Daily Papers

Self-evolving vision-language models train on questions they generate from unlabeled images. Since these questions have no gold answers, prior methods label them by majority vote over sampled answers or by a model judge. In a human evaluation, we find that 24\% of majority-vote labels and 18\% of model-judge labels produced during self-evolution are wrong. To address this problem, we present Verifiable QA Generation for Self-Evolving Models (VQS), which changes how the model judges answers. Instead of voting on an answer, the model parses each image into a structured record, such as a scene graph, a chart table, or a diagram graph. Fixed programs then write a question from the record and compute its answer. The model still acts as a visual checker, but it only confirms the individual facts the program reads, one short claim at a time. These claim-level checks select the parser's training targets, so the parser also improves without labels. Human raters find 94\% of VQS answers correct, against 76\% for majority voting. Across ten benchmarks, VQS improves Qwen3-VL by up to 3.18 points at the 2B, 4B, and 8B scales and outperforms the strongest self-evolving baseline at each. Gains keep growing over three training rounds, reaching 3.84 points at 2B. Code is released at https://github.com/ahmedheakl/VQS

Diagram-to-graph topology extraction aims to extract a graph of entities and their connections from a structural diagram. This task remains challenging for current vision-language models because it requires both fine-grained perceptual grounding and topology-aware reasoning with global consistency. We present TopoBench-180, a human-verified benchmark for diagram-to-graph topology extraction, and TopoAgent, a structure-aware perception-to-reasoning framework for reliable topology extraction using large vision-language models. TopoBench-180 contains 180 structural diagrams spanning Web-style and Network-style categories, paired with canonical graph annotations. TopoAgent progressively extracts the target graph by combining grounded perception, global structural priors, canonical node inventory construction, node-centric local-to-global relation reasoning, and topological consistency enforcement. Experiments on TopoBench-180 show that TopoAgent outperforms strong vision-language model baselines and recent visual reasoning frameworks, especially on edge extraction. More broadly, this work fills an important gap in multimodal structured understanding by establishing a benchmark and framework for diagram-to-graph topology extraction. The benchmark and associated resources will be publicly released at https://huggingface.co/datasets/WayneGuo0011/TopoBench-180.

Diagrams are common tools for representing complex concepts, relationships and events, often when it would be difficult to portray the same information with natural images. Understanding natural images has been extensively studied in computer vision, while diagram understanding has received little attention. In this paper, we study the problem of diagram interpretation and reasoning, the challenging task of identifying the structure of a diagram and the semantics of its constituents and their relationships. We introduce Diagram Parse Graphs (DPG) as our representation to model the structure of diagrams. We define syntactic parsing of diagrams as learning to infer DPGs for diagrams and study semantic interpretation and reasoning of diagrams in the context of diagram question answering. We devise an LSTM-based method for syntactic parsing of diagrams and introduce a DPG-based attention model for diagram question answering. We compile a new dataset of diagrams with exhaustive annotations of constituents and relationships for over 5,000 diagrams and 15,000 questions and answers. Our results show the significance of our models for syntactic parsing and question answering in diagrams using DPGs.

Structural diagrams are widely used to represent complex systems and relational information across scientific, engineering, procedural, and spatial domains. Recent vision-language models (VLMs) have become increasingly capable of recognizing diagram elements and reasoning about their content, while complete diagram topology extraction remains comparatively underexplored. In this paper, we study diagram-to-graph topology extraction: extracting all diagram entities and the complete relations among them. To enable large-scale supervised training and systematic evaluation of this task, we introduce Knossos, a benchmark of 19,200 diagrams across six diverse domains, with 245,179 nodes and 439,740 edges. Its symbolic generation process provides exact alignment between rendered diagrams and annotations of complete topology, relation types, and connector geometry. To address the modeling challenge of complete topology extraction, we also present Ariadne, a structured framework that decomposes the task into node inventory extraction and source-conditioned edge prediction. Extensive experiments show that training on Knossos substantially improves complete topology extraction in smaller open-source VLMs. Ariadne further improves over one-step extraction under matched supervision, demonstrating the additional benefit of structured decomposition. It achieves the highest average Edge F1 among the evaluated methods on Knossos, while both backbone variants also improve over their unadapted counterparts on the real-world external benchmark. Code and benchmark are available at https://github.com/bangwayne/knossos_Ariadne_Public.

Text-to-image (T2I) generation has seen significant growth over the past few years. Despite this, there has been little work on generating diagrams with T2I models. A diagram is a symbolic/schematic representation that explains information using structurally rich and spatially complex visualizations (e.g., a dense combination of related objects, text labels, directional arrows, connection lines, etc.). Existing state-of-the-art T2I models often fail at diagram generation because they lack fine-grained object layout control when many objects are densely connected via complex relations such as arrows/lines and also often fail to render comprehensible text labels. To address this gap, we present DiagrammerGPT, a novel two-stage text-to-diagram generation framework that leverages the layout guidance capabilities of LLMs (e.g., GPT-4) to generate more accurate open-domain, open-platform diagrams. In the first stage, we use LLMs to generate and iteratively refine 'diagram plans' (in a planner-auditor feedback loop) which describe all the entities (objects and text labels), their relationships (arrows or lines), and their bounding box layouts. In the second stage, we use a diagram generator, DiagramGLIGEN, and a text label rendering module to generate diagrams following the diagram plans. To benchmark the text-to-diagram generation task, we introduce AI2D-Caption, a densely annotated diagram dataset built on top of the AI2D dataset. We show quantitatively and qualitatively that our DiagrammerGPT framework produces more accurate diagrams, outperforming existing T2I models. We also provide comprehensive analysis including open-domain diagram generation, vector graphic diagram generation in different platforms, human-in-the-loop diagram plan editing, and multimodal planner/auditor LLMs (e.g., GPT-4Vision). We hope our work can inspire further research on diagram generation via T2I models and LLMs.

Motivated by recent observations of symmtry broken phases in lightly-doped multilayer graphene, we investigate magnetic phase transitions in a generalized electron gas model with four-component electron spin. This model simplifies the problem with a parabolic dispersion band, abstracting away the details of the graphene band structure to focus solely on the effects of the Coulomb interaction. We report four findings: 1) In the Hartree-Fock approximation, we observe that the paramagnetic state undergoes a sequence of density-driven, first-order phase transitions, progressively depopulating electrons from each spin component until achieving complete polarization within a very narrow density window where 1.2<r_s<2 (r_s being the electron gas parameter). 2) Further incorporating the correlation energy via the Bohm-Pines random-phase approximation shows that the cascade of transitions obtained within Hartree-Fock approximation is replaced by a single ferromagnetic phase transition at r_s = 6.12. 3) The disappearance of cascade is due to the correlation energy difference between the four-component paramagnetic state and symmetry-broken phases, which is nearly an order of magnitude more negative than the corresponding Hartree-Fock energy difference for 1.2 < r_s < 2. 4) The transition from the paramagnetic state to the fully polarized state at r_s=6.12 is governed by the balance between exchange and correlation energies, a competition that cannot be captured by mean-field approximations to models featuring effective (density-dependent) delta-function interactions, such as the Stoner model. We use the insights from our model to comment on the phase diagram of multilayer graphene electron gas.

A probability forecast or probabilistic classifier is reliable or calibrated if the predicted probabilities are matched by ex post observed frequencies, as examined visually in reliability diagrams. The classical binning and counting approach to plotting reliability diagrams has been hampered by a lack of stability under unavoidable, ad hoc implementation decisions. Here we introduce the CORP approach, which generates provably statistically Consistent, Optimally binned, and Reproducible reliability diagrams in an automated way. CORP is based on non-parametric isotonic regression and implemented via the Pool-adjacent-violators (PAV) algorithm - essentially, the CORP reliability diagram shows the graph of the PAV- (re)calibrated forecast probabilities. The CORP approach allows for uncertainty quantification via either resampling techniques or asymptotic theory, furnishes a new numerical measure of miscalibration, and provides a CORP based Brier score decomposition that generalizes to any proper scoring rule. We anticipate that judicious uses of the PAV algorithm yield improved tools for diagnostics and inference for a very wide range of statistical and machine learning methods.

Existing visual parsers for molecule diagrams translate pixel-based raster images such as PNGs to chemical structure representations (e.g., SMILES). However, PDFs created by word processors including LaTeX and Word provide explicit locations and shapes for characters, lines, and polygons. We extract symbols from born-digital PDF molecule images and then apply simple graph transformations to capture both visual and chemical structure in editable ChemDraw files (CDXML). Our fast ( PDF rightarrow visual graph rightarrow chemical graph ) pipeline does not require GPUs, Optical Character Recognition (OCR) or vectorization. We evaluate on standard benchmarks using SMILES strings, along with a novel evaluation that provides graph-based metrics and error compilation using LgEval. The geometric information in born-digital PDFs produces a highly accurate parser, motivating generating training data for visual parsers that recognize from raster images, with extracted graphics, visual structure, and chemical structure as annotations. To do this we render SMILES strings in Indigo, parse molecule structure, and then validate recognized structure to select correct files.

Geometry diagram parsing plays a key role in geometry problem solving, wherein the primitive extraction and relation parsing remain challenging due to the complex layout and between-primitive relationship. In this paper, we propose a powerful diagram parser based on deep learning and graph reasoning. Specifically, a modified instance segmentation method is proposed to extract geometric primitives, and the graph neural network (GNN) is leveraged to realize relation parsing and primitive classification incorporating geometric features and prior knowledge. All the modules are integrated into an end-to-end model called PGDPNet to perform all the sub-tasks simultaneously. In addition, we build a new large-scale geometry diagram dataset named PGDP5K with primitive level annotations. Experiments on PGDP5K and an existing dataset IMP-Geometry3K show that our model outperforms state-of-the-art methods in four sub-tasks remarkably. Our code, dataset and appendix material are available at https://github.com/mingliangzhang2018/PGDP.

Micro-Aerial Vehicles (MAVs) have the advantage of moving freely in 3D space. However, creating compact and sparse map representations that can be efficiently used for planning for such robots is still an open problem. In this paper, we take maps built from noisy sensor data and construct a sparse graph containing topological information that can be used for 3D planning. We use a Euclidean Signed Distance Field, extract a 3D Generalized Voronoi Diagram (GVD), and obtain a thin skeleton diagram representing the topological structure of the environment. We then convert this skeleton diagram into a sparse graph, which we show is resistant to noise and changes in resolution. We demonstrate global planning over this graph, and the orders of magnitude speed-up it offers over other common planning methods. We validate our planning algorithm in real maps built onboard an MAV, using RGB-D sensing.

Generating physics diagrams from text requires strict adherence to physical laws. While current generative models produce visually plausible outputs, they systematically hallucinate force vectors, ignore conservation laws, and violate geometric constraints. We present PhyDrawGen, a neuro-symbolic pipeline that decouples semantic scene understanding from physical constraint satisfaction. First, a large language model extracts a typed scene graph from the problem text. A deterministic solver then converts this graph into a Planar Straight-Line Graph (PSLG), encoding force balance, optical paths, and field topologies as exact geometric primitives. Finally, a fine-tuned Qwen-VL model implements a visually grounded propose-verify loop to iteratively correct any constraint violations. Evaluated on a benchmark of 1,449 problems spanning mechanics, optics, and electromagnetism, PhyDrawGen significantly outperforms GPT-5-image, Gemini 2.5 Flash, and Gemini 3 Pro, demonstrating robust physical accuracy even on unusual-object problems.

A bilayer formed by stacking two distinct materials creates a moiré lattice, which can serve as a platform for novel electronic phases. In this work we study a unique example of such a system: the graphene-black phosphorus heterostructure (G/BP), which has been suggested to have an intricate band structure. Most notably, the valence band hosts a quasi-one-dimensional region in the Brillouin zone of high density of states, suggesting that various many-body electronic phases are likely to emerge. We derive an effective tight-binding model that reproduces this band structure, and explore the emergent broken-symmetry phases when interactions are introduced. Employing a mean-field analysis, we find that the favored ground-state exhibits a striped spin density wave (SDW) order, characterized by either one of two-fold degenerate wave-vectors that are tunable by gating. Further exploring the phase-diagram controlled by gate voltage and the interaction strength, we find that the SDW-ordered state undergoes a metal to insulator transition via an intermediate metallic phase which supports striped SDW correlations. Possible experimental signatures are discussed, in particular a highly anisotropic dispersion of the collective excitations which should be manifested in electric and thermal transport.

Plane Geometry Diagram Synthesis has been a crucial task in computer graphics, with applications ranging from educational tools to AI-driven mathematical reasoning. Traditionally, we rely on manual tools (e.g., Matplotlib and GeoGebra) to generate precise diagrams, but this usually requires huge, complicated calculations. Recently, researchers start to work on model-based methods (e.g., Stable Diffusion and GPT5) to automatically generate diagrams, saving operational cost but usually suffering from limited realism and insufficient accuracy. In this paper, we propose a novel framework GeoSDF, to automatically generate diagrams efficiently and accurately with Signed Distance Field (SDF). Specifically, we first represent geometric elements (e.g., points, segments, and circles) in the SDF, then construct a series of constraint functions to represent geometric relationships. Next, we optimize those constructed constraint functions to get an optimized field of both elements and constraints. Finally, by rendering the optimized field, we can obtain the synthesized diagram. In our GeoSDF, we define a symbolic language to represent geometric elements and constraints, and our synthesized geometry diagrams can be self-verified in the SDF, ensuring both mathematical accuracy and visual plausibility. In experiments, through both qualitative and quantitative analysis, GeoSDF synthesized both normal high-school level and IMO-level geometry diagrams. We achieve 88.67\% synthesis accuracy by human evaluation in the IMO problem set. Furthermore, we obtain a very high accuracy of solving geometry problems (over 95\% while the current SOTA accuracy is around 75%) by leveraging our self-verification property. All of these demonstrate the advantage of GeoSDF, paving the way for more sophisticated, accurate, and flexible generation of geometric diagrams for a wide array of applications.

Legal documents including judgments and court orders require highly sophisticated legal knowledge for understanding. To disclose expert knowledge for non-experts, we explore the problem of visualizing legal texts with easy-to-understand diagrams and propose a novel dataset of LegalViz with 23 languages and 7,010 cases of legal document and visualization pairs, using the DOT graph description language of Graphviz. LegalViz provides a simple diagram from a complicated legal corpus identifying legal entities, transactions, legal sources, and statements at a glance, that are essential in each judgment. In addition, we provide new evaluation metrics for the legal diagram visualization by considering graph structures, textual similarities, and legal contents. We conducted empirical studies on few-shot and finetuning large language models for generating legal diagrams and evaluated them with these metrics, including legal content-based evaluation within 23 languages. Models trained with LegalViz outperform existing models including GPTs, confirming the effectiveness of our dataset.

DisCoPy is a Python toolkit for computing with monoidal categories. It comes with two flexible data structures for string diagrams: the first one for planar monoidal categories based on lists of layers, the second one for symmetric monoidal categories based on cospans of hypergraphs. Algorithms for functor application then allow to translate string diagrams into code for numerical computation, be it differentiable, probabilistic or quantum. This report gives an overview of the library and the new developments released in its version 1.0. In particular, we showcase the implementation of diagram equality for a large fragment of the hierarchy of graphical languages for monoidal categories, as well as a new syntax for defining string diagrams as Python functions.

Recent advances in autonomous ``AI scientist'' systems have demonstrated the ability to automatically write scientific manuscripts and codes with execution. However, producing a publication-grade scientific diagram (e.g., teaser figure) is still a major bottleneck in the ``end-to-end'' paper generation process. For example, a teaser figure acts as a strategic visual interface and serves a different purpose than derivative data plots. It demands conceptual synthesis and planning to translate complex logic workflow into a compelling graphic that guides intuition and sparks curiosity. Existing AI scientist systems usually omit this component or fall back to an inferior alternative. To bridge this gap, we present DiagramBank, a large-scale dataset consisting of 89,422 schematic diagrams curated from existing top-tier scientific publications, designed for multimodal retrieval and exemplar-driven scientific figure generation. DiagramBank is developed through our automated curation pipeline that extracts figures and corresponding in-text references, and uses a CLIP-based filter to differentiate schematic diagrams from standard plots or natural images. Each instance is paired with rich context from abstract, caption, to figure-reference pairs, enabling information retrieval under different query granularities. We release DiagramBank in a ready-to-index format and provide a retrieval-augmented generation codebase to demonstrate exemplar-conditioned synthesis of teaser figures. DiagramBank is publicly available at https://huggingface.co/datasets/zhangt20/DiagramBank with code at https://github.com/csml-rpi/DiagramBank.

We introduce Diagram of Thought (DoT), a framework that models iterative reasoning in large language models (LLMs) as the construction of a directed acyclic graph (DAG) within a single model. Unlike traditional approaches that represent reasoning as linear chains or trees, DoT organizes propositions, critiques, refinements, and verifications into a cohesive DAG structure, allowing the model to explore complex reasoning pathways while maintaining logical consistency. Each node in the diagram corresponds to a proposition that has been proposed, critiqued, refined, or verified, enabling the LLM to iteratively improve its reasoning through natural language feedback. By leveraging auto-regressive next-token prediction with role-specific tokens, DoT facilitates seamless transitions between proposing ideas and critically evaluating them, providing richer feedback than binary signals. Furthermore, we formalize the DoT framework using Topos Theory, providing a mathematical foundation that ensures logical consistency and soundness in the reasoning process. This approach enhances both the training and inference processes within a single LLM, eliminating the need for multiple models or external control mechanisms. DoT offers a conceptual framework for designing next-generation reasoning-specialized models, emphasizing training efficiency, robust reasoning capabilities, and theoretical grounding. The code is available at https://github.com/diagram-of-thought/diagram-of-thought.

Generating structured, editable diagrams remains a significant challenge for contemporary large language models, despite their proficiency in general-purpose vector code generation. The primary difficulty lies in the structural fragility of the output; minor errors such as misaligned connector endpoints, text labels overlapping borders, or complex layouts drifting beyond the canvas boundaries render the resulting SVG files functionally unusable for professional applications. To address these issues, we introduce GeoSVG-RL, a specialized reinforcement learning framework designed for layout-constrained text-to-SVG generation. Unlike standard training objectives that rely solely on maximizing token-level likelihood, our approach optimizes the policy against explicit, executable geometric feedback. The model first produces a structured layout plan that serves as a geometric contract for the subsequent generation of the SVG code. This code is then rendered through a browser-backed verifier, enabling the calculation of fine-grained rewards across six critical dimensions: rendering validity, canvas fitting, precise anchor placement, text containment, graph consistency, and code cleanliness. We utilize Group Relative Policy Optimization (GRPO) to refine the model, sampling multiple candidates per prompt to facilitate updates based on relative quality. Starting from a supervised warm-start phase on synthetic data, GeoSVG-RL achieves substantial gains in structural reliability, particularly in arrow-anchor accuracy and text-in-box rates. Quantitative evaluations demonstrate that our method consistently outperforms current state-of-the-art systems in local geometric precision and the preservation of graph connectivity, providing a robust pathway toward automated yet reliable technical illustration.

Scientific diagrams are vital tools for communicating structured knowledge across disciplines. However, they are often published as static raster images, losing symbolic semantics and limiting reuse. While Multimodal Large Language Models (MLLMs) offer a pathway to bridging vision and structure, existing methods lack semantic control and structural interpretability, especially on complex diagrams. We propose Draw with Thought (DwT), a training-free framework that guides MLLMs to reconstruct diagrams into editable mxGraph XML code through cognitively-grounded Chain-of-Thought reasoning. DwT enables interpretable and controllable outputs without model fine-tuning by dividing the task into two stages: Coarse-to-Fine Planning, which handles perceptual structuring and semantic specification, and Structure-Aware Code Generation, enhanced by format-guided refinement. To support evaluation, we release Plot2XML, a benchmark of 247 real-world scientific diagrams with gold-standard XML annotations. Extensive experiments across eight MLLMs show that our approach yields high-fidelity, semantically aligned, and structurally valid reconstructions, with human evaluations confirming strong alignment in both accuracy and visual aesthetics, offering a scalable solution for converting static visuals into executable representations and advancing machine understanding of scientific graphics.

Knot diagrams are among the most common visual tools in topology. Computer programs now make it possible to draw, manipulate and render them digitally, which proves to be useful in knot theory teaching and research. Still, an openly available tool to manipulate knot diagrams in a real-time, interactive way is yet to be developed. We introduce a method of operating on the geometry of the knot diagram itself without any underlying three-dimensional structure that can underpin such an application. This allows us to directly interact with vector graphics knot diagrams while at the same time computing knot invariants in ways proposed by previous work. An implementation of this method is provided.

Contrastive Vision-Language Models (VLMs) have demonstrated strong zero-shot capabilities. However, their cross-modal alignment remains biased toward English due to limited multilingual multimodal data. Recent multilingual extensions have alleviated this gap but enforce instance-level alignment while neglecting the global geometry of the shared embedding space. We address this problem by introducing ToMCLIP (Topological Alignment for Multilingual CLIP), a topology-aware framework aligning embedding spaces with topology-preserving constraints. The proposed method applies persistent homology to define a topological alignment loss and approximates persistence diagram with theoretical error bounds using graph sparsification strategy. This work validates the proposed approach, showing enhanced structural coherence of multilingual representations, higher zero-shot accuracy on the CIFAR-100, and stronger multilingual retrieval performance on the xFlickr&CO. Beyond VLMs, the proposed approach provides a general method for incorporating topological alignment into representation learning. Code is available at https://github.com/junwon0/ToMCLIP.git.

Despite deep learning models running well-defined mathematical functions, we lack a formal mathematical framework for describing model architectures. Ad-hoc notation, diagrams, and pseudocode poorly handle nonlinear broadcasting and the relationship between individual components and composed models. This paper introduces a categorical framework for deep learning models that formalizes broadcasting through the novel axis-stride and array-broadcasted categories. This allows the mathematical function underlying architectures to be precisely expressed and manipulated in a compositional manner. These mathematical definitions are translated into human manageable diagrams and machine manageable data structures. We provide a mirrored implementation in Python (pyncd) and TypeScript (tsncd) to show the universal aspect of our framework, along with features including algebraic construction, graph conversion, PyTorch compilation and diagram rendering. This lays the foundation for a systematic, formal approach to deep learning model design and analysis.

Hand-drawn sketches are a natural and efficient medium for capturing and conveying ideas. Despite significant advancements in controllable natural image generation, translating freehand sketches into structured, machine-readable diagrams remains a labor-intensive and predominantly manual task. The primary challenge stems from the inherent ambiguity of sketches, which lack the structural constraints and semantic precision required for automated diagram generation. To address this challenge, we introduce SketchAgent, a multi-agent system designed to automate the transformation of hand-drawn sketches into structured diagrams. SketchAgent integrates sketch recognition, symbolic reasoning, and iterative validation to produce semantically coherent and structurally accurate diagrams, significantly reducing the need for manual effort. To evaluate the effectiveness of our approach, we propose the Sketch2Diagram Benchmark, a comprehensive dataset and evaluation framework encompassing eight diverse diagram categories, such as flowcharts, directed graphs, and model architectures. The dataset comprises over 6,000 high-quality examples with token-level annotations, standardized preprocessing, and rigorous quality control. By streamlining the diagram generation process, SketchAgent holds great promise for applications in design, education, and engineering, while offering a significant step toward bridging the gap between intuitive sketching and machine-readable diagram generation. The benchmark is released at https://huggingface.co/datasets/DiagramAgent/Sketch2Diagram-Benchmark.

Visual language is a system of communication that conveys information through symbols, shapes, and spatial arrangements. Diagrams are a typical example of a visual language depicting complex concepts and their relationships in the form of an image. The symbolic nature of diagrams presents significant challenges for building models capable of understanding them. Yet, recent studies seem to suggest that Large Vision-Language Models (LVLMs) can even tackle complex reasoning tasks involving diagrams. In this paper, we investigate this phenomenon by developing a comprehensive test suite to evaluate the diagram comprehension capability of LVLMs. Our test suite uses a variety of questions focused on concept entities and their relationships over a set of synthetic as well as real diagrams across several domains to evaluate the recognition and reasoning abilities of models. Our evaluation of three LVLMs (GPT-4V, GPT-4o, and Gemini) shows that while these models can accurately identify and reason about entities, their ability to understand relationships is notably limited. Further testing reveals that the decent performance on diagram understanding largely stems from leveraging their background knowledge as shortcuts to identify and reason about the relational information. Thus, we conclude that LVLMs have a limited capability for genuine diagram understanding, and their impressive performance in diagram reasoning is an illusion emanating from other confounding factors, such as the background knowledge in the models.

We introduce the task of text-to-diagram generation, which focuses on creating structured visual representations directly from textual descriptions. Existing approaches in text-to-image and text-to-code generation lack the logical organization and flexibility needed to produce accurate, editable diagrams, often resulting in outputs that are either unstructured or difficult to modify. To address this gap, we introduce DiagramGenBenchmark, a comprehensive evaluation framework encompassing eight distinct diagram categories, including flowcharts, model architecture diagrams, and mind maps. Additionally, we present DiagramAgent, an innovative framework with four core modules-Plan Agent, Code Agent, Check Agent, and Diagram-to-Code Agent-designed to facilitate both the generation and refinement of complex diagrams. Our extensive experiments, which combine objective metrics with human evaluations, demonstrate that DiagramAgent significantly outperforms existing baseline models in terms of accuracy, structural coherence, and modifiability. This work not only establishes a foundational benchmark for the text-to-diagram generation task but also introduces a powerful toolset to advance research and applications in this emerging area.

Large Language Models (LLMs) are increasingly being adopted as tools for learning; however, most tools remain text-only, limiting their usefulness for domains where visualizations are essential, such as mathematics. Recent work shows that LLMs are capable of generating code that compiles to educational figures, but a major bottleneck remains: scalable evaluation of these diagrams. We address this by proposing DiagramIR: an automatic and scalable evaluation pipeline for geometric figures. Our method relies on intermediate representations (IRs) of LaTeX TikZ code. We compare our pipeline to other evaluation baselines such as LLM-as-a-Judge, showing that our approach has higher agreement with human raters. This evaluation approach also enables smaller models like GPT-4.1-Mini to perform comparably to larger models such as GPT-5 at a 10x lower inference cost, which is important for deploying accessible and scalable education technologies.

Diagrams matter. Unfortunately, the deep learning community has no standard method for diagramming architectures. The current combination of linear algebra notation and ad-hoc diagrams fails to offer the necessary precision to understand architectures in all their detail. However, this detail is critical for faithful implementation, mathematical analysis, further innovation, and ethical assurances. I present neural circuit diagrams, a graphical language tailored to the needs of communicating deep learning architectures. Neural circuit diagrams naturally keep track of the changing arrangement of data, precisely show how operations are broadcast over axes, and display the critical parallel behavior of linear operations. A lingering issue with existing diagramming methods is the inability to simultaneously express the detail of axes and the free arrangement of data, which neural circuit diagrams solve. Their compositional structure is analogous to code, creating a close correspondence between diagrams and implementation. In this work, I introduce neural circuit diagrams for an audience of machine learning researchers. After introducing neural circuit diagrams, I cover a host of architectures to show their utility and breed familiarity. This includes the transformer architecture, convolution (and its difficult-to-explain extensions), residual networks, the U-Net, and the vision transformer. I include a Jupyter notebook that provides evidence for the close correspondence between diagrams and code. Finally, I examine backpropagation using neural circuit diagrams. I show their utility in providing mathematical insight and analyzing algorithms' time and space complexities.

Large language models (LLMs) are increasingly adopted for a variety of tasks with implicit graphical structures, such as planning in robotics, multi-hop question answering or knowledge probing, structured commonsense reasoning, and more. While LLMs have advanced the state-of-the-art on these tasks with structure implications, whether LLMs could explicitly process textual descriptions of graphs and structures, map them to grounded conceptual spaces, and perform structured operations remains underexplored. To this end, we propose NLGraph (Natural Language Graph), a comprehensive benchmark of graph-based problem solving designed in natural language. NLGraph contains 29,370 problems, covering eight graph reasoning tasks with varying complexity from simple tasks such as connectivity and shortest path up to complex problems such as maximum flow and simulating graph neural networks. We evaluate LLMs (GPT-3/4) with various prompting approaches on the NLGraph benchmark and find that 1) language models do demonstrate preliminary graph reasoning abilities, 2) the benefit of advanced prompting and in-context learning diminishes on more complex graph problems, while 3) LLMs are also (un)surprisingly brittle in the face of spurious correlations in graph and problem settings. We then propose Build-a-Graph Prompting and Algorithmic Prompting, two instruction-based approaches to enhance LLMs in solving natural language graph problems. Build-a-Graph and Algorithmic prompting improve the performance of LLMs on NLGraph by 3.07% to 16.85% across multiple tasks and settings, while how to solve the most complicated graph reasoning tasks in our setup with language models remains an open research question. The NLGraph benchmark and evaluation code are available at https://github.com/Arthur-Heng/NLGraph.

Large Language Models (LLMs) have achieved impressive performance in text understanding and have become an essential tool for building smart assistants. Originally focusing on text, they have been enhanced with multimodal capabilities in recent works that successfully built visual instruction following assistants. As far as the graph modality goes, however, no such assistants have yet been developed. Graph structures are complex in that they represent relation between different features and are permutation invariant. Moreover, representing them in purely textual form does not always lead to good LLM performance even for finetuned models. As a result, there is a need to develop a new method to integrate graphs in LLMs for general graph understanding. This work explores the integration of the graph modality in LLM for general graph instruction following tasks. It aims at producing a deep learning model that enhances an underlying LLM with graph embeddings and trains it to understand them and to produce, given an instruction, an answer grounded in the graph representation. The approach performs significantly better than a graph to text approach and remains consistent even for larger graphs.

Charts are a primary medium for conveying quantitative and relational information, yet systematically evaluating chart parsing models remains difficult. Existing benchmarks focus on narrow chart types and leave diagrammatic structures such as flowcharts and mind maps largely unaddressed, while models produce outputs in incompatible formats, and datasets rarely include the printed or hand-drawn images encountered in practice. To address these issues, we introduce ChartArena, a comprehensive bilingual benchmark covering eight chart families spanning both numeric charts and diagrammatic structures, each evaluated across three visual scenarios: digital renderings, printed photos, and hand-drawn photos. The dataset is built via a human-agent collaborative annotation pipeline with multi-stage human verification to ensure annotation reliability. To enable fair cross-model comparison, we further design a format-agnostic evaluation protocol that maps heterogeneous outputs into two canonical semantic spaces, a normalized triple view and a directed graph view, and scores them with structure-aware metrics. Through extensive evaluation of 26 leading MLLMs, we observe three consistent findings: (i) frontier proprietary models such as Gemini 3.1 Pro lead overall, yet the strongest open-source systems are rapidly closing the gap; (ii) document parsing models handle numeric charts reasonably but fall sharply behind on diagrammatic structures; and (iii) expert chart parsers remain limited to narrow chart families. Across all models, radar charts and hand-drawn scenarios stay especially challenging. These findings show that ChartArena exposes clear capability gaps and provides a unified foundation for future progress. ChartArena is publicly available at https://github.com/pspdada/ChartArena.

Charts are high-density visualization carriers for complex data, serving as a crucial medium for information extraction and analysis. Automated chart understanding poses significant challenges to existing multimodal large language models (MLLMs) due to the need for precise and complex visual reasoning. Current step-by-step reasoning models primarily focus on text-based logical reasoning for chart understanding. However, they struggle to refine or correct their reasoning when errors stem from flawed visual understanding, as they lack the ability to leverage multimodal interaction for deeper comprehension. Inspired by human cognitive behavior, we propose ChartSketcher, a multimodal feedback-driven step-by-step reasoning method designed to address these limitations. ChartSketcher is a chart understanding model that employs Sketch-CoT, enabling MLLMs to annotate intermediate reasoning steps directly onto charts using a programmatic sketching library, iteratively feeding these visual annotations back into the reasoning process. This mechanism enables the model to visually ground its reasoning and refine its understanding over multiple steps. We employ a two-stage training strategy: a cold start phase to learn sketch-based reasoning patterns, followed by off-policy reinforcement learning to enhance reflection and generalization. Experiments demonstrate that ChartSketcher achieves promising performance on chart understanding benchmarks and general vision tasks, providing an interactive and interpretable approach to chart comprehension.

Large language models (LLMs) have demonstrated remarkable success across a wide range of tasks; however, they still encounter challenges in reasoning tasks that require understanding and inferring relationships between distinct pieces of information within text sequences. This challenge is particularly pronounced in tasks involving multi-step processes, such as logical reasoning and multi-hop question answering, where understanding implicit relationships between entities and leveraging multi-hop connections in the given context are crucial. Graphs, as fundamental data structures, explicitly represent pairwise relationships between entities, thereby offering the potential to enhance LLMs' reasoning capabilities. External graphs have proven effective in supporting LLMs across multiple tasks. However, in many reasoning tasks, no pre-existing graph structure is provided. Can we structure implicit knowledge derived from context into graphs to assist LLMs in reasoning? In this paper, we propose Reasoning with Graphs (RwG) by first constructing explicit graphs from the context and then leveraging these graphs to enhance LLM reasoning performance on reasoning tasks. Extensive experiments demonstrate the effectiveness of the proposed method in improving both logical reasoning and multi-hop question answering tasks.

Vision-language models (VLMs) have demonstrated strong performance in visual question answering with natural images. However, they continue to struggle with scientific diagrams, which are designed to convey functional or relational meaning rather than literal scenes. We therefore introduce a framework for generating large-scale diagram-grounded instruction data by leveraging terminology derived from scientific curricula. Our approach systematically extracts domain concepts, synthesizes atomic facts, retrieves relevant diagrams from the web, and generates multimodal supervision in the form of diagram captions and multiple-choice questions. Using this pipeline, we construct SciGram, a dataset of over 194K diagrams and 1.4M visual instructions across life, earth, and physical sciences. Despite relying on noisy web data and synthetic annotations, models fine-tuned on SciGram achieve substantial improvements on diagram-centric benchmarks, including TQA, ScienceQA, and AI2D, outperforming or matching state-of-the-art VLMs while using fewer training instances. Furthermore, augmenting existing models such as LLaVA OneVision with SciGram establishes new state-of-the-art performance on diagram question answering. Our results highlight the effectiveness of terminology-grounded instruction generation as a general strategy for improving vision-language reasoning in scientific domains. To support future research in scientific diagram understanding, we release both the SciGram dataset and models.

Despite the rapid advancements in Vision-Language Models (VLMs), a critical gap remains in their ability to handle structured, controllable diagrammatic tasks essential for professional workflows. Existing methods predominantly rely on pixel-based synthesis, which operates in probabilistic pixel spaces and is inherently limited in editability and fidelity. Instead, we propose a new Diagram-as-Code paradigm with symbolic logic that leverages mxGraph Extensible Markup Language (XML) for precise diagram generation and editing. We present VCG-Bench, a unified benchmark for visual-centric mxGraph tasks. VCG-Bench comprises: (1) a taxonomized dataset of 1,449 diverse diagrams spanning 6 domains and 15 sub-domains, (2) a paradigm definition that integrates Generation (Vision-to-Code) and Editability (Code-to-Code), (3) a Tailored Evaluation Protocol employing multi-dimensional metrics such as mxGraph Execution Success Rate, Style Consistency Score (SCS), etc. Experimental results highlight the challenges faced by current State-of-the-Art (SOTA) VLMs in structured fidelity and instruction compliance, reflecting their vision and reasoning capabilities.

Human reasoning relies on constructing and manipulating mental models-simplified internal representations of situations that we use to understand and solve problems. Conceptual diagrams (for example, sketches drawn by humans to aid reasoning) externalize these mental models, abstracting irrelevant details to efficiently capture relational and spatial information. In contrast, Large Language Models (LLMs) and Large Multimodal Models (LMMs) predominantly reason through textual representations, limiting their effectiveness in complex multi-step combinatorial and planning tasks. In this paper, we propose a zero-shot fully automatic framework that enables LMMs to reason through multiple chains of self-generated intermediate conceptual diagrams, significantly enhancing their combinatorial planning capabilities. Our approach does not require any human initialization beyond a natural language description of the task. It integrates both textual and diagrammatic reasoning within an optimized graph-of-thought inference framework, enhanced by beam search and depth-wise backtracking. Evaluated on multiple challenging PDDL planning domains, our method substantially improves GPT-4o's performance (for example, from 35.5% to 90.2% in Blocksworld). On more difficult planning domains with solution depths up to 40, our approach outperforms even the o1-preview reasoning model (for example, over 13% improvement in Parking). These results highlight the value of conceptual diagrams as a complementary reasoning medium in LMMs.

Graphs can be used to represent and reason about systems and a variety of metrics have been devised to quantify their global characteristics. However, little is currently known about how to construct a graph or improve an existing one given a target objective. In this work, we formulate the construction of a graph as a decision-making process in which a central agent creates topologies by trial and error and receives rewards proportional to the value of the target objective. By means of this conceptual framework, we propose an algorithm based on reinforcement learning and graph neural networks to learn graph construction and improvement strategies. Our core case study focuses on robustness to failures and attacks, a property relevant for the infrastructure and communication networks that power modern society. Experiments on synthetic and real-world graphs show that this approach can outperform existing methods while being cheaper to evaluate. It also allows generalization to out-of-sample graphs, as well as to larger out-of-distribution graphs in some cases. The approach is applicable to the optimization of other global structural properties of graphs.

Diagrams serve as a fundamental form of visual language, representing complex concepts and their inter-relationships through structured symbols, shapes, and spatial arrangements. Unlike natural images, their inherently symbolic and abstract nature poses significant challenges for Multimodal Large Language Models (MLLMs). However, current benchmarks conflate perceptual and reasoning tasks, making it difficult to assess whether MLLMs genuinely understand mathematical diagrams beyond superficial pattern recognition. To address this gap, we introduce MATHGLANCE, a benchmark specifically designed to isolate and evaluate mathematical perception in MLLMs. MATHGLANCE comprises 1.2K images and 1.6K carefully curated questions spanning four perception tasks: shape classification, object counting, relationship identification, and object grounding, covering diverse domains including plane geometry, solid geometry, and graphical representations. Our evaluation of MLLMs reveals that their ability to understand diagrams is notably limited, particularly in fine-grained grounding tasks. In response, we construct GeoPeP, a perception-oriented dataset of 200K structured geometry image-text pairs explicitly annotated with geometric primitives and precise spatial relationships. Training MLLM on GeoPeP leads to significant gains in perceptual accuracy, which in turn substantially improves mathematical reasoning. Our benchmark and dataset establish critical standards for evaluating and advancing multimodal mathematical understanding, providing valuable resources and insights to foster future MLLM research.

In this paper, we aim to develop a large language model (LLM) with the reasoning ability on complex graph data. Currently, LLMs have achieved very impressive performance on various natural language learning tasks, extensions of which have also been applied to study the vision tasks with multi-modal data. However, when it comes to the graph learning tasks, existing LLMs present very serious flaws due to their several inherited weaknesses in performing {multi-step logic reasoning}, {precise mathematical calculation} and {perception about the spatial and temporal factors}. To address such challenges, in this paper, we will investigate the principles, methodologies and algorithms to empower existing LLMs with graph reasoning ability, which will have tremendous impacts on the current research of both LLMs and graph learning. Inspired by the latest ChatGPT and Toolformer models, we propose the Graph-ToolFormer (Graph Reasoning oriented Toolformer) framework to teach LLMs themselves with prompts augmented by ChatGPT to use external graph reasoning API tools. Specifically, we will investigate to teach Graph-ToolFormer to handle various graph data reasoning tasks in this paper, including both (1) very basic graph data loading and graph property reasoning tasks, ranging from simple graph order and size to the graph diameter and periphery, and (2) more advanced reasoning tasks on real-world graph data, such as bibliographic networks, protein molecules, sequential recommender systems, social networks and knowledge graphs.

Computer science papers rely heavily on diagrams: architecture drawings, system flowcharts, and pipeline schematics that often carry more information than the text around them. There is currently no public dataset that pairs this specific kind of figure with captions, context, questions, answers, and step-by-step reasoning, which is exactly what is needed to train a vision-language model to understand them. We present SCAFFOLDhttps://github.com/theranjitraut/scaffold, a large-scale structured dataset of computer science research figures with diagram QA and Chain-of-Thought reasoning traces. This dataset consists of (image, caption, context, question-answer, chain-of-thought) tuples from arXiv computer science papers prepared using layout detection and PDF parsing, with an AI-assisted question-generation step. The resulting large-sized SCAFFOLD-157K dataset spans 3,058 papers with 29,887 figures (157,387 pairs), a medium-sized SCAFFOLD-37K dataset (36,797 pairs), and a small-sized SCAFFOLD-12K dataset (12,000 pairs). We used SCAFFOLD-12K for baseline experiments on Qwen2.5-VL-3B-Instruct.

The paradigm of programmable diagram generation is evolving rapidly, playing a crucial role in structured visualization. However, most existing studies are confined to a narrow range of task formulations and language support, constraining their applicability to diverse diagram types. In this work, we propose OmniDiagram, a unified framework that incorporates diverse diagram code languages and task definitions. To address the challenge of aligning code logic with visual fidelity in Reinforcement Learning (RL), we introduce a novel visual feedback strategy named Visual Interrogation Verifies All (Viva). Unlike brittle syntax-based rules or pixel-level matching, Viva rewards the visual structure of rendered diagrams through a generative approach. Specifically, Viva actively generates targeted visual inquiries to scrutinize diagram visual fidelity and provides fine-grained feedback for optimization. This mechanism facilitates a self-evolving training process, effectively obviating the need for manually annotated ground truth code. Furthermore, we construct M3^2Diagram, the first large-scale diagram code generation dataset, containing over 196k high-quality instances. Experimental results confirm that the combination of SFT and our Viva-based RL allows OmniDiagram to establish a new state-of-the-art (SOTA) across diagram code generation benchmarks.

This tutorial serves as a comprehensive guide for understanding graph databases, focusing on the fundamentals of graph theory while showcasing practical applications across various fields. It starts by introducing foundational concepts and delves into the structure of graphs through nodes and edges, covering different types such as undirected, directed, weighted, and unweighted graphs. Key graph properties, terminologies, and essential algorithms for network analysis are outlined, including Dijkstras shortest path algorithm and methods for calculating node centrality and graph connectivity. The tutorial highlights the advantages of graph databases over traditional relational databases, particularly in efficiently managing complex, interconnected data. It examines leading graph database systems such as Neo4j, Amazon Neptune, and ArangoDB, emphasizing their unique features for handling large datasets. Practical instructions on graph operations using NetworkX and Neo4j are provided, covering node and edge creation, attribute assignment, and advanced queries with Cypher. Additionally, the tutorial explores common graph visualization techniques using tools like Plotly and Neo4j Bloom, which enhance the interpretation and usability of graph data. It also delves into community detection algorithms, including the Louvain method, which facilitates clustering in large networks. Finally, the paper concludes with recommendations for researchers interested in exploring the vast potential of graph technologies.

Pre-trained sequence-to-sequence language models have led to widespread success in many natural language generation tasks. However, there has been relatively less work on analyzing their ability to generate structured outputs such as graphs. Unlike natural language, graphs have distinct structural and semantic properties in the context of a downstream NLP task, e.g., generating a graph that is connected and acyclic can be attributed to its structural constraints, while the semantics of a graph can refer to how meaningfully an edge represents the relation between two node concepts. In this work, we study pre-trained language models that generate explanation graphs in an end-to-end manner and analyze their ability to learn the structural constraints and semantics of such graphs. We first show that with limited supervision, pre-trained language models often generate graphs that either violate these constraints or are semantically incoherent. Since curating large amount of human-annotated graphs is expensive and tedious, we propose simple yet effective ways of graph perturbations via node and edge edit operations that lead to structurally and semantically positive and negative graphs. Next, we leverage these graphs in different contrastive learning models with Max-Margin and InfoNCE losses. Our methods lead to significant improvements in both structural and semantic accuracy of explanation graphs and also generalize to other similar graph generation tasks. Lastly, we show that human errors are the best negatives for contrastive learning and also that automatically generating more such human-like negative graphs can lead to further improvements. Our code and models are publicly available at https://github.com/swarnaHub/ExplagraphGen

Large language models (LLMs), such as ChatGPT and LLaMA, are creating significant advancements in natural language processing, due to their strong text encoding/decoding ability and newly found emergent capability (e.g., reasoning). While LLMs are mainly designed to process pure texts, there are many real-world scenarios where text data are associated with rich structure information in the form of graphs (e.g., academic networks, and e-commerce networks) or scenarios where graph data are paired with rich textual information (e.g., molecules with descriptions). Besides, although LLMs have shown their pure text-based reasoning ability, it is underexplored whether such ability can be generalized to graph scenarios (i.e., graph-based reasoning). In this paper, we provide a systematic review of scenarios and techniques related to large language models on graphs. We first summarize potential scenarios of adopting LLMs on graphs into three categories, namely pure graphs, text-rich graphs, and text-paired graphs. We then discuss detailed techniques for utilizing LLMs on graphs, including LLM as Predictor, LLM as Encoder, and LLM as Aligner, and compare the advantages and disadvantages of different schools of models. Furthermore, we mention the real-world applications of such methods and summarize open-source codes and benchmark datasets. Finally, we conclude with potential future research directions in this fast-growing field. The related source can be found at https://github.com/PeterGriffinJin/Awesome-Language-Model-on-Graphs.

Large Language Models (LLMs) have demonstrated exceptional abilities in reasoning for task planning. However, challenges remain under-explored for parallel schedules. This paper introduces a novel paradigm, plan-over-graph, in which the model first decomposes a real-life textual task into executable subtasks and constructs an abstract task graph. The model then understands this task graph as input and generates a plan for parallel execution. To enhance the planning capability of complex, scalable graphs, we design an automated and controllable pipeline to generate synthetic graphs and propose a two-stage training scheme. Experimental results show that our plan-over-graph method significantly improves task performance on both API-based LLMs and trainable open-sourced LLMs. By normalizing complex tasks as graphs, our method naturally supports parallel execution, demonstrating global efficiency. The code and data are available at https://github.com/zsq259/Plan-over-Graph.

A Harris Graph is a tough, Eulerian, non-Hamiltonian graph. Several approaches to creating new Harris graphs from existing ones are explored, including creating families of Harris graphs and combining Harris graphs. Pictures of all Harris Graphs through order 9 and the number of Harris graphs through order 12 are included. We also prove a result about barnacle-free Harris graphs.

Graphs are ubiquitous structures found in numerous real-world applications, such as drug discovery, recommender systems, and social network analysis. To model graph-structured data, graph neural networks (GNNs) have become a popular tool. However, existing GNN architectures encounter challenges in cross-graph learning where multiple graphs have different feature spaces. To address this, recent approaches introduce text-attributed graphs (TAGs), where each node is associated with a textual description, which can be projected into a unified feature space using textual encoders. While promising, this method relies heavily on the availability of text-attributed graph data, which is difficult to obtain in practice. To bridge this gap, we propose a novel method named Topology-Aware Node description Synthesis (TANS), leveraging large language models (LLMs) to convert existing graphs into text-attributed graphs. The key idea is to integrate topological information into LLMs to explain how graph topology influences node semantics. We evaluate our TANS on text-rich, text-limited, and text-free graphs, demonstrating its applicability. Notably, on text-free graphs, our method significantly outperforms existing approaches that manually design node features, showcasing the potential of LLMs for preprocessing graph-structured data in the absence of textual information. The code and data are available at https://github.com/Zehong-Wang/TANS.

Graphs are a powerful tool for representing and analyzing complex relationships in real-world applications such as social networks, recommender systems, and computational finance. Reasoning on graphs is essential for drawing inferences about the relationships between entities in a complex system, and to identify hidden patterns and trends. Despite the remarkable progress in automated reasoning with natural text, reasoning on graphs with large language models (LLMs) remains an understudied problem. In this work, we perform the first comprehensive study of encoding graph-structured data as text for consumption by LLMs. We show that LLM performance on graph reasoning tasks varies on three fundamental levels: (1) the graph encoding method, (2) the nature of the graph task itself, and (3) interestingly, the very structure of the graph considered. These novel results provide valuable insight on strategies for encoding graphs as text. Using these insights we illustrate how the correct choice of encoders can boost performance on graph reasoning tasks inside LLMs by 4.8% to 61.8%, depending on the task.

Visual language data such as plots, charts, and infographics are ubiquitous in the human world. However, state-of-the-art vision-language models do not perform well on these data. We propose MatCha (Math reasoning and Chart derendering pretraining) to enhance visual language models' capabilities in jointly modeling charts/plots and language data. Specifically, we propose several pretraining tasks that cover plot deconstruction and numerical reasoning which are the key capabilities in visual language modeling. We perform the MatCha pretraining starting from Pix2Struct, a recently proposed image-to-text visual language model. On standard benchmarks such as PlotQA and ChartQA, the MatCha model outperforms state-of-the-art methods by as much as nearly 20%. We also examine how well MatCha pretraining transfers to domains such as screenshots, textbook diagrams, and document figures and observe overall improvement, verifying the usefulness of MatCha pretraining on broader visual language tasks.

Causal reasoning is a cornerstone of how humans interpret the world. To model and reason about causality, causal graphs offer a concise yet effective solution. Given the impressive advancements in language models, a crucial question arises: can they really understand causal graphs? To this end, we pioneer an investigation into language models' understanding of causal graphs. Specifically, we develop a framework to define causal graph understanding, by assessing language models' behaviors through four practical criteria derived from diverse disciplines (e.g., philosophy and psychology). We then develop CLEAR, a novel benchmark that defines three complexity levels and encompasses 20 causal graph-based tasks across these levels. Finally, based on our framework and benchmark, we conduct extensive experiments on six leading language models and summarize five empirical findings. Our results indicate that while language models demonstrate a preliminary understanding of causal graphs, significant potential for improvement remains. Our project website is at https://github.com/OpenCausaLab/CLEAR.

Graphs are a fundamental data structure for representing relationships in real-world scenarios. With the success of Large Language Models (LLMs) across various natural language processing (NLP) tasks, there has been growing interest in integrating LLMs for graph learning. However, applying LLMs to graph-related tasks poses significant challenges, as these models are not inherently designed to capture the complex structural information present in graphs. Existing approaches address this challenge through two strategies: the chain of tasks approach, which uses Graph Neural Networks (GNNs) to encode the graph structure so that LLMs are relieved from understanding spatial positions; and Graph-to-Text Conversion, which translates graph structures into semantic text representations that LLMs can process. Despite their progress, these methods often struggle to fully preserve the topological information of graphs or require extensive computational resources, limiting their practical applicability. In this work, we introduce Node Tokenizer for Large Language Models (NT-LLM), a novel framework that efficiently encodes graph structures by selecting key nodes as anchors and representing each node based on its relative distance to these anchors. This position-anchored encoding effectively captures the graph topology, enabling enhanced reasoning capabilities in LLMs over graph data. Additionally, we implement a task-specific tuning procedure to further improve structural understanding within LLMs. Through extensive empirical evaluations, NT-LLM demonstrates significant performance improvements across a variety of graph-related tasks.

Flowcharts are a critical tool for visualizing decision-making processes. However, their non-linear structure and complex visual-textual relationships make it challenging to interpret them using LLMs, as vision-language models frequently hallucinate nonexistent connections and decision paths when analyzing these diagrams. This leads to compromised reliability for automated flowchart processing in critical domains such as logistics, health, and engineering. We introduce the task of Fine-grained Flowchart Attribution, which traces specific components grounding a flowchart referring LLM response. Flowchart Attribution ensures the verifiability of LLM predictions and improves explainability by linking generated responses to the flowchart's structure. We propose FlowPathAgent, a neurosymbolic agent that performs fine-grained post hoc attribution through graph-based reasoning. It first segments the flowchart, then converts it into a structured symbolic graph, and then employs an agentic approach to dynamically interact with the graph, to generate attribution paths. Additionally, we present FlowExplainBench, a novel benchmark for evaluating flowchart attributions across diverse styles, domains, and question types. Experimental results show that FlowPathAgent mitigates visual hallucinations in LLM answers over flowchart QA, outperforming strong baselines by 10-14% on our proposed FlowExplainBench dataset.

In recent years, Graph Neural Networks (GNNs) have made significant advances in processing structured data. However, most of them primarily adopted a model-centric approach, which simplifies graphs by converting them into undirected formats and emphasizes model designs. This approach is inherently limited in real-world applications due to the unavoidable information loss in simple undirected graphs and the model optimization challenges that arise when exceeding the upper bounds of this sub-optimal data representational capacity. As a result, there has been a shift toward data-centric methods that prioritize improving graph quality and representation. Specifically, various types of graphs can be derived from naturally structured data, including heterogeneous graphs, hypergraphs, and directed graphs. Among these, directed graphs offer distinct advantages in topological systems by modeling causal relationships, and directed GNNs have been extensively studied in recent years. However, a comprehensive survey of this emerging topic is still lacking. Therefore, we aim to provide a comprehensive review of directed graph learning, with a particular focus on a data-centric perspective. Specifically, we first introduce a novel taxonomy for existing studies. Subsequently, we re-examine these methods from the data-centric perspective, with an emphasis on understanding and improving data representation. It demonstrates that a deep understanding of directed graphs and their quality plays a crucial role in model performance. Additionally, we explore the diverse applications of directed GNNs across 10+ domains, highlighting their broad applicability. Finally, we identify key opportunities and challenges within the field, offering insights that can guide future research and development in directed graph learning.

Large language models are increasingly deployed as agents that plan over long horizons and act through external tools. Most agents select actions through unconstrained generation over an accumulating history, leaving implicit the procedural knowledge of what to do, in what order, and under which conditions. As trajectories lengthen, agents can lose track of their objectives, invoke tools out of order, and repeat unproductive actions. We introduce the Procedural Graph: just as a knowledge graph organizes factual knowledge into (entity, relation, entity) triplets for what-is questions, a Procedural Graph organizes procedural knowledge into (procedure, relation, procedure) triplets for what-to-do questions. At each decision step, the framework localizes the agent's active node, and a guidance model translates the surrounding subgraph into step-level situational guidance that biases the solver's next action without dictating it. The graph is self-evolving: an LLM refiner contrasts failed trajectories with successful ones and edits the graph's topology and attributes, committing edits that preserve or improve held-out validation performance while retaining rejected ones to discourage repetition. Starting from a minimal skeleton, the loop builds graphs that match or surpass hand-designed ones. It can also repair a flawed expert prior. Across multiple datasets, task types, and LLMs, the Procedural Graph delivers consistent gains over memory-based baselines, and self-evolution further improves performance without manual engineering.

We present a unified representation for actionable spatial perception: 3D Dynamic Scene Graphs. Scene graphs are directed graphs where nodes represent entities in the scene (e.g. objects, walls, rooms), and edges represent relations (e.g. inclusion, adjacency) among nodes. Dynamic scene graphs (DSGs) extend this notion to represent dynamic scenes with moving agents (e.g. humans, robots), and to include actionable information that supports planning and decision-making (e.g. spatio-temporal relations, topology at different levels of abstraction). Our second contribution is to provide the first fully automatic Spatial PerceptIon eNgine(SPIN) to build a DSG from visual-inertial data. We integrate state-of-the-art techniques for object and human detection and pose estimation, and we describe how to robustly infer object, robot, and human nodes in crowded scenes. To the best of our knowledge, this is the first paper that reconciles visual-inertial SLAM and dense human mesh tracking. Moreover, we provide algorithms to obtain hierarchical representations of indoor environments (e.g. places, structures, rooms) and their relations. Our third contribution is to demonstrate the proposed spatial perception engine in a photo-realistic Unity-based simulator, where we assess its robustness and expressiveness. Finally, we discuss the implications of our proposal on modern robotics applications. 3D Dynamic Scene Graphs can have a profound impact on planning and decision-making, human-robot interaction, long-term autonomy, and scene prediction. A video abstract is available at https://youtu.be/SWbofjhyPzI

Large Language Models (LLMs) reasoning processes are challenging to analyze due to their complexity and the lack of organized visualization tools. We present ReasonGraph, a web-based platform for visualizing and analyzing LLM reasoning processes. It supports both sequential and tree-based reasoning methods while integrating with major LLM providers and over fifty state-of-the-art models. ReasonGraph incorporates an intuitive UI with meta reasoning method selection, configurable visualization parameters, and a modular framework that facilitates efficient extension. Our evaluation shows high parsing reliability, efficient processing, and strong usability across various downstream applications. By providing a unified visualization framework, ReasonGraph reduces cognitive load in analyzing complex reasoning paths, improves error detection in logical processes, and enables more effective development of LLM-based applications. The platform is open-source, promoting accessibility and reproducibility in LLM reasoning analysis.

The need to analyze graphs is ubiquitous across various fields, from social networks to biological research and recommendation systems. Therefore, enabling the ability of large language models (LLMs) to process graphs is an important step toward more advanced general intelligence. However, current LLM benchmarks on graph analysis require models to directly reason over the prompts describing graph topology, and are thus limited to small graphs with only a few dozens of nodes. In contrast, human experts typically write programs based on popular libraries for task solving, and can thus handle graphs with different scales. To this end, a question naturally arises: can LLMs analyze graphs like professionals? In this paper, we introduce ProGraph, a manually crafted benchmark containing 3 categories of graph tasks. The benchmark expects solutions based on programming instead of directly reasoning over raw inputs. Our findings reveal that the performance of current LLMs is unsatisfactory, with the best model achieving only 36% accuracy. To bridge this gap, we propose LLM4Graph datasets, which include crawled documents and auto-generated codes based on 6 widely used graph libraries. By augmenting closed-source LLMs with document retrieval and fine-tuning open-source ones on the codes, we show 11-32% absolute improvements in their accuracies. Our results underscore that the capabilities of LLMs in handling structured data are still under-explored, and show the effectiveness of LLM4Graph in enhancing LLMs' proficiency of graph analysis. The benchmark, datasets and enhanced open-source models are available at https://github.com/BUPT-GAMMA/ProGraph.

Graph representation learning models aim to represent the graph structure and its features into low-dimensional vectors in a latent space, which can benefit various downstream tasks, such as node classification and link prediction. Due to its powerful graph data modelling capabilities, various graph embedding models and libraries have been proposed to learn embeddings and help researchers ease conducting experiments. In this paper, we introduce a novel graph representation framework covering various graph embedding models, ranging from shallow to state-of-the-art models, namely Connector. First, we consider graph generation by constructing various types of graphs with different structural relations, including homogeneous, signed, heterogeneous, and knowledge graphs. Second, we introduce various graph representation learning models, ranging from shallow to deep graph embedding models. Finally, we plan to build an efficient open-source framework that can provide deep graph embedding models to represent structural relations in graphs. The framework is available at https://github.com/NSLab-CUK/Connector.

Although Vision Language Models (VLMs) have seen tremendous progress across all kinds of use cases, they still fall behind in answering questions regard-ing diagrams compared to photos. Although progress has been made in the area of bar charts, line charts and other diagrams like that there is still few research concerned with other types of diagrams, e.g. in the computer science domain. Our work presents a benchmark for visual question answering based on UML class diagrams which is both challenging and manageable. We further construct a large-scale training dataset with 16.000 image-question-answer triples and show that a LoRA-based finetune easily outperforms Qwen 3.5 27B, which is a recent and well-performing VLM in many other benchmarks.

Large language models (LLMs) have demonstrated strong capabilities across various language tasks, notably through instruction-tuning methods. However, LLMs face challenges in visualizing complex, real-world data through charts and plots. Firstly, existing datasets rarely cover a full range of chart types, such as 3D, volumetric, and gridded charts. Secondly, supervised fine-tuning methods do not fully leverage the intricate relationships within rich datasets, including text, code, and figures. To address these challenges, we propose a hierarchical pipeline and a new dataset for chart generation. Our dataset, Text2Chart31, includes 31 unique plot types referring to the Matplotlib library, with 11.1K tuples of descriptions, code, data tables, and plots. Moreover, we introduce a reinforcement learning-based instruction tuning technique for chart generation tasks without requiring human feedback. Our experiments show that this approach significantly enhances the model performance, enabling smaller models to outperform larger open-source models and be comparable to state-of-the-art proprietary models in data visualization tasks. We make the code and dataset available at https://github.com/fatemehpesaran310/Text2Chart31.

Mathematical knowledge is organized around statements and their dependencies, but this structure is exposed unevenly: informal papers cite mostly at the document level, while formal libraries record fine-grained dependencies over a much smaller body of mathematics. We introduce TheoremGraph, a unified statement-level dependency graph spanning both informal and formal mathematics. On the informal side, we parse 11.7M theorem-like environments from mathematics arXiv and recover 18.3M candidate directed dependencies, each labeled by the extractor that proposed it so downstream users can trade coverage for precision. On the formal side, we release LeanGraph, a Lean 4 elaborator-level extractor producing 388,105 declaration nodes and 11.3M typed edges across 25 Lean projects. We bridge the two graphs by embedding generated natural-language slogans into a shared semantic space, linking related statements across papers and across the informal/formal divide; an LLM judge affirms 47,952 such matches above a 0.8 cosine floor, with the judge-acceptance rate rising from 48% across the floor to 87% in the >=0.9 tier. On formal concept retrieval, our name-and-signature representation with graph expansion comes within 0.5pp of LeanSearch v2's reranked Recall@10 (0.775 vs. 0.780) without an LM reranker. We release the dataset, extractors, HTTP API, and MCP interface as infrastructure for mathematical search, attribution, and retrieval-augmented reasoning, available at theoremsearch.com and huggingface.co/datasets/uw-math-ai/theorem-matching.

The advancement of Large Language Models (LLMs) has remarkably pushed the boundaries towards artificial general intelligence (AGI), with their exceptional ability on understanding diverse types of information, including but not limited to images and audio. Despite this progress, a critical gap remains in empowering LLMs to proficiently understand and reason on graph data. Recent studies underscore LLMs' underwhelming performance on fundamental graph reasoning tasks. In this paper, we endeavor to unearth the obstacles that impede LLMs in graph reasoning, pinpointing the common practice of converting graphs into natural language descriptions (Graph2Text) as a fundamental bottleneck. To overcome this impediment, we introduce GraphLLM, a pioneering end-to-end approach that synergistically integrates graph learning models with LLMs. This synergy equips LLMs with the ability to proficiently interpret and reason on graph data, harnessing the superior expressive power of graph learning models. Our empirical evaluations across four fundamental graph reasoning tasks validate the effectiveness of GraphLLM. The results exhibit a substantial average accuracy enhancement of 54.44%, alongside a noteworthy context reduction of 96.45% across various graph reasoning tasks.

Flowcharts are indispensable tools in software design and business-process analysis, yet current vision-language models (VLMs) frequently misinterpret the directional arrows and graph topology that set these diagrams apart from natural images. We introduce a seven-stage pipeline grouped into three broader processes: (1) arrow-aware detection of nodes and arrow endpoints; (2) optical character recognition (OCR) to extract node text; and (3) construction of a structured prompt that guides the VLMs. Tested on a 90-question benchmark distilled from 30 annotated flowcharts, the method raises overall accuracy from 80 % to 89 % (+9 percentage points) without any task-specific fine-tuning. The gain is most pronounced for next-step queries (25/30 -> 30/30; 100 %, +17 pp); branch-result questions improve more modestly, and before-step questions remain difficult. A parallel evaluation with an LLM-as-a-Judge protocol shows the same trends, reinforcing the advantage of explicit arrow encoding. Limitations include dependence on detector and OCR precision, the small evaluation set, and residual errors at nodes with multiple incoming edges. Future work will enlarge the benchmark with synthetic and handwritten flowcharts and assess the approach on Business Process Model and Notation (BPMN) and Unified Modeling Language (UML).

Chart understanding is crucial for deploying multimodal large language models (MLLMs) in real-world scenarios such as analyzing scientific papers and technical reports. Unlike natural images, charts pair a structured visual layout (spatial property) with an underlying data representation (textual property) -- grasping both is essential for precise, fine-grained chart reasoning. Motivated by this observation, we propose START, the Spatial and Textual learning for chART understanding. Specifically, we introduce (i) chart-element grounding and (ii) chart-to-code generation to strengthen an MLLM's understanding of both chart visual layout and data details. To facilitate spatial and textual learning, we propose the START-Dataset generated with a novel data-generation pipeline that first leverages an MLLM to translate real chart images into executable chart code, recovering the underlying data representation while preserving the visual distribution of real-world charts. We then evolve the code with a Large Language Model (LLM) to ascertain the positions of chart elements that capture the chart's visual structure, addressing challenges that existing methods cannot handle. To evaluate a model's ability to understand chart spatial structures, we propose the Chart Spatial understanding Benchmark (CS-Bench), filling a critical gap in comprehensive chart understanding evaluation. Leveraging spatial and textual learning, START delivers consistent gains across model sizes and benchmarks over the base models and surpasses prior state-of-the-art by a clear margin. Code, data and models will be publicly available.

Chain-of-thought (CoT) traces have been shown to improve performance of large language models on a plethora of reasoning tasks, yet there is no consensus on the mechanism by which this boost is achieved. To shed more light on this, we introduce Causal CoT Graphs (CCGraphs), which are directed acyclic graphs automatically extracted from reasoning traces that model fine-grained causal dependencies in language-model outputs. A collection of 1671 mathematical reasoning problems from MATH500, GSM8K, and AIME, together with their associated CCGraphs, has been compiled into our dataset -- KisMATH. Our detailed empirical analysis with 15 open-weight LLMs shows that (i) reasoning nodes in the CCGraphs are causal contributors to the final answer, which we argue is constitutive of reasoning; and (ii) LLMs emphasize the reasoning paths captured by the CCGraphs, indicating that the models internally realize structures similar to our graphs. KisMATH enables controlled, graph-aligned interventions and opens avenues for further investigation into the role of CoT in LLM reasoning.

Scaling vision-language models into Visual Multiagent Systems (VMAS) is hindered by two coupled issues. First, communication topologies are fixed before inference, leaving them blind to visual content and query context; second, agent reasoning abilities remain static during deployment. These issues reinforce each other: a rigid topology fails to leverage richer agent expertise, while static agents lack incentives to specialize for a given query. We address this with SkillGraph, a joint framework that evolves both agent expertise and communication topology. Within this framework, a Multimodal Graph Transformer (MMGT) encodes visual tokens, instruction semantics and active skill embeddings to predict a query-conditioned collaboration graph, replacing hand-crafted routing with dynamic, content-aware information flow. Complementing this, a Skill Designer distills and refines reasoning heuristics from failure cases, constructing a self-evolving multimodal Skill Bank. Crucially, updated skill embeddings are fed back into the MMGT, enabling the topology to adapt alongside capability growth. Experiments show that SkillGraph achieves consistent improvements across four benchmarks, five common MAS structures and four base models. Code is available at https://github.com/niez233/skillgraph.

The generation of explanation graphs is a significant task that aims to produce explanation graphs in response to user input, revealing the internal reasoning process. This task is challenging due to the significant discrepancy between unstructured user queries and structured explanation graphs. Current research commonly fine-tunes a text-based pre-trained language model on a small downstream dataset that is annotated with labeled graphs. However, due to the limited scale of available datasets, this approach may prove to be insufficient in bridging the gap between natural language text and structured graphs. In this paper, to alleviate the above limitations, we propose a novel pre-trained framework EG3P(for Explanation Graph Generation via Generative Pre-training over synthetic graphs) for the explanation graph generation task. Specifically, we first propose a text-to-graph generative task to pre-train the model with the goal of bridging the text-graph gap. Additionally, we propose an automatic corpus synthesis strategy for synthesizing a large scale of high-quality corpus, reducing the reliance on costly manual annotation methods. Experimental results on ExplaGraphs show the effectiveness of EG3P that our model surpasses all baseline systems with remarkable margins. Besides, further analysis demonstrates that EG3P is able to generate better explanation graphs on actual reasoning tasks such as CommonsenseQA and OpenbookQA.

Structured images, such as diagrams, charts, and flowcharts, are inherently symbolic and can be compactly represented in an editable format, yet in practice, they are often rendered as images, and therefore not graphically editable. This mismatch presents a significant challenge for researchers, engineers, and designers who wish to incorporate modified versions of existing graphic content into new materials without manually reconstructing it. In this study, we presentBack2Struct, which "makes structured images editable again" by directly recovering vector graphics code (SVG / XML) from image representations. Given an image of a structured graphic, Back2Struct predicts semantically object-level SVG / XML code that explicitly encodes text, shapes, topology, and layout, rather than performing low-level pixel vectorization. The generated code can be seamlessly imported into tools such as PowerPoint, allowing users to edit, refine, restyle, and reuse graphic content while preserving structural fidelity. Beyond supervised fine-tuning on ground-truth SVG token sequences, we further optimize Back2Struct with reward-based learning to better match deployment-time requirements: the output should be syntactically valid, properly concise, and visually faithful to the input diagram. Specifically, we design a composite reward that jointly encourages SVG / XML compilability, length consistency with the reference code, and structural or semantic similarity between the generated and ground-truth graphics. These complementary signals guide the model to produce SVGs that are not only closer to the training distribution, but also more complete, editable, and renderable in practice. Experiments show that Back2Struct improves accuracy, editability, validity, and user alignment over baselines. Dataset and code are available at: pengyu965.github.io/Back2Struct.github.io

Controllable 3D scene generation has extensive applications in virtual reality and interior design, where the generated scenes should exhibit high levels of realism and controllability in terms of geometry. Scene graphs provide a suitable data representation that facilitates these applications. However, current graph-based methods for scene generation are constrained to text-based inputs and exhibit insufficient adaptability to flexible user inputs, hindering the ability to precisely control object geometry. To address this issue, we propose MMGDreamer, a dual-branch diffusion model for scene generation that incorporates a novel Mixed-Modality Graph, visual enhancement module, and relation predictor. The mixed-modality graph allows object nodes to integrate textual and visual modalities, with optional relationships between nodes. It enhances adaptability to flexible user inputs and enables meticulous control over the geometry of objects in the generated scenes. The visual enhancement module enriches the visual fidelity of text-only nodes by constructing visual representations using text embeddings. Furthermore, our relation predictor leverages node representations to infer absent relationships between nodes, resulting in more coherent scene layouts. Extensive experimental results demonstrate that MMGDreamer exhibits superior control of object geometry, achieving state-of-the-art scene generation performance. Project page: https://yangzhifeio.github.io/project/MMGDreamer.

Large language models (LLMs), while exhibiting exceptional performance, suffer from hallucinations, especially on knowledge-intensive tasks. Existing works propose to augment LLMs with individual text units retrieved from external knowledge corpora to alleviate the issue. However, in many domains, texts are interconnected (e.g., academic papers in a bibliographic graph are linked by citations and co-authorships) which form a (text-attributed) graph. The knowledge in such graphs is encoded not only in single texts/nodes but also in their associated connections. To facilitate the research of augmenting LLMs with graphs, we manually construct a Graph Reasoning Benchmark dataset called GRBench, containing 1,740 questions that can be answered with the knowledge from 10 domain graphs. Then, we propose a simple and effective framework called Graph Chain-of-thought (Graph-CoT) to augment LLMs with graphs by encouraging LLMs to reason on the graph iteratively. Each Graph-CoT iteration consists of three sub-steps: LLM reasoning, LLM-graph interaction, and graph execution. We conduct systematic experiments with three LLM backbones on GRBench, where Graph-CoT outperforms the baselines consistently. The code is available at https://github.com/PeterGriffinJin/Graph-CoT.

Rationale discovery is defined as finding a subset of the input data that maximally supports the prediction of downstream tasks. In graph machine learning context, graph rationale is defined to locate the critical subgraph in the given graph topology, which fundamentally determines the prediction results. In contrast to the rationale subgraph, the remaining subgraph is named the environment subgraph. Graph rationalization can enhance the model performance as the mapping between the graph rationale and prediction label is viewed as invariant, by assumption. To ensure the discriminative power of the extracted rationale subgraphs, a key technique named "intervention" is applied. The core idea of intervention is that given any changing environment subgraphs, the semantics from the rationale subgraph is invariant, which guarantees the correct prediction result. However, most, if not all, of the existing rationalization works on graph data develop their intervention strategies on the graph level, which is coarse-grained. In this paper, we propose well-tailored intervention strategies on graph data. Our idea is driven by the development of Transformer models, whose self-attention module provides rich interactions between input nodes. Based on the self-attention module, our proposed invariant graph Transformer (IGT) can achieve fine-grained, more specifically, node-level and virtual node-level intervention. Our comprehensive experiments involve 7 real-world datasets, and the proposed IGT shows significant performance advantages compared to 13 baseline methods.

In this paper we introduce a novel family of attributed graphs for the purpose of shape discrimination. Our graphs typically arise from variations on the Mapper graph construction, which is an approximation of the Reeb graph for point cloud data. Our attributions enrich these constructions with (persistent) homology in ways that are provably stable, thereby recording extra topological information that is typically lost in these graph constructions. We provide experiments which illustrate the use of these invariants for shape representation and classification. In particular, we obtain competitive shape classification results when using our topologically attributed graphs as inputs to a simple graph neural network classifier.

Transformers have revolutionized performance in Natural Language Processing and Vision, paving the way for their integration with Graph Neural Networks (GNNs). One key challenge in enhancing graph transformers is strengthening the discriminative power of distinguishing isomorphisms of graphs, which plays a crucial role in boosting their predictive performances. To address this challenge, we introduce 'Topology-Informed Graph Transformer (TIGT)', a novel transformer enhancing both discriminative power in detecting graph isomorphisms and the overall performance of Graph Transformers. TIGT consists of four components: A topological positional embedding layer using non-isomorphic universal covers based on cyclic subgraphs of graphs to ensure unique graph representation: A dual-path message-passing layer to explicitly encode topological characteristics throughout the encoder layers: A global attention mechanism: And a graph information layer to recalibrate channel-wise graph features for better feature representation. TIGT outperforms previous Graph Transformers in classifying synthetic dataset aimed at distinguishing isomorphism classes of graphs. Additionally, mathematical analysis and empirical evaluations highlight our model's competitive edge over state-of-the-art Graph Transformers across various benchmark datasets.

Engineering diagrams pose a distinct challenge for vision-language models: unlike natural images or general documents, they encode information through dense spatial layouts, domain-specific symbols, and cross-references between visual callouts and structured parts tables. Despite their centrality to service, repair, and design workflows, there is no public benchmark for measuring VLM capabilities in this domain; existing datasets primarily focus on flowcharts, scientific figures, or business documents. To address this gap, we introduce Enginuity, the first open dataset and benchmark for evaluating VLMs on complex engineering diagrams. We define two tasks over a corpus of U.S. military service and repair manuals: structured parts-table extraction (Task 1) and free-form visual diagram question answering (VQA)(Task 2) for benchmarking. We evaluate four frontier VLMs (GPT-5.2 Chat, Claude Opus 4.7, Gemma 4, Qwen3-VL-32B-Instruct) under zero-shot and chain-of-thought prompting. On Task 1, models reach Recall@all of 0.61-0.87 but Token F1pen of only 0.03-0.18, exposing a systematic gap between part identification and description fidelity. Task 2 reveals a consistent factual-reasoning gap across all models. A supporting analysis shows that token-overlap metrics under-report model capability on technical descriptions by 2-6x relative to semantic similarity, motivating LLM-as-judge calibration for domain-specific evaluation. We release the dataset, annotations, evaluation harness, and per-sample model outputs to support a reproducible study of VLM capability on engineering content.

Recently, the strong text creation ability of Large Language Models(LLMs) has given rise to many tools for assisting paper reading or even writing. However, the weak diagram analysis abilities of LLMs or Multimodal LLMs greatly limit their application scenarios, especially for scientific academic paper writing. In this work, towards a more versatile copilot for academic paper writing, we mainly focus on strengthening the multi-modal diagram analysis ability of Multimodal LLMs. By parsing Latex source files of high-quality papers, we carefully build a multi-modal diagram understanding dataset M-Paper. By aligning diagrams in the paper with related paragraphs, we construct professional diagram analysis samples for training and evaluation. M-Paper is the first dataset to support joint comprehension of multiple scientific diagrams, including figures and tables in the format of images or Latex codes. Besides, to better align the copilot with the user's intention, we introduce the `outline' as the control signal, which could be directly given by the user or revised based on auto-generated ones. Comprehensive experiments with a state-of-the-art Mumtimodal LLM demonstrate that training on our dataset shows stronger scientific diagram understanding performance, including diagram captioning, diagram analysis, and outline recommendation. The dataset, code, and model are available at https://github.com/X-PLUG/mPLUG-DocOwl/tree/main/PaperOwl.

The digitization of complex technical systems, such as Piping and Instrumentation Diagrams (P&IDs), is crucial for efficient maintenance and operation of complex systems in hydraulic and process engineering. Previous approaches often rely on separate modules that analyze diagram elements individually, neglecting the diagram's overall structure. We address this limitation by proposing a novel approach that utilizes the Relationformer, a state-of-the-art deep learning architecture, to extract graphs from P&IDs. Our method leverages the ability of the Relationformer to simultaneously detect objects and their relationships in images, making it suitable for the task of graph extraction from engineering diagrams. We apply our proposed approach to both real-world and synthetically created P&ID datasets, and evaluate its effectiveness by comparing it with a modular digitization approach based on recent literature. We present PID2Graph, the first publicly accessible P&ID dataset featuring comprehensive labels for the graph structure, including symbols, nodes and their connections that is used for evaluation. To understand the effect of patching and stitching of both of the approaches, we compare values before and after merging the patches. For the real-world data, the Relationformer achieves convincing results, outperforming the modular digitization approach for edge detection by more than 25%. Our work provides a comprehensive framework for assessing the performance of P&ID digitization methods and opens up new avenues for research in this area using transformer architectures. The P&ID dataset used for evaluation will be published and publicly available upon acceptance of the paper.

In recent years, graph prompting has emerged as a promising research direction, enabling the learning of additional tokens or subgraphs appended to the original graphs without requiring retraining of pre-trained graph models across various applications. This novel paradigm, shifting from the traditional pretraining and finetuning to pretraining and prompting has shown significant empirical success in simulating graph data operations, with applications ranging from recommendation systems to biological networks and graph transferring. However, despite its potential, the theoretical underpinnings of graph prompting remain underexplored, raising critical questions about its fundamental effectiveness. The lack of rigorous theoretical proof of why and how much it works is more like a dark cloud over the graph prompt area to go further. To fill this gap, this paper introduces a theoretical framework that rigorously analyzes graph prompting from a data operation perspective. Our contributions are threefold: First, we provide a formal guarantee theorem, demonstrating graph prompts capacity to approximate graph transformation operators, effectively linking upstream and downstream tasks. Second, we derive upper bounds on the error of these data operations by graph prompts for a single graph and extend this discussion to batches of graphs, which are common in graph model training. Third, we analyze the distribution of data operation errors, extending our theoretical findings from linear graph models (e.g., GCN) to non-linear graph models (e.g., GAT). Extensive experiments support our theoretical results and confirm the practical implications of these guarantees.

Large language models can translate a researcher's intent into runnable matplotlib code, yet the resulting chart rarely lands in a paper without multiple rounds of manual revision. We argue that the open problem is not chart code generation but chart publication: making the output look like a top-venue figure, survive the target layout, and respond to precise author edits. We present chart-plot, an agentic harness that closes this last mile through three components: (1) a style-aware code generator conditioned on a textual style skill distilled from accepted figures at the target venue, (2) a deployment-aware render loop that compiles the chart inside the target LaTeX context and revises until layout constraints are met, and (3) a structured edit layer that exposes every chart element as a directly manipulable handle. We report early results on three chart-type case studies (grouped bar, scaling line, paired distributions) and a small user study.

In the past years, predictive process monitoring (PPM) techniques based on artificial neural networks have evolved as a method to monitor the future behavior of business processes. Existing approaches mostly focus on interpreting the processes as sequences, so-called traces, and feeding them to neural architectures designed to operate on sequential data such as recurrent neural networks (RNNs) or transformers. In this study, we investigate an alternative way to perform PPM: by transforming each process in its directly-follows-graph (DFG) representation we are able to apply graph neural networks (GNNs) for the prediction tasks. By this, we aim to develop models that are more suitable for complex processes that are long and contain an abundance of loops. In particular, we present different ways to create DFG representations depending on the particular GNN we use. The tested GNNs range from classical node-based to novel edge-based architectures. Further, we investigate the possibility of using multi-graphs. By these steps, we aim to design graph representations that minimize the information loss when transforming traces into graphs.

Recent efforts have aimed to automate scientific diagram generation from paper content (Lin et al., 2026; Zhu et al., 2026a). However, fully satisfying an author's visual and communicative preferences in a single turn is challenging: in our formative user study (N = 14), all participants requested further revisions after viewing an initial draft, and 86% of them rated the refined diagrams as more satisfactory. Despite the clear demand, the multi-turn workflow remains largely underexplored. To bridge this gap, we present MTPaperBananaBench, a benchmark for multi-turn diagram generation containing 292 images annotated with 3,518 user requirements. To reduce expensive human studies and enable scalable benchmarking, we construct a user simulator that, at each turn, identifies unsatisfied requirements and converts k of them into natural language feedback. Evaluating both requirement satisfaction and overall diagram quality reveals two key failure modes shared across baseline multiturn systems: (1) quality drift, where diagram quality progressively declines over turns, and (2) forgetting, where previously implemented features are lost in subsequent turns. To address these issues, we introduce PaperBanana-Interact, a multi-agent system that refines diagrams via an internal critique-and-refine loop. PaperBanana-Interact consistently improves rather than degrades diagram quality across turns, outperforming baselines by 11.9-18.6 points in quality score and reducing forgetting by 3.7-6.2 points.

Recent advances in large language models (LLMs) have opened new avenues for multimodal reasoning. Yet, most existing methods still rely on pretrained vision-language models (VLMs) to encode image-text pairs in isolation, ignoring the relational structure that real-world multimodal data naturally form. This motivates reasoning on multimodal graphs (MMGs), where each node has textual and visual attributes and edges provide structural cues. Enabling LLM-based reasoning on such heterogeneous multimodal signals while preserving graph topology introduces two key challenges: resolving weak cross-modal consistency and handling heterogeneous modality preference. To address this, we propose Mario, a unified framework that simultaneously resolves the two above challenges and enables effective LLM-based reasoning over MMGs. Mario consists of two innovative stages. Firstly, a graph-conditioned VLM design that jointly refines textual and visual features through fine-grained cross-modal contrastive learning guided by graph topology. Secondly, a modality-adaptive graph instruction tuning mechanism that organizes aligned multimodal features into graph-aware instruction views and employs a learnable router to surface, for each node and its neighborhood, the most informative modality configuration to the LLM. Extensive experiments across diverse MMG benchmarks demonstrate that Mario consistently outperforms state-of-the-art graph models in both supervised and zero-shot scenarios for node classification and link prediction. The code will be made available at https://github.com/sunyuanfu/Mario.

Chart understanding presents a critical test to the reasoning capabilities of Vision-Language Models (VLMs). Prior approaches face critical limitations: some rely on external tools, making them brittle and constrained by a predefined toolkit, while others fine-tune specialist models that often adopt a single reasoning strategy, such as text-based chain-of-thought (CoT). The intermediate steps of text-based reasoning are difficult to verify, which complicates the use of reinforcement-learning signals that reward factual accuracy. To address this, we propose a Code-as-Thought (CaT) approach to represent the visual information of a chart in a verifiable, symbolic format. Our key insight is that this strategy must be adaptive: a fixed, code-only implementation consistently fails on complex charts where symbolic representation is unsuitable. This finding leads us to introduce Visual Programmability: a learnable property that determines if a chart-question pair is better solved with code or direct visual analysis. We implement this concept in an adaptive framework where a VLM learns to choose between the CaT pathway and a direct visual reasoning pathway. The selection policy of the model is trained with reinforcement learning using a novel dual-reward system. This system combines a data-accuracy reward to ground the model in facts and prevent numerical hallucination, with a decision reward that teaches the model when to use each strategy, preventing it from defaulting to a single reasoning mode. Experiments demonstrate strong and robust performance across diverse chart-understanding benchmarks. Our work shows that VLMs can be taught not only to reason but also how to reason, dynamically selecting the optimal reasoning pathway for each task.

Graph is powerful for representing various types of real-world data. The topology (edges' presence) and edges' features of a graph decides the message passing mechanism among vertices within the graph. While most existing approaches only manually define a single-value edge to describe the connectivity or strength of association between a pair of vertices, task-specific and crucial relationship cues may be disregarded by such manually defined topology and single-value edge features. In this paper, we propose the first general graph representation learning framework (called GRATIS) which can generate a strong graph representation with a task-specific topology and task-specific multi-dimensional edge features from any arbitrary input. To learn each edge's presence and multi-dimensional feature, our framework takes both of the corresponding vertices pair and their global contextual information into consideration, enabling the generated graph representation to have a globally optimal message passing mechanism for different down-stream tasks. The principled investigation results achieved for various graph analysis tasks on 11 graph and non-graph datasets show that our GRATIS can not only largely enhance pre-defined graphs but also learns a strong graph representation for non-graph data, with clear performance improvements on all tasks. In particular, the learned topology and multi-dimensional edge features provide complementary task-related cues for graph analysis tasks. Our framework is effective, robust and flexible, and is a plug-and-play module that can be combined with different backbones and Graph Neural Networks (GNNs) to generate a task-specific graph representation from various graph and non-graph data. Our code is made publicly available at https://github.com/SSYSteve/Learning-Graph-Representation-with-Task-specific-Topology-and-Multi-dimensional-Edge-Features.

Being able to effectively read scientific plots, or chart understanding, is a central part toward building effective agents for science. However, existing multimodal large language models (MLLMs), especially open-source ones, are still falling behind with a typical success rate of 30%-50% on challenging benchmarks. Previous studies on fine-tuning MLLMs with synthetic charts are often restricted by their inadequate similarity to the real charts, which could compromise model training and performance on complex real-world charts. In this study, we show that modularizing chart generation and diversifying visual details improves chart understanding capabilities. In particular, we design a five-step data synthesis pipeline, where we separate data and function creation for single plot generation, condition the generation of later subplots on earlier ones for multi-subplot figures, visually diversify the generated figures, filter out low quality data, and finally generate the question-answer (QA) pairs with GPT-4o. This approach allows us to streamline the generation of fine-tuning datasets and introduce the effective chart dataset (ECD), which contains 10k+ chart images and 300k+ QA pairs, covering 25 topics and featuring 250+ chart type combinations with high visual complexity. We show that ECD consistently improves the performance of various MLLMs on a range of real-world and synthetic test sets. Code, data and models are available at: https://github.com/yuweiyang-anu/ECD.

Generating bitmap graphics from text has gained considerable attention, yet for scientific figures, vector graphics are often preferred. Given that vector graphics are typically encoded using low-level graphics primitives, generating them directly is difficult. To address this, we propose the use of TikZ, a well-known abstract graphics language that can be compiled to vector graphics, as an intermediate representation of scientific figures. TikZ offers human-oriented, high-level commands, thereby facilitating conditional language modeling with any large language model. To this end, we introduce DaTikZ the first large-scale TikZ dataset, consisting of 120k TikZ drawings aligned with captions. We fine-tune LLaMA on DaTikZ, as well as our new model CLiMA, which augments LLaMA with multimodal CLIP embeddings. In both human and automatic evaluation, CLiMA and LLaMA outperform commercial GPT-4 and Claude 2 in terms of similarity to human-created figures, with CLiMA additionally improving text-image alignment. Our detailed analysis shows that all models generalize well and are not susceptible to memorization. GPT-4 and Claude 2, however, tend to generate more simplistic figures compared to both humans and our models. We make our framework, AutomaTikZ, along with model weights and datasets, publicly available.

Methods that use Large Language Models (LLM) as planners for embodied instruction following tasks have become widespread. To successfully complete tasks, the LLM must be grounded in the environment in which the robot operates. One solution is to use a scene graph that contains all the necessary information. Modern methods rely on prebuilt scene graphs and assume that all task-relevant information is available at the start of planning. However, these approaches do not account for changes in the environment that may occur between the graph construction and the task execution. We propose LookPlanGraph - a method that leverages a scene graph composed of static assets and object priors. During plan execution, LookPlanGraph continuously updates the graph with relevant objects, either by verifying existing priors or discovering new entities. This is achieved by processing the agents egocentric camera view using a Vision Language Model. We conducted experiments with changed object positions VirtualHome and OmniGibson simulated environments, demonstrating that LookPlanGraph outperforms methods based on predefined static scene graphs. To demonstrate the practical applicability of our approach, we also conducted experiments in a real-world setting. Additionally, we introduce the GraSIF (Graph Scenes for Instruction Following) dataset with automated validation framework, comprising 514 tasks drawn from SayPlan Office, BEHAVIOR-1K, and VirtualHome RobotHow. Project page available at https://lookplangraph.github.io .

Understanding and reasoning over diagrams is a fundamental aspect of human intelligence. While Large Multimodal Models (LMMs) have demonstrated impressive capabilities across various tasks, existing benchmarks lack comprehensive evaluation of their diagram interpretation and reasoning abilities, particularly in coding contexts. We present HumanEval-V, a rigorous benchmark of human-annotated coding tasks that spans six task types and evaluates diverse visual reasoning capabilities. Each task features carefully crafted diagrams paired with function signatures and test cases, employing novel code generation tasks to thoroughly assess models' diagram comprehension. Through extensive experiments with 22 LMMs, we find that even top-performing models achieve modest success rates, with Claude 3.5 Sonnet reaching only 36.8% pass@1, highlighting substantial room for improvement. Our analysis reveals that current LMMs struggle with spatial transformations, topological relationships, and dynamic patterns that humans find intuitive. These findings provide valuable insights for advancing LMMs' visual reasoning abilities. We have open-sourced our code and benchmark at https://github.com/HumanEval-V/HumanEval-V-Benchmark.

Language models have been effective in a wide range of applications, yet the most sophisticated models are often proprietary. For example, GPT-4 by OpenAI and various models by Anthropic are expensive and consume substantial energy. In contrast, the open-source community has produced competitive models, like Llama3. Furthermore, niche-specific smaller language models, such as those tailored for legal, medical or financial tasks, have outperformed their proprietary counterparts. This paper introduces a novel approach that employs functional tokens to integrate multiple open-source models, each optimized for particular tasks. Our newly developed Octopus v4 model leverages functional tokens to intelligently direct user queries to the most appropriate vertical model and reformat the query to achieve the best performance. Octopus v4, an evolution of the Octopus v1, v2, and v3 models, excels in selection and parameter understanding and reformatting. Additionally, we explore the use of graph as a versatile data structure that effectively coordinates multiple open-source models by harnessing the capabilities of the Octopus model and functional tokens. Use our open-sourced GitHub (https://www.nexa4ai.com/) to try Octopus v4 models (https://huggingface.co/NexaAIDev/Octopus-v4), and contrite to a larger graph of language models. By activating models less than 10B parameters, we achieved SOTA MMLU score of 74.8 among the same level models.

Large language models (LLMs) have achieved impressive success across several fields, but their proficiency in understanding and resolving complex graph problems is less explored. To bridge this gap, we introduce GraphInstruct, a novel and comprehensive instruction-tuning dataset designed to equip language models with the ability to tackle a broad spectrum of graph problems using explicit reasoning paths. Utilizing GraphInstruct, we build GraphWiz, an open-source language model capable of resolving various graph problem types while generating clear reasoning processes. To enhance the model's capability and reliability, we incorporate the Direct Preference Optimization (DPO) framework into the graph problem-solving context. The enhanced model, GraphWiz-DPO, achieves an average accuracy of 65% across nine tasks with different complexity levels, surpassing GPT-4 which has an average accuracy of 43.8%. Moreover, our research delves into the delicate balance between training data volume and model performance, highlighting the potential for overfitting with increased data. We also explore the transferability of the model's reasoning ability across different graph tasks, indicating the model's adaptability and practical application potential. Our investigation offers a new blueprint and valuable insights for developing LLMs specialized in graph reasoning and problem-solving.

We study the implications of the modeling choice to use a graph, instead of a hypergraph, to represent real-world interconnected systems whose constituent relationships are of higher order by nature. Such a modeling choice typically involves an underlying projection process that maps the original hypergraph onto a graph, and is common in graph-based analysis. While hypergraph projection can potentially lead to loss of higher-order relations, there exists very limited studies on the consequences of doing so, as well as its remediation. This work fills this gap by doing two things: (1) we develop analysis based on graph and set theory, showing two ubiquitous patterns of hyperedges that are root to structural information loss in all hypergraph projections; we also quantify the combinatorial impossibility of recovering the lost higher-order structures if no extra help is provided; (2) we still seek to recover the lost higher-order structures in hypergraph projection, and in light of (1)'s findings we propose to relax the problem into a learning-based setting. Under this setting, we develop a learning-based hypergraph reconstruction method based on an important statistic of hyperedge distributions that we find. Our reconstruction method is evaluated on 8 real-world datasets under different settings, and exhibits consistently good performance. We also demonstrate benefits of the reconstructed hypergraphs via use cases of protein rankings and link predictions.

Evaluating and enhancing the general capabilities of large language models (LLMs) has been an important research topic. Graph is a common data structure in the real world, and understanding graph data is a crucial part for advancing general intelligence. To evaluate and enhance the graph understanding abilities of LLMs, in this paper, we propose a benchmark named GraphInstruct, which comprehensively includes 21 classical graph reasoning tasks, providing diverse graph generation pipelines and detailed reasoning steps. Based on GraphInstruct, we further construct GraphLM through efficient instruction-tuning, which shows prominent graph understanding capability. In order to enhance the LLM with graph reasoning capability as well, we propose a step mask training strategy, and construct a model named GraphLM+. As one of the pioneering efforts to enhance the graph understanding and reasoning abilities of LLMs, extensive experiments have demonstrated the superiority of GraphLM and GraphLM+ over other LLMs. We look forward to more researchers exploring the potential of LLMs in the graph data mining domain through GraphInstruct. Our code for generating GraphInstruct is released publicly at: https://github.com/CGCL-codes/GraphInstruct.

Multimodal Large Language Models (MLLMs) excel at recognizing individual visual elements and reasoning over simple linear diagrams. However, when faced with complex topological structures involving branching paths, converging flows, and cyclic dependencies, their reasoning capabilities degrade sharply, even on tasks as basic as counting endpoints. Existing benchmarks fail to probe this gap, focusing on semantic comprehension rather than structural reasoning. We introduce ReactBench, a benchmark that reveals fundamental limitations in structural reasoning through chemical reaction diagrams. These real-world scientific diagrams offer an ideal testbed because they naturally span diverse structures from linear chains to cyclic graphs, while requiring both precise local recognition and coherent global reasoning. Our benchmark comprises 1,618 expert-annotated QA pairs across four hierarchical task dimensions. Extensive evaluation across 17 MLLMs reveals a significant performance gap exceeding 30% between anchor-based tasks and holistic structural reasoning tasks. Controlled ablations confirm this bottleneck lies in reasoning, not perception. These findings expose a fundamental deficit in structural understanding and establish directions for advancing visual reasoning.

Biomedical knowledge graphs (KGs) are widely used in the life sciences, yet many are derived from unstructured documents and therefore lack schema-level constrains, whereas graphs assembled from structured resources are difficult to harmonize into a unified representation. We present OptimusKG, a multimodal biomedical labeled property graph (LPG) built from structured and semi-structured resources to preserve factual, type-specific metadata across molecular, anatomical, clinical, and environmental domains. OptimusKG contains 190,531 nodes across 10 entity types, 21,813,816 edges across 26 relation types, and 67,249,863 property instances encoding 110,276,843 values across 150 distinct property keys, derived from 18 ontologies and controlled vocabularies. The graph enforces a top-level schema for nodes and edges and retains granular, type-specific properties, cross-references, and provenance across molecular, anatomical, clinical, and environmental domains. We assessed the validity of OptimusKG by evaluating whether graph relationships are supported by evidence from the scientific literature using a multimodal agent, PaperQA3. PaperQA3 identified supporting evidence for 70.0% of sampled edges, whereas 83.4% of sampled false edges received no supporting evidence. Edges without literature support were concentrated in associations derived from experimental and functional genomics resources, suggesting that OptimusKG captures biomedical knowledge that may precede synthesis in the scientific literature. OptimusKG is distributed as Apache Parquet files, providing a standardized resource for graph-based machine learning, knowledge-grounded retrieval with large language models, and biomedical discovery use cases such as hypothesis generation.

Forecasting future links is a central task in temporal graph (TG) reasoning, requiring models to leverage historical interactions to predict upcoming ones. Traditional neural approaches, such as temporal graph neural networks, achieve strong performance but lack explainability and cannot be applied to unseen graphs without retraining. Recent studies have begun to explore using large language models (LLMs) for graph reasoning, but most of them are constrained to static graphs or small synthetic TGs and lack the evaluation of the quality of reasoning traces generated by LLMs. In this work, we present Reasoning-Enhanced Learning for Temporal Graphs (ReaL-TG), a reinforcement learning framework that fine-tunes LLMs to perform explainable link forecasting on real-world TGs. ReaL-TG uses outcome-based reward to encourage models to self-explore reasoning strategies from graph structure and to produce explanations that directly justify their predictions. To enable evaluation on LLM-generated reasoning traces, we propose a new evaluation protocol combining ranking metrics with an LLM-as-a-Judge system that assesses both the quality of reasoning and the impact of hallucinations. Experiments with ReaL-TG-4B, obtained by fine-tuning Qwen3-4B under our framework, show that it outperforms much larger frontier LLMs, including GPT-5 mini, on ranking metrics, while producing high-quality explanations confirmed by both the LLM judge and human evaluation.

Recent advances in search-augmented large reasoning models (LRMs) enable the retrieval of external knowledge to reduce hallucinations in multistep reasoning. However, their ability to operate on graph-structured data, prevalent in domains such as e-commerce, social networks, and scientific citations, remains underexplored. Unlike plain text corpora, graphs encode rich topological signals that connect related entities and can serve as valuable priors for retrieval, enabling more targeted search and improved reasoning efficiency. Yet, effectively leveraging such structure poses unique challenges, including the difficulty of generating graph-expressive queries and ensuring reliable retrieval that balances structural and semantic relevance. To address this gap, we introduce GraphSearch, the first framework that extends search-augmented reasoning to graph learning, enabling zero-shot graph learning without task-specific fine-tuning. GraphSearch combines a Graph-aware Query Planner, which disentangles search space (e.g., 1-hop, multi-hop, or global neighbors) from semantic queries, with a Graph-aware Retriever, which constructs candidate sets based on topology and ranks them using a hybrid scoring function. We further instantiate two traversal modes: GraphSearch-R, which recursively expands neighborhoods hop by hop, and GraphSearch-F, which flexibly retrieves across local and global neighborhoods without hop constraints. Extensive experiments across diverse benchmarks show that GraphSearch achieves competitive or even superior performance compared to supervised graph learning methods, setting state-of-the-art results in zero-shot node classification and link prediction. These findings position GraphSearch as a flexible and generalizable paradigm for agentic reasoning over graphs.

Various human-designed prompt engineering techniques have been proposed to improve problem solvers based on Large Language Models (LLMs), yielding many disparate code bases. We unify these approaches by describing LLM-based agents as computational graphs. The nodes implement functions to process multimodal data or query LLMs, and the edges describe the information flow between operations. Graphs can be recursively combined into larger composite graphs representing hierarchies of inter-agent collaboration (where edges connect operations of different agents). Our novel automatic graph optimizers (1) refine node-level LLM prompts (node optimization) and (2) improve agent orchestration by changing graph connectivity (edge optimization). Experiments demonstrate that our framework can be used to efficiently develop, integrate, and automatically improve various LLM agents. The code can be found at https://github.com/metauto-ai/gptswarm.

Although most current large multimodal models (LMMs) can already understand photos of natural scenes and portraits, their understanding of abstract images, e.g., charts, maps, or layouts, and visual reasoning capabilities remains quite rudimentary. They often struggle with simple daily tasks, such as reading time from a clock, understanding a flowchart, or planning a route using a road map. In light of this, we design a multi-modal self-instruct, utilizing large language models and their code capabilities to synthesize massive abstract images and visual reasoning instructions across daily scenarios. Our strategy effortlessly creates a multimodal benchmark with 11,193 instructions for eight visual scenarios: charts, tables, simulated maps, dashboards, flowcharts, relation graphs, floor plans, and visual puzzles. This benchmark, constructed with simple lines and geometric elements, exposes the shortcomings of most advanced LMMs like Claude-3.5-Sonnet and GPT-4o in abstract image understanding, spatial relations reasoning, and visual element induction. Besides, to verify the quality of our synthetic data, we fine-tune an LMM using 62,476 synthetic chart, table and road map instructions. The results demonstrate improved chart understanding and map navigation performance, and also demonstrate potential benefits for other visual reasoning tasks. Our code is available at: https://github.com/zwq2018/Multi-modal-Self-instruct.

For robots to perform a wide variety of tasks, they require a 3D representation of the world that is semantically rich, yet compact and efficient for task-driven perception and planning. Recent approaches have attempted to leverage features from large vision-language models to encode semantics in 3D representations. However, these approaches tend to produce maps with per-point feature vectors, which do not scale well in larger environments, nor do they contain semantic spatial relationships between entities in the environment, which are useful for downstream planning. In this work, we propose ConceptGraphs, an open-vocabulary graph-structured representation for 3D scenes. ConceptGraphs is built by leveraging 2D foundation models and fusing their output to 3D by multi-view association. The resulting representations generalize to novel semantic classes, without the need to collect large 3D datasets or finetune models. We demonstrate the utility of this representation through a number of downstream planning tasks that are specified through abstract (language) prompts and require complex reasoning over spatial and semantic concepts. (Project page: https://concept-graphs.github.io/ Explainer video: https://youtu.be/mRhNkQwRYnc )

Associating unstructured data with structured information is crucial for real-world tasks that require relevance search. However, existing graph learning benchmarks often overlook the rich semantic information associate with each node. To bridge such gap, we introduce the Multimodal Graph Benchmark (MM-GRAPH), the first comprehensive multi-modal graph benchmark that incorporates both textual and visual information. MM-GRAPH surpasses previous efforts, which have primarily focused on text-attributed graphs with various connectivity patterns. MM-GRAPH consists of five graph learning datasets of various scales that are appropriate for different learning tasks. Their multimodal node features, enabling a more comprehensive evaluation of graph learning algorithms in real-world scenarios. To facilitate research on multimodal graph learning, we further provide an extensive study on the performance of various graph neural networks in the presence of features from various modalities. MM-GRAPH aims to foster research on multimodal graph learning and drive the development of more advanced and robust graph learning algorithms. By providing a diverse set of datasets and benchmarks, MM-GRAPH enables researchers to evaluate and compare their models in realistic settings, ultimately leading to improved performance on real-world applications that rely on multimodal graph data.

Recently, there has been a surge of interest in employing neural networks for graph generation, a fundamental statistical learning problem with critical applications like molecule design and community analysis. However, most approaches encounter significant limitations when generating large-scale graphs. This is due to their requirement to output the full adjacency matrices whose size grows quadratically with the number of nodes. In response to this challenge, we introduce a new, simple, and scalable graph representation named gap encoded edge list (GEEL) that has a small representation size that aligns with the number of edges. In addition, GEEL significantly reduces the vocabulary size by incorporating the gap encoding and bandwidth restriction schemes. GEEL can be autoregressively generated with the incorporation of node positional encoding, and we further extend GEEL to deal with attributed graphs by designing a new grammar. Our findings reveal that the adoption of this compact representation not only enhances scalability but also bolsters performance by simplifying the graph generation process. We conduct a comprehensive evaluation across ten non-attributed and two molecular graph generation tasks, demonstrating the effectiveness of GEEL.

Graph-structured data are the commonly used and have wide application scenarios in the real world. For these diverse applications, the vast variety of learning tasks, graph domains, and complex graph learning procedures present challenges for human experts when designing versatile graph learning approaches. Facing these challenges, large language models (LLMs) offer a potential solution due to the extensive knowledge and the human-like intelligence. This paper proposes a novel conceptual prototype for designing versatile graph learning methods with LLMs, with a particular focus on the "where" and "how" perspectives. From the "where" perspective, we summarize four key graph learning procedures, including task definition, graph data feature engineering, model selection and optimization, deployment and serving. We then explore the application scenarios of LLMs in these procedures across a wider spectrum. In the "how" perspective, we align the abilities of LLMs with the requirements of each procedure. Finally, we point out the promising directions that could better leverage the strength of LLMs towards versatile graph learning methods.

Neuronal morphology encodes critical information about circuit function, development, and disease, yet current methods analyze topology or graph structure in isolation. We introduce GraPHFormer, a multimodal architecture that unifies these complementary views through CLIP-style contrastive learning. Our vision branch processes a novel three-channel persistence image encoding unweighted, persistence-weighted, and radius-weighted topological densities via DINOv2-ViT-S. In parallel, a TreeLSTM encoder captures geometric and radial attributes from skeleton graphs. Both project to a shared embedding space trained with symmetric InfoNCE loss, augmented by persistence-space transformations that preserve topological semantics. Evaluated on six benchmarks (BIL-6, ACT-4, JML-4, N7, M1-Cell, M1-REG) spanning self-supervised and supervised settings, GraPHFormer achieves state-of-the-art performance on five benchmarks, significantly outperforming topology-only, graph-only, and morphometrics baselines. We demonstrate practical utility by discriminating glial morphologies across cortical regions and species, and detecting signatures of developmental and degenerative processes. Code: https://github.com/Uzshah/GraPHFormer

Scene graph representations enable structured visual understanding by modeling objects and their relationships, and have been widely used for multiview and 3D scene reasoning. Existing methods such as MSG learn scene graph embeddings in Euclidean space using contrastive learning and attention based association. However, Euclidean geometry does not explicitly capture hierarchical entailment relationships between places and objects, limiting the structural consistency of learned representations. To address this, we propose Hyperbolic Scene Graph (HSG), which learns scene graph embeddings in hyperbolic space where hierarchical relationships are naturally encoded through geometric distance. Our results show that HSG improves hierarchical structure quality while maintaining strong retrieval performance. The largest gains are observed in graph level metrics: HSG achieves a PP IoU of 33.17 and the highest Graph IoU of 33.51, outperforming the best AoMSG variant (25.37) by 8.14, highlighting the effectiveness of hyperbolic representation learning for scene graph modeling. Code: https://github.com/AIGeeksGroup/HSG.

Auxiliary lines are essential for solving complex geometric problems but remain challenging for large vision-language models (LVLMs). Recent attempts construct auxiliary lines via code-driven rendering, a strategy that relies on accurate and executable code generation to produce visual renderings of the auxiliary lines for subsequent reasoning. However, in complex solid geometry settings, such a strong dependence on precise specifications substantially restricts the robustness of this strategy. Alternatively, we turn to a simpler and more stable solution, representing auxiliary-line constructions as structured textual descriptions. To bridge the gap between textual descriptions and spatial structure, we propose a reinforcement learning framework that enhances diagram-text alignment. The core is a cross-modal reward model that evaluates how well the generated auxiliary-line description matches the ground-truth auxiliary-line diagram. The reward signal drives a GRPO-based RL stage to yield informative auxiliary-line descriptions for the reasoning. To support the training and evaluation, we develop a scalable data pipeline and construct AuxSolidMath, a dataset of 3,018 real-exam geometry problems with paired diagrams and aligned textual fields. Based on this framework, we derive GeoVLMath, an LVLM for solving complex solid geometry.

3D indoor scenes are widely used in computer graphics, with applications ranging from interior design to gaming to virtual and augmented reality. They also contain rich information, including room layout, as well as furniture type, geometry, and placement. High-quality 3D indoor scenes are highly demanded while it requires expertise and is time-consuming to design high-quality 3D indoor scenes manually. Existing research only addresses partial problems: some works learn to generate room layout, and other works focus on generating detailed structure and geometry of individual furniture objects. However, these partial steps are related and should be addressed together for optimal synthesis. We propose SCENEHGN, a hierarchical graph network for 3D indoor scenes that takes into account the full hierarchy from the room level to the object level, then finally to the object part level. Therefore for the first time, our method is able to directly generate plausible 3D room content, including furniture objects with fine-grained geometry, and their layout. To address the challenge, we introduce functional regions as intermediate proxies between the room and object levels to make learning more manageable. To ensure plausibility, our graph-based representation incorporates both vertical edges connecting child nodes with parent nodes from different levels, and horizontal edges encoding relationships between nodes at the same level. Extensive experiments demonstrate that our method produces superior generation results, even when comparing results of partial steps with alternative methods that can only achieve these. We also demonstrate that our method is effective for various applications such as part-level room editing, room interpolation, and room generation by arbitrary room boundaries.

Captions that describe or explain charts help improve recall and comprehension of the depicted data and provide a more accessible medium for people with visual disabilities. However, current approaches for automatically generating such captions struggle to articulate the perceptual or cognitive features that are the hallmark of charts (e.g., complex trends and patterns). In response, we introduce VisText: a dataset of 12,441 pairs of charts and captions that describe the charts' construction, report key statistics, and identify perceptual and cognitive phenomena. In VisText, a chart is available as three representations: a rasterized image, a backing data table, and a scene graph -- a hierarchical representation of a chart's visual elements akin to a web page's Document Object Model (DOM). To evaluate the impact of VisText, we fine-tune state-of-the-art language models on our chart captioning task and apply prefix-tuning to produce captions that vary the semantic content they convey. Our models generate coherent, semantically rich captions and perform on par with state-of-the-art chart captioning models across machine translation and text generation metrics. Through qualitative analysis, we identify six broad categories of errors that our models make that can inform future work.

Understanding charts requires models to jointly reason over geometric visual patterns, structured numerical data, and natural language -- a capability where current vision-language models (VLMs) remain limited. We introduce ChartNet, a high-quality, million-scale multimodal dataset designed to advance chart interpretation and reasoning. ChartNet leverages a novel code-guided synthesis pipeline to generate 1.5 million diverse chart samples spanning 24 chart types and 6 plotting libraries. Each sample consists of five aligned components: plotting code, rendered chart image, data table, natural language summary, and question-answering with reasoning, providing fine-grained cross-modal alignment. To capture the full spectrum of chart comprehension, ChartNet additionally includes specialized subsets encompassing human annotated data, real-world data, safety, and grounding. Moreover, a rigorous quality-filtering pipeline ensures visual fidelity, semantic accuracy, and diversity across chart representations. Fine-tuning on ChartNet consistently improves results across benchmarks, demonstrating its utility as large-scale supervision for multimodal models. As the largest open-source dataset of its kind, ChartNet aims to support the development of foundation models with robust and generalizable capabilities for data visualization understanding. The dataset is publicly available at https://huggingface.co/datasets/ibm-granite/ChartNet

Large Language Models (LLMs) have gained the ability to assimilate human knowledge and facilitate natural language interactions with both humans and other LLMs. However, despite their impressive achievements, LLMs have not made significant advancements in the realm of graph machine learning. This limitation arises because graphs encapsulate distinct relational data, making it challenging to transform them into natural language that LLMs understand. In this paper, we bridge this gap with a novel framework, GraphText, that translates graphs into natural language. GraphText derives a graph-syntax tree for each graph that encapsulates both the node attributes and inter-node relationships. Traversal of the tree yields a graph text sequence, which is then processed by an LLM to treat graph tasks as text generation tasks. Notably, GraphText offers multiple advantages. It introduces training-free graph reasoning: even without training on graph data, GraphText with ChatGPT can achieve on par with, or even surpassing, the performance of supervised-trained graph neural networks through in-context learning (ICL). Furthermore, GraphText paves the way for interactive graph reasoning, allowing both humans and LLMs to communicate with the model seamlessly using natural language. These capabilities underscore the vast, yet-to-be-explored potential of LLMs in the domain of graph machine learning.

Knowledge graphs (KGs) provide reliable external knowledge for multi-hop factual reasoning with large language models (LLMs), yet most KGs in real-world domains such as finance and industry lack question--answer (QA) annotations. Without such annotations, existing methods struggle to improve LLM graph reasoning: training-free agents cannot improve their exploration through interaction; reinforcement learning (RL) agents depend on QA data annotated by humans or synthesized by closed-source models; and training data is typically built offline, so its topology mix is fixed and cannot follow the agent's ability. We propose Evolve on Graph (EoG), a framework that lets an LLM self-evolve its graph reasoning without any QA annotations. Through Graph Self-Play, a single LLM alternates between a Proposer that poses questions and a Solver that answers them. To make questions verifiable, Symbolically Verifiable Topology Synthesis (SVTS) samples reasoning topologies on the KG and executes the corresponding first-order logic queries, yielding topology skeletons with correct and complete answer sets; guided by a skeleton, the Proposer explores the graph to pose a multi-hop question. To let task topologies follow the Solver, a Boundary-Aware Graph Curriculum rewards the Proposer by the Solver's score variance, keeping questions at the Solver's capability boundary so that complex topologies enter training as the Solver improves. On six benchmarks over Freebase, Wikidata, and an industrial KG, EoG consistently outperforms prompting-, retrieval-, and agent-based methods, showing that LLM graph reasoning can improve through self-play without QA annotations. Our code is available at https://github.com/Szy5/EoG

A 3D scene graph represents a compact scene model, storing information about the objects and the semantic relationships between them, making its use promising for robotic tasks. When interacting with a user, an embodied intelligent agent should be capable of responding to various queries about the scene formulated in natural language. Large Language Models (LLMs) are beneficial solutions for user-robot interaction due to their natural language understanding and reasoning abilities. Recent methods for creating learnable representations of 3D scenes have demonstrated the potential to improve the quality of LLMs responses by adapting to the 3D world. However, the existing methods do not explicitly utilize information about the semantic relationships between objects, limiting themselves to information about their coordinates. In this work, we propose a method 3DGraphLLM for constructing a learnable representation of a 3D scene graph. The learnable representation is used as input for LLMs to perform 3D vision-language tasks. In our experiments on popular ScanRefer, RIORefer, Multi3DRefer, ScanQA, Sqa3D, and Scan2cap datasets, we demonstrate the advantage of this approach over baseline methods that do not use information about the semantic relationships between objects. The code is publicly available at https://github.com/CognitiveAISystems/3DGraphLLM.

Real-world documents distribute evidence across text, tables, figures, and captions within complex page layouts. Answering complex questions over such documents therefore requires more than retrieving relevant passages: systems must recover the evidence topology that connects heterogeneous evidence units. Existing GraphRAG evaluations remain largely text-centered, while multimodal document RAG benchmarks assess cross-modal retrieval and generation without directly evaluating recovery of the intended evidence topology. We introduce TOPOGRAPHRAG-BENCH, a layout-grounded benchmark for multimodal evidence reasoning in GraphRAG, comprising 2,024 questions over 201 long, visually rich documents. Questions are constructed bottom-up from text, figure, and table evidence units under three controlled topologies: single-hop retrieval, bridge-chain reasoning, and multi-source synthesis. To ensure that questions preserve their intended structure, we apply counterfactual validation for shortcut resistance, modality necessity, and evidence necessity. We evaluate text-only GraphRAG, page-level visual retrieval, and multimodal GraphRAG systems using retrieval, generation, and topology-aware reasoning metrics. Multimodal GraphRAG systems achieve the strongest overall performance, but still fail when visual-textual evidence alignment or multi-unit composition is incomplete. Text-only GraphRAG struggles when key dependencies are grounded in figures or tables, while page-level visual retrieval lacks the fine-grained structure needed for topology recovery. These findings motivate GraphRAG systems that move beyond text-derived entity relation graphs to explicitly model document layouts, cross-modal evidence alignment, and the reasoning roles of evidence units. Code and data are available at https://richardlrc.github.io/TopoGraphRAG-Bench/.

This paper introduces layout-aware graph modeling for multimodal RAG. Different from traditional RAG methods that mostly deal with flat text chunks, the proposed method takes into account the relationship of multimodalities by using a graph structure. To do that, a graph modeling structure is defined based on document layout parsing. The structure of an input document is retained with the connection of text chunks, tables, and figures. This representation allows the method to handle complex questions that require information from multimodalities. To confirm the efficiency of the graph modeling, a flexible RAG pipeline is developed using robust components. Experimental results on four benchmark test sets confirm the contribution of the layout-aware modeling for performance improvement of the RAG pipeline.

The exponential growth of scientific literature requires effective management and extraction of valuable insights. While existing scientific search engines excel at delivering search results based on relational databases, they often neglect the analysis of collaborations between scientific entities and the evolution of ideas, as well as the in-depth analysis of content within scientific publications. The representation of heterogeneous graphs and the effective measurement, analysis, and mining of such graphs pose significant challenges. To address these challenges, we present AceMap, an academic system designed for knowledge discovery through academic graph. We present advanced database construction techniques to build the comprehensive AceMap database with large-scale academic entities that contain rich visual, textual, and numerical information. AceMap also employs innovative visualization, quantification, and analysis methods to explore associations and logical relationships among academic entities. AceMap introduces large-scale academic network visualization techniques centered on nebular graphs, providing a comprehensive view of academic networks from multiple perspectives. In addition, AceMap proposes a unified metric based on structural entropy to quantitatively measure the knowledge content of different academic entities. Moreover, AceMap provides advanced analysis capabilities, including tracing the evolution of academic ideas through citation relationships and concept co-occurrence, and generating concise summaries informed by this evolutionary process. In addition, AceMap uses machine reading methods to generate potential new ideas at the intersection of different fields. Exploring the integration of large language models and knowledge graphs is a promising direction for future research in idea evolution. Please visit https://www.acemap.info for further exploration.

Understanding how events in a scenario causally connect with each other is important for effectively modeling and reasoning about events. But event reasoning remains a difficult challenge, and despite recent advances, Large Language Models (LLMs) still struggle to accurately identify causal connections between events. This struggle leads to poor performance on deeper reasoning tasks like event forecasting and timeline understanding. To address this challenge, we investigate the generation of causal event graphs (e.g., A enables B) as a parallel mechanism to help LLMs explicitly represent causality during inference. This paper evaluates both how to generate correct graphs as well as how graphs can assist reasoning. We propose a collaborative approach to causal graph generation where we use LLMs to simulate experts that focus on specific semantic relations. The experts engage in multiple rounds of discussions which are then consolidated by a final expert. Then, to demonstrate the utility of causal graphs, we use them on multiple downstream applications, and also introduce a new explainable event prediction task that requires a causal chain of events in the explanation. These explanations are more informative and coherent than baseline generations. Finally, our overall approach not finetuned on any downstream task, achieves competitive results with state-of-the-art models on both forecasting and next event prediction tasks.

Artificial general intelligence on graphs has shown significant advancements across various applications, yet the traditional 'Pre-train & Fine-tune' paradigm faces inefficiencies and negative transfer issues, particularly in complex and few-shot settings. Graph prompt learning emerges as a promising alternative, leveraging lightweight prompts to manipulate data and fill the task gap by reformulating downstream tasks to the pretext. However, several critical challenges still remain: how to unify diverse graph prompt models, how to evaluate the quality of graph prompts, and to improve their usability for practical comparisons and selection. In response to these challenges, we introduce the first comprehensive benchmark for graph prompt learning. Our benchmark integrates SIX pre-training methods and FIVE state-of-the-art graph prompt techniques, evaluated across FIFTEEN diverse datasets to assess performance, flexibility, and efficiency. We also present 'ProG', an easy-to-use open-source library that streamlines the execution of various graph prompt models, facilitating objective evaluations. Additionally, we propose a unified framework that categorizes existing graph prompt methods into two main approaches: prompts as graphs and prompts as tokens. This framework enhances the applicability and comparison of graph prompt techniques. The code is available at: https://github.com/sheldonresearch/ProG.

Complex chart understanding tasks demand advanced visual recognition and reasoning capabilities from multimodal large language models (MLLMs). However, current research provides limited coverage of complex chart scenarios and computation-intensive reasoning tasks prevalent in real-world applications. This study proposes an automated multi-stage code-driven pipeline for systematically generating visual reasoning datasets to address these limitations. The pipeline integrates retrieval-augmented generation (RAG) to retrieve professional chart templates and employs chain-of-thought (CoT) strategies to generate reasoning codes that simulate real data distributions, thereby driving chart rendering and question-related statistical computations. Through model-based evaluation, the pipeline enhances chart diversity and data quality. Using this framework, we construct ChartM^3, a multi-dimensional and multi-step dataset containing 38K charts and 142K Q&A pairs for training, along with 2,871 high-quality evaluation samples for enabling practical performance assessment. Supervised fine-tuning (SFT) and reinforcement learning (RL) experiments demonstrate that our dataset significantly improves reasoning capabilities and cross-domain generalization performance, enabling smaller models to achieve performance comparable to larger-scale models in complex chart comprehension.

Synthetic image generation has recently experienced significant improvements in domains such as natural image or art generation. However, the problem of figure and diagram generation remains unexplored. A challenging aspect of generating figures and diagrams is effectively rendering readable texts within the images. To alleviate this problem, we present OCR-VQGAN, an image encoder, and decoder that leverages OCR pre-trained features to optimize a text perceptual loss, encouraging the architecture to preserve high-fidelity text and diagram structure. To explore our approach, we introduce the Paper2Fig100k dataset, with over 100k images of figures and texts from research papers. The figures show architecture diagrams and methodologies of articles available at arXiv.org from fields like artificial intelligence and computer vision. Figures usually include text and discrete objects, e.g., boxes in a diagram, with lines and arrows that connect them. We demonstrate the effectiveness of OCR-VQGAN by conducting several experiments on the task of figure reconstruction. Additionally, we explore the qualitative and quantitative impact of weighting different perceptual metrics in the overall loss function. We release code, models, and dataset at https://github.com/joanrod/ocr-vqgan.

Visual language such as charts and plots is ubiquitous in the human world. Comprehending plots and charts requires strong reasoning skills. Prior state-of-the-art (SOTA) models require at least tens of thousands of training examples and their reasoning capabilities are still much limited, especially on complex human-written queries. This paper presents the first one-shot solution to visual language reasoning. We decompose the challenge of visual language reasoning into two steps: (1) plot-to-text translation, and (2) reasoning over the translated text. The key in this method is a modality conversion module, named as DePlot, which translates the image of a plot or chart to a linearized table. The output of DePlot can then be directly used to prompt a pretrained large language model (LLM), exploiting the few-shot reasoning capabilities of LLMs. To obtain DePlot, we standardize the plot-to-table task by establishing unified task formats and metrics, and train DePlot end-to-end on this task. DePlot can then be used off-the-shelf together with LLMs in a plug-and-play fashion. Compared with a SOTA model finetuned on more than >28k data points, DePlot+LLM with just one-shot prompting achieves a 24.0% improvement over finetuned SOTA on human-written queries from the task of chart QA.

With the goal of understanding the visual concepts that CLIP associates with text prompts, we show that the latent space of CLIP can be visualized solely in terms of linear transformations on simple geometric primitives like circles and straight lines. Although existing approaches achieve this by sketch-synthesis-through-optimization, they do so on the space of B\'ezier curves, which exhibit a wastefully large set of structures that they can evolve into, as most of them are non-essential for generating meaningful sketches. We present CLIPDrawX, an algorithm that provides significantly better visualizations for CLIP text embeddings, using only simple primitive shapes like straight lines and circles. This constrains the set of possible outputs to linear transformations on these primitives, thereby exhibiting an inherently simpler mathematical form. The synthesis process of CLIPDrawX can be tracked end-to-end, with each visual concept being explained exclusively in terms of primitives. Implementation will be released upon acceptance. Project Page: https://clipdrawx.github.io/{https://clipdrawx.github.io/}.

In this paper, we introduce a novel way to use geometric deep learning for knot data by constructing a functor that takes knots to graphs and using graph neural networks. We will attempt to predict several knot invariants with this approach. This approach demonstrates high generalization capabilities.

Multimodal large language models are increasingly capable of complex reasoning, yet their performance often degrades when they must externalize a problem through a tool and then reason over the tool's output, specifically when they rely on visual aids. This gap is especially important because real engineering and scientific workflows often rely on visualization tools for analysis, validation, and decision-making. To study this discrepancy, we introduce VAMPS (Visual-Assisted Mathematical Problem Solving), a benchmark for graph-assisted mathematics. VAMPS contains 1,168 multimodal, bilingual multiple-choice question-answer pairs drawn from Iranian University Entrance Exam algebra and calculus problems and expanded with human-reviewed LLM-generated synthetic variants, all selected so that plotting provides a natural solution strategy by revealing intersections, extrema, asymptotes, etc. Designed for both benchmarking and diagnosis, VAMPS goes beyond prior multimodal benchmarks that primarily evaluate reasoning over fixed visual inputs by testing whether a model can benefit from constructing a useful graph and grounding its answer in the resulting visualization. Overall, we found that across a diverse set of models, direct analytical solving surprisingly outperforms tool-enabled visual solving, even on problems where plotting is a natural strategy.