Daily Papers

This paper presents an unpaired method for creating line drawings from photographs. Current methods often rely on high quality paired datasets to generate line drawings. However, these datasets often have limitations due to the subjects of the drawings belonging to a specific domain, or in the amount of data collected. Although recent work in unsupervised image-to-image translation has shown much progress, the latest methods still struggle to generate compelling line drawings. We observe that line drawings are encodings of scene information and seek to convey 3D shape and semantic meaning. We build these observations into a set of objectives and train an image translation to map photographs into line drawings. We introduce a geometry loss which predicts depth information from the image features of a line drawing, and a semantic loss which matches the CLIP features of a line drawing with its corresponding photograph. Our approach outperforms state-of-the-art unpaired image translation and line drawing generation methods on creating line drawings from arbitrary photographs. For code and demo visit our webpage carolineec.github.io/informative_drawings

3D textured face reconstruction from sketches applicable in many scenarios such as animation, 3D avatars, artistic design, missing people search, etc., is a highly promising but underdeveloped research topic. On the one hand, the stylistic diversity of sketches leads to existing sketch-to-3D-face methods only being able to handle pose-limited and realistically shaded sketches. On the other hand, texture plays a vital role in representing facial appearance, yet sketches lack this information, necessitating additional texture control in the reconstruction process. This paper proposes a novel method for reconstructing controllable textured and detailed 3D faces from sketches, named S2TD-Face. S2TD-Face introduces a two-stage geometry reconstruction framework that directly reconstructs detailed geometry from the input sketch. To keep geometry consistent with the delicate strokes of the sketch, we propose a novel sketch-to-geometry loss that ensures the reconstruction accurately fits the input features like dimples and wrinkles. Our training strategies do not rely on hard-to-obtain 3D face scanning data or labor-intensive hand-drawn sketches. Furthermore, S2TD-Face introduces a texture control module utilizing text prompts to select the most suitable textures from a library and seamlessly integrate them into the geometry, resulting in a 3D detailed face with controllable texture. S2TD-Face surpasses existing state-of-the-art methods in extensive quantitative and qualitative experiments. Our project is available at https://github.com/wang-zidu/S2TD-Face .

Neural surface reconstruction is sensitive to the camera pose noise, even if state-of-the-art pose estimators like COLMAP or ARKit are used. More importantly, existing Pose-NeRF joint optimisation methods have struggled to improve pose accuracy in challenging real-world scenarios. To overcome the challenges, we introduce the pose residual field (PoRF), a novel implicit representation that uses an MLP for regressing pose updates. This is more robust than the conventional pose parameter optimisation due to parameter sharing that leverages global information over the entire sequence. Furthermore, we propose an epipolar geometry loss to enhance the supervision that leverages the correspondences exported from COLMAP results without the extra computational overhead. Our method yields promising results. On the DTU dataset, we reduce the rotation error by 78\% for COLMAP poses, leading to the decreased reconstruction Chamfer distance from 3.48mm to 0.85mm. On the MobileBrick dataset that contains casually captured unbounded 360-degree videos, our method refines ARKit poses and improves the reconstruction F1 score from 69.18 to 75.67, outperforming that with the dataset provided ground-truth pose (75.14). These achievements demonstrate the efficacy of our approach in refining camera poses and improving the accuracy of neural surface reconstruction in real-world scenarios.

Synthesizing semantic-aware, long-horizon, human-object interaction is critical to simulate realistic human behaviors. In this work, we address the challenging problem of generating synchronized object motion and human motion guided by language descriptions in 3D scenes. We propose Controllable Human-Object Interaction Synthesis (CHOIS), an approach that generates object motion and human motion simultaneously using a conditional diffusion model given a language description, initial object and human states, and sparse object waypoints. While language descriptions inform style and intent, waypoints ground the motion in the scene and can be effectively extracted using high-level planning methods. Naively applying a diffusion model fails to predict object motion aligned with the input waypoints and cannot ensure the realism of interactions that require precise hand-object contact and appropriate contact grounded by the floor. To overcome these problems, we introduce an object geometry loss as additional supervision to improve the matching between generated object motion and input object waypoints. In addition, we design guidance terms to enforce contact constraints during the sampling process of the trained diffusion model.

In this paper, we introduce Splatt3R, a pose-free, feed-forward method for in-the-wild 3D reconstruction and novel view synthesis from stereo pairs. Given uncalibrated natural images, Splatt3R can predict 3D Gaussian Splats without requiring any camera parameters or depth information. For generalizability, we build Splatt3R upon a ``foundation'' 3D geometry reconstruction method, MASt3R, by extending it to deal with both 3D structure and appearance. Specifically, unlike the original MASt3R which reconstructs only 3D point clouds, we predict the additional Gaussian attributes required to construct a Gaussian primitive for each point. Hence, unlike other novel view synthesis methods, Splatt3R is first trained by optimizing the 3D point cloud's geometry loss, and then a novel view synthesis objective. By doing this, we avoid the local minima present in training 3D Gaussian Splats from stereo views. We also propose a novel loss masking strategy that we empirically find is critical for strong performance on extrapolated viewpoints. We train Splatt3R on the ScanNet++ dataset and demonstrate excellent generalisation to uncalibrated, in-the-wild images. Splatt3R can reconstruct scenes at 4FPS at 512 x 512 resolution, and the resultant splats can be rendered in real-time.

Large foundation models have recently emerged as a prominent focus of interest, attaining superior performance in widespread scenarios. Due to the scarcity of 3D data, many efforts have been made to adapt pre-trained transformers from vision to 3D domains. However, such 2D-to-3D approaches are still limited, due to the potential loss of spatial geometries and high computation cost. More importantly, their frameworks are mainly designed for 2D models, lacking a general any-to-3D paradigm. In this paper, we introduce Any2Point, a parameter-efficient method to empower any-modality large models (vision, language, audio) for 3D understanding. Given a frozen transformer from any source modality, we propose a 3D-to-any (1D or 2D) virtual projection strategy that correlates the input 3D points to the original 1D or 2D positions within the source modality. This mechanism enables us to assign each 3D token with a positional encoding paired with the pre-trained model, which avoids 3D geometry loss caused by the true projection and better motivates the transformer for 3D learning with 1D/2D positional priors. Then, within each transformer block, we insert an any-to-3D guided adapter module for parameter-efficient fine-tuning. The adapter incorporates prior spatial knowledge from the source modality to guide the local feature aggregation of 3D tokens, compelling the semantic adaption of any-modality transformers. We conduct extensive experiments to showcase the effectiveness and efficiency of our method. Code and models are released at https://github.com/Ivan-Tang-3D/Any2Point.

Adam outperforms SGD when training language models. Yet this advantage is not well-understood theoretically -- previous convergence analysis for Adam and SGD mainly focuses on the number of steps T and is already minimax-optimal in non-convex cases, which are both O(T^{-1/4}). In this work, we argue that the exploitation of nice ell_infty-geometry is the key advantage of Adam over SGD. More specifically, we give a new convergence analysis for Adam under novel assumptions that loss is smooth under ell_infty-geometry rather than the more common ell_2-geometry, which yields a much better empirical smoothness constant for GPT-2 and ResNet models. Our experiments confirm that Adam performs much worse when the favorable ell_infty-geometry is changed while SGD provably remains unaffected. We also extend the convergence analysis to blockwise Adam under novel blockwise smoothness assumptions.

3D room layout estimation by a single panorama using deep neural networks has made great progress. However, previous approaches can not obtain efficient geometry awareness of room layout with the only latitude of boundaries or horizon-depth. We present that using horizon-depth along with room height can obtain omnidirectional-geometry awareness of room layout in both horizontal and vertical directions. In addition, we propose a planar-geometry aware loss function with normals and gradients of normals to supervise the planeness of walls and turning of corners. We propose an efficient network, LGT-Net, for room layout estimation, which contains a novel Transformer architecture called SWG-Transformer to model geometry relations. SWG-Transformer consists of (Shifted) Window Blocks and Global Blocks to combine the local and global geometry relations. Moreover, we design a novel relative position embedding of Transformer to enhance the spatial identification ability for the panorama. Experiments show that the proposed LGT-Net achieves better performance than current state-of-the-arts (SOTA) on benchmark datasets.

The loss landscape of neural networks is a critical aspect of their training, and understanding its properties is essential for improving their performance. In this paper, we investigate how the loss surface changes when the sample size increases, a previously unexplored issue. We theoretically analyze the convergence of the loss landscape in a fully connected neural network and derive upper bounds for the difference in loss function values when adding a new object to the sample. Our empirical study confirms these results on various datasets, demonstrating the convergence of the loss function surface for image classification tasks. Our findings provide insights into the local geometry of neural loss landscapes and have implications for the development of sample size determination techniques.

Vision Transformers (ViTs) and MLPs signal further efforts on replacing hand-wired features or inductive biases with general-purpose neural architectures. Existing works empower the models by massive data, such as large-scale pre-training and/or repeated strong data augmentations, and still report optimization-related problems (e.g., sensitivity to initialization and learning rates). Hence, this paper investigates ViTs and MLP-Mixers from the lens of loss geometry, intending to improve the models' data efficiency at training and generalization at inference. Visualization and Hessian reveal extremely sharp local minima of converged models. By promoting smoothness with a recently proposed sharpness-aware optimizer, we substantially improve the accuracy and robustness of ViTs and MLP-Mixers on various tasks spanning supervised, adversarial, contrastive, and transfer learning (e.g., +5.3\% and +11.0\% top-1 accuracy on ImageNet for ViT-B/16 and Mixer-B/16, respectively, with the simple Inception-style preprocessing). We show that the improved smoothness attributes to sparser active neurons in the first few layers. The resultant ViTs outperform ResNets of similar size and throughput when trained from scratch on ImageNet without large-scale pre-training or strong data augmentations. Model checkpoints are available at https://github.com/google-research/vision_transformer.

In representation learning, uniformity refers to the uniform feature distribution in the latent space (i.e., unit hypersphere). Previous work has shown that improving uniformity contributes to the learning of under-represented classes. However, most of the previous work focused on classification; the representation space of imbalanced regression remains unexplored. Classification-based methods are not suitable for regression tasks because they cluster features into distinct groups without considering the continuous and ordered nature essential for regression. In a geometric aspect, we uniquely focus on ensuring uniformity in the latent space for imbalanced regression through two key losses: enveloping and homogeneity. The enveloping loss encourages the induced trace to uniformly occupy the surface of a hypersphere, while the homogeneity loss ensures smoothness, with representations evenly spaced at consistent intervals. Our method integrates these geometric principles into the data representations via a Surrogate-driven Representation Learning (SRL) framework. Experiments with real-world regression and operator learning tasks highlight the importance of uniformity in imbalanced regression and validate the efficacy of our geometry-based loss functions.

We study the properties of common loss surfaces through their Hessian matrix. In particular, in the context of deep learning, we empirically show that the spectrum of the Hessian is composed of two parts: (1) the bulk centered near zero, (2) and outliers away from the bulk. We present numerical evidence and mathematical justifications to the following conjectures laid out by Sagun et al. (2016): Fixing data, increasing the number of parameters merely scales the bulk of the spectrum; fixing the dimension and changing the data (for instance adding more clusters or making the data less separable) only affects the outliers. We believe that our observations have striking implications for non-convex optimization in high dimensions. First, the flatness of such landscapes (which can be measured by the singularity of the Hessian) implies that classical notions of basins of attraction may be quite misleading. And that the discussion of wide/narrow basins may be in need of a new perspective around over-parametrization and redundancy that are able to create large connected components at the bottom of the landscape. Second, the dependence of small number of large eigenvalues to the data distribution can be linked to the spectrum of the covariance matrix of gradients of model outputs. With this in mind, we may reevaluate the connections within the data-architecture-algorithm framework of a model, hoping that it would shed light into the geometry of high-dimensional and non-convex spaces in modern applications. In particular, we present a case that links the two observations: small and large batch gradient descent appear to converge to different basins of attraction but we show that they are in fact connected through their flat region and so belong to the same basin.

Stochastic Gradient Descent (SGD) stands as a cornerstone optimization algorithm with proven real-world empirical successes but relatively limited theoretical understanding. Recent research has illuminated a key factor contributing to its practical efficacy: the implicit regularization it instigates. Several studies have investigated the linear stability property of SGD in the vicinity of a stationary point as a predictive proxy for sharpness and generalization error in overparameterized neural networks (Wu et al., 2022; Jastrzebski et al., 2019; Cohen et al., 2021). In this paper, we delve deeper into the relationship between linear stability and sharpness. More specifically, we meticulously delineate the necessary and sufficient conditions for linear stability, contingent on hyperparameters of SGD and the sharpness at the optimum. Towards this end, we introduce a novel coherence measure of the loss Hessian that encapsulates pertinent geometric properties of the loss function that are relevant to the linear stability of SGD. It enables us to provide a simplified sufficient condition for identifying linear instability at an optimum. Notably, compared to previous works, our analysis relies on significantly milder assumptions and is applicable for a broader class of loss functions than known before, encompassing not only mean-squared error but also cross-entropy loss.

Respiratory sound classification is hindered by the limited size, high noise levels, and severe class imbalance of benchmark datasets like ICBHI 2017. While Transformer-based models offer powerful feature extraction capabilities, they are prone to overfitting and often converge to sharp minima in the loss landscape when trained on such constrained medical data. To address this, we introduce a framework that enhances the Audio Spectrogram Transformer (AST) using Sharpness-Aware Minimization (SAM). Instead of merely minimizing the training loss, our approach optimizes the geometry of the loss surface, guiding the model toward flatter minima that generalize better to unseen patients. We also implement a weighted sampling strategy to handle class imbalance effectively. Our method achieves a state-of-the-art score of 68.10% on the ICBHI 2017 dataset, outperforming existing CNN and hybrid baselines. More importantly, it reaches a sensitivity of 68.31%, a crucial improvement for reliable clinical screening. Further analysis using t-SNE and attention maps confirms that the model learns robust, discriminative features rather than memorizing background noise.

Neural signed distance functions (SDFs) have been a vital representation to represent 3D shapes or scenes with neural networks. An SDF is an implicit function that can query signed distances at specific coordinates for recovering a 3D surface. Although implicit functions work well on a single shape or scene, they pose obstacles when analyzing multiple SDFs with high-fidelity geometry details, due to the limited information encoded in the latent space for SDFs and the loss of geometry details. To overcome these obstacles, we introduce a method to represent multiple SDFs in a common space, aiming to recover more high-fidelity geometry details with more compact latent representations. Our key idea is to take full advantage of the benefits of generalization-based and overfitting-based learning strategies, which manage to preserve high-fidelity geometry details with compact latent codes. Based on this framework, we also introduce a novel sampling strategy to sample training queries. The sampling can improve the training efficiency and eliminate artifacts caused by the influence of other SDFs. We report numerical and visual evaluations on widely used benchmarks to validate our designs and show advantages over the latest methods in terms of the representative ability and compactness.

Research on loss surface geometry, such as Sharpness-Aware Minimization (SAM), shows that flatter minima improve generalization. Recent studies further reveal that flatter minima can also reduce the domain generalization (DG) gap. However, existing flatness-based DG techniques predominantly operate within a full-precision training process, which is impractical for deployment on resource-constrained edge devices that typically rely on lower bit-width representations (e.g., 4 bits, 3 bits). Consequently, low-precision quantization-aware training is critical for optimizing these techniques in real-world applications. In this paper, we observe a significant degradation in performance when applying state-of-the-art DG-SAM methods to quantized models, suggesting that current approaches fail to preserve generalizability during the low-precision training process. To address this limitation, we propose a novel Gradient-Adaptive Quantization-Aware Training (GAQAT) framework for DG. Our approach begins by identifying the scale-gradient conflict problem in low-precision quantization, where the task loss and smoothness loss induce conflicting gradients for the scaling factors of quantizers, with certain layers exhibiting opposing gradient directions. This conflict renders the optimization of quantized weights highly unstable. To mitigate this, we further introduce a mechanism to quantify gradient inconsistencies and selectively freeze the gradients of scaling factors, thereby stabilizing the training process and enhancing out-of-domain generalization. Extensive experiments validate the effectiveness of the proposed GAQAT framework. On PACS, our 3-bit and 4-bit models outperform direct DG-QAT integration by up to 4.5%. On DomainNet, the 4-bit model achieves near-lossless performance compared to full precision, with improvements of 1.39% (4-bit) and 1.06% (3-bit) over the SOTA QAT baseline.

In today's heavily overparameterized models, the value of the training loss provides few guarantees on model generalization ability. Indeed, optimizing only the training loss value, as is commonly done, can easily lead to suboptimal model quality. Motivated by prior work connecting the geometry of the loss landscape and generalization, we introduce a novel, effective procedure for instead simultaneously minimizing loss value and loss sharpness. In particular, our procedure, Sharpness-Aware Minimization (SAM), seeks parameters that lie in neighborhoods having uniformly low loss; this formulation results in a min-max optimization problem on which gradient descent can be performed efficiently. We present empirical results showing that SAM improves model generalization across a variety of benchmark datasets (e.g., CIFAR-10, CIFAR-100, ImageNet, finetuning tasks) and models, yielding novel state-of-the-art performance for several. Additionally, we find that SAM natively provides robustness to label noise on par with that provided by state-of-the-art procedures that specifically target learning with noisy labels. We open source our code at https://github.com/google-research/sam.

Cross-scene generalizable NeRF models, which can directly synthesize novel views of unseen scenes, have become a new spotlight of the NeRF field. Several existing attempts rely on increasingly end-to-end "neuralized" architectures, i.e., replacing scene representation and/or rendering modules with performant neural networks such as transformers, and turning novel view synthesis into a feed-forward inference pipeline. While those feedforward "neuralized" architectures still do not fit diverse scenes well out of the box, we propose to bridge them with the powerful Mixture-of-Experts (MoE) idea from large language models (LLMs), which has demonstrated superior generalization ability by balancing between larger overall model capacity and flexible per-instance specialization. Starting from a recent generalizable NeRF architecture called GNT, we first demonstrate that MoE can be neatly plugged in to enhance the model. We further customize a shared permanent expert and a geometry-aware consistency loss to enforce cross-scene consistency and spatial smoothness respectively, which are essential for generalizable view synthesis. Our proposed model, dubbed GNT with Mixture-of-View-Experts (GNT-MOVE), has experimentally shown state-of-the-art results when transferring to unseen scenes, indicating remarkably better cross-scene generalization in both zero-shot and few-shot settings. Our codes are available at https://github.com/VITA-Group/GNT-MOVE.

Modern deep neural networks (DNNs) have achieved state-of-the-art performances but are typically over-parameterized. The over-parameterization may result in undesirably large generalization error in the absence of other customized training strategies. Recently, a line of research under the name of Sharpness-Aware Minimization (SAM) has shown that minimizing a sharpness measure, which reflects the geometry of the loss landscape, can significantly reduce the generalization error. However, SAM-like methods incur a two-fold computational overhead of the given base optimizer (e.g. SGD) for approximating the sharpness measure. In this paper, we propose Sharpness-Aware Training for Free, or SAF, which mitigates the sharp landscape at almost zero additional computational cost over the base optimizer. Intuitively, SAF achieves this by avoiding sudden drops in the loss in the sharp local minima throughout the trajectory of the updates of the weights. Specifically, we suggest a novel trajectory loss, based on the KL-divergence between the outputs of DNNs with the current weights and past weights, as a replacement of the SAM's sharpness measure. This loss captures the rate of change of the training loss along the model's update trajectory. By minimizing it, SAF ensures the convergence to a flat minimum with improved generalization capabilities. Extensive empirical results show that SAF minimizes the sharpness in the same way that SAM does, yielding better results on the ImageNet dataset with essentially the same computational cost as the base optimizer.

Multi-view image generation attracts particular attention these days due to its promising 3D-related applications, e.g., image viewpoint editing. Most existing methods follow a paradigm where a 3D representation is first synthesized, and then rendered into 2D images to ensure photo-consistency across viewpoints. However, such explicit bias for photo-consistency sacrifices photo-realism, causing geometry artifacts and loss of fine-scale details when these methods are applied to edit real images. To address this issue, we propose ray conditioning, a geometry-free alternative that relaxes the photo-consistency constraint. Our method generates multi-view images by conditioning a 2D GAN on a light field prior. With explicit viewpoint control, state-of-the-art photo-realism and identity consistency, our method is particularly suited for the viewpoint editing task.

Neural surface representation has demonstrated remarkable success in the areas of novel view synthesis and 3D reconstruction. However, assessing the geometric quality of 3D reconstructions in the absence of ground truth mesh remains a significant challenge, due to its rendering-based optimization process and entangled learning of appearance and geometry with photometric losses. In this paper, we present a novel framework, i.e, GURecon, which establishes a geometric uncertainty field for the neural surface based on geometric consistency. Different from existing methods that rely on rendering-based measurement, GURecon models a continuous 3D uncertainty field for the reconstructed surface, and is learned by an online distillation approach without introducing real geometric information for supervision. Moreover, in order to mitigate the interference of illumination on geometric consistency, a decoupled field is learned and exploited to finetune the uncertainty field. Experiments on various datasets demonstrate the superiority of GURecon in modeling 3D geometric uncertainty, as well as its plug-and-play extension to various neural surface representations and improvement on downstream tasks such as incremental reconstruction. The code and supplementary material are available on the project website: https://zju3dv.github.io/GURecon/.

Numerous deep learning applications benefit from multi-task learning with multiple regression and classification objectives. In this paper we make the observation that the performance of such systems is strongly dependent on the relative weighting between each task's loss. Tuning these weights by hand is a difficult and expensive process, making multi-task learning prohibitive in practice. We propose a principled approach to multi-task deep learning which weighs multiple loss functions by considering the homoscedastic uncertainty of each task. This allows us to simultaneously learn various quantities with different units or scales in both classification and regression settings. We demonstrate our model learning per-pixel depth regression, semantic and instance segmentation from a monocular input image. Perhaps surprisingly, we show our model can learn multi-task weightings and outperform separate models trained individually on each task.

Standard training metrics like loss fail to explain the emergence of complex capabilities in large language models. We take a spectral approach to investigate the geometry of learned representations across pretraining and post-training, measuring effective rank (RankMe) and eigenspectrum decay (α-ReQ). With OLMo (1B-7B) and Pythia (160M-12B) models, we uncover a consistent non-monotonic sequence of three geometric phases during autoregressive pretraining. The initial "warmup" phase exhibits rapid representational collapse. This is followed by an "entropy-seeking" phase, where the manifold's dimensionality expands substantially, coinciding with peak n-gram memorization. Subsequently, a "compression-seeking" phase imposes anisotropic consolidation, selectively preserving variance along dominant eigendirections while contracting others, a transition marked with significant improvement in downstream task performance. We show these phases can emerge from a fundamental interplay of cross-entropy optimization under skewed token frequencies and representational bottlenecks (d ll |V|). Post-training further transforms geometry: SFT and DPO drive "entropy-seeking" dynamics to integrate specific instructional or preferential data, improving in-distribution performance while degrading out-of-distribution robustness. Conversely, RLVR induces "compression-seeking", enhancing reward alignment but reducing generation diversity.

This paper introduces YOLOv8-TO, a novel approach for reverse engineering of topology-optimized structures into interpretable geometric parameters using the YOLOv8 instance segmentation model. Density-based topology optimization methods require post-processing to convert the optimal density distribution into a parametric representation for design exploration and integration with CAD tools. Traditional methods such as skeletonization struggle with complex geometries and require manual intervention. YOLOv8-TO addresses these challenges by training a custom YOLOv8 model to automatically detect and reconstruct structural components from binary density distributions. The model is trained on a diverse dataset of both optimized and random structures generated using the Moving Morphable Components method. A custom reconstruction loss function based on the dice coefficient of the predicted geometry is used to train the new regression head of the model via self-supervised learning. The method is evaluated on test sets generated from different topology optimization methods, including out-of-distribution samples, and compared against a skeletonization approach. Results show that YOLOv8-TO significantly outperforms skeletonization in reconstructing visually and structurally similar designs. The method showcases an average improvement of 13.84% in the Dice coefficient, with peak enhancements reaching 20.78%. The method demonstrates good generalization to complex geometries and fast inference times, making it suitable for integration into design workflows using regular workstations. Limitations include the sensitivity to non-max suppression thresholds. YOLOv8-TO represents a significant advancement in topology optimization post-processing, enabling efficient and accurate reverse engineering of optimized structures for design exploration and manufacturing.

Recent advances in language and vision have demonstrated that scaling up model capacity consistently improves performance across diverse tasks. In 3D visual geometry reconstruction, large-scale training has likewise proven effective for learning versatile representations. However, further scaling of 3D models is challenging due to the complexity of geometric supervision and the diversity of 3D data. To overcome these limitations, we propose MoRE, a dense 3D visual foundation model based on a Mixture-of-Experts (MoE) architecture that dynamically routes features to task-specific experts, allowing them to specialize in complementary data aspects and enhance both scalability and adaptability. Aiming to improve robustness under real-world conditions, MoRE incorporates a confidence-based depth refinement module that stabilizes and refines geometric estimation. In addition, it integrates dense semantic features with globally aligned 3D backbone representations for high-fidelity surface normal prediction. MoRE is further optimized with tailored loss functions to ensure robust learning across diverse inputs and multiple geometric tasks. Extensive experiments demonstrate that MoRE achieves state-of-the-art performance across multiple benchmarks and supports effective downstream applications without extra computation.

We present NeRFVS, a novel neural radiance fields (NeRF) based method to enable free navigation in a room. NeRF achieves impressive performance in rendering images for novel views similar to the input views while suffering for novel views that are significantly different from the training views. To address this issue, we utilize the holistic priors, including pseudo depth maps and view coverage information, from neural reconstruction to guide the learning of implicit neural representations of 3D indoor scenes. Concretely, an off-the-shelf neural reconstruction method is leveraged to generate a geometry scaffold. Then, two loss functions based on the holistic priors are proposed to improve the learning of NeRF: 1) A robust depth loss that can tolerate the error of the pseudo depth map to guide the geometry learning of NeRF; 2) A variance loss to regularize the variance of implicit neural representations to reduce the geometry and color ambiguity in the learning procedure. These two loss functions are modulated during NeRF optimization according to the view coverage information to reduce the negative influence brought by the view coverage imbalance. Extensive results demonstrate that our NeRFVS outperforms state-of-the-art view synthesis methods quantitatively and qualitatively on indoor scenes, achieving high-fidelity free navigation results.

In this study, we address the challenge of 3D scene structure recovery from monocular depth estimation. While traditional depth estimation methods leverage labeled datasets to directly predict absolute depth, recent advancements advocate for mix-dataset training, enhancing generalization across diverse scenes. However, such mixed dataset training yields depth predictions only up to an unknown scale and shift, hindering accurate 3D reconstructions. Existing solutions necessitate extra 3D datasets or geometry-complete depth annotations, constraints that limit their versatility. In this paper, we propose a learning framework that trains models to predict geometry-preserving depth without requiring extra data or annotations. To produce realistic 3D structures, we render novel views of the reconstructed scenes and design loss functions to promote depth estimation consistency across different views. Comprehensive experiments underscore our framework's superior generalization capabilities, surpassing existing state-of-the-art methods on several benchmark datasets without leveraging extra training information. Moreover, our innovative loss functions empower the model to autonomously recover domain-specific scale-and-shift coefficients using solely unlabeled images.

Self-supervised learning converts raw perceptual data such as images to a compact space where simple Euclidean distances measure meaningful variations in data. In this paper, we extend this formulation by adding additional geometric structure to the embedding space by enforcing transformations of input space to correspond to simple (i.e., linear) transformations of embedding space. Specifically, in the contrastive learning setting, we introduce an equivariance objective and theoretically prove that its minima forces augmentations on input space to correspond to rotations on the spherical embedding space. We show that merely combining our equivariant loss with a non-collapse term results in non-trivial representations, without requiring invariance to data augmentations. Optimal performance is achieved by also encouraging approximate invariance, where input augmentations correspond to small rotations. Our method, CARE: Contrastive Augmentation-induced Rotational Equivariance, leads to improved performance on downstream tasks, and ensures sensitivity in embedding space to important variations in data (e.g., color) that standard contrastive methods do not achieve. Code is available at https://github.com/Sharut/CARE.

Supervised contrastive loss (SCL) is a competitive and often superior alternative to the cross-entropy loss for classification. While prior studies have demonstrated that both losses yield symmetric training representations under balanced data, this symmetry breaks under class imbalances. This paper presents an intriguing discovery: the introduction of a ReLU activation at the final layer effectively restores the symmetry in SCL-learned representations. We arrive at this finding analytically, by establishing that the global minimizers of an unconstrained features model with SCL loss and entry-wise non-negativity constraints form an orthogonal frame. Extensive experiments conducted across various datasets, architectures, and imbalance scenarios corroborate our finding. Importantly, our experiments reveal that the inclusion of the ReLU activation restores symmetry without compromising test accuracy. This constitutes the first geometry characterization of SCL under imbalances. Additionally, our analysis and experiments underscore the pivotal role of batch selection strategies in representation geometry. By proving necessary and sufficient conditions for mini-batch choices that ensure invariant symmetric representations, we introduce batch-binding as an efficient strategy that guarantees these conditions hold.

Vision--language models (VLMs) often process visual inputs through a pretrained vision encoder, followed by a projection into the language model's embedding space via a connector component. While crucial for modality fusion, the potential information loss induced by this projection step and its direct impact on model capabilities remain understudied. We introduce two complementary approaches to examine and quantify this loss by analyzing the latent representation space. First, we evaluate semantic information preservation by analyzing changes in k-nearest neighbor relationships between image representations, before and after projection. Second, we directly measure information loss by reconstructing visual embeddings from the projected representation, localizing loss at an image patch level. Experiments reveal that connectors substantially distort the local geometry of visual representations, with k-nearest neighbors diverging by 40--60\% post-projection, correlating with degradation in retrieval performance. The patch-level embedding reconstruction provides interpretable insights for model behavior on visually grounded question-answering tasks, finding that areas of high information loss reliably predict instances where models struggle.

Knowledge distillation aims to train a compact student network using soft supervision from a larger teacher network and hard supervision from ground truths. However, determining an optimal knowledge fusion ratio that balances these supervisory signals remains challenging. Prior methods generally resort to a constant or heuristic-based fusion ratio, which often falls short of a proper balance. In this study, we introduce a novel adaptive method for learning a sample-wise knowledge fusion ratio, exploiting both the correctness of teacher and student, as well as how well the student mimics the teacher on each sample. Our method naturally leads to the intra-sample trilateral geometric relations among the student prediction (S), teacher prediction (T), and ground truth (G). To counterbalance the impact of outliers, we further extend to the inter-sample relations, incorporating the teacher's global average prediction T for samples within the same class. A simple neural network then learns the implicit mapping from the intra- and inter-sample relations to an adaptive, sample-wise knowledge fusion ratio in a bilevel-optimization manner. Our approach provides a simple, practical, and adaptable solution for knowledge distillation that can be employed across various architectures and model sizes. Extensive experiments demonstrate consistent improvements over other loss re-weighting methods on image classification, attack detection, and click-through rate prediction.

In this paper, we study the problem of 3D scene geometry decomposition and manipulation from 2D views. By leveraging the recent implicit neural representation techniques, particularly the appealing neural radiance fields, we introduce an object field component to learn unique codes for all individual objects in 3D space only from 2D supervision. The key to this component is a series of carefully designed loss functions to enable every 3D point, especially in non-occupied space, to be effectively optimized even without 3D labels. In addition, we introduce an inverse query algorithm to freely manipulate any specified 3D object shape in the learned scene representation. Notably, our manipulation algorithm can explicitly tackle key issues such as object collisions and visual occlusions. Our method, called DM-NeRF, is among the first to simultaneously reconstruct, decompose, manipulate and render complex 3D scenes in a single pipeline. Extensive experiments on three datasets clearly show that our method can accurately decompose all 3D objects from 2D views, allowing any interested object to be freely manipulated in 3D space such as translation, rotation, size adjustment, and deformation.

We present a method for 3D object detection and pose estimation from a single image. In contrast to current techniques that only regress the 3D orientation of an object, our method first regresses relatively stable 3D object properties using a deep convolutional neural network and then combines these estimates with geometric constraints provided by a 2D object bounding box to produce a complete 3D bounding box. The first network output estimates the 3D object orientation using a novel hybrid discrete-continuous loss, which significantly outperforms the L2 loss. The second output regresses the 3D object dimensions, which have relatively little variance compared to alternatives and can often be predicted for many object types. These estimates, combined with the geometric constraints on translation imposed by the 2D bounding box, enable us to recover a stable and accurate 3D object pose. We evaluate our method on the challenging KITTI object detection benchmark both on the official metric of 3D orientation estimation and also on the accuracy of the obtained 3D bounding boxes. Although conceptually simple, our method outperforms more complex and computationally expensive approaches that leverage semantic segmentation, instance level segmentation and flat ground priors and sub-category detection. Our discrete-continuous loss also produces state of the art results for 3D viewpoint estimation on the Pascal 3D+ dataset.

3D LiDAR sensors are essential for autonomous navigation, environmental monitoring, and precision mapping in remote sensing applications. To efficiently process the massive point clouds generated by these sensors, LiDAR data is often projected into 2D range images that organize points by their angular positions and distances. While these range image representations enable efficient processing, conventional projection methods suffer from fundamental geometric inconsistencies that cause irreversible information loss, compromising high-fidelity applications. We present ALICE-LRI (Automatic LiDAR Intrinsic Calibration Estimation for Lossless Range Images), the first general, sensor-agnostic method that achieves lossless range image generation from spinning LiDAR point clouds without requiring manufacturer metadata or calibration files. Our algorithm automatically reverse-engineers the intrinsic geometry of any spinning LiDAR sensor by inferring critical parameters including laser beam configuration, angular distributions, and per-beam calibration corrections, enabling lossless projection and complete point cloud reconstruction with zero point loss. Comprehensive evaluation across the complete KITTI and DurLAR datasets demonstrates that ALICE-LRI achieves perfect point preservation, with zero points lost across all point clouds. Geometric accuracy is maintained well within sensor precision limits, establishing geometric losslessness with real-time performance. We also present a compression case study that validates substantial downstream benefits, demonstrating significant quality improvements in practical applications. This paradigm shift from approximate to lossless LiDAR projections opens new possibilities for high-precision remote sensing applications requiring complete geometric preservation.

We investigate the relationship between the geometry of token embeddings and their role in the next token prediction within transformer models. An important aspect of this connection uses the notion of empirical measure, which encodes the distribution of token point clouds across transformer layers and drives the evolution of token representations in the mean-field interacting picture. We use metrics such as intrinsic dimension, neighborhood overlap, and cosine similarity to observationally probe these empirical measures across layers. To validate our approach, we compare these metrics to a dataset where the tokens are shuffled, which disrupts the syntactic and semantic structure. Our findings reveal a correlation between the geometric properties of token embeddings and the cross-entropy loss of next token predictions, implying that prompts with higher loss values have tokens represented in higher-dimensional spaces.

Score distillation sampling (SDS), the methodology in which the score from pretrained 2D diffusion models is distilled into 3D representation, has recently brought significant advancements in text-to-3D generation task. However, this approach is still confronted with critical geometric inconsistency problems such as the Janus problem. Starting from a hypothesis that such inconsistency problems may be induced by multiview inconsistencies between 2D scores predicted from various viewpoints, we introduce GSD, a simple and general plug-and-play framework for incorporating 3D consistency and therefore geometry awareness into the SDS process. Our methodology is composed of three components: 3D consistent noising, designed to produce 3D consistent noise maps that perfectly follow the standard Gaussian distribution, geometry-based gradient warping for identifying correspondences between predicted gradients of different viewpoints, and novel gradient consistency loss to optimize the scene geometry toward producing more consistent gradients. We demonstrate that our method significantly improves performance, successfully addressing the geometric inconsistency problems in text-to-3D generation task with minimal computation cost and being compatible with existing score distillation-based models. Our project page is available at https://ku-cvlab.github.io/GSD/.

Maps are a key component in image-based camera localization and visual SLAM systems: they are used to establish geometric constraints between images, correct drift in relative pose estimation, and relocalize cameras after lost tracking. The exact definitions of maps, however, are often application-specific and hand-crafted for different scenarios (e.g. 3D landmarks, lines, planes, bags of visual words). We propose to represent maps as a deep neural net called MapNet, which enables learning a data-driven map representation. Unlike prior work on learning maps, MapNet exploits cheap and ubiquitous sensory inputs like visual odometry and GPS in addition to images and fuses them together for camera localization. Geometric constraints expressed by these inputs, which have traditionally been used in bundle adjustment or pose-graph optimization, are formulated as loss terms in MapNet training and also used during inference. In addition to directly improving localization accuracy, this allows us to update the MapNet (i.e., maps) in a self-supervised manner using additional unlabeled video sequences from the scene. We also propose a novel parameterization for camera rotation which is better suited for deep-learning based camera pose regression. Experimental results on both the indoor 7-Scenes dataset and the outdoor Oxford RobotCar dataset show significant performance improvement over prior work. The MapNet project webpage is https://goo.gl/mRB3Au.

Training recurrent neural networks (RNNs) is a high-dimensional process that requires updating numerous parameters. Therefore, it is often difficult to pinpoint the underlying learning mechanisms. To address this challenge, we propose to gain mechanistic insights into the phenomenon of abrupt learning by studying RNNs trained to perform diverse short-term memory tasks. In these tasks, RNN training begins with an initial search phase. Following a long period of plateau in accuracy, the values of the loss function suddenly drop, indicating abrupt learning. Analyzing the neural computation performed by these RNNs reveals geometric restructuring (GR) in their phase spaces prior to the drop. To promote these GR events, we introduce a temporal consistency regularization that accelerates (bioplausible) training, facilitates attractor formation, and enables efficient learning in strongly connected networks. Our findings offer testable predictions for neuroscientists and emphasize the need for goal-agnostic secondary mechanisms to facilitate learning in biological and artificial networks.

The ability of gaze estimation models to generalize is often significantly hindered by various factors unrelated to gaze, especially when the training dataset is limited. Current strategies aim to address this challenge through different domain generalization techniques, yet they have had limited success due to the risk of overfitting when solely relying on value labels for regression. Recent progress in pre-trained vision-language models has motivated us to capitalize on the abundant semantic information available. We propose a novel approach in this paper, reframing the gaze estimation task as a vision-language alignment issue. Our proposed framework, named Language-Guided Gaze Estimation (LG-Gaze), learns continuous and geometry-sensitive features for gaze estimation benefit from the rich prior knowledges of vision-language models. Specifically, LG-Gaze aligns gaze features with continuous linguistic features through our proposed multimodal contrastive regression loss, which customizes adaptive weights for different negative samples. Furthermore, to better adapt to the labels for gaze estimation task, we propose a geometry-aware interpolation method to obtain more precise gaze embeddings. Through extensive experiments, we validate the efficacy of our framework in four different cross-domain evaluation tasks.

Perspective projection has been extensively utilized in monocular 3D object detection methods. It introduces geometric priors from 2D bounding boxes and 3D object dimensions to reduce the uncertainty of depth estimation. However, due to depth errors originating from the object's visual surface, the height of the bounding box often fails to represent the actual projected central height, which undermines the effectiveness of geometric depth. Direct prediction for the projected height unavoidably results in a loss of 2D priors, while multi-depth prediction with complex branches does not fully leverage geometric depth. This paper presents a Transformer-based monocular 3D object detection method called MonoDGP, which adopts perspective-invariant geometry errors to modify the projection formula. We also try to systematically discuss and explain the mechanisms and efficacy behind geometry errors, which serve as a simple but effective alternative to multi-depth prediction. Additionally, MonoDGP decouples the depth-guided decoder and constructs a 2D decoder only dependent on visual features, providing 2D priors and initializing object queries without the disturbance of 3D detection. To further optimize and fine-tune input tokens of the transformer decoder, we also introduce a Region Segment Head (RSH) that generates enhanced features and segment embeddings. Our monocular method demonstrates state-of-the-art performance on the KITTI benchmark without extra data. Code is available at https://github.com/PuFanqi23/MonoDGP.

Graph foundation models represent a transformative paradigm for learning transferable representations across diverse graph domains. Recent methods leverage large language models to unify graph and text modalities into a shared representation space using contrastive learning. However, systematic evaluations reveal significant performance degradation at structural boundaries where distinct topological patterns converge, with accuracy losses exceeding 20 percentage points. This issue arises from a key limitation: current methods assume all graph structures can be encoded within a single Euclidean space. In reality, tree structures require hyperbolic geometry to preserve hierarchical branching, while cyclic patterns depend on spherical geometry for closure properties. At structural boundaries, nodes experience conflicting geometric constraints that uniform encoding spaces cannot resolve. This raises a crucial challenge: Can alignment frameworks be designed to respect the intrinsic geometric diversity of graph structures? We introduce GraphShaper, a geometry-aware framework that enhances graph encoding through multi-geometric specialization. Our approach employs expert networks tailored to different geometric spaces, dynamically computing fusion weights to adaptively integrate geometric properties based on local structural characteristics. This adaptive fusion preserves structural integrity before alignment with text embeddings. Extensive experiments demonstrate that GraphShaper achieves 9.47\% accuracy improvements on citation networks and 7.63\% on social networks in zero-shot settings.

Accurate, real-time 3D reconstruction of human heads from monocular images and videos underlies numerous visual applications. As 3D ground truth data is hard to come by at scale, previous methods have sought to learn from abundant 2D videos in a self-supervised manner. Typically, this involves the use of differentiable mesh rendering, which is effective but faces limitations. To improve on this, we propose SHeaP (Self-supervised Head Geometry Predictor Learned via 2D Gaussians). Given a source image, we predict a 3DMM mesh and a set of Gaussians that are rigged to this mesh. We then reanimate this rigged head avatar to match a target frame, and backpropagate photometric losses to both the 3DMM and Gaussian prediction networks. We find that using Gaussians for rendering substantially improves the effectiveness of this self-supervised approach. Training solely on 2D data, our method surpasses existing self-supervised approaches in geometric evaluations on the NoW benchmark for neutral faces and a new benchmark for non-neutral expressions. Our method also produces highly expressive meshes, outperforming state-of-the-art in emotion classification.

Leveraging visual priors from pre-trained text-to-image (T2I) generative models has shown success in dense prediction. However, dense prediction is inherently an image-to-image task, suggesting that image editing models, rather than T2I generative models, may be a more suitable foundation for fine-tuning. Motivated by this, we conduct a systematic analysis of the fine-tuning behaviors of both editors and generators for dense geometry estimation. Our findings show that editing models possess inherent structural priors, which enable them to converge more stably by ``refining" their innate features, and ultimately achieve higher performance than their generative counterparts. Based on these findings, we introduce FE2E, a framework that pioneeringly adapts an advanced editing model based on Diffusion Transformer (DiT) architecture for dense geometry prediction. Specifically, to tailor the editor for this deterministic task, we reformulate the editor's original flow matching loss into the ``consistent velocity" training objective. And we use logarithmic quantization to resolve the precision conflict between the editor's native BFloat16 format and the high precision demand of our tasks. Additionally, we leverage the DiT's global attention for a cost-free joint estimation of depth and normals in a single forward pass, enabling their supervisory signals to mutually enhance each other. Without scaling up the training data, FE2E achieves impressive performance improvements in zero-shot monocular depth and normal estimation across multiple datasets. Notably, it achieves over 35\% performance gains on the ETH3D dataset and outperforms the DepthAnything series, which is trained on 100times data. The project page can be accessed https://amap-ml.github.io/FE2E/{here}.

Manual modeling of material parameters and 3D geometry is a time consuming yet essential task in the gaming and film industries. While recent advances in 3D reconstruction have enabled accurate approximations of scene geometry and appearance, these methods often fall short in relighting scenarios due to the lack of precise, spatially varying material parameters. At the same time, diffusion models operating on 2D images have shown strong performance in predicting physically based rendering (PBR) properties such as albedo, roughness, and metallicity. However, transferring these 2D material maps onto reconstructed 3D geometry remains a significant challenge. We propose a framework for fusing 2D material data into 3D geometry using a combination of novel learning-based and projection-based approaches. We begin by reconstructing scene geometry via Gaussian Splatting. From the input images, a diffusion model generates 2D maps for albedo, roughness, and metallic parameters. Any existing diffusion model that can convert images or videos to PBR materials can be applied. The predictions are further integrated into the 3D representation either by optimizing an image-based loss or by directly projecting the material parameters onto the Gaussians using Gaussian ray tracing. To enhance fine-scale accuracy and multi-view consistency, we further introduce a light-weight neural refinement step (Neural Merger), which takes ray-traced material features as input and produces detailed adjustments. Our results demonstrate that the proposed methods outperform existing techniques in both quantitative metrics and perceived visual realism. This enables more accurate, relightable, and photorealistic renderings from reconstructed scenes, significantly improving the realism and efficiency of asset creation workflows in content production pipelines.

We present a novel appearance model that simultaneously realizes explicit high-quality 3D surface mesh recovery and photorealistic novel view synthesis from sparse view samples. Our key idea is to model the underlying scene geometry Mesh as an Atlas of Charts which we render with 2D Gaussian surfels (MAtCha Gaussians). MAtCha distills high-frequency scene surface details from an off-the-shelf monocular depth estimator and refines it through Gaussian surfel rendering. The Gaussian surfels are attached to the charts on the fly, satisfying photorealism of neural volumetric rendering and crisp geometry of a mesh model, i.e., two seemingly contradicting goals in a single model. At the core of MAtCha lies a novel neural deformation model and a structure loss that preserve the fine surface details distilled from learned monocular depths while addressing their fundamental scale ambiguities. Results of extensive experimental validation demonstrate MAtCha's state-of-the-art quality of surface reconstruction and photorealism on-par with top contenders but with dramatic reduction in the number of input views and computational time. We believe MAtCha will serve as a foundational tool for any visual application in vision, graphics, and robotics that require explicit geometry in addition to photorealism. Our project page is the following: https://anttwo.github.io/matcha/

Learning-based multi-view stereo (MVS) methods deal with predicting accurate depth maps to achieve an accurate and complete 3D representation. Despite the excellent performance, existing methods ignore the fact that a suitable depth geometry is also critical in MVS. In this paper, we demonstrate that different depth geometries have significant performance gaps, even using the same depth prediction error. Therefore, we introduce an ideal depth geometry composed of Saddle-Shaped Cells, whose predicted depth map oscillates upward and downward around the ground-truth surface, rather than maintaining a continuous and smooth depth plane. To achieve it, we develop a coarse-to-fine framework called Dual-MVSNet (DMVSNet), which can produce an oscillating depth plane. Technically, we predict two depth values for each pixel (Dual-Depth), and propose a novel loss function and a checkerboard-shaped selecting strategy to constrain the predicted depth geometry. Compared to existing methods,DMVSNet achieves a high rank on the DTU benchmark and obtains the top performance on challenging scenes of Tanks and Temples, demonstrating its strong performance and generalization ability. Our method also points to a new research direction for considering depth geometry in MVS.

We introduce a differentiable estimator of range-partition entropy, a recent concept from computational geometry that enables algorithms to adapt to the "sortedness" of their input. While range-partition entropy provides strong guarantees in algorithm design, it has not yet been made accessible to deep learning. In this work, we (i) propose the first differentiable approximation of range-partition entropy, enabling its use as a trainable loss or regularizer; (ii) design EntropyNet, a neural module that restructures data into low-entropy forms to accelerate downstream instance-optimal algorithms; and (iii) extend this principle beyond geometry by applying entropy regularization directly to Transformer attention. Across tasks, we demonstrate that differentiable entropy improves efficiency without degrading correctness: in geometry, our method achieves up to 4.1times runtime speedups with negligible error (<0.2%); in deep learning, it induces structured attention patterns that yield 6% higher accuracy at 80% sparsity compared to L1 baselines. Our theoretical analysis provides approximation bounds for the estimator, and extensive ablations validate design choices. These results suggest that entropy-bounded computation is not only theoretically elegant but also a practical mechanism for adaptive learning, efficiency, and structured representation.

Developing a unified pipeline that enables users to remove, re-texture, or replace objects in a versatile manner is crucial for text-guided 3D inpainting. However, there are still challenges in performing multiple 3D inpainting tasks within a unified framework: 1) Single reference inpainting methods lack robustness when dealing with views that are far from the reference view. 2) Appearance inconsistency arises when independently inpainting multi-view images with 2D diffusion priors; 3) Geometry inconsistency limits performance when there are significant geometric changes in the inpainting regions. To tackle these challenges, we introduce DiGA3D, a novel and versatile 3D inpainting pipeline that leverages diffusion models to propagate consistent appearance and geometry in a coarse-to-fine manner. First, DiGA3D develops a robust strategy for selecting multiple reference views to reduce errors during propagation. Next, DiGA3D designs an Attention Feature Propagation (AFP) mechanism that propagates attention features from the selected reference views to other views via diffusion models to maintain appearance consistency. Furthermore, DiGA3D introduces a Texture-Geometry Score Distillation Sampling (TG-SDS) loss to further improve the geometric consistency of inpainted 3D scenes. Extensive experiments on multiple 3D inpainting tasks demonstrate the effectiveness of our method. The project page is available at https://rorisis.github.io/DiGA3D/.

This study explores cardiovascular stents fabricated using laser powder bed fusion (LPBF); an emerging method to offer patient-specific customisable parts. Here, the shape memory alloy NiTi, in a near equiatomic composition, was investigated to deconvolve the material response from macroscopic component effects. Specifically, stress-geometry interactions were revealed, in-situ, for a minaturised cardiovascular stent subjected to an externally applied cylindrical stress whilst acquiring synchrotron X-ray imaging and diffraction data. The approach enabled the collection of spatially resolved micromechanical deformation data; the formation of stress-induced martensite and R-phase was evident, occurring in locations near junctions between stent ligaments where stress concentrations exist. In the as-fabricated condition, hardness maps were obtained through nanoindentation, demonstrating that the localised deformation and deformation patterning is further controlled by porosity and microstructural heterogeneity. Electron backscatter diffraction (EBSD) supported these observations, showing a finer grain structure near stent junctions with higher associated lattice curvature. These features, combined with stress concentrations when loaded will initiate localised phase transformations. If the stent was subjected to repeated loading, representing in-vivo conditions, these regions would be susceptible to cyclic damage through transformation memory loss, leading to premature component failure. This study highlights the challenges that must be addressed for the post-processing treatment of LABF-processed stents for healthcare-related applications.

We present Meta 3D AssetGen (AssetGen), a significant advancement in text-to-3D generation which produces faithful, high-quality meshes with texture and material control. Compared to works that bake shading in the 3D object's appearance, AssetGen outputs physically-based rendering (PBR) materials, supporting realistic relighting. AssetGen generates first several views of the object with factored shaded and albedo appearance channels, and then reconstructs colours, metalness and roughness in 3D, using a deferred shading loss for efficient supervision. It also uses a sign-distance function to represent 3D shape more reliably and introduces a corresponding loss for direct shape supervision. This is implemented using fused kernels for high memory efficiency. After mesh extraction, a texture refinement transformer operating in UV space significantly improves sharpness and details. AssetGen achieves 17% improvement in Chamfer Distance and 40% in LPIPS over the best concurrent work for few-view reconstruction, and a human preference of 72% over the best industry competitors of comparable speed, including those that support PBR. Project page with generated assets: https://assetgen.github.io

We present PI3DETR, an end-to-end framework that directly predicts 3D parametric curve instances from raw point clouds, avoiding the intermediate representations and multi-stage processing common in prior work. Extending 3DETR, our model introduces a geometry-aware matching strategy and specialized loss functions that enable unified detection of differently parameterized curve types, including cubic B\'ezier curves, line segments, circles, and arcs, in a single forward pass. Optional post-processing steps further refine predictions without adding complexity. This streamlined design improves robustness to noise and varying sampling densities, addressing critical challenges in real world LiDAR and 3D sensing scenarios. PI3DETR sets a new state-of-the-art on the ABC dataset and generalizes effectively to real sensor data, offering a simple yet powerful solution for 3D edge and curve estimation.

Shape optimization is essential in aerospace vehicle design, including reentry systems, and propulsion system components, as it directly influences aerodynamic efficiency, structural integrity, and overall mission success. Rapid and accurate prediction of external and internal flows accelerates design iterations. To this end, we develop a new variant of DeepONet, called Fusion-DeepONet as a fast surrogate model for geometry-dependent hypersonic and supersonic flow fields. We evaluated Fusion-DeepONet in learning two external hypersonic flows and a supersonic shape-dependent internal flow problem. First, we compare the performance of Fusion-DeepONet with state-of-the-art neural operators to learn inviscid hypersonic flow around semi-elliptic blunt bodies for two grid types: uniform Cartesian and irregular grids. Fusion-DeepONet provides comparable accuracy to parameter-conditioned U-Net on uniform grids while outperforming MeshGraphNet and Vanilla-DeepONet on irregular grids. Fusion-DeepONet requires significantly fewer trainable parameters than U-Net, MeshGraphNet, and FNO. For the second hypersonic problem, we set up Fusion-DeepONet to map from geometry and free stream Mach number to the temperature field around a reentry capsule traveling at hypersonic speed. This fast surrogate is then improved to predict the spatial derivative of the temperature, resulting in an accurate prediction of heat flux at the surfaces of the capsule. To enhance the accuracy of spatial derivative prediction, we introduce a derivative-enhanced loss term with the least computation overhead. For the third problem, we show that Fusion-DeepONet outperforms MeshGraphNet in learning geometry-dependent supersonic flow in a converging-diverging nozzle configuration. For all the problems, we used high-fidelity simulations with a high-order entropy-stable DGSEM solver to generate training datasets with limited samples.

Neural field methods have seen great progress in various long-standing tasks in computer vision and computer graphics, including novel view synthesis and geometry reconstruction. As existing neural field methods try to predict some coordinate-based continuous target values, such as RGB for Neural Radiance Field (NeRF), all of these methods are regression models and are optimized by some regression loss. However, are regression models really better than classification models for neural field methods? In this work, we try to visit this very fundamental but overlooked question for neural fields from a machine learning perspective. We successfully propose a novel Neural Field Classifier (NFC) framework which formulates existing neural field methods as classification tasks rather than regression tasks. The proposed NFC can easily transform arbitrary Neural Field Regressor (NFR) into its classification variant via employing a novel Target Encoding module and optimizing a classification loss. By encoding a continuous regression target into a high-dimensional discrete encoding, we naturally formulate a multi-label classification task. Extensive experiments demonstrate the impressive effectiveness of NFC at the nearly free extra computational costs. Moreover, NFC also shows robustness to sparse inputs, corrupted images, and dynamic scenes.

A significant weakness of most current deep Convolutional Neural Networks is the need to train them using vast amounts of manu- ally labelled data. In this work we propose a unsupervised framework to learn a deep convolutional neural network for single view depth predic- tion, without requiring a pre-training stage or annotated ground truth depths. We achieve this by training the network in a manner analogous to an autoencoder. At training time we consider a pair of images, source and target, with small, known camera motion between the two such as a stereo pair. We train the convolutional encoder for the task of predicting the depth map for the source image. To do so, we explicitly generate an inverse warp of the target image using the predicted depth and known inter-view displacement, to reconstruct the source image; the photomet- ric error in the reconstruction is the reconstruction loss for the encoder. The acquisition of this training data is considerably simpler than for equivalent systems, requiring no manual annotation, nor calibration of depth sensor to camera. We show that our network trained on less than half of the KITTI dataset (without any further augmentation) gives com- parable performance to that of the state of art supervised methods for single view depth estimation.

Despite significant progress in 4D content generation, the conversion of monocular videos into high-quality animated 3D assets with explicit 4D meshes remains considerably challenging. The scarcity of large-scale, naturally captured 4D mesh datasets further limits the ability to train generalizable video-to-4D models from scratch in a purely data-driven manner. Meanwhile, advances in image-to-3D generation, supported by extensive datasets, offer powerful prior models that can be leveraged. To better utilize these priors while minimizing reliance on 4D supervision, we introduce SWiT-4D, a Sliding-Window Transformer for lossless, parameter-free temporal 4D mesh generation. SWiT-4D integrates seamlessly with any Diffusion Transformer (DiT)-based image-to-3D generator, adding spatial-temporal modeling across video frames while preserving the original single-image forward process, enabling 4D mesh reconstruction from videos of arbitrary length. To recover global translation, we further introduce an optimization-based trajectory module tailored for static-camera monocular videos. SWiT-4D demonstrates strong data efficiency: with only a single short (<10s) video for fine-tuning, it achieves high-fidelity geometry and stable temporal consistency, indicating practical deployability under extremely limited 4D supervision. Comprehensive experiments on both in-domain zoo-test sets and challenging out-of-domain benchmarks (C4D, Objaverse, and in-the-wild videos) show that SWiT-4D consistently outperforms existing baselines in temporal smoothness. Project page: https://animotionlab.github.io/SWIT4D/

A well-known challenge in applying deep-learning methods to omnidirectional images is spherical distortion. In dense regression tasks such as depth estimation, where structural details are required, using a vanilla CNN layer on the distorted 360 image results in undesired information loss. In this paper, we propose a 360 monocular depth estimation pipeline, OmniFusion, to tackle the spherical distortion issue. Our pipeline transforms a 360 image into less-distorted perspective patches (i.e. tangent images) to obtain patch-wise predictions via CNN, and then merge the patch-wise results for final output. To handle the discrepancy between patch-wise predictions which is a major issue affecting the merging quality, we propose a new framework with the following key components. First, we propose a geometry-aware feature fusion mechanism that combines 3D geometric features with 2D image features to compensate for the patch-wise discrepancy. Second, we employ the self-attention-based transformer architecture to conduct a global aggregation of patch-wise information, which further improves the consistency. Last, we introduce an iterative depth refinement mechanism, to further refine the estimated depth based on the more accurate geometric features. Experiments show that our method greatly mitigates the distortion issue, and achieves state-of-the-art performances on several 360 monocular depth estimation benchmark datasets.

Medical vision-language models enable co-learning and integrating features from medical imaging and clinical text. However, these models are not easy to train and the latent representation space can be complex. Here we propose a novel way for pre-training and regularising medical vision-language models. The proposed method, named Medical vision-language pre-training with Frozen language models and Latent spAce Geometry optimization (M-FLAG), leverages a frozen language model for training stability and efficiency and introduces a novel orthogonality loss to harmonize the latent space geometry. We demonstrate the potential of the pre-trained model on three downstream tasks: medical image classification, segmentation, and object detection. Extensive experiments across five public datasets demonstrate that M-FLAG significantly outperforms existing medical vision-language pre-training approaches and reduces the number of parameters by 78\%. Notably, M-FLAG achieves outstanding performance on the segmentation task while using only 1\% of the RSNA dataset, even outperforming ImageNet pre-trained models that have been fine-tuned using 100\% of the data.

We propose a new sampler for robust estimators that always selects the sample with the highest probability of consisting only of inliers. After every unsuccessful iteration, the inlier probabilities are updated in a principled way via a Bayesian approach. The probabilities obtained by the deep network are used as prior (so-called neural guidance) inside the sampler. Moreover, we introduce a new loss that exploits, in a geometrically justifiable manner, the orientation and scale that can be estimated for any type of feature, e.g., SIFT or SuperPoint, to estimate two-view geometry. The new loss helps to learn higher-order information about the underlying scene geometry. Benefiting from the new sampler and the proposed loss, we combine the neural guidance with the state-of-the-art MAGSAC++. Adaptive Reordering Sampler with Neurally Guided MAGSAC (ARS-MAGSAC) is superior to the state-of-the-art in terms of accuracy and run-time on the PhotoTourism and KITTI datasets for essential and fundamental matrix estimation. The code and trained models are available at https://github.com/weitong8591/ars_magsac.

We present a class of novel optimisers for training neural networks that makes use of the Riemannian metric naturally induced when the loss landscape is embedded in higher-dimensional space. This is the same metric that underlies common visualisations of loss landscapes. By taking this geometric perspective literally and using the induced metric, we develop a new optimiser and compare it to existing methods, namely: SGD, Adam, AdamW, and Muon, across a range of tasks and architectures. Empirically, we conclude that this new class of optimisers is highly effective in low dimensional examples, and provides slight improvement over state-of-the-art methods for training neural networks. These new optimisers have theoretically desirable properties. In particular, the effective learning rate is automatically decreased in regions of high curvature acting as a smoothed out form of gradient clipping. Similarly, one variant of these optimisers can also be viewed as inducing an effective scheduled learning rate and decoupled weight decay is the natural choice from our geometric perspective. The basic method can be used to modify any existing preconditioning method. The new optimiser has a computational complexity comparable to that of Adam.

Non-parametric quantization has received much attention due to its efficiency on parameters and scalability to a large codebook. In this paper, we present a unified formulation of different non-parametric quantization methods through the lens of lattice coding. The geometry of lattice codes explains the necessity of auxiliary loss terms when training auto-encoders with certain existing lookup-free quantization variants such as BSQ. As a step forward, we explore a few possible candidates, including random lattices, generalized Fibonacci lattices, and densest sphere packing lattices. Among all, we find the Leech lattice-based quantization method, which is dubbed as Spherical Leech Quantization (Λ_{24}-SQ), leads to both a simplified training recipe and an improved reconstruction-compression tradeoff thanks to its high symmetry and even distribution on the hypersphere. In image tokenization and compression tasks, this quantization approach achieves better reconstruction quality across all metrics than BSQ, the best prior art, while consuming slightly fewer bits. The improvement also extends to state-of-the-art auto-regressive image generation frameworks.

While existing methods for 3D face reconstruction from in-the-wild images excel at recovering the overall face shape, they commonly miss subtle, extreme, asymmetric, or rarely observed expressions. We improve upon these methods with SMIRK (Spatial Modeling for Image-based Reconstruction of Kinesics), which faithfully reconstructs expressive 3D faces from images. We identify two key limitations in existing methods: shortcomings in their self-supervised training formulation, and a lack of expression diversity in the training images. For training, most methods employ differentiable rendering to compare a predicted face mesh with the input image, along with a plethora of additional loss functions. This differentiable rendering loss not only has to provide supervision to optimize for 3D face geometry, camera, albedo, and lighting, which is an ill-posed optimization problem, but the domain gap between rendering and input image further hinders the learning process. Instead, SMIRK replaces the differentiable rendering with a neural rendering module that, given the rendered predicted mesh geometry, and sparsely sampled pixels of the input image, generates a face image. As the neural rendering gets color information from sampled image pixels, supervising with neural rendering-based reconstruction loss can focus solely on the geometry. Further, it enables us to generate images of the input identity with varying expressions while training. These are then utilized as input to the reconstruction model and used as supervision with ground truth geometry. This effectively augments the training data and enhances the generalization for diverse expressions. Our qualitative, quantitative and particularly our perceptual evaluations demonstrate that SMIRK achieves the new state-of-the art performance on accurate expression reconstruction. Project webpage: https://georgeretsi.github.io/smirk/.

In this paper, we present Gaussian Splatting based text-to-3D generation (GSGEN), a novel approach for generating high-quality 3D objects. Previous methods suffer from inaccurate geometry and limited fidelity due to the absence of 3D prior and proper representation. We leverage 3D Gaussian Splatting, a recent state-of-the-art representation, to address existing shortcomings by exploiting the explicit nature that enables the incorporation of 3D prior. Specifically, our method adopts a progressive optimization strategy, which includes a geometry optimization stage and an appearance refinement stage. In geometry optimization, a coarse representation is established under a 3D geometry prior along with the ordinary 2D SDS loss, ensuring a sensible and 3D-consistent rough shape. Subsequently, the obtained Gaussians undergo an iterative refinement to enrich details. In this stage, we increase the number of Gaussians by compactness-based densification to enhance continuity and improve fidelity. With these designs, our approach can generate 3D content with delicate details and more accurate geometry. Extensive evaluations demonstrate the effectiveness of our method, especially for capturing high-frequency components. Video results are provided at https://gsgen3d.github.io. Our code is available at https://github.com/gsgen3d/gsgen

We introduce Representation Tokenizer (RepTok), a generative modeling framework that represents an image using a single continuous latent token obtained from self-supervised vision transformers. Building on a pre-trained SSL encoder, we fine-tune only the semantic token embedding and pair it with a generative decoder trained jointly using a standard flow matching objective. This adaptation enriches the token with low-level, reconstruction-relevant details, enabling faithful image reconstruction. To preserve the favorable geometry of the original SSL space, we add a cosine-similarity loss that regularizes the adapted token, ensuring the latent space remains smooth and suitable for generation. Our single-token formulation resolves spatial redundancies of 2D latent spaces and significantly reduces training costs. Despite its simplicity and efficiency, RepTok achieves competitive results on class-conditional ImageNet generation and naturally extends to text-to-image synthesis, reaching competitive zero-shot performance on MS-COCO under extremely limited training budgets. Our findings highlight the potential of fine-tuned SSL representations as compact and effective latent spaces for efficient generative modeling.

We present a novel framework to regularize Neural Radiance Field (NeRF) in a few-shot setting with a geometry-aware consistency regularization. The proposed approach leverages a rendered depth map at unobserved viewpoint to warp sparse input images to the unobserved viewpoint and impose them as pseudo ground truths to facilitate learning of NeRF. By encouraging such geometry-aware consistency at a feature-level instead of using pixel-level reconstruction loss, we regularize the NeRF at semantic and structural levels while allowing for modeling view dependent radiance to account for color variations across viewpoints. We also propose an effective method to filter out erroneous warped solutions, along with training strategies to stabilize training during optimization. We show that our model achieves competitive results compared to state-of-the-art few-shot NeRF models. Project page is available at https://ku-cvlab.github.io/GeCoNeRF/.

Recent advances in text-guided 3D avatar generation have made substantial progress by distilling knowledge from diffusion models. Despite the plausible generated appearance, existing methods cannot achieve fine-grained disentanglement or high-fidelity modeling between inner body and outfit. In this paper, we propose Barbie, a novel framework for generating 3D avatars that can be dressed in diverse and high-quality Barbie-like garments and accessories. Instead of relying on a holistic model, Barbie achieves fine-grained disentanglement on avatars by semantic-aligned separated models for human body and outfits. These disentangled 3D representations are then optimized by different expert models to guarantee the domain-specific fidelity. To balance geometry diversity and reasonableness, we propose a series of losses for template-preserving and human-prior evolving. The final avatar is enhanced by unified texture refinement for superior texture consistency. Extensive experiments demonstrate that Barbie outperforms existing methods in both dressed human and outfit generation, supporting flexible apparel combination and animation. The code will be released for research purposes. Our project page is: https://xiaokunsun.github.io/Barbie.github.io/.

We present GALA, a framework that takes as input a single-layer clothed 3D human mesh and decomposes it into complete multi-layered 3D assets. The outputs can then be combined with other assets to create novel clothed human avatars with any pose. Existing reconstruction approaches often treat clothed humans as a single-layer of geometry and overlook the inherent compositionality of humans with hairstyles, clothing, and accessories, thereby limiting the utility of the meshes for downstream applications. Decomposing a single-layer mesh into separate layers is a challenging task because it requires the synthesis of plausible geometry and texture for the severely occluded regions. Moreover, even with successful decomposition, meshes are not normalized in terms of poses and body shapes, failing coherent composition with novel identities and poses. To address these challenges, we propose to leverage the general knowledge of a pretrained 2D diffusion model as geometry and appearance prior for humans and other assets. We first separate the input mesh using the 3D surface segmentation extracted from multi-view 2D segmentations. Then we synthesize the missing geometry of different layers in both posed and canonical spaces using a novel pose-guided Score Distillation Sampling (SDS) loss. Once we complete inpainting high-fidelity 3D geometry, we also apply the same SDS loss to its texture to obtain the complete appearance including the initially occluded regions. Through a series of decomposition steps, we obtain multiple layers of 3D assets in a shared canonical space normalized in terms of poses and human shapes, hence supporting effortless composition to novel identities and reanimation with novel poses. Our experiments demonstrate the effectiveness of our approach for decomposition, canonicalization, and composition tasks compared to existing solutions.

2D-to-3D reconstruction is an ill-posed problem, yet humans are good at solving this problem due to their prior knowledge of the 3D world developed over years. Driven by this observation, we propose NeRDi, a single-view NeRF synthesis framework with general image priors from 2D diffusion models. Formulating single-view reconstruction as an image-conditioned 3D generation problem, we optimize the NeRF representations by minimizing a diffusion loss on its arbitrary view renderings with a pretrained image diffusion model under the input-view constraint. We leverage off-the-shelf vision-language models and introduce a two-section language guidance as conditioning inputs to the diffusion model. This is essentially helpful for improving multiview content coherence as it narrows down the general image prior conditioned on the semantic and visual features of the single-view input image. Additionally, we introduce a geometric loss based on estimated depth maps to regularize the underlying 3D geometry of the NeRF. Experimental results on the DTU MVS dataset show that our method can synthesize novel views with higher quality even compared to existing methods trained on this dataset. We also demonstrate our generalizability in zero-shot NeRF synthesis for in-the-wild images.

3D surface reconstruction from images is essential for numerous applications. Recently, Neural Radiance Fields (NeRFs) have emerged as a promising framework for 3D modeling. However, NeRFs require accurate camera poses as input, and existing methods struggle to handle significantly noisy pose estimates (i.e., outliers), which are commonly encountered in real-world scenarios. To tackle this challenge, we present a novel approach that optimizes radiance fields with scene graphs to mitigate the influence of outlier poses. Our method incorporates an adaptive inlier-outlier confidence estimation scheme based on scene graphs, emphasizing images of high compatibility with the neighborhood and consistency in the rendering quality. We also introduce an effective intersection-over-union (IoU) loss to optimize the camera pose and surface geometry, together with a coarse-to-fine strategy to facilitate the training. Furthermore, we propose a new dataset containing typical outlier poses for a detailed evaluation. Experimental results on various datasets consistently demonstrate the effectiveness and superiority of our method over existing approaches, showcasing its robustness in handling outliers and producing high-quality 3D reconstructions. Our code and data are available at: https://github.com/Iris-cyy/SG-NeRF.

Reconstructing complex structures from planar cross-sections is a challenging problem, with wide-reaching applications in medical imaging, manufacturing, and topography. Out-of-the-box point cloud reconstruction methods can often fail due to the data sparsity between slicing planes, while current bespoke methods struggle to reconstruct thin geometric structures and preserve topological continuity. This is important for medical applications where thin vessel structures are present in CT and MRI scans. This paper introduces CrossSDF, a novel approach for extracting a 3D signed distance field from 2D signed distances generated from planar contours. Our approach makes the training of neural SDFs contour-aware by using losses designed for the case where geometry is known within 2D slices. Our results demonstrate a significant improvement over existing methods, effectively reconstructing thin structures and producing accurate 3D models without the interpolation artifacts or over-smoothing of prior approaches.

Text-guided 3D face synthesis has achieved remarkable results by leveraging text-to-image (T2I) diffusion models. However, most existing works focus solely on the direct generation, ignoring the editing, restricting them from synthesizing customized 3D faces through iterative adjustments. In this paper, we propose a unified text-guided framework from face generation to editing. In the generation stage, we propose a geometry-texture decoupled generation to mitigate the loss of geometric details caused by coupling. Besides, decoupling enables us to utilize the generated geometry as a condition for texture generation, yielding highly geometry-texture aligned results. We further employ a fine-tuned texture diffusion model to enhance texture quality in both RGB and YUV space. In the editing stage, we first employ a pre-trained diffusion model to update facial geometry or texture based on the texts. To enable sequential editing, we introduce a UV domain consistency preservation regularization, preventing unintentional changes to irrelevant facial attributes. Besides, we propose a self-guided consistency weight strategy to improve editing efficacy while preserving consistency. Through comprehensive experiments, we showcase our method's superiority in face synthesis. Project page: https://faceg2e.github.io/.

Latent variable collaborative filtering methods have been a standard approach to modelling user-click interactions due to their simplicity and effectiveness. However, there is limited work on analyzing the mathematical properties of these methods in particular on preventing the overfitting towards the identity, and such methods typically utilize loss functions that overlook the geometry between items. In this work, we introduce a notion of generalization gap in collaborative filtering and analyze this with respect to latent collaborative filtering models. We present a geometric upper bound that gives rise to loss functions, and a way to meaningfully utilize the geometry of item-metadata to improve recommendations. We show how these losses can be minimized and gives the recipe to a new latent collaborative filtering algorithm, which we refer to as GeoCF, due to the geometric nature of our results. We then show experimentally that our proposed GeoCF algorithm can outperform other all existing methods on the Movielens20M and Netflix datasets, as well as two large-scale internal datasets. In summary, our work proposes a theoretically sound method which paves a way to better understand generalization of collaborative filtering at large.

Unified visual grounding pursues a simple and generic technical route to leverage multi-task data with less task-specific design. The most advanced methods typically present boxes and masks as vertex sequences to model referring detection and segmentation as an autoregressive sequential vertex generation paradigm. However, generating high-dimensional vertex sequences sequentially is error-prone because the upstream of the sequence remains static and cannot be refined based on downstream vertex information, even if there is a significant location gap. Besides, with limited vertexes, the inferior fitting of objects with complex contours restricts the performance upper bound. To deal with this dilemma, we propose a parallel vertex generation paradigm for superior high-dimension scalability with a diffusion model by simply modifying the noise dimension. An intuitive materialization of our paradigm is Parallel Vertex Diffusion (PVD) to directly set vertex coordinates as the generation target and use a diffusion model to train and infer. We claim that it has two flaws: (1) unnormalized coordinate caused a high variance of loss value; (2) the original training objective of PVD only considers point consistency but ignores geometry consistency. To solve the first flaw, Center Anchor Mechanism (CAM) is designed to convert coordinates as normalized offset values to stabilize the training loss value. For the second flaw, Angle summation loss (ASL) is designed to constrain the geometry difference of prediction and ground truth vertexes for geometry-level consistency. Empirical results show that our PVD achieves state-of-the-art in both referring detection and segmentation, and our paradigm is more scalable and efficient than sequential vertex generation with high-dimension data.

Learning neural implicit surfaces from volume rendering has become popular for multi-view reconstruction. Neural surface reconstruction approaches can recover complex 3D geometry that are difficult for classical Multi-view Stereo (MVS) approaches, such as non-Lambertian surfaces and thin structures. However, one key assumption for these methods is knowing accurate camera parameters for the input multi-view images, which are not always available. In this paper, we present NoPose-NeuS, a neural implicit surface reconstruction method that extends NeuS to jointly optimize camera poses with the geometry and color networks. We encode the camera poses as a multi-layer perceptron (MLP) and introduce two additional losses, which are multi-view feature consistency and rendered depth losses, to constrain the learned geometry for better estimated camera poses and scene surfaces. Extensive experiments on the DTU dataset show that the proposed method can estimate relatively accurate camera poses, while maintaining a high surface reconstruction quality with 0.89 mean Chamfer distance.

Text-to-3D generation has recently garnered significant attention, fueled by 2D diffusion models trained on billions of image-text pairs. Existing methods primarily rely on score distillation to leverage the 2D diffusion priors to supervise the generation of 3D models, e.g., NeRF. However, score distillation is prone to suffer the view inconsistency problem, and implicit NeRF modeling can also lead to an arbitrary shape, thus leading to less realistic and uncontrollable 3D generation. In this work, we propose a flexible framework of Points-to-3D to bridge the gap between sparse yet freely available 3D points and realistic shape-controllable 3D generation by distilling the knowledge from both 2D and 3D diffusion models. The core idea of Points-to-3D is to introduce controllable sparse 3D points to guide the text-to-3D generation. Specifically, we use the sparse point cloud generated from the 3D diffusion model, Point-E, as the geometric prior, conditioned on a single reference image. To better utilize the sparse 3D points, we propose an efficient point cloud guidance loss to adaptively drive the NeRF's geometry to align with the shape of the sparse 3D points. In addition to controlling the geometry, we propose to optimize the NeRF for a more view-consistent appearance. To be specific, we perform score distillation to the publicly available 2D image diffusion model ControlNet, conditioned on text as well as depth map of the learned compact geometry. Qualitative and quantitative comparisons demonstrate that Points-to-3D improves view consistency and achieves good shape controllability for text-to-3D generation. Points-to-3D provides users with a new way to improve and control text-to-3D generation.

Surface reconstruction from sparse views aims to reconstruct a 3D shape or scene from few RGB images. The latest methods are either generalization-based or overfitting-based. However, the generalization-based methods do not generalize well on views that were unseen during training, while the reconstruction quality of overfitting-based methods is still limited by the limited geometry clues. To address this issue, we propose SparseRecon, a novel neural implicit reconstruction method for sparse views with volume rendering-based feature consistency and uncertainty-guided depth constraint. Firstly, we introduce a feature consistency loss across views to constrain the neural implicit field. This design alleviates the ambiguity caused by insufficient consistency information of views and ensures completeness and smoothness in the reconstruction results. Secondly, we employ an uncertainty-guided depth constraint to back up the feature consistency loss in areas with occlusion and insignificant features, which recovers geometry details for better reconstruction quality. Experimental results demonstrate that our method outperforms the state-of-the-art methods, which can produce high-quality geometry with sparse-view input, especially in the scenarios with small overlapping views. Project page: https://hanl2010.github.io/SparseRecon/.

3D human generation is increasingly significant in various applications. However, the direct use of 2D generative methods in 3D generation often results in significant loss of local details, while methods that reconstruct geometry from generated images struggle with global view consistency. In this work, we introduce Joint2Human, a novel method that leverages 2D diffusion models to generate detailed 3D human geometry directly, ensuring both global structure and local details. To achieve this, we employ the Fourier occupancy field (FOF) representation, enabling the direct production of 3D shapes as preliminary results using 2D generative models. With the proposed high-frequency enhancer and the multi-view recarving strategy, our method can seamlessly integrate the details from different views into a uniform global shape.To better utilize the 3D human prior and enhance control over the generated geometry, we introduce a compact spherical embedding of 3D joints. This allows for effective application of pose guidance during the generation process. Additionally, our method is capable of generating 3D humans guided by textual inputs. Our experimental results demonstrate the capability of our method to ensure global structure, local details, high resolution, and low computational cost, simultaneously. More results and code can be found on our project page at http://cic.tju.edu.cn/faculty/likun/projects/Joint2Human.

3D Morphable Models (3DMMs) provide promising 3D face reconstructions in various applications. However, existing methods struggle to reconstruct faces with extreme expressions due to deficiencies in supervisory signals, such as sparse or inaccurate landmarks. Segmentation information contains effective geometric contexts for face reconstruction. Certain attempts intuitively depend on differentiable renderers to compare the rendered silhouettes of reconstruction with segmentation, which is prone to issues like local optima and gradient instability. In this paper, we fully utilize the facial part segmentation geometry by introducing Part Re-projection Distance Loss (PRDL). Specifically, PRDL transforms facial part segmentation into 2D points and re-projects the reconstruction onto the image plane. Subsequently, by introducing grid anchors and computing different statistical distances from these anchors to the point sets, PRDL establishes geometry descriptors to optimize the distribution of the point sets for face reconstruction. PRDL exhibits a clear gradient compared to the renderer-based methods and presents state-of-the-art reconstruction performance in extensive quantitative and qualitative experiments. Our project is available at https://github.com/wang-zidu/3DDFA-V3 .

In the field of monocular 3D detection, it is common practice to utilize scene geometric clues to enhance the detector's performance. However, many existing works adopt these clues explicitly such as estimating a depth map and back-projecting it into 3D space. This explicit methodology induces sparsity in 3D representations due to the increased dimensionality from 2D to 3D, and leads to substantial information loss, especially for distant and occluded objects. To alleviate this issue, we propose MonoNeRD, a novel detection framework that can infer dense 3D geometry and occupancy. Specifically, we model scenes with Signed Distance Functions (SDF), facilitating the production of dense 3D representations. We treat these representations as Neural Radiance Fields (NeRF) and then employ volume rendering to recover RGB images and depth maps. To the best of our knowledge, this work is the first to introduce volume rendering for M3D, and demonstrates the potential of implicit reconstruction for image-based 3D perception. Extensive experiments conducted on the KITTI-3D benchmark and Waymo Open Dataset demonstrate the effectiveness of MonoNeRD. Codes are available at https://github.com/cskkxjk/MonoNeRD.

Despite recent research advancements in reconstructing clothed humans from a single image, accurately restoring the "unseen regions" with high-level details remains an unsolved challenge that lacks attention. Existing methods often generate overly smooth back-side surfaces with a blurry texture. But how to effectively capture all visual attributes of an individual from a single image, which are sufficient to reconstruct unseen areas (e.g., the back view)? Motivated by the power of foundation models, TeCH reconstructs the 3D human by leveraging 1) descriptive text prompts (e.g., garments, colors, hairstyles) which are automatically generated via a garment parsing model and Visual Question Answering (VQA), 2) a personalized fine-tuned Text-to-Image diffusion model (T2I) which learns the "indescribable" appearance. To represent high-resolution 3D clothed humans at an affordable cost, we propose a hybrid 3D representation based on DMTet, which consists of an explicit body shape grid and an implicit distance field. Guided by the descriptive prompts + personalized T2I diffusion model, the geometry and texture of the 3D humans are optimized through multi-view Score Distillation Sampling (SDS) and reconstruction losses based on the original observation. TeCH produces high-fidelity 3D clothed humans with consistent & delicate texture, and detailed full-body geometry. Quantitative and qualitative experiments demonstrate that TeCH outperforms the state-of-the-art methods in terms of reconstruction accuracy and rendering quality. The code will be publicly available for research purposes at https://huangyangyi.github.io/tech

Accurately segmenting thin tubular structures, such as vessels, nerves, roads or concrete cracks, is a crucial task in computer vision. Standard deep learning-based segmentation loss functions, such as Dice or Cross-Entropy, focus on volumetric overlap, often at the expense of preserving structural connectivity or topology. This can lead to segmentation errors that adversely affect downstream tasks, including flow calculation, navigation, and structural inspection. Although current topology-focused losses mark an improvement, they introduce significant computational and memory overheads. This is particularly relevant for 3D data, rendering these losses infeasible for larger volumes as well as increasingly important multi-class segmentation problems. To mitigate this, we propose a novel Skeleton Recall Loss, which effectively addresses these challenges by circumventing intensive GPU-based calculations with inexpensive CPU operations. It demonstrates overall superior performance to current state-of-the-art approaches on five public datasets for topology-preserving segmentation, while substantially reducing computational overheads by more than 90%. In doing so, we introduce the first multi-class capable loss function for thin structure segmentation, excelling in both efficiency and efficacy for topology-preservation.

We extend the recently proposed sparse voxel rasterization paradigm to the task of high-fidelity surface reconstruction by integrating Signed Distance Function (SDF), named SVRecon. Unlike 3D Gaussians, sparse voxels are spatially disentangled from their neighbors and have sharp boundaries, which makes them prone to local minima during optimization. Although SDF values provide a naturally smooth and continuous geometric field, preserving this smoothness across independently parameterized sparse voxels is nontrivial. To address this challenge, we promote coherent and smooth voxel-wise structure through (1) robust geometric initialization using a visual geometry model and (2) a spatial smoothness loss that enforces coherent relationships across parent-child and sibling voxel groups. Extensive experiments across various benchmarks show that our method achieves strong reconstruction accuracy while having consistently speedy convergence. The code will be made public.

Improving the quality of hyperspectral images (HSIs), such as through super-resolution, is a crucial research area. However, generative modeling for HSIs presents several challenges. Due to their high spectral dimensionality, HSIs are too memory-intensive for direct input into conventional diffusion models. Furthermore, general generative models lack an understanding of the topological and geometric structures of ground objects in remote sensing imagery. In addition, most diffusion models optimize loss functions at the noise level, leading to a non-intuitive convergence behavior and suboptimal generation quality for complex data. To address these challenges, we propose a Geometric Enhanced Wavelet-based Diffusion Model (GEWDiff), a novel framework for reconstructing hyperspectral images at 4-times super-resolution. A wavelet-based encoder-decoder is introduced that efficiently compresses HSIs into a latent space while preserving spectral-spatial information. To avoid distortion during generation, we incorporate a geometry-enhanced diffusion process that preserves the geometric features. Furthermore, a multi-level loss function was designed to guide the diffusion process, promoting stable convergence and improved reconstruction fidelity. Our model demonstrated state-of-the-art results across multiple dimensions, including fidelity, spectral accuracy, visual realism, and clarity.

In this paper, we introduce Geometry-Inverse-Meet-Pixel-Insert, short for GEO, an exceptionally versatile image editing technique designed to cater to customized user requirements at both local and global scales. Our approach seamlessly integrates text prompts and image prompts to yield diverse and precise editing outcomes. Notably, our method operates without the need for training and is driven by two key contributions: (i) a novel geometric accumulation loss that enhances DDIM inversion to faithfully preserve pixel space geometry and layout, and (ii) an innovative boosted image prompt technique that combines pixel-level editing for text-only inversion with latent space geometry guidance for standard classifier-free reversion. Leveraging the publicly available Stable Diffusion model, our approach undergoes extensive evaluation across various image types and challenging prompt editing scenarios, consistently delivering high-fidelity editing results for real images.

Multi-task learning (MTL) is an inductive transfer mechanism designed to leverage useful information from multiple tasks to improve generalization performance compared to single-task learning. It has been extensively explored in traditional machine learning to address issues such as data sparsity and overfitting in neural networks. In this work, we apply MTL to problems in science and engineering governed by partial differential equations (PDEs). However, implementing MTL in this context is complex, as it requires task-specific modifications to accommodate various scenarios representing different physical processes. To this end, we present a multi-task deep operator network (MT-DeepONet) to learn solutions across various functional forms of source terms in a PDE and multiple geometries in a single concurrent training session. We introduce modifications in the branch network of the vanilla DeepONet to account for various functional forms of a parameterized coefficient in a PDE. Additionally, we handle parameterized geometries by introducing a binary mask in the branch network and incorporating it into the loss term to improve convergence and generalization to new geometry tasks. Our approach is demonstrated on three benchmark problems: (1) learning different functional forms of the source term in the Fisher equation; (2) learning multiple geometries in a 2D Darcy Flow problem and showcasing better transfer learning capabilities to new geometries; and (3) learning 3D parameterized geometries for a heat transfer problem and demonstrate the ability to predict on new but similar geometries. Our MT-DeepONet framework offers a novel approach to solving PDE problems in engineering and science under a unified umbrella based on synergistic learning that reduces the overall training cost for neural operators.

Molecule pretraining has quickly become the go-to schema to boost the performance of AI-based drug discovery. Naturally, molecules can be represented as 2D topological graphs or 3D geometric point clouds. Although most existing pertaining methods focus on merely the single modality, recent research has shown that maximizing the mutual information (MI) between such two modalities enhances the molecule representation ability. Meanwhile, existing molecule multi-modal pretraining approaches approximate MI based on the representation space encoded from the topology and geometry, thus resulting in the loss of critical structural information of molecules. To address this issue, we propose MoleculeSDE. MoleculeSDE leverages group symmetric (e.g., SE(3)-equivariant and reflection-antisymmetric) stochastic differential equation models to generate the 3D geometries from 2D topologies, and vice versa, directly in the input space. It not only obtains tighter MI bound but also enables prosperous downstream tasks than the previous work. By comparing with 17 pretraining baselines, we empirically verify that MoleculeSDE can learn an expressive representation with state-of-the-art performance on 26 out of 32 downstream tasks.

Previous methods solve feature matching and pose estimation using a two-stage process by first finding matches and then estimating the pose. As they ignore the geometric relationships between the two tasks, they focus on either improving the quality of matches or filtering potential outliers, leading to limited efficiency or accuracy. In contrast, we propose an iterative matching and pose estimation framework (IMP) leveraging the geometric connections between the two tasks: a few good matches are enough for a roughly accurate pose estimation; a roughly accurate pose can be used to guide the matching by providing geometric constraints. To this end, we implement a geometry-aware recurrent attention-based module which jointly outputs sparse matches and camera poses. Specifically, for each iteration, we first implicitly embed geometric information into the module via a pose-consistency loss, allowing it to predict geometry-aware matches progressively. Second, we introduce an efficient IMP, called EIMP, to dynamically discard keypoints without potential matches, avoiding redundant updating and significantly reducing the quadratic time complexity of attention computation in transformers. Experiments on YFCC100m, Scannet, and Aachen Day-Night datasets demonstrate that the proposed method outperforms previous approaches in terms of accuracy and efficiency.

This paper addresses the challenge of reconstructing 3D indoor scenes from multi-view images. Many previous works have shown impressive reconstruction results on textured objects, but they still have difficulty in handling low-textured planar regions, which are common in indoor scenes. An approach to solving this issue is to incorporate planer constraints into the depth map estimation in multi-view stereo-based methods, but the per-view plane estimation and depth optimization lack both efficiency and multi-view consistency. In this work, we show that the planar constraints can be conveniently integrated into the recent implicit neural representation-based reconstruction methods. Specifically, we use an MLP network to represent the signed distance function as the scene geometry. Based on the Manhattan-world assumption, planar constraints are employed to regularize the geometry in floor and wall regions predicted by a 2D semantic segmentation network. To resolve the inaccurate segmentation, we encode the semantics of 3D points with another MLP and design a novel loss that jointly optimizes the scene geometry and semantics in 3D space. Experiments on ScanNet and 7-Scenes datasets show that the proposed method outperforms previous methods by a large margin on 3D reconstruction quality. The code is available at https://zju3dv.github.io/manhattan_sdf.

In the realm of text-to-3D generation, utilizing 2D diffusion models through score distillation sampling (SDS) frequently leads to issues such as blurred appearances and multi-faced geometry, primarily due to the intrinsically noisy nature of the SDS loss. Our analysis identifies the core of these challenges as the interaction among noise levels in the 2D diffusion process, the architecture of the diffusion network, and the 3D model representation. To overcome these limitations, we present StableDreamer, a methodology incorporating three advances. First, inspired by InstructNeRF2NeRF, we formalize the equivalence of the SDS generative prior and a simple supervised L2 reconstruction loss. This finding provides a novel tool to debug SDS, which we use to show the impact of time-annealing noise levels on reducing multi-faced geometries. Second, our analysis shows that while image-space diffusion contributes to geometric precision, latent-space diffusion is crucial for vivid color rendition. Based on this observation, StableDreamer introduces a two-stage training strategy that effectively combines these aspects, resulting in high-fidelity 3D models. Third, we adopt an anisotropic 3D Gaussians representation, replacing Neural Radiance Fields (NeRFs), to enhance the overall quality, reduce memory usage during training, and accelerate rendering speeds, and better capture semi-transparent objects. StableDreamer reduces multi-face geometries, generates fine details, and converges stably.

We present SLICK, a novel framework for precise and robust car damage segmentation that leverages structural priors and domain knowledge to tackle real-world automotive inspection challenges. SLICK introduces five key components: (1) Selective Part Segmentation using a high-resolution semantic backbone guided by structural priors to achieve surgical accuracy in segmenting vehicle parts even under occlusion, deformation, or paint loss; (2) Localization-Aware Attention blocks that dynamically focus on damaged regions, enhancing fine-grained damage detection in cluttered and complex street scenes; (3) an Instance-Sensitive Refinement head that leverages panoptic cues and shape priors to disentangle overlapping or adjacent parts, enabling precise boundary alignment; (4) Cross-Channel Calibration through multi-scale channel attention that amplifies subtle damage signals such as scratches and dents while suppressing noise like reflections and decals; and (5) a Knowledge Fusion Module that integrates synthetic crash data, part geometry, and real-world insurance datasets to improve generalization and handle rare cases effectively. Experiments on large-scale automotive datasets demonstrate SLICK's superior segmentation performance, robustness, and practical applicability for insurance and automotive inspection workflows.

Reconstructing 3D objects from a single image is an intriguing but challenging problem. One promising solution is to utilize multi-view (MV) 3D reconstruction to fuse generated MV images into consistent 3D objects. However, the generated images usually suffer from inconsistent lighting, misaligned geometry, and sparse views, leading to poor reconstruction quality. To cope with these problems, we present a novel 3D reconstruction framework that leverages intrinsic decomposition guidance, transient-mono prior guidance, and view augmentation to cope with the three issues, respectively. Specifically, we first leverage to decouple the shading information from the generated images to reduce the impact of inconsistent lighting; then, we introduce mono prior with view-dependent transient encoding to enhance the reconstructed normal; and finally, we design a view augmentation fusion strategy that minimizes pixel-level loss in generated sparse views and semantic loss in augmented random views, resulting in view-consistent geometry and detailed textures. Our approach, therefore, enables the integration of a pre-trained MV image generator and a neural network-based volumetric signed distance function (SDF) representation for a single image to 3D object reconstruction. We evaluate our framework on various datasets and demonstrate its superior performance in both quantitative and qualitative assessments, signifying a significant advancement in 3D object reconstruction. Compared with the latest state-of-the-art method Syncdreamer~liu2023syncdreamer, we reduce the Chamfer Distance error by about 36\% and improve PSNR by about 30\% .

Plasticity, the ability of a neural network to quickly change its predictions in response to new information, is essential for the adaptability and robustness of deep reinforcement learning systems. Deep neural networks are known to lose plasticity over the course of training even in relatively simple learning problems, but the mechanisms driving this phenomenon are still poorly understood. This paper conducts a systematic empirical analysis into plasticity loss, with the goal of understanding the phenomenon mechanistically in order to guide the future development of targeted solutions. We find that loss of plasticity is deeply connected to changes in the curvature of the loss landscape, but that it typically occurs in the absence of saturated units or divergent gradient norms. Based on this insight, we identify a number of parameterization and optimization design choices which enable networks to better preserve plasticity over the course of training. We validate the utility of these findings in larger-scale learning problems by applying the best-performing intervention, layer normalization, to a deep RL agent trained on the Arcade Learning Environment.

Modern deep neural networks have achieved impressive performance on tasks from image classification to natural language processing. Surprisingly, these complex systems with massive amounts of parameters exhibit the same structural properties in their last-layer features and classifiers across canonical datasets when training until convergence. In particular, it has been observed that the last-layer features collapse to their class-means, and those class-means are the vertices of a simplex Equiangular Tight Frame (ETF). This phenomenon is known as Neural Collapse (NC). Recent papers have theoretically shown that NC emerges in the global minimizers of training problems with the simplified "unconstrained feature model". In this context, we take a step further and prove the NC occurrences in deep linear networks for the popular mean squared error (MSE) and cross entropy (CE) losses, showing that global solutions exhibit NC properties across the linear layers. Furthermore, we extend our study to imbalanced data for MSE loss and present the first geometric analysis of NC under bias-free setting. Our results demonstrate the convergence of the last-layer features and classifiers to a geometry consisting of orthogonal vectors, whose lengths depend on the amount of data in their corresponding classes. Finally, we empirically validate our theoretical analyses on synthetic and practical network architectures with both balanced and imbalanced scenarios.

Deep learning approaches have provided state-of-the-art performance in many applications by relying on large and overparameterized neural networks. However, such networks have been shown to be very brittle and are difficult to deploy on resource-limited platforms. Model pruning, i.e., reducing the size of the network, is a widely adopted strategy that can lead to a more robust and compact model. Many heuristics exist for model pruning, but empirical studies show that some heuristics improve performance whereas others can make models more brittle or have other side effects. This work aims to shed light on how different pruning methods alter the network's internal feature representation and the corresponding impact on model performance. To facilitate a comprehensive comparison and characterization of the high-dimensional model feature space, we introduce a visual geometric analysis of feature representations. We decomposed and evaluated a set of critical geometric concepts from the common adopted classification loss, and used them to design a visualization system to compare and highlight the impact of pruning on model performance and feature representation. The proposed tool provides an environment for in-depth comparison of pruning methods and a comprehensive understanding of how model response to common data corruption. By leveraging the proposed visualization, machine learning researchers can reveal the similarities between pruning methods and redundant in robustness evaluation benchmarks, obtain geometric insights about the differences between pruned models that achieve superior robustness performance, and identify samples that are robust or fragile to model pruning and common data corruption to model pruning and data corruption but also obtain insights and explanations on how some pruned models achieve superior robustness performance.

Affine correspondences have received significant attention due to their benefits in tasks like image matching and pose estimation. Existing methods for extracting affine correspondences still have many limitations in terms of performance; thus, exploring a new paradigm is crucial. In this paper, we present a new pipeline designed for extracting accurate affine correspondences by integrating dense matching and geometric constraints. Specifically, a novel extraction framework is introduced, with the aid of dense matching and a novel keypoint scale and orientation estimator. For this purpose, we propose loss functions based on geometric constraints, which can effectively improve accuracy by supervising neural networks to learn feature geometry. The experimental show that the accuracy and robustness of our method outperform the existing ones in image matching tasks. To further demonstrate the effectiveness of the proposed method, we applied it to relative pose estimation. Affine correspondences extracted by our method lead to more accurate poses than the baselines on a range of real-world datasets. The code is available at https://github.com/stilcrad/DenseAffine.

Depth maps are widely used in feed-forward 3D Gaussian Splatting (3DGS) pipelines by unprojecting them into 3D point clouds for novel view synthesis. This approach offers advantages such as efficient training, the use of known camera poses, and accurate geometry estimation. However, depth discontinuities at object boundaries often lead to fragmented or sparse point clouds, degrading rendering quality -- a well-known limitation of depth-based representations. To tackle this issue, we introduce PM-Loss, a novel regularization loss based on a pointmap predicted by a pre-trained transformer. Although the pointmap itself may be less accurate than the depth map, it effectively enforces geometric smoothness, especially around object boundaries. With the improved depth map, our method significantly improves the feed-forward 3DGS across various architectures and scenes, delivering consistently better rendering results. Our project page: https://aim-uofa.github.io/PMLoss

We address the problem of regressing 3D human pose and shape from a single image, with a focus on 3D accuracy. The current best methods leverage large datasets of 3D pseudo-ground-truth (p-GT) and 2D keypoints, leading to robust performance. With such methods, we observe a paradoxical decline in 3D pose accuracy with increasing 2D accuracy. This is caused by biases in the p-GT and the use of an approximate camera projection model. We quantify the error induced by current camera models and show that fitting 2D keypoints and p-GT accurately causes incorrect 3D poses. Our analysis defines the invalid distances within which minimizing 2D and p-GT losses is detrimental. We use this to formulate a new loss Threshold-Adaptive Loss Scaling (TALS) that penalizes gross 2D and p-GT losses but not smaller ones. With such a loss, there are many 3D poses that could equally explain the 2D evidence. To reduce this ambiguity we need a prior over valid human poses but such priors can introduce unwanted bias. To address this, we exploit a tokenized representation of human pose and reformulate the problem as token prediction. This restricts the estimated poses to the space of valid poses, effectively providing a uniform prior. Extensive experiments on the EMDB and 3DPW datasets show that our reformulated keypoint loss and tokenization allows us to train on in-the-wild data while improving 3D accuracy over the state-of-the-art. Our models and code are available for research at https://tokenhmr.is.tue.mpg.de.

3D Gaussian Splatting (3DGS) has exhibited remarkable efficacy in novel view synthesis (NVS). However, it suffers from a significant drawback: achieving high-fidelity rendering typically necessitates a large number of 3D Gaussians, resulting in substantial memory consumption and storage requirements. To address this challenge, we propose the first knowledge distillation framework for 3DGS, featuring various teacher models, including vanilla 3DGS, noise-augmented variants, and dropout-regularized versions. The outputs of these teachers are aggregated to guide the optimization of a lightweight student model. To distill the hidden geometric structure, we propose a structural similarity loss to boost the consistency of spatial geometric distributions between the student and teacher model. Through comprehensive quantitative and qualitative evaluations across diverse datasets, the proposed Distilled-3DGS, a simple yet effective framework without bells and whistles, achieves promising rendering results in both rendering quality and storage efficiency compared to state-of-the-art methods. Project page: https://distilled3dgs.github.io . Code: https://github.com/lt-xiang/Distilled-3DGS .

Nearly all practical neural models for classification are trained using cross-entropy loss. Yet this ubiquitous choice is supported by little theoretical or empirical evidence. Recent work (Hui & Belkin, 2020) suggests that training using the (rescaled) square loss is often superior in terms of the classification accuracy. In this paper we propose the "squentropy" loss, which is the sum of two terms: the cross-entropy loss and the average square loss over the incorrect classes. We provide an extensive set of experiments on multi-class classification problems showing that the squentropy loss outperforms both the pure cross entropy and rescaled square losses in terms of the classification accuracy. We also demonstrate that it provides significantly better model calibration than either of these alternative losses and, furthermore, has less variance with respect to the random initialization. Additionally, in contrast to the square loss, squentropy loss can typically be trained using exactly the same optimization parameters, including the learning rate, as the standard cross-entropy loss, making it a true "plug-and-play" replacement. Finally, unlike the rescaled square loss, multiclass squentropy contains no parameters that need to be adjusted.

Large language models (LLMs) have shown remarkable proficiency in human-level reasoning and generation capabilities, which encourages extensive research on their application in mathematical problem solving. However, current work has been largely focused on text-based mathematical problems, with limited investigation in problems involving geometric information. Addressing this gap, we aim to enable LLMs to solve geometric problems by understanding image input. We first analyze the limitations of current Multimodal Large Language Models (MLLMs) in this area: they struggle to accurately comprehending basic geometric elements and their relationships. To overcome these challenges, we take advantage of the unique characteristics of geometric problems (such as unique geometric logical form, and geometric scalability) and the capacity of the textual LLMs to build an enriched multimodal geometry dataset based on existing data. The augmented dataset, Geo170K, contains more than 170K geometric image-caption and question-answer pairs. Utilizing our constructed Geo170K dataset, we develop G-LLaVA, which demonstrates exceptional performance in solving geometric problems, significantly outperforming GPT-4-V on the MathVista benchmark with only 7B parameters.

Despite their proficiency in general tasks, Multi-modal Large Language Models (MLLMs) struggle with automatic Geometry Problem Solving (GPS), which demands understanding diagrams, interpreting symbols, and performing complex reasoning. This limitation arises from their pre-training on natural images and texts, along with the lack of automated verification in the problem-solving process. Besides, current geometric specialists are limited by their task-specific designs, making them less effective for broader geometric problems. To this end, we present GeoX, a multi-modal large model focusing on geometric understanding and reasoning tasks. Given the significant differences between geometric diagram-symbol and natural image-text, we introduce unimodal pre-training to develop a diagram encoder and symbol decoder, enhancing the understanding of geometric images and corpora. Furthermore, we introduce geometry-language alignment, an effective pre-training paradigm that bridges the modality gap between unimodal geometric experts. We propose a Generator-And-Sampler Transformer (GS-Former) to generate discriminative queries and eliminate uninformative representations from unevenly distributed geometric signals. Finally, GeoX benefits from visual instruction tuning, empowering it to take geometric images and questions as input and generate verifiable solutions. Experiments show that GeoX outperforms both generalists and geometric specialists on publicly recognized benchmarks, such as GeoQA, UniGeo, Geometry3K, and PGPS9k.

The process of camera calibration involves estimating the intrinsic and extrinsic parameters, which are essential for accurately performing tasks such as 3D reconstruction, object tracking and augmented reality. In this work, we propose a novel constraints-based loss for measuring the intrinsic (focal length: (f_x, f_y) and principal point: (p_x, p_y)) and extrinsic (baseline: (b), disparity: (d), translation: (t_x, t_y, t_z), and rotation specifically pitch: (theta_p)) camera parameters. Our novel constraints are based on geometric properties inherent in the camera model, including the anatomy of the projection matrix (vanishing points, image of world origin, axis planes) and the orthonormality of the rotation matrix. Thus we proposed a novel Unsupervised Geometric Constraint Loss (UGCL) via a multitask learning framework. Our methodology is a hybrid approach that employs the learning power of a neural network to estimate the desired parameters along with the underlying mathematical properties inherent in the camera projection matrix. This distinctive approach not only enhances the interpretability of the model but also facilitates a more informed learning process. Additionally, we introduce a new CVGL Camera Calibration dataset, featuring over 900 configurations of camera parameters, incorporating 63,600 image pairs that closely mirror real-world conditions. By training and testing on both synthetic and real-world datasets, our proposed approach demonstrates improvements across all parameters when compared to the state-of-the-art (SOTA) benchmarks. The code and the updated dataset can be found here: https://github.com/CVLABLUMS/CVGL-Camera-Calibration

This paper presents GPSM4K, a comprehensive geometry multimodal dataset tailored to augment the problem-solving capabilities of Large Vision Language Models (LVLMs). GPSM4K encompasses 2157 multimodal question-answer pairs manually extracted from mathematics textbooks spanning grades 7-12 and is further augmented to 5340 problems, consisting of both numerical and theorem-proving questions. In contrast to PGPS9k, Geometry3K, and Geo170K which feature only objective-type questions, GPSM4K offers detailed step-by-step solutions in a consistent format, facilitating a comprehensive evaluation of problem-solving approaches. This dataset serves as an excellent benchmark for assessing the geometric reasoning capabilities of LVLMs. Evaluation of our test set shows that there is scope for improvement needed in open-source language models in geometry problem-solving. Finetuning on our training set increases the geometry problem-solving capabilities of models. Further, We also evaluate the effectiveness of techniques such as image captioning and Retrieval Augmentation generation (RAG) on model performance. We leveraged LLM to automate the task of final answer evaluation by providing ground truth and predicted solutions. This research will help to assess and improve the geometric reasoning capabilities of LVLMs.

Recent advances in large language models (LLMs) have demonstrated remarkable capabilities across diverse domains, particularly in mathematical reasoning, amid which geometry problem solving remains a challenging area where auxiliary construction plays a enssential role. Existing approaches either achieve suboptimal performance or rely on massive LLMs (e.g., GPT-4o), incurring massive computational costs. We posit that reinforcement learning with verifiable reward (e.g., GRPO) offers a promising direction for training smaller models that effectively combine auxiliary construction with robust geometric reasoning. However, directly applying GRPO to geometric reasoning presents fundamental limitations due to its dependence on unconditional rewards, which leads to indiscriminate and counterproductive auxiliary constructions. To address these challenges, we propose Group Contrastive Policy Optimization (GCPO), a novel reinforcement learning framework featuring two key innovations: (1) Group Contrastive Masking, which adaptively provides positive or negative reward signals for auxiliary construction based on contextual utility, and a (2) length reward that promotes longer reasoning chains. Building on GCPO, we develop GeometryZero, a family of affordable-size geometric reasoning models that judiciously determine when to employ auxiliary construction. Our extensive empirical evaluation across popular geometric benchmarks (Geometry3K, MathVista) demonstrates that GeometryZero models consistently outperform baselines (e.g. GRPO), achieving an average improvement of 4.29% across all benchmarks.

Neural network training relies on our ability to find "good" minimizers of highly non-convex loss functions. It is well-known that certain network architecture designs (e.g., skip connections) produce loss functions that train easier, and well-chosen training parameters (batch size, learning rate, optimizer) produce minimizers that generalize better. However, the reasons for these differences, and their effects on the underlying loss landscape, are not well understood. In this paper, we explore the structure of neural loss functions, and the effect of loss landscapes on generalization, using a range of visualization methods. First, we introduce a simple "filter normalization" method that helps us visualize loss function curvature and make meaningful side-by-side comparisons between loss functions. Then, using a variety of visualizations, we explore how network architecture affects the loss landscape, and how training parameters affect the shape of minimizers.

A growing literature in computational neuroscience leverages gradient descent and learning algorithms that approximate it to study synaptic plasticity in the brain. However, the vast majority of this work ignores a critical underlying assumption: the choice of distance for synaptic changes - i.e. the geometry of synaptic plasticity. Gradient descent assumes that the distance is Euclidean, but many other distances are possible, and there is no reason that biology necessarily uses Euclidean geometry. Here, using the theoretical tools provided by mirror descent, we show that the distribution of synaptic weights will depend on the geometry of synaptic plasticity. We use these results to show that experimentally-observed log-normal weight distributions found in several brain areas are not consistent with standard gradient descent (i.e. a Euclidean geometry), but rather with non-Euclidean distances. Finally, we show that it should be possible to experimentally test for different synaptic geometries by comparing synaptic weight distributions before and after learning. Overall, our work shows that the current paradigm in theoretical work on synaptic plasticity that assumes Euclidean synaptic geometry may be misguided and that it should be possible to experimentally determine the true geometry of synaptic plasticity in the brain.

Neural representations of 3D data have been widely adopted across various applications, particularly in recent work leveraging coordinate-based networks to model scalar or vector fields. However, these approaches face inherent challenges, such as handling thin structures and non-watertight geometries, which limit their flexibility and accuracy. In contrast, we propose a novel geometric data representation that models geometry as distributions-a powerful representation that makes no assumptions about surface genus, connectivity, or boundary conditions. Our approach uses diffusion models with a novel network architecture to learn surface point distributions, capturing fine-grained geometric details. We evaluate our representation qualitatively and quantitatively across various object types, demonstrating its effectiveness in achieving high geometric fidelity. Additionally, we explore applications using our representation, such as textured mesh representation, neural surface compression, dynamic object modeling, and rendering, highlighting its potential to advance 3D geometric learning.

Geometric methods for solving open-world off-road navigation tasks, by learning occupancy and metric maps, provide good generalization but can be brittle in outdoor environments that violate their assumptions (e.g., tall grass). Learning-based methods can directly learn collision-free behavior from raw observations, but are difficult to integrate with standard geometry-based pipelines. This creates an unfortunate conflict -- either use learning and lose out on well-understood geometric navigational components, or do not use it, in favor of extensively hand-tuned geometry-based cost maps. In this work, we reject this dichotomy by designing the learning and non-learning-based components in a way such that they can be effectively combined in a self-supervised manner. Both components contribute to a planning criterion: the learned component contributes predicted traversability as rewards, while the geometric component contributes obstacle cost information. We instantiate and comparatively evaluate our system in both in-distribution and out-of-distribution environments, showing that this approach inherits complementary gains from the learned and geometric components and significantly outperforms either of them. Videos of our results are hosted at https://sites.google.com/view/hybrid-imitative-planning

Mathematics olympiads are prestigious competitions, with problem proposing and solving highly honored. Building artificial intelligence that proposes and solves olympiads presents an unresolved challenge in automated theorem discovery and proving, especially in geometry for its combination of numerical and spatial elements. We introduce TongGeometry, a Euclidean geometry system supporting tree-search-based guided problem proposing and solving. The efficient geometry system establishes the most extensive repository of geometry theorems to date: within the same computational budget as the existing state-of-the-art, TongGeometry discovers 6.7 billion geometry theorems requiring auxiliary constructions, including 4.1 billion exhibiting geometric symmetry. Among them, 10 theorems were proposed to regional mathematical olympiads with 3 of TongGeometry's proposals selected in real competitions, earning spots in a national team qualifying exam or a top civil olympiad in China and the US. Guided by fine-tuned large language models, TongGeometry solved all International Mathematical Olympiad geometry in IMO-AG-30, outperforming gold medalists for the first time. It also surpasses the existing state-of-the-art across a broader spectrum of olympiad-level problems. The full capabilities of the system can be utilized on a consumer-grade machine, making the model more accessible and fostering widespread democratization of its use. By analogy, unlike existing systems that merely solve problems like students, TongGeometry acts like a geometry coach, discovering, presenting, and proving theorems.

Deep neural networks are prone to adversarial examples that maliciously alter the network's outcome. Due to the increasing popularity of 3D sensors in safety-critical systems and the vast deployment of deep learning models for 3D point sets, there is a growing interest in adversarial attacks and defenses for such models. So far, the research has focused on the semantic level, namely, deep point cloud classifiers. However, point clouds are also widely used in a geometric-related form that includes encoding and reconstructing the geometry. In this work, we are the first to consider the problem of adversarial examples at a geometric level. In this setting, the question is how to craft a small change to a clean source point cloud that leads, after passing through an autoencoder model, to the reconstruction of a different target shape. Our attack is in sharp contrast to existing semantic attacks on 3D point clouds. While such works aim to modify the predicted label by a classifier, we alter the entire reconstructed geometry. Additionally, we demonstrate the robustness of our attack in the case of defense, where we show that remnant characteristics of the target shape are still present at the output after applying the defense to the adversarial input. Our code is publicly available at https://github.com/itailang/geometric_adv.

Benefiting from contrastively trained visual encoders on large-scale natural scene images, Large Multimodal Models (LMMs) have achieved remarkable performance across various visual perception tasks. However, the inherent limitations of contrastive learning upon summarized descriptions fundamentally restrict the capabilities of models in meticulous reasoning, particularly in crucial scenarios of geometric problem-solving. To enhance geometric understanding, we propose a novel hard negative contrastive learning framework for the vision encoder, which combines image-based contrastive learning using generation-based hard negatives created by perturbing diagram generation code, and text-based contrastive learning using rule-based negatives derived from modified geometric descriptions and retrieval-based negatives selected based on caption similarity. We train CLIP using our strong negative learning method, namely MMCLIP (Multimodal Math CLIP), and subsequently train an LMM for geometric problem-solving. Experiments show that our trained model, MMGeoLM, significantly outperforms other open-source models on three geometric reasoning benchmarks. Even with a size of 7B, it can rival powerful closed-source models like GPT-4o. We further study the impact of different negative sample construction methods and the number of negative samples on the geometric reasoning performance of LMM, yielding fruitful conclusions. The code and dataset are available at https://github.com/THU-KEG/MMGeoLM.

Learning discriminative shape representations is a crucial issue for large-scale 3D shape retrieval. In this paper, we propose the Collaborative Inner Product Loss (CIP Loss) to obtain ideal shape embedding that discriminative among different categories and clustered within the same class. Utilizing simple inner product operation, CIP loss explicitly enforces the features of the same class to be clustered in a linear subspace, while inter-class subspaces are constrained to be at least orthogonal. Compared to previous metric loss functions, CIP loss could provide more clear geometric interpretation for the embedding than Euclidean margin, and is easy to implement without normalization operation referring to cosine margin. Moreover, our proposed loss term can combine with other commonly used loss functions and can be easily plugged into existing off-the-shelf architectures. Extensive experiments conducted on the two public 3D object retrieval datasets, ModelNet and ShapeNetCore 55, demonstrate the effectiveness of our proposal, and our method has achieved state-of-the-art results on both datasets.

Multimodal large language models (MLLMs) have made rapid progress in recent years, yet continue to struggle with low-level visual perception (LLVP) -- particularly the ability to accurately describe the geometric details of an image. This capability is crucial for applications in areas such as robotics, medical image analysis, and manufacturing. In this paper, we first introduce Geoperception, a benchmark designed to evaluate an MLLM's ability to accurately transcribe 2D geometric information from an image. Using this benchmark, we demonstrate the limitations of leading MLLMs, and then conduct a comprehensive empirical study to explore strategies for improving their performance on geometric tasks. Our findings highlight the benefits of certain model architectures, training techniques, and data strategies, including the use of high-fidelity synthetic data and multi-stage training with a data curriculum. Notably, we find that a data curriculum enables models to learn challenging geometry understanding tasks which they fail to learn from scratch. Leveraging these insights, we develop Euclid, a family of models specifically optimized for strong low-level geometric perception. Although purely trained on synthetic multimodal data, Euclid shows strong generalization ability to novel geometry shapes. For instance, Euclid outperforms the best closed-source model, Gemini-1.5-Pro, by up to 58.56% on certain Geoperception benchmark tasks and 10.65% on average across all tasks.

Recent advances in video generation have enabled the synthesis of high-quality and visually realistic clips using diffusion transformer models. However, most existing approaches operate purely in the 2D pixel space and lack explicit mechanisms for modeling 3D structures, often resulting in temporally inconsistent geometries, implausible motions, and structural artifacts. In this work, we introduce geometric regularization losses into video generation by augmenting latent diffusion models with per-frame depth prediction. We adopted depth as the geometric representation because of the great progress in depth prediction and its compatibility with image-based latent encoders. Specifically, to enforce structural consistency over time, we propose a multi-view geometric loss that aligns the predicted depth maps across frames within a shared 3D coordinate system. Our method bridges the gap between appearance generation and 3D structure modeling, leading to improved spatio-temporal coherence, shape consistency, and physical plausibility. Experiments across multiple datasets show that our approach produces significantly more stable and geometrically consistent results than existing baselines.

The aerodynamic coefficients of aircrafts are significantly impacted by its geometry, especially when the angle of attack (AoA) is large. In the field of aerodynamics, traditional polynomial-based parameterization uses as few parameters as possible to describe the geometry of an airfoil. However, because the 3D geometry of a wing is more complicated than the 2D airfoil, polynomial-based parameterizations have difficulty in accurately representing the entire shape of a wing in 3D space. Existing deep learning-based methods can extract massive latent neural representations for the shape of 2D airfoils or 2D slices of wings. Recent studies highlight that directly taking geometric features as inputs to the neural networks can improve the accuracy of predicted aerodynamic coefficients. Motivated by geometry theory, we propose to incorporate Riemannian geometric features for learning Coefficient of Pressure (CP) distributions on wing surfaces. Our method calculates geometric features (Riemannian metric, connection, and curvature) and further inputs the geometric features, coordinates and flight conditions into a deep learning model to predict the CP distribution. Experimental results show that our method, compared to state-of-the-art Deep Attention Network (DAN), reduces the predicted mean square error (MSE) of CP by an average of 8.41% for the DLR-F11 aircraft test set.

To accelerate diffusion model inference, numerical solvers perform poorly at extremely small steps, while distillation techniques often introduce complexity and instability. This work presents an intermediate strategy, balancing performance and cost, by learning ODE integration using loss functions derived from the derivative-integral relationship, inspired by Monte Carlo integration and Picard iteration. From a geometric perspective, the losses operate by gradually extending the tangent to the secant, thus are named as secant losses. The target of secant losses is the same as that of diffusion models, or the diffusion model itself, leading to great training stability. By fine-tuning or distillation, the secant version of EDM achieves a 10-step FID of 2.14 on CIFAR-10, while the secant version of SiT-XL/2 attains a 4-step FID of 2.27 and an 8-step FID of 1.96 on ImageNet-256times256. Code is available at https://github.com/poppuppy/secant-expectation.

We present AlphaGeometry2, a significantly improved version of AlphaGeometry introduced in Trinh et al. (2024), which has now surpassed an average gold medalist in solving Olympiad geometry problems. To achieve this, we first extend the original AlphaGeometry language to tackle harder problems involving movements of objects, and problems containing linear equations of angles, ratios, and distances. This, together with other additions, has markedly improved the coverage rate of the AlphaGeometry language on International Math Olympiads (IMO) 2000-2024 geometry problems from 66% to 88%. The search process of AlphaGeometry2 has also been greatly improved through the use of Gemini architecture for better language modeling, and a novel knowledge-sharing mechanism that combines multiple search trees. Together with further enhancements to the symbolic engine and synthetic data generation, we have significantly boosted the overall solving rate of AlphaGeometry2 to 84% for all geometry problems over the last 25 years, compared to 54% previously. AlphaGeometry2 was also part of the system that achieved silver-medal standard at IMO 2024 https://dpmd.ai/imo-silver. Last but not least, we report progress towards using AlphaGeometry2 as a part of a fully automated system that reliably solves geometry problems directly from natural language input.

In deep metric learning, the Triplet Loss has emerged as a popular method to learn many computer vision and natural language processing tasks such as facial recognition, object detection, and visual-semantic embeddings. One issue that plagues the Triplet Loss is network collapse, an undesirable phenomenon where the network projects the embeddings of all data onto a single point. Researchers predominately solve this problem by using triplet mining strategies. While hard negative mining is the most effective of these strategies, existing formulations lack strong theoretical justification for their empirical success. In this paper, we utilize the mathematical theory of isometric approximation to show an equivalence between the Triplet Loss sampled by hard negative mining and an optimization problem that minimizes a Hausdorff-like distance between the neural network and its ideal counterpart function. This provides the theoretical justifications for hard negative mining's empirical efficacy. In addition, our novel application of the isometric approximation theorem provides the groundwork for future forms of hard negative mining that avoid network collapse. Our theory can also be extended to analyze other Euclidean space-based metric learning methods like Ladder Loss or Contrastive Learning.

The enduring legacy of Euclidean geometry underpins classical machine learning, which, for decades, has been primarily developed for data lying in Euclidean space. Yet, modern machine learning increasingly encounters richly structured data that is inherently nonEuclidean. This data can exhibit intricate geometric, topological and algebraic structure: from the geometry of the curvature of space-time, to topologically complex interactions between neurons in the brain, to the algebraic transformations describing symmetries of physical systems. Extracting knowledge from such non-Euclidean data necessitates a broader mathematical perspective. Echoing the 19th-century revolutions that gave rise to non-Euclidean geometry, an emerging line of research is redefining modern machine learning with non-Euclidean structures. Its goal: generalizing classical methods to unconventional data types with geometry, topology, and algebra. In this review, we provide an accessible gateway to this fast-growing field and propose a graphical taxonomy that integrates recent advances into an intuitive unified framework. We subsequently extract insights into current challenges and highlight exciting opportunities for future development in this field.

Transformers achieve strong performance across diverse domains but implicitly assume Euclidean geometry in their attention mechanisms, limiting their effectiveness on data with non-Euclidean structure. While recent extensions to hyperbolic and spherical spaces show promise for hierarchical and cyclical patterns, respectively, they require committing to a single geometry a priori, reducing flexibility when data exhibits mixed geometric properties. We introduce the Curvature-Adaptive Transformer (CAT), a novel architecture that dynamically learns per-token routing across three geometric attention branches through a lightweight, differentiable gating mechanism. Unlike fixed-geometry approaches, CAT enables adaptive geometric specialization, routing tokens to the appropriate curvature based on their local relational structure. The routing network provides interpretable curvature preferences while each branch employs geometry-specific operations optimized for its respective manifold. On knowledge graph completion benchmarks (FB15k-237, WN18RR), CAT achieves approximately 10% improvements in MRR and Hits@10 over fixed-geometry baselines with minimal overhead (5% parameter increase, comparable inference time). These results demonstrate that learned geometric adaptation outperforms any single fixed geometry for complex relational reasoning, establishing CAT as a scalable and interpretable foundation for mixture-of-geometry architectures across language, vision, and multimodal domains.

In this work, we study the evolution of the loss Hessian across many classification tasks in order to understand the effect the curvature of the loss has on the training dynamics. Whereas prior work has focused on how different learning rates affect the loss Hessian observed during training, we also analyze the effects of model initialization, architectural choices, and common training heuristics such as gradient clipping and learning rate warmup. Our results demonstrate that successful model and hyperparameter choices allow the early optimization trajectory to either avoid -- or navigate out of -- regions of high curvature and into flatter regions that tolerate a higher learning rate. Our results suggest a unifying perspective on how disparate mitigation strategies for training instability ultimately address the same underlying failure mode of neural network optimization, namely poor conditioning. Inspired by the conditioning perspective, we show that learning rate warmup can improve training stability just as much as batch normalization, layer normalization, MetaInit, GradInit, and Fixup initialization.