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# HierarchicalTopK SAE decoder Triton kernels
# Copyright 2025 T-Tech
from typing import Tuple
import torch
import triton
import triton.language as tl
@triton.jit
def hierarchical_sae_forward_kernel(
loss_per_batch_ptr, # [B]
final_recon_ptr, # [B, D]
indices_ptr, # [B, K]
weight_ptr, # [F, D]
bias_ptr, # [D]
vals_ptr, # [B, K]
target_ptr, # [B, D]
B: tl.constexpr,
D: tl.constexpr,
K: tl.constexpr,
BLOCK_D: tl.constexpr,
LOOP_NUM_STAGES: tl.constexpr,
BLOCK_B: tl.constexpr,
):
tl.static_assert((D % BLOCK_D) == 0)
tl.static_assert((B % BLOCK_B) == 0)
tl.static_assert((K & (K - 1)) == 0, f"{K=} must be a power of 2")
tl.static_assert((BLOCK_D & (BLOCK_D - 1)) == 0, f"{BLOCK_D=} must be a power of 2")
tl.static_assert((BLOCK_B & (BLOCK_B - 1)) == 0, f"{BLOCK_B=} must be a power of 2")
pid_b = tl.program_id(axis=0).to(tl.int64)
pid_d = tl.program_id(axis=1).to(tl.int64)
batch_offsets = pid_b * BLOCK_B + tl.arange(0, BLOCK_B)
batch_offsets = batch_offsets.to(tl.int64)
tl.multiple_of(batch_offsets, BLOCK_B)
offset_d = pid_d * BLOCK_D + tl.arange(0, BLOCK_D)
offset_d = offset_d.to(tl.int64)
tl.multiple_of(offset_d, BLOCK_D)
tl.max_contiguous(offset_d, BLOCK_D)
batch_d_offset = batch_offsets[:, None] * D + offset_d[None, :]
bias_tile = tl.load(bias_ptr + offset_d).to(tl.float32)
recon = tl.zeros([BLOCK_B, BLOCK_D], dtype=tl.float32)
recon += bias_tile[None, :]
target = tl.load(target_ptr + batch_d_offset).to(tl.float32)
loss_accum = tl.zeros([BLOCK_B, BLOCK_D], dtype=tl.float32)
row_idx_ptr = indices_ptr + batch_offsets * K
row_val_ptr = vals_ptr + batch_offsets * K
idx = tl.load(row_idx_ptr).to(tl.int64)
val = tl.load(row_val_ptr).to(tl.float32)
val = val[:, None]
weight_tile = tl.load(weight_ptr + idx[:, None] * D + offset_d[None, :]).to(tl.float32)
for t in tl.range(0, K, num_stages=LOOP_NUM_STAGES):
recon += weight_tile * val
diff = recon - target
loss_accum += diff * diff
if t + 1 < K:
idx_next = tl.load(row_idx_ptr + (t + 1)).to(tl.int64)
val_next = tl.load(row_val_ptr + (t + 1)).to(tl.float32)
weight_next = tl.load(weight_ptr + idx_next[:, None] * D + offset_d[None, :]).to(tl.float32)
idx = idx_next
val = val_next[:, None]
weight_tile = weight_next
loss_tile = tl.sum(loss_accum, axis=1)
tl.atomic_add(
loss_per_batch_ptr + batch_offsets,
loss_tile,
sem="relaxed",
)
tl.store(
final_recon_ptr + batch_d_offset,
recon,
)
@triton.jit
def hierarchical_sae_backward_kernel(
weight_grad_ptr, # [F, D]
vals_grad_ptr, # [B, K]
bias_grad_ptr, # [D]
final_recon_ptr, # [B, D]
indices_ptr, # [B, K]
weight_ptr, # [F, D]
vals_ptr, # [B, K]
target_ptr, # [B, D]
B: tl.constexpr,
D: tl.constexpr,
K: tl.constexpr,
BLOCK_D: tl.constexpr,
LOOP_NUM_STAGES: tl.constexpr,
BLOCK_B: tl.constexpr,
):
tl.static_assert((D % BLOCK_D) == 0)
tl.static_assert((B % BLOCK_B) == 0)
tl.static_assert((K & (K - 1)) == 0, f"{K=} must be a power of 2")
tl.static_assert((BLOCK_D & (BLOCK_D - 1)) == 0, f"{BLOCK_D=} must be a power of 2")
tl.static_assert((BLOCK_B & (BLOCK_B - 1)) == 0, f"{BLOCK_B=} must be a power of 2")
pid_b = tl.program_id(axis=0).to(tl.int64)
pid_d = tl.program_id(axis=1).to(tl.int64)
batch_offsets = pid_b * BLOCK_B + tl.arange(0, BLOCK_B)
batch_offsets = batch_offsets.to(tl.int64)
tl.multiple_of(batch_offsets, BLOCK_B)
offset_d = pid_d * BLOCK_D + tl.arange(0, BLOCK_D)
offset_d = offset_d.to(tl.int64)
tl.multiple_of(offset_d, BLOCK_D)
tl.max_contiguous(offset_d, BLOCK_D)
batch_d_offset = batch_offsets[:, None] * D + offset_d[None, :]
recon = tl.load(final_recon_ptr + batch_d_offset).to(tl.float32)
target = tl.load(target_ptr + batch_d_offset).to(tl.float32)
suffix = tl.zeros([BLOCK_B, BLOCK_D], dtype=tl.float32)
bias_accum = tl.zeros([BLOCK_B, BLOCK_D], dtype=tl.float32)
scale = tl.full((), 2.0 / (B * K * D), dtype=tl.float32)
row_idx_ptr = indices_ptr + batch_offsets * K
row_val_ptr = vals_ptr + batch_offsets * K
k_offsets = tl.arange(0, K)
val_grad_tile = tl.zeros([BLOCK_B, K], dtype=tl.float32)
step = K - 1
idx = tl.load(row_idx_ptr + step).to(tl.int64)
val = tl.load(row_val_ptr + step).to(tl.float32)
weight_tile = tl.load(weight_ptr + idx[:, None] * D + offset_d[None, :]).to(tl.float32)
for _ in tl.range(0, K, num_stages=LOOP_NUM_STAGES):
curr_step = step
diff = recon - target
grad_curr = diff * scale
suffix += grad_curr
bias_accum += grad_curr
val_broadcast = val[:, None]
contrib = suffix * val_broadcast
tl.atomic_add(
weight_grad_ptr + idx[:, None] * D + offset_d[None, :],
contrib,
sem="relaxed",
)
dot_partial = tl.sum(weight_tile * suffix, axis=1)
mask_curr = k_offsets[None, :] == curr_step
val_grad_tile = tl.where(mask_curr, dot_partial[:, None], val_grad_tile)
recon -= weight_tile * val_broadcast
if curr_step > 0:
step = curr_step - 1
idx = tl.load(row_idx_ptr + step).to(tl.int64)
val = tl.load(row_val_ptr + step).to(tl.float32)
weight_tile = tl.load(weight_ptr + idx[:, None] * D + offset_d[None, :]).to(tl.float32)
bias_grad_tile = tl.sum(bias_accum, axis=0)
tl.atomic_add(
bias_grad_ptr + offset_d,
bias_grad_tile,
sem="relaxed",
)
row_val_grad_ptr = vals_grad_ptr + batch_offsets[:, None] * K + k_offsets[None, :]
tl.atomic_add(
row_val_grad_ptr,
val_grad_tile,
sem="relaxed",
)
def _hierarchical_sae_forward(
indices: torch.Tensor, # [B, K]
weight: torch.Tensor, # [F, D]
vals: torch.Tensor, # [B, K]
bias: torch.Tensor, # [D]
target: torch.Tensor, # [B, D]
) -> Tuple[torch.Tensor, torch.Tensor]:
B, K = indices.shape
F, D = weight.shape
loss_per_batch = torch.zeros((B,), dtype=torch.float32, device=weight.device)
final_recon = torch.empty((B, D), dtype=torch.float32, device=weight.device)
def _forward_grid(meta):
return (
B // meta["BLOCK_B"],
D // meta["BLOCK_D"],
)
hierarchical_sae_forward_kernel[_forward_grid](
loss_per_batch,
final_recon,
indices,
weight,
bias,
vals,
target,
B=B,
D=D,
K=K,
BLOCK_D=64,
LOOP_NUM_STAGES=4,
BLOCK_B=1,
num_warps=2,
num_stages=2,
)
loss = loss_per_batch.sum() / (B * K * D)
return loss, final_recon
def _hierarchical_sae_backward(
indices: torch.Tensor, # [B, K]
weight: torch.Tensor, # [F, D]
vals: torch.Tensor, # [B, K]
target: torch.Tensor, # [B, D]
final_recon: torch.Tensor, # [B, D]
) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor]:
device = weight.device
B, K = indices.shape
F, D = weight.shape
dW = torch.zeros((F, D), dtype=torch.float32, device=device)
dVals = torch.zeros((B, K), dtype=torch.float32, device=device)
db = torch.zeros((D,), dtype=torch.float32, device=device)
def _backward_grid(meta):
return (
B // meta["BLOCK_B"],
D // meta["BLOCK_D"],
)
hierarchical_sae_backward_kernel[_backward_grid](
dW,
dVals,
db,
final_recon,
indices,
weight,
vals,
target,
B=B,
D=D,
K=K,
BLOCK_D=32,
LOOP_NUM_STAGES=16,
BLOCK_B=16,
num_warps=8,
num_stages=8,
)
return dW, dVals, db
class HierarchicalSAELossFunction(torch.autograd.Function):
@staticmethod
@torch.amp.custom_fwd(device_type="cuda")
def forward(
ctx,
indices: torch.Tensor, # [B, K]
weight: torch.Tensor, # [F, D]
vals: torch.Tensor, # [B, K]
bias: torch.Tensor, # [D]
target: torch.Tensor, # [B, D]
):
loss, final_recon = _hierarchical_sae_forward(indices, weight, vals, bias, target)
ctx.save_for_backward(indices, weight, vals, target, final_recon)
return loss
@staticmethod
@torch.amp.custom_bwd(device_type="cuda")
def backward(ctx, grad):
indices, weight, vals, target, final_recon = ctx.saved_tensors
dW, dVals, db = _hierarchical_sae_backward(indices, weight, vals, target, final_recon)
if grad is not None:
dW.mul_(grad)
dVals.mul_(grad)
db.mul_(grad)
return None, dW, dVals, db, None
def triton_hierarchical_sae_loss(
indices: torch.Tensor, # [B, K]
weight: torch.Tensor, # [F, D]
vals: torch.Tensor, # [B, K]
bias: torch.Tensor, # [D]
target: torch.Tensor, # [B, D]
) -> torch.Tensor:
return HierarchicalSAELossFunction.apply(indices, weight, vals, bias, target)
def hierarchical_sae_loss(
indices: torch.Tensor, # [B, K]
weight: torch.Tensor, # [F, D]
vals: torch.Tensor, # [B, K]
bias: torch.Tensor, # [D]
target: torch.Tensor, # [B, D]
) -> torch.Tensor:
emb = weight[indices].to(torch.float32) # [K, D]
recon_cum = bias.to(torch.float32) + (emb * vals.unsqueeze(-1)).cumsum(dim=1)
diff = recon_cum.to(torch.float32) - target.to(torch.float32).unsqueeze(1)
loss = diff.pow(2).mean()
return loss
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