FW-GLM-5-1 · popcorn · pop_l123_all_gpt
correct 22_SE3InvariantLinear.py
model
FW-GLM-5-1
turns / max
14 / 15
tool calls
14
tokens (total)
253394
wall clock
5795.9s
truncated
no
backend
cuda fp32
variant
popcorn
runtime
0.06 μs
ref runtime
0.43 μs
speedup
7.56x
started
2026-05-11T21:17:53Z
timingkernelbench.timing
kernel runtime
0.06 μs
ref runtime
0.43 μs
speedup
7.56x
kernel mean / median / std
0.06 / — / 0.09 μs
ref mean / median / std
0.43 / — / 0.03 μs
numerical precisioneval_kernel_against_ref
max abs error
7.15e-07
mean abs error
4.16e-08
max rel error
0.03
mean rel error
4.75e-07
gpu memoryextended_metrics.measure_memory
kernel peak
33.93 MB
ref peak
34.55 MB
kernel / ref
0.98x
kernel launches / fusiontorch.profiler
kernel launches
9
ref launches
51
fusion ratio (ref / kernel)
5.67x
total cuda time
66 μs
SOL (speed-of-light)nsight_hardware_counters
SOL score (0–1)
0.007
dram util %
0.7%
compute util %
0.0%
bottleneck
unknown
dominant pipe
None
arithmetic intensity
—
ridge point
20.00
roofline / occupancynsight_hardware_counters
dram bandwidth
24.31 GB/s
dram util %
0.7%
fp32 tflops
—
fp32 util %
—
fp16 tflops
—
occupancy %
80.5%
bottleneck
unknown
dominant pipe %
—
arithmetic intensity
—
ridge point
20.00
L1 hit %
—
L2 hit %
85.3%
ld sectors / req
17.38
st sectors / req
—
regs / thread
32
smem / block
1536 B
block size
256
peak bw
3350.00 GB/s
peak fp32 tflops
67.00
peak fp16 tflops
1979.00
warp stalls (top 5)nsight
long_scoreboard
2246.8%
mio_throttle
555.2%
short_scoreboard
335.2%
reference PyTorch source (the prompt the agent sees)
import torch
import torch.nn as nn


class Model(nn.Module):
    """
    SE(3)-invariant linear layer.  Maps node features that are augmented
    with 3-D coordinate information through a linear transform that
    respects rotational and translational invariance.  The layer operates
    on (scalar_features, vector_features) pairs where scalar features
    transform trivially and vector features transform as 3-D vectors.
    Used in equivariant GNNs (EGNN, PaiNN, TFN).
    """

    def __init__(self, scalar_in, scalar_out, vector_in, vector_out):
        super().__init__()
        self.scalar_linear = nn.Linear(scalar_in + vector_in, scalar_out)
        self.vector_weight = nn.Parameter(torch.randn(vector_out, vector_in))
        nn.init.xavier_uniform_(self.vector_weight)
        self.vector_gate = nn.Linear(scalar_in + vector_in, vector_out)

    def forward(
        self, scalar_feat: torch.Tensor, vector_feat: torch.Tensor
    ) -> tuple:
        """
        Args:
            scalar_feat: (B, N, scalar_in) – invariant node features
            vector_feat: (B, N, vector_in, 3) – equivariant vector features
        Returns:
            (scalar_out, vector_out):
                scalar_out: (B, N, scalar_out)
                vector_out: (B, N, vector_out, 3)
        """
        # Invariant scalars from vector norms
        vec_norm = vector_feat.norm(dim=-1)  # (B, N, vector_in)
        combined = torch.cat([scalar_feat, vec_norm], dim=-1)

        s_out = self.scalar_linear(combined)

        # Equivariant vector transform: linear combination of input vectors
        v_out = torch.einsum("oi,bnid->bnod", self.vector_weight, vector_feat)
        # Gating by scalar-derived signal
        gate = torch.sigmoid(self.vector_gate(combined)).unsqueeze(-1)  # (B, N, vector_out, 1)
        v_out = gate * v_out

        return s_out, v_out


scalar_in = 64
scalar_out = 64
vector_in = 16
vector_out = 16
num_nodes = 128
batch_size = 8


def get_inputs():
    p = popcorn_pri
    bs = p.jitter_int(batch_size)
    nn = p.jitter_int(num_nodes)
    s = torch.randn(bs, nn, scalar_in)
    v = torch.randn(bs, nn, vector_in, 3)
    return [s, v]


def get_init_inputs():
    return [scalar_in, scalar_out, vector_in, vector_out]
turn 0272.8s turn · 5.2s LLM · 267.7s tools · tokens in=2,355 · out=545 · total=2,900
reasoning
Let me analyze this SE(3)-invariant linear layer and understand what computations need to be performed: 1. **Input shapes:** - `scalar_feat`: (B, N, scalar_in) = (8, 128, 64) - `vector_feat`: (B, N, vector_in, 3) = (8, 128, 16, 3) 2. **Computations:** - `vec_norm = vector_feat.norm(dim=-1)` → (B, N, vector_in) = (8, 128, 16) - `combined = torch.cat([scalar_feat, vec_norm], dim=-1)` → (B, N, scalar_in + vector_in) = (8, 128, 80) - `s_out = self.scalar_linear(combined)` → Linear(80, 64) → (8, 128, 64) - `v_out = torch.einsum("oi,bnid->bnod", self.vector_weight, vector_feat)` → (8, 128, 16, 3) - `gate = torch.sigmoid(self.vector_gate(combined)).unsqueeze(-1)` → (8, 128, 16, 1) - `v_out = gate * v_out` → (8, 128, 16, 3) 3. **Parameters:** - `scalar_linear.weight`: (scalar_out, scalar_in + vector_in) = (64, 80) - `scalar_linear.bias`: (scalar_out,) = (64,) - `vector_weight`: (vector_out, vector_in) = (16, 16) - `vector_gate.weight`: (vector_out, scalar_in + vector_in) = (16, 80) - `vector_gate.bias`: (vector_out,) = (16,) Let me start by writing a CUDA kernel for this. The key operations are: 1. Vector norm computation (compute sqrt of sum of squares along the last dimension) 2. Concatenation of scalar features with vector norms 3. Linear transformations (matrix-vector products) 4. Sigmoid gating 5. Element-wise multiplication I'll write a fused kernel that handles all these operations efficiently.
assistantLooking at this SE(3)-invariant linear layer, I need to: 1. Compute vector norms 2. Concatenate scalar features with norms 3. Apply linear transformations for scalar output and gating 4. Apply einsum for vector transformation 5. Apply sigmoid gate Let me start by getting the GPU specs and understanding the problem better.
call → get_gpu_specs
callget_gpu_specs {}
result ← get_gpu_specs (ok)
okget_gpu_specs GPU specs for NVIDIA H100 80GB HBM3: total memory (runtime): 79.1 GB spec entry: H100 GPU Architecture: Hopper GPU Memory: 80GB Memory Bandwidth: 3.35 TB/s FP64 TFLOPS: 34 FP64 Tensor Core TFLOPS: 67 FP32 TFLOPS: 67 TF32 Tensor Core TFLOPS: 989 with sparsity BFLOAT16 Tensore Core TFLOPS: 1979 with sparsity FP16 Tensor Core TFLOPS: 1979 with sparsity FP8 Tensor Core TFLOPS: 3958 with sparsity INT8 Tensor Core TOPS: 3958 with sparsity Register File Size: 64K 32-bit registers per SM Maximum number of registers per thread: 255 Maximum number of thread blocks per SM: 32 Shared memory capacity per SM: 228 KB Maximum shared memory per thread block: 227 KB
turn 1 · 1 tool call(s) · 362.7s turn · 18.4s LLM · tokens in=2,674 · out=2,156 · total=4,830 · 9,473 chars (click to expand)
turn 1362.7s turn · 18.4s LLM · 344.4s tools · tokens in=2,674 · out=2,156 · total=4,830
reasoning
Now let me write my first CUDA kernel. I need to be careful about: 1. Vector norm computation: sum of squares, then sqrt 2. Concatenation: scalar_feat and vec_norm concatenated 3. Linear transforms: matrix multiplication 4. Einsum for vector transformation 5. Sigmoid gating Let me start with a basic implementation:
assistantLet me write the initial CUDA kernel implementation:
call → compile_kernel
callcompile_kernel { "kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\ncuda_source = \"\"\"\n#include <torch/extension.h>\n#include <cuda.h>\n#include <cuda_runtime.h>\n#include <cmath>\n\n// Vectorized memory access helper - process 4 floats at once\n__device__ __forceinline__ float4 load_float4(const float* ptr) {\n return *reinterpret_cast<const float4*>(ptr);\n}\n\n__device__ __forceinline__ void store_float4(float* ptr, float4 val) {\n *reinterpret_cast<float4*>(ptr) = val;\n}\n\n// Optimized sigmoid\n__device__ __forceinline__ float fast_sigmoid(float x) {\n return 1.0f / (1.0f + expf(-x));\n}\n\n// Kernel 1: Compute vector norms and concatenate with scalar features\n// Output: combined (B, N, scalar_in + vector_in)\n__global__ void compute_norms_and_combine_kernel(\n const float* __restrict__ scalar_feat, // (B, N, scalar_in)\n const float* __restrict__ vector_feat, // (B, N, vector_in, 3)\n float* __restrict__ combined, // (B, N, scalar_in + vector_in)\n int batch_size, int num_nodes, int scalar_in, int vector_in\n) {\n const int total = batch_size * num_nodes;\n const int idx = blockIdx.x * blockDim.x + threadIdx.x;\n \n if (idx >= total) return;\n \n const int b = idx / num_nodes;\n const int n = idx % num_nodes;\n \n const int scalar_offset = b * num_nodes * scalar_in + n * scalar_in;\n const int vector_offset = b * num_nodes * vector_in * 3 + n * vector_in * 3;\n const int combined_offset = b * num_nodes * (scalar_in + vector_in) + n * (scalar_in + vector_in);\n \n // Copy scalar features to combined\n for (int s = 0; s < scalar_in; s++) {\n combined[combined_offset + s] = scalar_feat[scalar_offset + s];\n }\n \n // Compute norms and store in combined\n for (int v = 0; v < vector_in; v++) {\n const float vx = vector_feat[vector_offset + v * 3 + 0];\n const float vy = vector_feat[vector_offset + v * 3 + 1];\n const float vz = vector_feat[vector_offset + v * 3 + 2];\n const float norm = sqrtf(vx * vx + vy * vy + vz * vz);\n combined[combined_offset + scalar_in + v] = norm;\n }\n}\n\n// Kernel 2: Scalar linear transform\n// s_out = combined @ W_scalar.T + bias\n__global__ void scalar_linear_kernel(\n const float* __restrict__ combined, // (B, N, combined_dim)\n const float* __restrict__ weight, // (scalar_out, combined_dim)\n const float* __restrict__ bias, // (scalar_out,)\n float* __restrict__ s_out, // (B, N, scalar_out)\n int batch_size, int num_nodes, int combined_dim, int scalar_out\n) {\n const int total = batch_size * num_nodes;\n const int idx = blockIdx.x * blockDim.x + threadIdx.x;\n \n if (idx >= total) return;\n \n const int b = idx / num_nodes;\n const int n = idx % num_nodes;\n \n const int combined_offset = b * num_nodes * combined_dim + n * combined_dim;\n const int out_offset = b * num_nodes * scalar_out + n * scalar_out;\n \n for (int o = 0; o < scalar_out; o++) {\n float sum = bias[o];\n for (int i = 0; i < combined_dim; i++) {\n sum += combined[combined_offset + i] * weight[o * combined_dim + i];\n }\n s_out[out_offset + o] = sum;\n }\n}\n\n// Kernel 3: Vector linear transform (einsum: oi,bnid->bnod)\n__global__ void vector_linear_kernel(\n const float* __restrict__ vector_feat, // (B, N, vector_in, 3)\n const float* __restrict__ weight, // (vector_out, vector_in)\n float* __restrict__ v_out, // (B, N, vector_out, 3)\n int batch_size, int num_nodes, int vector_in, int vector_out\n) {\n const int total = batch_size * num_nodes;\n const int idx = blockIdx.x * blockDim.x + threadIdx.x;\n \n if (idx >= total) return;\n \n const int b = idx / num_nodes;\n const int n = idx % num_nodes;\n \n const int in_offset = b * num_nodes * vector_in * 3 + n * vector_in * 3;\n const int out_offset = b * num_nodes * vector_out * 3 + n * vector_out * 3;\n \n for (int o = 0; o < vector_out; o++) {\n float sum_x = 0.0f, sum_y = 0.0f, sum_z = 0.0f;\n for (int i = 0; i < vector_in; i++) {\n const float w = weight[o * vector_in + i];\n sum_x += w * vector_feat[in_offset + i * 3 + 0];\n sum_y += w * vector_feat[in_offset + i * 3 + 1];\n sum_z += w * vector_feat[in_offset + i * 3 + 2];\n }\n v_out[out_offset + o * 3 + 0] = sum_x;\n v_out[out_offset + o * 3 + 1] = sum_y;\n v_out[out_offset + o * 3 + 2] = sum_z;\n }\n}\n\n// Kernel 4: Gating and final output\n// gate = sigmoid(combined @ W_gate.T + bias)\n// v_out = gate * v_out\n__global__ void apply_gate_kernel(\n const float* __restrict__ combined, // (B, N, combined_dim)\n const float* __restrict__ weight, // (vector_out, combined_dim)\n const float* __restrict__ bias, // (vector_out,)\n float* __restrict__ v_out, // (B, N, vector_out, 3)\n int batch_size, int num_nodes, int combined_dim, int vector_out\n) {\n const int total = batch_size * num_nodes;\n const int idx = blockIdx.x * blockDim.x + threadIdx.x;\n \n if (idx >= total) return;\n \n const int b = idx / num_nodes;\n const int n = idx % num_nodes;\n \n const int combined_offset = b * num_nodes * combined_dim + n * combined_dim;\n const int out_offset = b * num_nodes * vector_out * 3 + n * vector_out * 3;\n \n for (int o = 0; o < vector_out; o++) {\n float sum = bias[o];\n for (int i = 0; i < combined_dim; i++) {\n sum += combined[combined_offset + i] * weight[o * combined_dim + i];\n }\n const float gate = fast_sigmoid(sum);\n \n v_out[out_offset + o * 3 + 0] *= gate;\n v_out[out_offset + o * 3 + 1] *= gate;\n v_out[out_offset + o * 3 + 2] *= gate;\n }\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor se3_forward_cuda(\n torch::Tensor scalar_feat,\n torch::Tensor vector_feat,\n torch::Tensor scalar_weight,\n torch::Tensor scalar_bias,\n torch::Tensor vector_weight,\n torch::Tensor gate_weight,\n torch::Tensor gate_bias\n);\n\"\"\"\n\nse3_cuda = load_inline(\n name='se3_cuda',\n cuda_sources=cuda_source,\n cpp_sources=cpp_source,\n functions=['se3_forward_cuda'],\n verbose=False,\n extra_cuda_cflags=['-O3', '--use_fast_math']\n)\n\nclass ModelNew(nn.Module):\n def __init__(self, scalar_in, scalar_out, vector_in, vector_out):\n super().__init__()\n self.scalar_in = scalar_in\n self.scalar_out = scalar_out\n self.vector_in = vector_in\n self.vector_out = vector_out\n \n self.scalar_linear = nn.Linear(scalar_in + vector_in, scalar_out)\n self.vector_weight = nn.Parameter(torch.randn(vector_out, vector_in))\n nn.init.xavier_uniform_(self.vector_weight)\n self.vector_gate = nn.Linear(scalar_in + vector_in, vector_out)\n \n def forward(self, scalar_feat: torch.Tensor, vector_feat: torch.Tensor) -> tuple:\n # Ensure inputs are contiguous float32\n scalar_feat = scalar_feat.contiguous().float()\n vector_feat = vector_feat.contiguous().float()\n \n # Get parameters\n scalar_weight = self.scalar_linear.weight.contiguous().float()\n scalar_bias = self.scalar_linear.bias.contiguous().float()\n vector_weight = self.vector_weight.contiguous().float()\n gate_weight = self.vector_gate.weight.contiguous().float()\n gate_bias = self.vector_gate.bias.contiguous().float()\n \n # Call CUDA kernel\n s_out, v_out = se3_cuda.se3_forward_cuda(\n scalar_feat, vector_feat,\n scalar_weight, scalar_bias,\n vector_weight, gate_weight, gate_bias\n )\n \n return s_out, v_out" }
result ← compile_kernel (fail)
failcompile_kernel compile_kernel FAILED: ImportError. ImportError: /scratch/abaner/KernelBench/runs/pop_l123_all_gpt/popcorn/FW-GLM-5-1/level_1_problem_22_cache/k_ea8314d774ed/se3_cuda/se3_cuda.so: undefined symbol: _Z16se3_forward_cudaN2at6TensorES0_S0_S0_S0_S0_S0_
turn 2 · 1 tool call(s) · 362.2s turn · 20.4s LLM · tokens in=4,851 · out=2,540 · total=7,391 · 11,193 chars (click to expand)
turn 2362.2s turn · 20.4s LLM · 341.8s tools · tokens in=4,851 · out=2,540 · total=7,391
reasoning
I need to add the C++ function definition that actually calls the CUDA kernels. The `cpp_sources` should have the actual implementation that torch::jit can use.
assistantI need to add the actual C++ function implementation. Let me fix this:
call → compile_kernel
callcompile_kernel { "kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\ncuda_source = \"\"\"\n#include <torch/extension.h>\n#include <cuda.h>\n#include <cuda_runtime.h>\n#include <cmath>\n\n// Optimized sigmoid\n__device__ __forceinline__ float fast_sigmoid(float x) {\n return 1.0f / (1.0f + expf(-x));\n}\n\n// Kernel 1: Compute vector norms and concatenate with scalar features\n__global__ void compute_norms_and_combine_kernel(\n const float* __restrict__ scalar_feat, // (B, N, scalar_in)\n const float* __restrict__ vector_feat, // (B, N, vector_in, 3)\n float* __restrict__ combined, // (B, N, scalar_in + vector_in)\n int batch_size, int num_nodes, int scalar_in, int vector_in\n) {\n const int total = batch_size * num_nodes;\n const int idx = blockIdx.x * blockDim.x + threadIdx.x;\n \n if (idx >= total) return;\n \n const int b = idx / num_nodes;\n const int n = idx % num_nodes;\n \n const int scalar_offset = b * num_nodes * scalar_in + n * scalar_in;\n const int vector_offset = b * num_nodes * vector_in * 3 + n * vector_in * 3;\n const int combined_offset = b * num_nodes * (scalar_in + vector_in) + n * (scalar_in + vector_in);\n \n // Copy scalar features to combined\n for (int s = 0; s < scalar_in; s++) {\n combined[combined_offset + s] = scalar_feat[scalar_offset + s];\n }\n \n // Compute norms and store in combined\n for (int v = 0; v < vector_in; v++) {\n const float vx = vector_feat[vector_offset + v * 3 + 0];\n const float vy = vector_feat[vector_offset + v * 3 + 1];\n const float vz = vector_feat[vector_offset + v * 3 + 2];\n const float norm = sqrtf(vx * vx + vy * vy + vz * vz);\n combined[combined_offset + scalar_in + v] = norm;\n }\n}\n\n// Kernel 2: Scalar linear transform\n__global__ void scalar_linear_kernel(\n const float* __restrict__ combined, // (B, N, combined_dim)\n const float* __restrict__ weight, // (scalar_out, combined_dim)\n const float* __restrict__ bias, // (scalar_out,)\n float* __restrict__ s_out, // (B, N, scalar_out)\n int batch_size, int num_nodes, int combined_dim, int scalar_out\n) {\n const int total = batch_size * num_nodes;\n const int idx = blockIdx.x * blockDim.x + threadIdx.x;\n \n if (idx >= total) return;\n \n const int b = idx / num_nodes;\n const int n = idx % num_nodes;\n \n const int combined_offset = b * num_nodes * combined_dim + n * combined_dim;\n const int out_offset = b * num_nodes * scalar_out + n * scalar_out;\n \n for (int o = 0; o < scalar_out; o++) {\n float sum = bias[o];\n for (int i = 0; i < combined_dim; i++) {\n sum += combined[combined_offset + i] * weight[o * combined_dim + i];\n }\n s_out[out_offset + o] = sum;\n }\n}\n\n// Kernel 3: Vector linear transform (einsum: oi,bnid->bnod)\n__global__ void vector_linear_kernel(\n const float* __restrict__ vector_feat, // (B, N, vector_in, 3)\n const float* __restrict__ weight, // (vector_out, vector_in)\n float* __restrict__ v_out, // (B, N, vector_out, 3)\n int batch_size, int num_nodes, int vector_in, int vector_out\n) {\n const int total = batch_size * num_nodes;\n const int idx = blockIdx.x * blockDim.x + threadIdx.x;\n \n if (idx >= total) return;\n \n const int b = idx / num_nodes;\n const int n = idx % num_nodes;\n \n const int in_offset = b * num_nodes * vector_in * 3 + n * vector_in * 3;\n const int out_offset = b * num_nodes * vector_out * 3 + n * vector_out * 3;\n \n for (int o = 0; o < vector_out; o++) {\n float sum_x = 0.0f, sum_y = 0.0f, sum_z = 0.0f;\n for (int i = 0; i < vector_in; i++) {\n const float w = weight[o * vector_in + i];\n sum_x += w * vector_feat[in_offset + i * 3 + 0];\n sum_y += w * vector_feat[in_offset + i * 3 + 1];\n sum_z += w * vector_feat[in_offset + i * 3 + 2];\n }\n v_out[out_offset + o * 3 + 0] = sum_x;\n v_out[out_offset + o * 3 + 1] = sum_y;\n v_out[out_offset + o * 3 + 2] = sum_z;\n }\n}\n\n// Kernel 4: Gating and final output\n__global__ void apply_gate_kernel(\n const float* __restrict__ combined, // (B, N, combined_dim)\n const float* __restrict__ weight, // (vector_out, combined_dim)\n const float* __restrict__ bias, // (vector_out,)\n float* __restrict__ v_out, // (B, N, vector_out, 3)\n int batch_size, int num_nodes, int combined_dim, int vector_out\n) {\n const int total = batch_size * num_nodes;\n const int idx = blockIdx.x * blockDim.x + threadIdx.x;\n \n if (idx >= total) return;\n \n const int b = idx / num_nodes;\n const int n = idx % num_nodes;\n \n const int combined_offset = b * num_nodes * combined_dim + n * combined_dim;\n const int out_offset = b * num_nodes * vector_out * 3 + n * vector_out * 3;\n \n for (int o = 0; o < vector_out; o++) {\n float sum = bias[o];\n for (int i = 0; i < combined_dim; i++) {\n sum += combined[combined_offset + i] * weight[o * combined_dim + i];\n }\n const float gate = fast_sigmoid(sum);\n \n v_out[out_offset + o * 3 + 0] *= gate;\n v_out[out_offset + o * 3 + 1] *= gate;\n v_out[out_offset + o * 3 + 2] *= gate;\n }\n}\n\n// Host function\nstd::tuple<torch::Tensor, torch::Tensor> se3_forward_cuda(\n torch::Tensor scalar_feat,\n torch::Tensor vector_feat,\n torch::Tensor scalar_weight,\n torch::Tensor scalar_bias,\n torch::Tensor vector_weight,\n torch::Tensor gate_weight,\n torch::Tensor gate_bias\n) {\n const int batch_size = scalar_feat.size(0);\n const int num_nodes = scalar_feat.size(1);\n const int scalar_in = scalar_feat.size(2);\n const int vector_in = vector_feat.size(2);\n const int scalar_out = scalar_weight.size(0);\n const int vector_out = vector_weight.size(0);\n const int combined_dim = scalar_in + vector_in;\n \n const int total = batch_size * num_nodes;\n const int block_size = 256;\n const int grid_size = (total + block_size - 1) / block_size;\n \n // Allocate outputs\n auto combined = torch::empty({batch_size, num_nodes, combined_dim}, scalar_feat.options());\n auto s_out = torch::empty({batch_size, num_nodes, scalar_out}, scalar_feat.options());\n auto v_out = torch::empty({batch_size, num_nodes, vector_out, 3}, scalar_feat.options());\n \n // Kernel 1: Compute norms and combine\n compute_norms_and_combine_kernel<<<grid_size, block_size>>>(\n scalar_feat.data_ptr<float>(),\n vector_feat.data_ptr<float>(),\n combined.data_ptr<float>(),\n batch_size, num_nodes, scalar_in, vector_in\n );\n \n // Kernel 2: Scalar linear\n scalar_linear_kernel<<<grid_size, block_size>>>(\n combined.data_ptr<float>(),\n scalar_weight.data_ptr<float>(),\n scalar_bias.data_ptr<float>(),\n s_out.data_ptr<float>(),\n batch_size, num_nodes, combined_dim, scalar_out\n );\n \n // Kernel 3: Vector linear\n vector_linear_kernel<<<grid_size, block_size>>>(\n vector_feat.data_ptr<float>(),\n vector_weight.data_ptr<float>(),\n v_out.data_ptr<float>(),\n batch_size, num_nodes, vector_in, vector_out\n );\n \n // Kernel 4: Apply gating\n apply_gate_kernel<<<grid_size, block_size>>>(\n combined.data_ptr<float>(),\n gate_weight.data_ptr<float>(),\n gate_bias.data_ptr<float>(),\n v_out.data_ptr<float>(),\n batch_size, num_nodes, combined_dim, vector_out\n );\n \n return std::make_tuple(s_out, v_out);\n}\n\"\"\"\n\ncpp_source = \"\"\"\nstd::tuple<torch::Tensor, torch::Tensor> se3_forward_cuda(\n torch::Tensor scalar_feat,\n torch::Tensor vector_feat,\n torch::Tensor scalar_weight,\n torch::Tensor scalar_bias,\n torch::Tensor vector_weight,\n torch::Tensor gate_weight,\n torch::Tensor gate_bias\n);\n\"\"\"\n\nse3_cuda = load_inline(\n name='se3_cuda_v2',\n cuda_sources=cuda_source,\n cpp_sources=cpp_source,\n functions=['se3_forward_cuda'],\n verbose=False,\n extra_cuda_cflags=['-O3', '--use_fast_math']\n)\n\nclass ModelNew(nn.Module):\n def __init__(self, scalar_in, scalar_out, vector_in, vector_out):\n super().__init__()\n self.scalar_in = scalar_in\n self.scalar_out = scalar_out\n self.vector_in = vector_in\n self.vector_out = vector_out\n \n self.scalar_linear = nn.Linear(scalar_in + vector_in, scalar_out)\n self.vector_weight = nn.Parameter(torch.randn(vector_out, vector_in))\n nn.init.xavier_uniform_(self.vector_weight)\n self.vector_gate = nn.Linear(scalar_in + vector_in, vector_out)\n \n def forward(self, scalar_feat: torch.Tensor, vector_feat: torch.Tensor) -> tuple:\n # Ensure inputs are contiguous float32\n scalar_feat = scalar_feat.contiguous().float()\n vector_feat = vector_feat.contiguous().float()\n \n # Get parameters\n scalar_weight = self.scalar_linear.weight.contiguous().float()\n scalar_bias = self.scalar_linear.bias.contiguous().float()\n vector_weight = self.vector_weight.contiguous().float()\n gate_weight = self.vector_gate.weight.contiguous().float()\n gate_bias = self.vector_gate.bias.contiguous().float()\n \n # Call CUDA kernel\n s_out, v_out = se3_cuda.se3_forward_cuda(\n scalar_feat, vector_feat,\n scalar_weight, scalar_bias,\n vector_weight, gate_weight, gate_bias\n )\n \n return s_out, v_out" }
result ← compile_kernel (ok)
okcompile_kernel compile_kernel PASSED: kernel compiled without errors.
turn 3 · 1 tool call(s) · 483.2s turn · 19.5s LLM · tokens in=7,371 · out=2,505 · total=9,876 · 11,046 chars (click to expand)
turn 3483.2s turn · 19.5s LLM · 463.7s tools · tokens in=7,371 · out=2,505 · total=9,876
reasoning
Good, the kernel compiles. Now let me check correctness.
call → run_correctness
callrun_correctness { "kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\ncuda_source = \"\"\"\n#include <torch/extension.h>\n#include <cuda.h>\n#include <cuda_runtime.h>\n#include <cmath>\n\n// Optimized sigmoid\n__device__ __forceinline__ float fast_sigmoid(float x) {\n return 1.0f / (1.0f + expf(-x));\n}\n\n// Kernel 1: Compute vector norms and concatenate with scalar features\n__global__ void compute_norms_and_combine_kernel(\n const float* __restrict__ scalar_feat, // (B, N, scalar_in)\n const float* __restrict__ vector_feat, // (B, N, vector_in, 3)\n float* __restrict__ combined, // (B, N, scalar_in + vector_in)\n int batch_size, int num_nodes, int scalar_in, int vector_in\n) {\n const int total = batch_size * num_nodes;\n const int idx = blockIdx.x * blockDim.x + threadIdx.x;\n \n if (idx >= total) return;\n \n const int b = idx / num_nodes;\n const int n = idx % num_nodes;\n \n const int scalar_offset = b * num_nodes * scalar_in + n * scalar_in;\n const int vector_offset = b * num_nodes * vector_in * 3 + n * vector_in * 3;\n const int combined_offset = b * num_nodes * (scalar_in + vector_in) + n * (scalar_in + vector_in);\n \n // Copy scalar features to combined\n for (int s = 0; s < scalar_in; s++) {\n combined[combined_offset + s] = scalar_feat[scalar_offset + s];\n }\n \n // Compute norms and store in combined\n for (int v = 0; v < vector_in; v++) {\n const float vx = vector_feat[vector_offset + v * 3 + 0];\n const float vy = vector_feat[vector_offset + v * 3 + 1];\n const float vz = vector_feat[vector_offset + v * 3 + 2];\n const float norm = sqrtf(vx * vx + vy * vy + vz * vz);\n combined[combined_offset + scalar_in + v] = norm;\n }\n}\n\n// Kernel 2: Scalar linear transform\n__global__ void scalar_linear_kernel(\n const float* __restrict__ combined, // (B, N, combined_dim)\n const float* __restrict__ weight, // (scalar_out, combined_dim)\n const float* __restrict__ bias, // (scalar_out,)\n float* __restrict__ s_out, // (B, N, scalar_out)\n int batch_size, int num_nodes, int combined_dim, int scalar_out\n) {\n const int total = batch_size * num_nodes;\n const int idx = blockIdx.x * blockDim.x + threadIdx.x;\n \n if (idx >= total) return;\n \n const int b = idx / num_nodes;\n const int n = idx % num_nodes;\n \n const int combined_offset = b * num_nodes * combined_dim + n * combined_dim;\n const int out_offset = b * num_nodes * scalar_out + n * scalar_out;\n \n for (int o = 0; o < scalar_out; o++) {\n float sum = bias[o];\n for (int i = 0; i < combined_dim; i++) {\n sum += combined[combined_offset + i] * weight[o * combined_dim + i];\n }\n s_out[out_offset + o] = sum;\n }\n}\n\n// Kernel 3: Vector linear transform (einsum: oi,bnid->bnod)\n__global__ void vector_linear_kernel(\n const float* __restrict__ vector_feat, // (B, N, vector_in, 3)\n const float* __restrict__ weight, // (vector_out, vector_in)\n float* __restrict__ v_out, // (B, N, vector_out, 3)\n int batch_size, int num_nodes, int vector_in, int vector_out\n) {\n const int total = batch_size * num_nodes;\n const int idx = blockIdx.x * blockDim.x + threadIdx.x;\n \n if (idx >= total) return;\n \n const int b = idx / num_nodes;\n const int n = idx % num_nodes;\n \n const int in_offset = b * num_nodes * vector_in * 3 + n * vector_in * 3;\n const int out_offset = b * num_nodes * vector_out * 3 + n * vector_out * 3;\n \n for (int o = 0; o < vector_out; o++) {\n float sum_x = 0.0f, sum_y = 0.0f, sum_z = 0.0f;\n for (int i = 0; i < vector_in; i++) {\n const float w = weight[o * vector_in + i];\n sum_x += w * vector_feat[in_offset + i * 3 + 0];\n sum_y += w * vector_feat[in_offset + i * 3 + 1];\n sum_z += w * vector_feat[in_offset + i * 3 + 2];\n }\n v_out[out_offset + o * 3 + 0] = sum_x;\n v_out[out_offset + o * 3 + 1] = sum_y;\n v_out[out_offset + o * 3 + 2] = sum_z;\n }\n}\n\n// Kernel 4: Gating and final output\n__global__ void apply_gate_kernel(\n const float* __restrict__ combined, // (B, N, combined_dim)\n const float* __restrict__ weight, // (vector_out, combined_dim)\n const float* __restrict__ bias, // (vector_out,)\n float* __restrict__ v_out, // (B, N, vector_out, 3)\n int batch_size, int num_nodes, int combined_dim, int vector_out\n) {\n const int total = batch_size * num_nodes;\n const int idx = blockIdx.x * blockDim.x + threadIdx.x;\n \n if (idx >= total) return;\n \n const int b = idx / num_nodes;\n const int n = idx % num_nodes;\n \n const int combined_offset = b * num_nodes * combined_dim + n * combined_dim;\n const int out_offset = b * num_nodes * vector_out * 3 + n * vector_out * 3;\n \n for (int o = 0; o < vector_out; o++) {\n float sum = bias[o];\n for (int i = 0; i < combined_dim; i++) {\n sum += combined[combined_offset + i] * weight[o * combined_dim + i];\n }\n const float gate = fast_sigmoid(sum);\n \n v_out[out_offset + o * 3 + 0] *= gate;\n v_out[out_offset + o * 3 + 1] *= gate;\n v_out[out_offset + o * 3 + 2] *= gate;\n }\n}\n\n// Host function\nstd::tuple<torch::Tensor, torch::Tensor> se3_forward_cuda(\n torch::Tensor scalar_feat,\n torch::Tensor vector_feat,\n torch::Tensor scalar_weight,\n torch::Tensor scalar_bias,\n torch::Tensor vector_weight,\n torch::Tensor gate_weight,\n torch::Tensor gate_bias\n) {\n const int batch_size = scalar_feat.size(0);\n const int num_nodes = scalar_feat.size(1);\n const int scalar_in = scalar_feat.size(2);\n const int vector_in = vector_feat.size(2);\n const int scalar_out = scalar_weight.size(0);\n const int vector_out = vector_weight.size(0);\n const int combined_dim = scalar_in + vector_in;\n \n const int total = batch_size * num_nodes;\n const int block_size = 256;\n const int grid_size = (total + block_size - 1) / block_size;\n \n // Allocate outputs\n auto combined = torch::empty({batch_size, num_nodes, combined_dim}, scalar_feat.options());\n auto s_out = torch::empty({batch_size, num_nodes, scalar_out}, scalar_feat.options());\n auto v_out = torch::empty({batch_size, num_nodes, vector_out, 3}, scalar_feat.options());\n \n // Kernel 1: Compute norms and combine\n compute_norms_and_combine_kernel<<<grid_size, block_size>>>(\n scalar_feat.data_ptr<float>(),\n vector_feat.data_ptr<float>(),\n combined.data_ptr<float>(),\n batch_size, num_nodes, scalar_in, vector_in\n );\n \n // Kernel 2: Scalar linear\n scalar_linear_kernel<<<grid_size, block_size>>>(\n combined.data_ptr<float>(),\n scalar_weight.data_ptr<float>(),\n scalar_bias.data_ptr<float>(),\n s_out.data_ptr<float>(),\n batch_size, num_nodes, combined_dim, scalar_out\n );\n \n // Kernel 3: Vector linear\n vector_linear_kernel<<<grid_size, block_size>>>(\n vector_feat.data_ptr<float>(),\n vector_weight.data_ptr<float>(),\n v_out.data_ptr<float>(),\n batch_size, num_nodes, vector_in, vector_out\n );\n \n // Kernel 4: Apply gating\n apply_gate_kernel<<<grid_size, block_size>>>(\n combined.data_ptr<float>(),\n gate_weight.data_ptr<float>(),\n gate_bias.data_ptr<float>(),\n v_out.data_ptr<float>(),\n batch_size, num_nodes, combined_dim, vector_out\n );\n \n return std::make_tuple(s_out, v_out);\n}\n\"\"\"\n\ncpp_source = \"\"\"\nstd::tuple<torch::Tensor, torch::Tensor> se3_forward_cuda(\n torch::Tensor scalar_feat,\n torch::Tensor vector_feat,\n torch::Tensor scalar_weight,\n torch::Tensor scalar_bias,\n torch::Tensor vector_weight,\n torch::Tensor gate_weight,\n torch::Tensor gate_bias\n);\n\"\"\"\n\nse3_cuda = load_inline(\n name='se3_cuda_v3',\n cuda_sources=cuda_source,\n cpp_sources=cpp_source,\n functions=['se3_forward_cuda'],\n verbose=False,\n extra_cuda_cflags=['-O3', '--use_fast_math']\n)\n\nclass ModelNew(nn.Module):\n def __init__(self, scalar_in, scalar_out, vector_in, vector_out):\n super().__init__()\n self.scalar_in = scalar_in\n self.scalar_out = scalar_out\n self.vector_in = vector_in\n self.vector_out = vector_out\n \n self.scalar_linear = nn.Linear(scalar_in + vector_in, scalar_out)\n self.vector_weight = nn.Parameter(torch.randn(vector_out, vector_in))\n nn.init.xavier_uniform_(self.vector_weight)\n self.vector_gate = nn.Linear(scalar_in + vector_in, vector_out)\n \n def forward(self, scalar_feat: torch.Tensor, vector_feat: torch.Tensor) -> tuple:\n # Ensure inputs are contiguous float32\n scalar_feat = scalar_feat.contiguous().float()\n vector_feat = vector_feat.contiguous().float()\n \n # Get parameters\n scalar_weight = self.scalar_linear.weight.contiguous().float()\n scalar_bias = self.scalar_linear.bias.contiguous().float()\n vector_weight = self.vector_weight.contiguous().float()\n gate_weight = self.vector_gate.weight.contiguous().float()\n gate_bias = self.vector_gate.bias.contiguous().float()\n \n # Call CUDA kernel\n s_out, v_out = se3_cuda.se3_forward_cuda(\n scalar_feat, vector_feat,\n scalar_weight, scalar_bias,\n vector_weight, gate_weight, gate_bias\n )\n \n return s_out, v_out" }
result ← run_correctness (ok)
okrun_correctness run_correctness PASSED: (3 / 3) trials all matched the reference. Numerical precision: max_abs_err=7.15e-07 mean_abs_err=4.16e-08 max_rel_err=3.50e-02
turn 4 · 1 tool call(s) · 358.7s turn · 19.4s LLM · tokens in=9,920 · out=2,527 · total=12,447 · 12,725 chars (click to expand)
turn 4358.7s turn · 19.4s LLM · 339.3s tools · tokens in=9,920 · out=2,527 · total=12,447
reasoning
The kernel passes correctness! Now let me profile it to see what performance we're getting and identify optimization opportunities.
assistantThe kernel passes correctness. Let me profile it to understand the performance:
call → profile_kernel
callprofile_kernel { "kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\ncuda_source = \"\"\"\n#include <torch/extension.h>\n#include <cuda.h>\n#include <cuda_runtime.h>\n#include <cmath>\n\n// Optimized sigmoid\n__device__ __forceinline__ float fast_sigmoid(float x) {\n return 1.0f / (1.0f + expf(-x));\n}\n\n// Kernel 1: Compute vector norms and concatenate with scalar features\n__global__ void compute_norms_and_combine_kernel(\n const float* __restrict__ scalar_feat, // (B, N, scalar_in)\n const float* __restrict__ vector_feat, // (B, N, vector_in, 3)\n float* __restrict__ combined, // (B, N, scalar_in + vector_in)\n int batch_size, int num_nodes, int scalar_in, int vector_in\n) {\n const int total = batch_size * num_nodes;\n const int idx = blockIdx.x * blockDim.x + threadIdx.x;\n \n if (idx >= total) return;\n \n const int b = idx / num_nodes;\n const int n = idx % num_nodes;\n \n const int scalar_offset = b * num_nodes * scalar_in + n * scalar_in;\n const int vector_offset = b * num_nodes * vector_in * 3 + n * vector_in * 3;\n const int combined_offset = b * num_nodes * (scalar_in + vector_in) + n * (scalar_in + vector_in);\n \n // Copy scalar features to combined\n for (int s = 0; s < scalar_in; s++) {\n combined[combined_offset + s] = scalar_feat[scalar_offset + s];\n }\n \n // Compute norms and store in combined\n for (int v = 0; v < vector_in; v++) {\n const float vx = vector_feat[vector_offset + v * 3 + 0];\n const float vy = vector_feat[vector_offset + v * 3 + 1];\n const float vz = vector_feat[vector_offset + v * 3 + 2];\n const float norm = sqrtf(vx * vx + vy * vy + vz * vz);\n combined[combined_offset + scalar_in + v] = norm;\n }\n}\n\n// Kernel 2: Scalar linear transform\n__global__ void scalar_linear_kernel(\n const float* __restrict__ combined, // (B, N, combined_dim)\n const float* __restrict__ weight, // (scalar_out, combined_dim)\n const float* __restrict__ bias, // (scalar_out,)\n float* __restrict__ s_out, // (B, N, scalar_out)\n int batch_size, int num_nodes, int combined_dim, int scalar_out\n) {\n const int total = batch_size * num_nodes;\n const int idx = blockIdx.x * blockDim.x + threadIdx.x;\n \n if (idx >= total) return;\n \n const int b = idx / num_nodes;\n const int n = idx % num_nodes;\n \n const int combined_offset = b * num_nodes * combined_dim + n * combined_dim;\n const int out_offset = b * num_nodes * scalar_out + n * scalar_out;\n \n for (int o = 0; o < scalar_out; o++) {\n float sum = bias[o];\n for (int i = 0; i < combined_dim; i++) {\n sum += combined[combined_offset + i] * weight[o * combined_dim + i];\n }\n s_out[out_offset + o] = sum;\n }\n}\n\n// Kernel 3: Vector linear transform (einsum: oi,bnid->bnod)\n__global__ void vector_linear_kernel(\n const float* __restrict__ vector_feat, // (B, N, vector_in, 3)\n const float* __restrict__ weight, // (vector_out, vector_in)\n float* __restrict__ v_out, // (B, N, vector_out, 3)\n int batch_size, int num_nodes, int vector_in, int vector_out\n) {\n const int total = batch_size * num_nodes;\n const int idx = blockIdx.x * blockDim.x + threadIdx.x;\n \n if (idx >= total) return;\n \n const int b = idx / num_nodes;\n const int n = idx % num_nodes;\n \n const int in_offset = b * num_nodes * vector_in * 3 + n * vector_in * 3;\n const int out_offset = b * num_nodes * vector_out * 3 + n * vector_out * 3;\n \n for (int o = 0; o < vector_out; o++) {\n float sum_x = 0.0f, sum_y = 0.0f, sum_z = 0.0f;\n for (int i = 0; i < vector_in; i++) {\n const float w = weight[o * vector_in + i];\n sum_x += w * vector_feat[in_offset + i * 3 + 0];\n sum_y += w * vector_feat[in_offset + i * 3 + 1];\n sum_z += w * vector_feat[in_offset + i * 3 + 2];\n }\n v_out[out_offset + o * 3 + 0] = sum_x;\n v_out[out_offset + o * 3 + 1] = sum_y;\n v_out[out_offset + o * 3 + 2] = sum_z;\n }\n}\n\n// Kernel 4: Gating and final output\n__global__ void apply_gate_kernel(\n const float* __restrict__ combined, // (B, N, combined_dim)\n const float* __restrict__ weight, // (vector_out, combined_dim)\n const float* __restrict__ bias, // (vector_out,)\n float* __restrict__ v_out, // (B, N, vector_out, 3)\n int batch_size, int num_nodes, int combined_dim, int vector_out\n) {\n const int total = batch_size * num_nodes;\n const int idx = blockIdx.x * blockDim.x + threadIdx.x;\n \n if (idx >= total) return;\n \n const int b = idx / num_nodes;\n const int n = idx % num_nodes;\n \n const int combined_offset = b * num_nodes * combined_dim + n * combined_dim;\n const int out_offset = b * num_nodes * vector_out * 3 + n * vector_out * 3;\n \n for (int o = 0; o < vector_out; o++) {\n float sum = bias[o];\n for (int i = 0; i < combined_dim; i++) {\n sum += combined[combined_offset + i] * weight[o * combined_dim + i];\n }\n const float gate = fast_sigmoid(sum);\n \n v_out[out_offset + o * 3 + 0] *= gate;\n v_out[out_offset + o * 3 + 1] *= gate;\n v_out[out_offset + o * 3 + 2] *= gate;\n }\n}\n\n// Host function\nstd::tuple<torch::Tensor, torch::Tensor> se3_forward_cuda(\n torch::Tensor scalar_feat,\n torch::Tensor vector_feat,\n torch::Tensor scalar_weight,\n torch::Tensor scalar_bias,\n torch::Tensor vector_weight,\n torch::Tensor gate_weight,\n torch::Tensor gate_bias\n) {\n const int batch_size = scalar_feat.size(0);\n const int num_nodes = scalar_feat.size(1);\n const int scalar_in = scalar_feat.size(2);\n const int vector_in = vector_feat.size(2);\n const int scalar_out = scalar_weight.size(0);\n const int vector_out = vector_weight.size(0);\n const int combined_dim = scalar_in + vector_in;\n \n const int total = batch_size * num_nodes;\n const int block_size = 256;\n const int grid_size = (total + block_size - 1) / block_size;\n \n // Allocate outputs\n auto combined = torch::empty({batch_size, num_nodes, combined_dim}, scalar_feat.options());\n auto s_out = torch::empty({batch_size, num_nodes, scalar_out}, scalar_feat.options());\n auto v_out = torch::empty({batch_size, num_nodes, vector_out, 3}, scalar_feat.options());\n \n // Kernel 1: Compute norms and combine\n compute_norms_and_combine_kernel<<<grid_size, block_size>>>(\n scalar_feat.data_ptr<float>(),\n vector_feat.data_ptr<float>(),\n combined.data_ptr<float>(),\n batch_size, num_nodes, scalar_in, vector_in\n );\n \n // Kernel 2: Scalar linear\n scalar_linear_kernel<<<grid_size, block_size>>>(\n combined.data_ptr<float>(),\n scalar_weight.data_ptr<float>(),\n scalar_bias.data_ptr<float>(),\n s_out.data_ptr<float>(),\n batch_size, num_nodes, combined_dim, scalar_out\n );\n \n // Kernel 3: Vector linear\n vector_linear_kernel<<<grid_size, block_size>>>(\n vector_feat.data_ptr<float>(),\n vector_weight.data_ptr<float>(),\n v_out.data_ptr<float>(),\n batch_size, num_nodes, vector_in, vector_out\n );\n \n // Kernel 4: Apply gating\n apply_gate_kernel<<<grid_size, block_size>>>(\n combined.data_ptr<float>(),\n gate_weight.data_ptr<float>(),\n gate_bias.data_ptr<float>(),\n v_out.data_ptr<float>(),\n batch_size, num_nodes, combined_dim, vector_out\n );\n \n return std::make_tuple(s_out, v_out);\n}\n\"\"\"\n\ncpp_source = \"\"\"\nstd::tuple<torch::Tensor, torch::Tensor> se3_forward_cuda(\n torch::Tensor scalar_feat,\n torch::Tensor vector_feat,\n torch::Tensor scalar_weight,\n torch::Tensor scalar_bias,\n torch::Tensor vector_weight,\n torch::Tensor gate_weight,\n torch::Tensor gate_bias\n);\n\"\"\"\n\nse3_cuda = load_inline(\n name='se3_cuda_v4',\n cuda_sources=cuda_source,\n cpp_sources=cpp_source,\n functions=['se3_forward_cuda'],\n verbose=False,\n extra_cuda_cflags=['-O3', '--use_fast_math']\n)\n\nclass ModelNew(nn.Module):\n def __init__(self, scalar_in, scalar_out, vector_in, vector_out):\n super().__init__()\n self.scalar_in = scalar_in\n self.scalar_out = scalar_out\n self.vector_in = vector_in\n self.vector_out = vector_out\n \n self.scalar_linear = nn.Linear(scalar_in + vector_in, scalar_out)\n self.vector_weight = nn.Parameter(torch.randn(vector_out, vector_in))\n nn.init.xavier_uniform_(self.vector_weight)\n self.vector_gate = nn.Linear(scalar_in + vector_in, vector_out)\n \n def forward(self, scalar_feat: torch.Tensor, vector_feat: torch.Tensor) -> tuple:\n # Ensure inputs are contiguous float32\n scalar_feat = scalar_feat.contiguous().float()\n vector_feat = vector_feat.contiguous().float()\n \n # Get parameters\n scalar_weight = self.scalar_linear.weight.contiguous().float()\n scalar_bias = self.scalar_linear.bias.contiguous().float()\n vector_weight = self.vector_weight.contiguous().float()\n gate_weight = self.vector_gate.weight.contiguous().float()\n gate_bias = self.vector_gate.bias.contiguous().float()\n \n # Call CUDA kernel\n s_out, v_out = se3_cuda.se3_forward_cuda(\n scalar_feat, vector_feat,\n scalar_weight, scalar_bias,\n vector_weight, gate_weight, gate_bias\n )\n \n return s_out, v_out" }
result ← profile_kernel (ok)
okprofile_kernel profile_kernel PASSED: profiling complete. === Kernel Profile Summary === --- Kernel Breakdown (by GPU time) --- #1: aten::empty 31.0μs (32%) calls=1 #2: aten::empty 19.0μs (20%) calls=1 #3: aten::to 17.0μs (18%) calls=1 #4: aten::empty 7.0μs (7%) calls=1 #5: aten::to 4.0μs (4%) calls=1 ... +5 more kernels --- Timing --- GPU time: 619.49 μs --- Memory Bandwidth --- DRAM BW: 23.0/3350 GB/s (0.7%) read=23.0 write=0.0 GB/s Hit rates: L2=370.7% --- Compute Throughput --- Pipe util: FMA=4.9%, Tensor=0.0% --- Roofline Analysis --- Ridge point (FP32): 20.00 FLOPs/byte Classification: UNKNOWN --- Occupancy --- Achieved: 49.6% Eligible warps/cycle: 0.17 WARNING: <1 eligible warp/cycle = latency-bound, needs more parallelism Launch: regs/thread=128, smem/blk=4096B, block=1024, grid=16 --- Memory Access Quality --- Global ld coalescing: 89.34 sectors/req (89.3x wasted BW) --- Warp Stall Reasons (% of issue cycles) --- long_scoreboard 18465.2% #################### short_scoreboard 143.9% #################### --- Optimization Hints --- -> 18465% stalls: global memory latency (waiting for DRAM/L2). + sectors/req=89.3 -> uncoalesced global loads, restructure access pattern or use __ldg Try shared-memory tiling, prefetching, or reducing working set. -> Global load coalescing=89.3x (ideal=1.0) -> 89x wasted DRAM BW. Make per-warp accesses contiguous. -> Low eligible warps + low BW% + low compute% = LATENCY-BOUND. Need more parallelism (larger grid, more ILP, prefetching).
turn 5 · 1 tool call(s) · 565.9s turn · 18.8s LLM · tokens in=12,956 · out=2,138 · total=15,094 · 9,816 chars (click to expand)
turn 5565.9s turn · 18.8s LLM · 547.2s tools · tokens in=12,956 · out=2,138 · total=15,094
reasoning
The profiling shows significant issues: 1. Memory access is uncoalesced (89.3 sectors/request instead of 1) 2. Long scoreboard stalls (18465%) - waiting for memory 3. Low occupancy (49.6%) 4. Latency bound - need more parallelism The main issue is uncoalesced memory access. Let me rewrite the kernel with better memory access patterns: - Each thread should access contiguous memory - Use shared memory to cache weights - Better thread organization Let me design a more optimized kernel where threads in a warp access contiguous memory locations.
assistantThe profiling shows major issues with memory coalescing (89x wasted bandwidth). Let me rewrite with better memory access patterns - each thread should access contiguous memory:
call → compile_kernel
callcompile_kernel { "kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\ncuda_source = \"\"\"\n#include <torch/extension.h>\n#include <cuda.h>\n#include <cuda_runtime.h>\n#include <cmath>\n\n// Optimized sigmoid\n__device__ __forceinline__ float fast_sigmoid(float x) {\n return 1.0f / (1.0f + expf(-x));\n}\n\n// Optimized unified kernel - processes all operations with better memory access\n// Each thread block handles one (b, n) pair, threads cooperate on output features\n__global__ void se3_unified_kernel(\n const float* __restrict__ scalar_feat, // (B, N, scalar_in)\n const float* __restrict__ vector_feat, // (B, N, vector_in, 3)\n const float* __restrict__ scalar_weight, // (scalar_out, combined_dim)\n const float* __restrict__ scalar_bias, // (scalar_out,)\n const float* __restrict__ vector_weight, // (vector_out, vector_in)\n const float* __restrict__ gate_weight, // (vector_out, combined_dim)\n const float* __restrict__ gate_bias, // (vector_out,)\n float* __restrict__ s_out, // (B, N, scalar_out)\n float* __restrict__ v_out, // (B, N, vector_out, 3)\n int batch_size, int num_nodes, int scalar_in, int vector_in, \n int scalar_out, int vector_out, int combined_dim\n) {\n // Each block handles one (b, n) pair\n const int total = batch_size * num_nodes;\n const int bn_idx = blockIdx.x;\n \n if (bn_idx >= total) return;\n \n const int b = bn_idx / num_nodes;\n const int n = bn_idx % num_nodes;\n \n const int scalar_offset = b * num_nodes * scalar_in + n * scalar_in;\n const int vector_offset = b * num_nodes * vector_in * 3 + n * vector_in * 3;\n const int s_out_offset = b * num_nodes * scalar_out + n * scalar_out;\n const int v_out_offset = b * num_nodes * vector_out * 3 + n * vector_out * 3;\n \n // Use shared memory for combined features and vector linear output\n extern __shared__ float smem[];\n float* combined = smem; // combined_dim elements\n float* v_linear = smem + combined_dim; // vector_out * 3 elements\n \n // Load scalar features into combined (first scalar_in elements)\n for (int s = threadIdx.x; s < scalar_in; s += blockDim.x) {\n combined[s] = scalar_feat[scalar_offset + s];\n }\n \n // Compute vector norms and store in combined\n for (int v = threadIdx.x; v < vector_in; v += blockDim.x) {\n const float vx = vector_feat[vector_offset + v * 3 + 0];\n const float vy = vector_feat[vector_offset + v * 3 + 1];\n const float vz = vector_feat[vector_offset + v * 3 + 2];\n combined[scalar_in + v] = sqrtf(vx * vx + vy * vy + vz * vz);\n }\n \n __syncthreads();\n \n // Compute scalar linear output\n // Each thread handles a subset of output features\n for (int o = threadIdx.x; o < scalar_out; o += blockDim.x) {\n float sum = scalar_bias[o];\n for (int i = 0; i < combined_dim; i++) {\n sum += combined[i] * scalar_weight[o * combined_dim + i];\n }\n s_out[s_out_offset + o] = sum;\n }\n \n // Compute vector linear output: einsum(\"oi,bnid->bnod\")\n // Each thread handles a subset of (output_vec, xyz) pairs\n const int total_vec_out = vector_out * 3;\n for (int idx = threadIdx.x; idx < total_vec_out; idx += blockDim.x) {\n const int o = idx / 3;\n const int c = idx % 3;\n float sum = 0.0f;\n for (int i = 0; i < vector_in; i++) {\n sum += vector_weight[o * vector_in + i] * vector_feat[vector_offset + i * 3 + c];\n }\n v_linear[o * 3 + c] = sum;\n }\n \n __syncthreads();\n \n // Compute gating and apply to vector output\n for (int idx = threadIdx.x; idx < total_vec_out; idx += blockDim.x) {\n const int o = idx / 3;\n const int c = idx % 3;\n \n // Compute gate for this output vector\n float gate_sum = gate_bias[o];\n for (int i = 0; i < combined_dim; i++) {\n gate_sum += combined[i] * gate_weight[o * combined_dim + i];\n }\n const float gate = fast_sigmoid(gate_sum);\n \n v_out[v_out_offset + o * 3 + c] = gate * v_linear[o * 3 + c];\n }\n}\n\n// Host function\nstd::tuple<torch::Tensor, torch::Tensor> se3_forward_cuda(\n torch::Tensor scalar_feat,\n torch::Tensor vector_feat,\n torch::Tensor scalar_weight,\n torch::Tensor scalar_bias,\n torch::Tensor vector_weight,\n torch::Tensor gate_weight,\n torch::Tensor gate_bias\n) {\n const int batch_size = scalar_feat.size(0);\n const int num_nodes = scalar_feat.size(1);\n const int scalar_in = scalar_feat.size(2);\n const int vector_in = vector_feat.size(2);\n const int scalar_out = scalar_weight.size(0);\n const int vector_out = vector_weight.size(0);\n const int combined_dim = scalar_in + vector_in;\n \n const int total = batch_size * num_nodes;\n const int block_size = 128; // One block per (b, n) pair\n const int grid_size = total;\n \n // Shared memory: combined (scalar_in + vector_in) + v_linear (vector_out * 3)\n const size_t smem_size = (combined_dim + vector_out * 3) * sizeof(float);\n \n // Allocate outputs\n auto s_out = torch::empty({batch_size, num_nodes, scalar_out}, scalar_feat.options());\n auto v_out = torch::empty({batch_size, num_nodes, vector_out, 3}, scalar_feat.options());\n \n se3_unified_kernel<<<grid_size, block_size, smem_size>>>(\n scalar_feat.data_ptr<float>(),\n vector_feat.data_ptr<float>(),\n scalar_weight.data_ptr<float>(),\n scalar_bias.data_ptr<float>(),\n vector_weight.data_ptr<float>(),\n gate_weight.data_ptr<float>(),\n gate_bias.data_ptr<float>(),\n s_out.data_ptr<float>(),\n v_out.data_ptr<float>(),\n batch_size, num_nodes, scalar_in, vector_in, scalar_out, vector_out, combined_dim\n );\n \n return std::make_tuple(s_out, v_out);\n}\n\"\"\"\n\ncpp_source = \"\"\"\nstd::tuple<torch::Tensor, torch::Tensor> se3_forward_cuda(\n torch::Tensor scalar_feat,\n torch::Tensor vector_feat,\n torch::Tensor scalar_weight,\n torch::Tensor scalar_bias,\n torch::Tensor vector_weight,\n torch::Tensor gate_weight,\n torch::Tensor gate_bias\n);\n\"\"\"\n\nse3_cuda = load_inline(\n name='se3_cuda_v5',\n cuda_sources=cuda_source,\n cpp_sources=cpp_source,\n functions=['se3_forward_cuda'],\n verbose=False,\n extra_cuda_cflags=['-O3', '--use_fast_math']\n)\n\nclass ModelNew(nn.Module):\n def __init__(self, scalar_in, scalar_out, vector_in, vector_out):\n super().__init__()\n self.scalar_in = scalar_in\n self.scalar_out = scalar_out\n self.vector_in = vector_in\n self.vector_out = vector_out\n \n self.scalar_linear = nn.Linear(scalar_in + vector_in, scalar_out)\n self.vector_weight = nn.Parameter(torch.randn(vector_out, vector_in))\n nn.init.xavier_uniform_(self.vector_weight)\n self.vector_gate = nn.Linear(scalar_in + vector_in, vector_out)\n \n def forward(self, scalar_feat: torch.Tensor, vector_feat: torch.Tensor) -> tuple:\n # Ensure inputs are contiguous float32\n scalar_feat = scalar_feat.contiguous().float()\n vector_feat = vector_feat.contiguous().float()\n \n # Get parameters\n scalar_weight = self.scalar_linear.weight.contiguous().float()\n scalar_bias = self.scalar_linear.bias.contiguous().float()\n vector_weight = self.vector_weight.contiguous().float()\n gate_weight = self.vector_gate.weight.contiguous().float()\n gate_bias = self.vector_gate.bias.contiguous().float()\n \n # Call CUDA kernel\n s_out, v_out = se3_cuda.se3_forward_cuda(\n scalar_feat, vector_feat,\n scalar_weight, scalar_bias,\n vector_weight, gate_weight, gate_bias\n )\n \n return s_out, v_out" }
result ← compile_kernel (ok)
okcompile_kernel compile_kernel PASSED: kernel compiled without errors.
turn 6 · 1 tool call(s) · 342.9s turn · 16.6s LLM · tokens in=14,986 · out=1,998 · total=16,984 · 9,171 chars (click to expand)
turn 6342.9s turn · 16.6s LLM · 326.3s tools · tokens in=14,986 · out=1,998 · total=16,984
reasoning
Good, it compiled. Let me run correctness to verify.
call → run_correctness
callrun_correctness { "kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\ncuda_source = \"\"\"\n#include <torch/extension.h>\n#include <cuda.h>\n#include <cuda_runtime.h>\n#include <cmath>\n\n// Optimized sigmoid\n__device__ __forceinline__ float fast_sigmoid(float x) {\n return 1.0f / (1.0f + expf(-x));\n}\n\n// Optimized unified kernel - processes all operations with better memory access\n// Each thread block handles one (b, n) pair, threads cooperate on output features\n__global__ void se3_unified_kernel(\n const float* __restrict__ scalar_feat, // (B, N, scalar_in)\n const float* __restrict__ vector_feat, // (B, N, vector_in, 3)\n const float* __restrict__ scalar_weight, // (scalar_out, combined_dim)\n const float* __restrict__ scalar_bias, // (scalar_out,)\n const float* __restrict__ vector_weight, // (vector_out, vector_in)\n const float* __restrict__ gate_weight, // (vector_out, combined_dim)\n const float* __restrict__ gate_bias, // (vector_out,)\n float* __restrict__ s_out, // (B, N, scalar_out)\n float* __restrict__ v_out, // (B, N, vector_out, 3)\n int batch_size, int num_nodes, int scalar_in, int vector_in, \n int scalar_out, int vector_out, int combined_dim\n) {\n // Each block handles one (b, n) pair\n const int total = batch_size * num_nodes;\n const int bn_idx = blockIdx.x;\n \n if (bn_idx >= total) return;\n \n const int b = bn_idx / num_nodes;\n const int n = bn_idx % num_nodes;\n \n const int scalar_offset = b * num_nodes * scalar_in + n * scalar_in;\n const int vector_offset = b * num_nodes * vector_in * 3 + n * vector_in * 3;\n const int s_out_offset = b * num_nodes * scalar_out + n * scalar_out;\n const int v_out_offset = b * num_nodes * vector_out * 3 + n * vector_out * 3;\n \n // Use shared memory for combined features and vector linear output\n extern __shared__ float smem[];\n float* combined = smem; // combined_dim elements\n float* v_linear = smem + combined_dim; // vector_out * 3 elements\n \n // Load scalar features into combined (first scalar_in elements)\n for (int s = threadIdx.x; s < scalar_in; s += blockDim.x) {\n combined[s] = scalar_feat[scalar_offset + s];\n }\n \n // Compute vector norms and store in combined\n for (int v = threadIdx.x; v < vector_in; v += blockDim.x) {\n const float vx = vector_feat[vector_offset + v * 3 + 0];\n const float vy = vector_feat[vector_offset + v * 3 + 1];\n const float vz = vector_feat[vector_offset + v * 3 + 2];\n combined[scalar_in + v] = sqrtf(vx * vx + vy * vy + vz * vz);\n }\n \n __syncthreads();\n \n // Compute scalar linear output\n // Each thread handles a subset of output features\n for (int o = threadIdx.x; o < scalar_out; o += blockDim.x) {\n float sum = scalar_bias[o];\n for (int i = 0; i < combined_dim; i++) {\n sum += combined[i] * scalar_weight[o * combined_dim + i];\n }\n s_out[s_out_offset + o] = sum;\n }\n \n // Compute vector linear output: einsum(\"oi,bnid->bnod\")\n // Each thread handles a subset of (output_vec, xyz) pairs\n const int total_vec_out = vector_out * 3;\n for (int idx = threadIdx.x; idx < total_vec_out; idx += blockDim.x) {\n const int o = idx / 3;\n const int c = idx % 3;\n float sum = 0.0f;\n for (int i = 0; i < vector_in; i++) {\n sum += vector_weight[o * vector_in + i] * vector_feat[vector_offset + i * 3 + c];\n }\n v_linear[o * 3 + c] = sum;\n }\n \n __syncthreads();\n \n // Compute gating and apply to vector output\n for (int idx = threadIdx.x; idx < total_vec_out; idx += blockDim.x) {\n const int o = idx / 3;\n const int c = idx % 3;\n \n // Compute gate for this output vector\n float gate_sum = gate_bias[o];\n for (int i = 0; i < combined_dim; i++) {\n gate_sum += combined[i] * gate_weight[o * combined_dim + i];\n }\n const float gate = fast_sigmoid(gate_sum);\n \n v_out[v_out_offset + o * 3 + c] = gate * v_linear[o * 3 + c];\n }\n}\n\n// Host function\nstd::tuple<torch::Tensor, torch::Tensor> se3_forward_cuda(\n torch::Tensor scalar_feat,\n torch::Tensor vector_feat,\n torch::Tensor scalar_weight,\n torch::Tensor scalar_bias,\n torch::Tensor vector_weight,\n torch::Tensor gate_weight,\n torch::Tensor gate_bias\n) {\n const int batch_size = scalar_feat.size(0);\n const int num_nodes = scalar_feat.size(1);\n const int scalar_in = scalar_feat.size(2);\n const int vector_in = vector_feat.size(2);\n const int scalar_out = scalar_weight.size(0);\n const int vector_out = vector_weight.size(0);\n const int combined_dim = scalar_in + vector_in;\n \n const int total = batch_size * num_nodes;\n const int block_size = 128; // One block per (b, n) pair\n const int grid_size = total;\n \n // Shared memory: combined (scalar_in + vector_in) + v_linear (vector_out * 3)\n const size_t smem_size = (combined_dim + vector_out * 3) * sizeof(float);\n \n // Allocate outputs\n auto s_out = torch::empty({batch_size, num_nodes, scalar_out}, scalar_feat.options());\n auto v_out = torch::empty({batch_size, num_nodes, vector_out, 3}, scalar_feat.options());\n \n se3_unified_kernel<<<grid_size, block_size, smem_size>>>(\n scalar_feat.data_ptr<float>(),\n vector_feat.data_ptr<float>(),\n scalar_weight.data_ptr<float>(),\n scalar_bias.data_ptr<float>(),\n vector_weight.data_ptr<float>(),\n gate_weight.data_ptr<float>(),\n gate_bias.data_ptr<float>(),\n s_out.data_ptr<float>(),\n v_out.data_ptr<float>(),\n batch_size, num_nodes, scalar_in, vector_in, scalar_out, vector_out, combined_dim\n );\n \n return std::make_tuple(s_out, v_out);\n}\n\"\"\"\n\ncpp_source = \"\"\"\nstd::tuple<torch::Tensor, torch::Tensor> se3_forward_cuda(\n torch::Tensor scalar_feat,\n torch::Tensor vector_feat,\n torch::Tensor scalar_weight,\n torch::Tensor scalar_bias,\n torch::Tensor vector_weight,\n torch::Tensor gate_weight,\n torch::Tensor gate_bias\n);\n\"\"\"\n\nse3_cuda = load_inline(\n name='se3_cuda_v6',\n cuda_sources=cuda_source,\n cpp_sources=cpp_source,\n functions=['se3_forward_cuda'],\n verbose=False,\n extra_cuda_cflags=['-O3', '--use_fast_math']\n)\n\nclass ModelNew(nn.Module):\n def __init__(self, scalar_in, scalar_out, vector_in, vector_out):\n super().__init__()\n self.scalar_in = scalar_in\n self.scalar_out = scalar_out\n self.vector_in = vector_in\n self.vector_out = vector_out\n \n self.scalar_linear = nn.Linear(scalar_in + vector_in, scalar_out)\n self.vector_weight = nn.Parameter(torch.randn(vector_out, vector_in))\n nn.init.xavier_uniform_(self.vector_weight)\n self.vector_gate = nn.Linear(scalar_in + vector_in, vector_out)\n \n def forward(self, scalar_feat: torch.Tensor, vector_feat: torch.Tensor) -> tuple:\n # Ensure inputs are contiguous float32\n scalar_feat = scalar_feat.contiguous().float()\n vector_feat = vector_feat.contiguous().float()\n \n # Get parameters\n scalar_weight = self.scalar_linear.weight.contiguous().float()\n scalar_bias = self.scalar_linear.bias.contiguous().float()\n vector_weight = self.vector_weight.contiguous().float()\n gate_weight = self.vector_gate.weight.contiguous().float()\n gate_bias = self.vector_gate.bias.contiguous().float()\n \n # Call CUDA kernel\n s_out, v_out = se3_cuda.se3_forward_cuda(\n scalar_feat, vector_feat,\n scalar_weight, scalar_bias,\n vector_weight, gate_weight, gate_bias\n )\n \n return s_out, v_out" }
result ← run_correctness (ok)
okrun_correctness run_correctness PASSED: (3 / 3) trials all matched the reference. Numerical precision: max_abs_err=7.15e-07 mean_abs_err=4.16e-08 max_rel_err=3.50e-02
turn 7 · 1 tool call(s) · 498.0s turn · 16.9s LLM · tokens in=17,029 · out=1,998 · total=19,027 · 11,023 chars (click to expand)
turn 7498.0s turn · 16.9s LLM · 481.0s tools · tokens in=17,029 · out=1,998 · total=19,027
reasoning
Good, correctness passes. Now let me profile this optimized version.
call → profile_kernel
callprofile_kernel { "kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\ncuda_source = \"\"\"\n#include <torch/extension.h>\n#include <cuda.h>\n#include <cuda_runtime.h>\n#include <cmath>\n\n// Optimized sigmoid\n__device__ __forceinline__ float fast_sigmoid(float x) {\n return 1.0f / (1.0f + expf(-x));\n}\n\n// Optimized unified kernel - processes all operations with better memory access\n// Each thread block handles one (b, n) pair, threads cooperate on output features\n__global__ void se3_unified_kernel(\n const float* __restrict__ scalar_feat, // (B, N, scalar_in)\n const float* __restrict__ vector_feat, // (B, N, vector_in, 3)\n const float* __restrict__ scalar_weight, // (scalar_out, combined_dim)\n const float* __restrict__ scalar_bias, // (scalar_out,)\n const float* __restrict__ vector_weight, // (vector_out, vector_in)\n const float* __restrict__ gate_weight, // (vector_out, combined_dim)\n const float* __restrict__ gate_bias, // (vector_out,)\n float* __restrict__ s_out, // (B, N, scalar_out)\n float* __restrict__ v_out, // (B, N, vector_out, 3)\n int batch_size, int num_nodes, int scalar_in, int vector_in, \n int scalar_out, int vector_out, int combined_dim\n) {\n // Each block handles one (b, n) pair\n const int total = batch_size * num_nodes;\n const int bn_idx = blockIdx.x;\n \n if (bn_idx >= total) return;\n \n const int b = bn_idx / num_nodes;\n const int n = bn_idx % num_nodes;\n \n const int scalar_offset = b * num_nodes * scalar_in + n * scalar_in;\n const int vector_offset = b * num_nodes * vector_in * 3 + n * vector_in * 3;\n const int s_out_offset = b * num_nodes * scalar_out + n * scalar_out;\n const int v_out_offset = b * num_nodes * vector_out * 3 + n * vector_out * 3;\n \n // Use shared memory for combined features and vector linear output\n extern __shared__ float smem[];\n float* combined = smem; // combined_dim elements\n float* v_linear = smem + combined_dim; // vector_out * 3 elements\n \n // Load scalar features into combined (first scalar_in elements)\n for (int s = threadIdx.x; s < scalar_in; s += blockDim.x) {\n combined[s] = scalar_feat[scalar_offset + s];\n }\n \n // Compute vector norms and store in combined\n for (int v = threadIdx.x; v < vector_in; v += blockDim.x) {\n const float vx = vector_feat[vector_offset + v * 3 + 0];\n const float vy = vector_feat[vector_offset + v * 3 + 1];\n const float vz = vector_feat[vector_offset + v * 3 + 2];\n combined[scalar_in + v] = sqrtf(vx * vx + vy * vy + vz * vz);\n }\n \n __syncthreads();\n \n // Compute scalar linear output\n // Each thread handles a subset of output features\n for (int o = threadIdx.x; o < scalar_out; o += blockDim.x) {\n float sum = scalar_bias[o];\n for (int i = 0; i < combined_dim; i++) {\n sum += combined[i] * scalar_weight[o * combined_dim + i];\n }\n s_out[s_out_offset + o] = sum;\n }\n \n // Compute vector linear output: einsum(\"oi,bnid->bnod\")\n // Each thread handles a subset of (output_vec, xyz) pairs\n const int total_vec_out = vector_out * 3;\n for (int idx = threadIdx.x; idx < total_vec_out; idx += blockDim.x) {\n const int o = idx / 3;\n const int c = idx % 3;\n float sum = 0.0f;\n for (int i = 0; i < vector_in; i++) {\n sum += vector_weight[o * vector_in + i] * vector_feat[vector_offset + i * 3 + c];\n }\n v_linear[o * 3 + c] = sum;\n }\n \n __syncthreads();\n \n // Compute gating and apply to vector output\n for (int idx = threadIdx.x; idx < total_vec_out; idx += blockDim.x) {\n const int o = idx / 3;\n const int c = idx % 3;\n \n // Compute gate for this output vector\n float gate_sum = gate_bias[o];\n for (int i = 0; i < combined_dim; i++) {\n gate_sum += combined[i] * gate_weight[o * combined_dim + i];\n }\n const float gate = fast_sigmoid(gate_sum);\n \n v_out[v_out_offset + o * 3 + c] = gate * v_linear[o * 3 + c];\n }\n}\n\n// Host function\nstd::tuple<torch::Tensor, torch::Tensor> se3_forward_cuda(\n torch::Tensor scalar_feat,\n torch::Tensor vector_feat,\n torch::Tensor scalar_weight,\n torch::Tensor scalar_bias,\n torch::Tensor vector_weight,\n torch::Tensor gate_weight,\n torch::Tensor gate_bias\n) {\n const int batch_size = scalar_feat.size(0);\n const int num_nodes = scalar_feat.size(1);\n const int scalar_in = scalar_feat.size(2);\n const int vector_in = vector_feat.size(2);\n const int scalar_out = scalar_weight.size(0);\n const int vector_out = vector_weight.size(0);\n const int combined_dim = scalar_in + vector_in;\n \n const int total = batch_size * num_nodes;\n const int block_size = 128; // One block per (b, n) pair\n const int grid_size = total;\n \n // Shared memory: combined (scalar_in + vector_in) + v_linear (vector_out * 3)\n const size_t smem_size = (combined_dim + vector_out * 3) * sizeof(float);\n \n // Allocate outputs\n auto s_out = torch::empty({batch_size, num_nodes, scalar_out}, scalar_feat.options());\n auto v_out = torch::empty({batch_size, num_nodes, vector_out, 3}, scalar_feat.options());\n \n se3_unified_kernel<<<grid_size, block_size, smem_size>>>(\n scalar_feat.data_ptr<float>(),\n vector_feat.data_ptr<float>(),\n scalar_weight.data_ptr<float>(),\n scalar_bias.data_ptr<float>(),\n vector_weight.data_ptr<float>(),\n gate_weight.data_ptr<float>(),\n gate_bias.data_ptr<float>(),\n s_out.data_ptr<float>(),\n v_out.data_ptr<float>(),\n batch_size, num_nodes, scalar_in, vector_in, scalar_out, vector_out, combined_dim\n );\n \n return std::make_tuple(s_out, v_out);\n}\n\"\"\"\n\ncpp_source = \"\"\"\nstd::tuple<torch::Tensor, torch::Tensor> se3_forward_cuda(\n torch::Tensor scalar_feat,\n torch::Tensor vector_feat,\n torch::Tensor scalar_weight,\n torch::Tensor scalar_bias,\n torch::Tensor vector_weight,\n torch::Tensor gate_weight,\n torch::Tensor gate_bias\n);\n\"\"\"\n\nse3_cuda = load_inline(\n name='se3_cuda_v7',\n cuda_sources=cuda_source,\n cpp_sources=cpp_source,\n functions=['se3_forward_cuda'],\n verbose=False,\n extra_cuda_cflags=['-O3', '--use_fast_math']\n)\n\nclass ModelNew(nn.Module):\n def __init__(self, scalar_in, scalar_out, vector_in, vector_out):\n super().__init__()\n self.scalar_in = scalar_in\n self.scalar_out = scalar_out\n self.vector_in = vector_in\n self.vector_out = vector_out\n \n self.scalar_linear = nn.Linear(scalar_in + vector_in, scalar_out)\n self.vector_weight = nn.Parameter(torch.randn(vector_out, vector_in))\n nn.init.xavier_uniform_(self.vector_weight)\n self.vector_gate = nn.Linear(scalar_in + vector_in, vector_out)\n \n def forward(self, scalar_feat: torch.Tensor, vector_feat: torch.Tensor) -> tuple:\n # Ensure inputs are contiguous float32\n scalar_feat = scalar_feat.contiguous().float()\n vector_feat = vector_feat.contiguous().float()\n \n # Get parameters\n scalar_weight = self.scalar_linear.weight.contiguous().float()\n scalar_bias = self.scalar_linear.bias.contiguous().float()\n vector_weight = self.vector_weight.contiguous().float()\n gate_weight = self.vector_gate.weight.contiguous().float()\n gate_bias = self.vector_gate.bias.contiguous().float()\n \n # Call CUDA kernel\n s_out, v_out = se3_cuda.se3_forward_cuda(\n scalar_feat, vector_feat,\n scalar_weight, scalar_bias,\n vector_weight, gate_weight, gate_bias\n )\n \n return s_out, v_out" }
result ← profile_kernel (ok)
okprofile_kernel profile_kernel PASSED: profiling complete. === Kernel Profile Summary === --- Kernel Breakdown (by GPU time) --- #1: aten::empty 23.0μs (35%) calls=1 #2: aten::to 14.0μs (22%) calls=1 #3: aten::empty 7.0μs (11%) calls=1 #4: aten::to 5.0μs (8%) calls=1 #5: aten::to 4.0μs (6%) calls=1 ... +4 more kernels --- Timing --- GPU time: 20.29 μs [↓599.2μs ok] --- Memory Bandwidth --- DRAM BW: 24.6/3350 GB/s (0.7%) [↑0.0% ok] read=24.6 write=0.0 GB/s Hit rates: L2=87.2% --- Compute Throughput --- Pipe util: FMA=3.3%, Tensor=0.1% --- Roofline Analysis --- Ridge point (FP32): 20.00 FLOPs/byte Classification: UNKNOWN --- Occupancy --- Achieved: 42.9% [↓6.7% REGRESSED] Eligible warps/cycle: 0.12 WARNING: <1 eligible warp/cycle = latency-bound, needs more parallelism Launch: regs/thread=36, smem/blk=1536B, block=128, grid=1024 --- Memory Access Quality --- Global ld coalescing: 17.38 sectors/req (17.4x wasted BW) --- Warp Stall Reasons (% of issue cycles) --- long_scoreboard 2168.0% #################### short_scoreboard 800.2% #################### mio_throttle 757.1% #################### --- Optimization Hints --- -> 2168% stalls: global memory latency (waiting for DRAM/L2). + sectors/req=17.4 -> uncoalesced global loads, restructure access pattern or use __ldg Try shared-memory tiling, prefetching, or reducing working set. -> Global load coalescing=17.4x (ideal=1.0) -> 17x wasted DRAM BW. Make per-warp accesses contiguous. -> Low eligible warps + low BW% + low compute% = LATENCY-BOUND. Need more parallelism (larger grid, more ILP, prefetching). --- Delta vs Previous Iteration --- GPU time: 619.49→20.29μs (↓599.20) ok DRAM BW%: 0.69→0.73% (↑0.05) ok Occupancy: 49.64→42.94% (↓6.70) REGRESSED Eligible warps/cyc: 0.17→0.12 (↓0.05) REGRESSED Ld sectors/req: 89.34→17.38 (↓71.97) ok L2 hit%: 370.73→87.19% (↓283.54) REGRESSED
turn 8 · 1 tool call(s) · 484.6s turn · 20.2s LLM · tokens in=19,733 · out=2,243 · total=21,976 · 10,030 chars (click to expand)
turn 8484.6s turn · 20.2s LLM · 464.4s tools · tokens in=19,733 · out=2,243 · total=21,976
reasoning
Good progress - GPU time went from 619μs to 20μs, which is a 30x speedup! Memory coalescing improved from 89x to 17x wasted bandwidth. But we're still latency-bound with low occupancy. The issue is that with 1024 blocks and 128 threads per block, we have limited parallelism. Each block handles one (b, n) pair but only 128 threads are used. Let me try a different approach where I use larger blocks with more threads to improve occupancy, and also use vectorized loads where possible.
assistantGreat improvement! GPU time went from 619μs to 20μs. Let me optimize further by improving thread utilization and using vectorized loads:
call → compile_kernel
callcompile_kernel { "kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\ncuda_source = \"\"\"\n#include <torch/extension.h>\n#include <cuda.h>\n#include <cuda_runtime.h>\n#include <cmath>\n\n// Vector load/store helpers\n__device__ __forceinline__ void load_float4(float4& dst, const float* ptr) {\n dst = *reinterpret_cast<const float4*>(ptr);\n}\n\n__device__ __forceinline__ void store_float4(float* ptr, float4 val) {\n *reinterpret_cast<float4*>(ptr) = val;\n}\n\n// Optimized sigmoid\n__device__ __forceinline__ float fast_sigmoid(float x) {\n return 1.0f / (1.0f + expf(-x));\n}\n\n// Fused kernel with better parallelism\n// Grid: batch_size * num_nodes blocks\n// Block: up to 256 threads, cooperatively compute outputs\n__global__ void se3_fused_kernel(\n const float* __restrict__ scalar_feat, // (B, N, scalar_in)\n const float* __restrict__ vector_feat, // (B, N, vector_in, 3)\n const float* __restrict__ scalar_weight, // (scalar_out, combined_dim)\n const float* __restrict__ scalar_bias, // (scalar_out,)\n const float* __restrict__ vector_weight, // (vector_out, vector_in)\n const float* __restrict__ gate_weight, // (vector_out, combined_dim)\n const float* __restrict__ gate_bias, // (vector_out,)\n float* __restrict__ s_out, // (B, N, scalar_out)\n float* __restrict__ v_out, // (B, N, vector_out, 3)\n int batch_size, int num_nodes, int scalar_in, int vector_in, \n int scalar_out, int vector_out, int combined_dim\n) {\n const int bn_idx = blockIdx.x;\n const int total_bn = batch_size * num_nodes;\n if (bn_idx >= total_bn) return;\n \n const int b = bn_idx / num_nodes;\n const int n = bn_idx % num_nodes;\n const int tid = threadIdx.x;\n const int block_dim = blockDim.x;\n \n // Input offsets\n const int scalar_offset = b * num_nodes * scalar_in + n * scalar_in;\n const int vector_offset = b * num_nodes * vector_in * 3 + n * vector_in * 3;\n \n // Output offsets\n const int s_out_offset = b * num_nodes * scalar_out + n * scalar_out;\n const int v_out_offset = b * num_nodes * vector_out * 3 + n * vector_out * 3;\n \n // Shared memory allocation\n extern __shared__ float smem[];\n float* combined = smem; // combined_dim floats\n float* v_linear = smem + combined_dim; // vector_out * 3 floats\n \n // Load scalar features to shared memory (coalesced)\n for (int i = tid; i < scalar_in; i += block_dim) {\n combined[i] = scalar_feat[scalar_offset + i];\n }\n \n // Compute vector norms and store (each thread handles multiple vectors)\n for (int v = tid; v < vector_in; v += block_dim) {\n const float* v_ptr = vector_feat + vector_offset + v * 3;\n float vx = v_ptr[0], vy = v_ptr[1], vz = v_ptr[2];\n combined[scalar_in + v] = sqrtf(vx*vx + vy*vy + vz*vz);\n }\n \n __syncthreads();\n \n // Compute scalar linear output: each thread handles one output element\n for (int o = tid; o < scalar_out; o += block_dim) {\n float sum = scalar_bias[o];\n const float* w_row = scalar_weight + o * combined_dim;\n \n // Unrolled loop for better ILP\n #pragma unroll 8\n for (int i = 0; i < combined_dim; i++) {\n sum = fmaf(combined[i], w_row[i], sum);\n }\n s_out[s_out_offset + o] = sum;\n }\n \n // Compute vector linear output (einsum) - store in shared memory\n // Each thread handles one (output_idx, coord) pair\n const int total_v_out = vector_out * 3;\n for (int idx = tid; idx < total_v_out; idx += block_dim) {\n const int o = idx / 3;\n const int c = idx % 3;\n \n float sum = 0.0f;\n const float* w_row = vector_weight + o * vector_in;\n \n #pragma unroll 4\n for (int i = 0; i < vector_in; i++) {\n sum = fmaf(w_row[i], vector_feat[vector_offset + i * 3 + c], sum);\n }\n v_linear[o * 3 + c] = sum;\n }\n \n __syncthreads();\n \n // Apply gating to vector output\n for (int idx = tid; idx < total_v_out; idx += block_dim) {\n const int o = idx / 3;\n const int c = idx % 3;\n \n // Compute gate\n float gate_sum = gate_bias[o];\n const float* g_row = gate_weight + o * combined_dim;\n \n #pragma unroll 8\n for (int i = 0; i < combined_dim; i++) {\n gate_sum = fmaf(combined[i], g_row[i], gate_sum);\n }\n float gate = fast_sigmoid(gate_sum);\n \n v_out[v_out_offset + o * 3 + c] = gate * v_linear[o * 3 + c];\n }\n}\n\n// Host function\nstd::tuple<torch::Tensor, torch::Tensor> se3_forward_cuda(\n torch::Tensor scalar_feat,\n torch::Tensor vector_feat,\n torch::Tensor scalar_weight,\n torch::Tensor scalar_bias,\n torch::Tensor vector_weight,\n torch::Tensor gate_weight,\n torch::Tensor gate_bias\n) {\n const int batch_size = scalar_feat.size(0);\n const int num_nodes = scalar_feat.size(1);\n const int scalar_in = scalar_feat.size(2);\n const int vector_in = vector_feat.size(2);\n const int scalar_out = scalar_weight.size(0);\n const int vector_out = vector_weight.size(0);\n const int combined_dim = scalar_in + vector_in;\n \n const int total_bn = batch_size * num_nodes;\n const int block_size = 256; // Larger block for more parallelism\n const int grid_size = total_bn;\n \n // Shared memory: combined + v_linear\n const size_t smem_size = (combined_dim + vector_out * 3) * sizeof(float);\n \n // Allocate outputs\n auto s_out = torch::empty({batch_size, num_nodes, scalar_out}, scalar_feat.options());\n auto v_out = torch::empty({batch_size, num_nodes, vector_out, 3}, scalar_feat.options());\n \n se3_fused_kernel<<<grid_size, block_size, smem_size>>>(\n scalar_feat.data_ptr<float>(),\n vector_feat.data_ptr<float>(),\n scalar_weight.data_ptr<float>(),\n scalar_bias.data_ptr<float>(),\n vector_weight.data_ptr<float>(),\n gate_weight.data_ptr<float>(),\n gate_bias.data_ptr<float>(),\n s_out.data_ptr<float>(),\n v_out.data_ptr<float>(),\n batch_size, num_nodes, scalar_in, vector_in, scalar_out, vector_out, combined_dim\n );\n \n return std::make_tuple(s_out, v_out);\n}\n\"\"\"\n\ncpp_source = \"\"\"\nstd::tuple<torch::Tensor, torch::Tensor> se3_forward_cuda(\n torch::Tensor scalar_feat,\n torch::Tensor vector_feat,\n torch::Tensor scalar_weight,\n torch::Tensor scalar_bias,\n torch::Tensor vector_weight,\n torch::Tensor gate_weight,\n torch::Tensor gate_bias\n);\n\"\"\"\n\nse3_cuda = load_inline(\n name='se3_cuda_v8',\n cuda_sources=cuda_source,\n cpp_sources=cpp_source,\n functions=['se3_forward_cuda'],\n verbose=False,\n extra_cuda_cflags=['-O3', '--use_fast_math', '-Xptxas=-v']\n)\n\nclass ModelNew(nn.Module):\n def __init__(self, scalar_in, scalar_out, vector_in, vector_out):\n super().__init__()\n self.scalar_in = scalar_in\n self.scalar_out = scalar_out\n self.vector_in = vector_in\n self.vector_out = vector_out\n \n self.scalar_linear = nn.Linear(scalar_in + vector_in, scalar_out)\n self.vector_weight = nn.Parameter(torch.randn(vector_out, vector_in))\n nn.init.xavier_uniform_(self.vector_weight)\n self.vector_gate = nn.Linear(scalar_in + vector_in, vector_out)\n \n def forward(self, scalar_feat: torch.Tensor, vector_feat: torch.Tensor) -> tuple:\n scalar_feat = scalar_feat.contiguous().float()\n vector_feat = vector_feat.contiguous().float()\n \n scalar_weight = self.scalar_linear.weight.contiguous().float()\n scalar_bias = self.scalar_linear.bias.contiguous().float()\n vector_weight = self.vector_weight.contiguous().float()\n gate_weight = self.vector_gate.weight.contiguous().float()\n gate_bias = self.vector_gate.bias.contiguous().float()\n \n s_out, v_out = se3_cuda.se3_forward_cuda(\n scalar_feat, vector_feat,\n scalar_weight, scalar_bias,\n vector_weight, gate_weight, gate_bias\n )\n \n return s_out, v_out" }
result ← compile_kernel (ok)
okcompile_kernel compile_kernel PASSED: kernel compiled without errors.
turn 9 · 1 tool call(s) · 448.5s turn · 17.7s LLM · tokens in=21,869 · out=2,102 · total=23,971 · 9,488 chars (click to expand)
turn 9448.5s turn · 17.7s LLM · 430.7s tools · tokens in=21,869 · out=2,102 · total=23,971
reasoning
Let me check correctness and profile this improved version.
call → run_correctness
callrun_correctness { "kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\ncuda_source = \"\"\"\n#include <torch/extension.h>\n#include <cuda.h>\n#include <cuda_runtime.h>\n#include <cmath>\n\n// Vector load/store helpers\n__device__ __forceinline__ void load_float4(float4& dst, const float* ptr) {\n dst = *reinterpret_cast<const float4*>(ptr);\n}\n\n__device__ __forceinline__ void store_float4(float* ptr, float4 val) {\n *reinterpret_cast<float4*>(ptr) = val;\n}\n\n// Optimized sigmoid\n__device__ __forceinline__ float fast_sigmoid(float x) {\n return 1.0f / (1.0f + expf(-x));\n}\n\n// Fused kernel with better parallelism\n// Grid: batch_size * num_nodes blocks\n// Block: up to 256 threads, cooperatively compute outputs\n__global__ void se3_fused_kernel(\n const float* __restrict__ scalar_feat, // (B, N, scalar_in)\n const float* __restrict__ vector_feat, // (B, N, vector_in, 3)\n const float* __restrict__ scalar_weight, // (scalar_out, combined_dim)\n const float* __restrict__ scalar_bias, // (scalar_out,)\n const float* __restrict__ vector_weight, // (vector_out, vector_in)\n const float* __restrict__ gate_weight, // (vector_out, combined_dim)\n const float* __restrict__ gate_bias, // (vector_out,)\n float* __restrict__ s_out, // (B, N, scalar_out)\n float* __restrict__ v_out, // (B, N, vector_out, 3)\n int batch_size, int num_nodes, int scalar_in, int vector_in, \n int scalar_out, int vector_out, int combined_dim\n) {\n const int bn_idx = blockIdx.x;\n const int total_bn = batch_size * num_nodes;\n if (bn_idx >= total_bn) return;\n \n const int b = bn_idx / num_nodes;\n const int n = bn_idx % num_nodes;\n const int tid = threadIdx.x;\n const int block_dim = blockDim.x;\n \n // Input offsets\n const int scalar_offset = b * num_nodes * scalar_in + n * scalar_in;\n const int vector_offset = b * num_nodes * vector_in * 3 + n * vector_in * 3;\n \n // Output offsets\n const int s_out_offset = b * num_nodes * scalar_out + n * scalar_out;\n const int v_out_offset = b * num_nodes * vector_out * 3 + n * vector_out * 3;\n \n // Shared memory allocation\n extern __shared__ float smem[];\n float* combined = smem; // combined_dim floats\n float* v_linear = smem + combined_dim; // vector_out * 3 floats\n \n // Load scalar features to shared memory (coalesced)\n for (int i = tid; i < scalar_in; i += block_dim) {\n combined[i] = scalar_feat[scalar_offset + i];\n }\n \n // Compute vector norms and store (each thread handles multiple vectors)\n for (int v = tid; v < vector_in; v += block_dim) {\n const float* v_ptr = vector_feat + vector_offset + v * 3;\n float vx = v_ptr[0], vy = v_ptr[1], vz = v_ptr[2];\n combined[scalar_in + v] = sqrtf(vx*vx + vy*vy + vz*vz);\n }\n \n __syncthreads();\n \n // Compute scalar linear output: each thread handles one output element\n for (int o = tid; o < scalar_out; o += block_dim) {\n float sum = scalar_bias[o];\n const float* w_row = scalar_weight + o * combined_dim;\n \n // Unrolled loop for better ILP\n #pragma unroll 8\n for (int i = 0; i < combined_dim; i++) {\n sum = fmaf(combined[i], w_row[i], sum);\n }\n s_out[s_out_offset + o] = sum;\n }\n \n // Compute vector linear output (einsum) - store in shared memory\n // Each thread handles one (output_idx, coord) pair\n const int total_v_out = vector_out * 3;\n for (int idx = tid; idx < total_v_out; idx += block_dim) {\n const int o = idx / 3;\n const int c = idx % 3;\n \n float sum = 0.0f;\n const float* w_row = vector_weight + o * vector_in;\n \n #pragma unroll 4\n for (int i = 0; i < vector_in; i++) {\n sum = fmaf(w_row[i], vector_feat[vector_offset + i * 3 + c], sum);\n }\n v_linear[o * 3 + c] = sum;\n }\n \n __syncthreads();\n \n // Apply gating to vector output\n for (int idx = tid; idx < total_v_out; idx += block_dim) {\n const int o = idx / 3;\n const int c = idx % 3;\n \n // Compute gate\n float gate_sum = gate_bias[o];\n const float* g_row = gate_weight + o * combined_dim;\n \n #pragma unroll 8\n for (int i = 0; i < combined_dim; i++) {\n gate_sum = fmaf(combined[i], g_row[i], gate_sum);\n }\n float gate = fast_sigmoid(gate_sum);\n \n v_out[v_out_offset + o * 3 + c] = gate * v_linear[o * 3 + c];\n }\n}\n\n// Host function\nstd::tuple<torch::Tensor, torch::Tensor> se3_forward_cuda(\n torch::Tensor scalar_feat,\n torch::Tensor vector_feat,\n torch::Tensor scalar_weight,\n torch::Tensor scalar_bias,\n torch::Tensor vector_weight,\n torch::Tensor gate_weight,\n torch::Tensor gate_bias\n) {\n const int batch_size = scalar_feat.size(0);\n const int num_nodes = scalar_feat.size(1);\n const int scalar_in = scalar_feat.size(2);\n const int vector_in = vector_feat.size(2);\n const int scalar_out = scalar_weight.size(0);\n const int vector_out = vector_weight.size(0);\n const int combined_dim = scalar_in + vector_in;\n \n const int total_bn = batch_size * num_nodes;\n const int block_size = 256; // Larger block for more parallelism\n const int grid_size = total_bn;\n \n // Shared memory: combined + v_linear\n const size_t smem_size = (combined_dim + vector_out * 3) * sizeof(float);\n \n // Allocate outputs\n auto s_out = torch::empty({batch_size, num_nodes, scalar_out}, scalar_feat.options());\n auto v_out = torch::empty({batch_size, num_nodes, vector_out, 3}, scalar_feat.options());\n \n se3_fused_kernel<<<grid_size, block_size, smem_size>>>(\n scalar_feat.data_ptr<float>(),\n vector_feat.data_ptr<float>(),\n scalar_weight.data_ptr<float>(),\n scalar_bias.data_ptr<float>(),\n vector_weight.data_ptr<float>(),\n gate_weight.data_ptr<float>(),\n gate_bias.data_ptr<float>(),\n s_out.data_ptr<float>(),\n v_out.data_ptr<float>(),\n batch_size, num_nodes, scalar_in, vector_in, scalar_out, vector_out, combined_dim\n );\n \n return std::make_tuple(s_out, v_out);\n}\n\"\"\"\n\ncpp_source = \"\"\"\nstd::tuple<torch::Tensor, torch::Tensor> se3_forward_cuda(\n torch::Tensor scalar_feat,\n torch::Tensor vector_feat,\n torch::Tensor scalar_weight,\n torch::Tensor scalar_bias,\n torch::Tensor vector_weight,\n torch::Tensor gate_weight,\n torch::Tensor gate_bias\n);\n\"\"\"\n\nse3_cuda = load_inline(\n name='se3_cuda_v9',\n cuda_sources=cuda_source,\n cpp_sources=cpp_source,\n functions=['se3_forward_cuda'],\n verbose=False,\n extra_cuda_cflags=['-O3', '--use_fast_math', '-Xptxas=-v']\n)\n\nclass ModelNew(nn.Module):\n def __init__(self, scalar_in, scalar_out, vector_in, vector_out):\n super().__init__()\n self.scalar_in = scalar_in\n self.scalar_out = scalar_out\n self.vector_in = vector_in\n self.vector_out = vector_out\n \n self.scalar_linear = nn.Linear(scalar_in + vector_in, scalar_out)\n self.vector_weight = nn.Parameter(torch.randn(vector_out, vector_in))\n nn.init.xavier_uniform_(self.vector_weight)\n self.vector_gate = nn.Linear(scalar_in + vector_in, vector_out)\n \n def forward(self, scalar_feat: torch.Tensor, vector_feat: torch.Tensor) -> tuple:\n scalar_feat = scalar_feat.contiguous().float()\n vector_feat = vector_feat.contiguous().float()\n \n scalar_weight = self.scalar_linear.weight.contiguous().float()\n scalar_bias = self.scalar_linear.bias.contiguous().float()\n vector_weight = self.vector_weight.contiguous().float()\n gate_weight = self.vector_gate.weight.contiguous().float()\n gate_bias = self.vector_gate.bias.contiguous().float()\n \n s_out, v_out = se3_cuda.se3_forward_cuda(\n scalar_feat, vector_feat,\n scalar_weight, scalar_bias,\n vector_weight, gate_weight, gate_bias\n )\n \n return s_out, v_out" }
result ← run_correctness (ok)
okrun_correctness run_correctness PASSED: (3 / 3) trials all matched the reference. Numerical precision: max_abs_err=7.15e-07 mean_abs_err=4.16e-08 max_rel_err=3.50e-02
turn 10 · 1 tool call(s) · 358.7s turn · 17.9s LLM · tokens in=24,018 · out=2,102 · total=26,120 · 11,215 chars (click to expand)
turn 10358.7s turn · 17.9s LLM · 340.8s tools · tokens in=24,018 · out=2,102 · total=26,120
reasoning
Let me profile this version to see if it improved.
call → profile_kernel
callprofile_kernel { "kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\ncuda_source = \"\"\"\n#include <torch/extension.h>\n#include <cuda.h>\n#include <cuda_runtime.h>\n#include <cmath>\n\n// Vector load/store helpers\n__device__ __forceinline__ void load_float4(float4& dst, const float* ptr) {\n dst = *reinterpret_cast<const float4*>(ptr);\n}\n\n__device__ __forceinline__ void store_float4(float* ptr, float4 val) {\n *reinterpret_cast<float4*>(ptr) = val;\n}\n\n// Optimized sigmoid\n__device__ __forceinline__ float fast_sigmoid(float x) {\n return 1.0f / (1.0f + expf(-x));\n}\n\n// Fused kernel with better parallelism\n// Grid: batch_size * num_nodes blocks\n// Block: up to 256 threads, cooperatively compute outputs\n__global__ void se3_fused_kernel(\n const float* __restrict__ scalar_feat, // (B, N, scalar_in)\n const float* __restrict__ vector_feat, // (B, N, vector_in, 3)\n const float* __restrict__ scalar_weight, // (scalar_out, combined_dim)\n const float* __restrict__ scalar_bias, // (scalar_out,)\n const float* __restrict__ vector_weight, // (vector_out, vector_in)\n const float* __restrict__ gate_weight, // (vector_out, combined_dim)\n const float* __restrict__ gate_bias, // (vector_out,)\n float* __restrict__ s_out, // (B, N, scalar_out)\n float* __restrict__ v_out, // (B, N, vector_out, 3)\n int batch_size, int num_nodes, int scalar_in, int vector_in, \n int scalar_out, int vector_out, int combined_dim\n) {\n const int bn_idx = blockIdx.x;\n const int total_bn = batch_size * num_nodes;\n if (bn_idx >= total_bn) return;\n \n const int b = bn_idx / num_nodes;\n const int n = bn_idx % num_nodes;\n const int tid = threadIdx.x;\n const int block_dim = blockDim.x;\n \n // Input offsets\n const int scalar_offset = b * num_nodes * scalar_in + n * scalar_in;\n const int vector_offset = b * num_nodes * vector_in * 3 + n * vector_in * 3;\n \n // Output offsets\n const int s_out_offset = b * num_nodes * scalar_out + n * scalar_out;\n const int v_out_offset = b * num_nodes * vector_out * 3 + n * vector_out * 3;\n \n // Shared memory allocation\n extern __shared__ float smem[];\n float* combined = smem; // combined_dim floats\n float* v_linear = smem + combined_dim; // vector_out * 3 floats\n \n // Load scalar features to shared memory (coalesced)\n for (int i = tid; i < scalar_in; i += block_dim) {\n combined[i] = scalar_feat[scalar_offset + i];\n }\n \n // Compute vector norms and store (each thread handles multiple vectors)\n for (int v = tid; v < vector_in; v += block_dim) {\n const float* v_ptr = vector_feat + vector_offset + v * 3;\n float vx = v_ptr[0], vy = v_ptr[1], vz = v_ptr[2];\n combined[scalar_in + v] = sqrtf(vx*vx + vy*vy + vz*vz);\n }\n \n __syncthreads();\n \n // Compute scalar linear output: each thread handles one output element\n for (int o = tid; o < scalar_out; o += block_dim) {\n float sum = scalar_bias[o];\n const float* w_row = scalar_weight + o * combined_dim;\n \n // Unrolled loop for better ILP\n #pragma unroll 8\n for (int i = 0; i < combined_dim; i++) {\n sum = fmaf(combined[i], w_row[i], sum);\n }\n s_out[s_out_offset + o] = sum;\n }\n \n // Compute vector linear output (einsum) - store in shared memory\n // Each thread handles one (output_idx, coord) pair\n const int total_v_out = vector_out * 3;\n for (int idx = tid; idx < total_v_out; idx += block_dim) {\n const int o = idx / 3;\n const int c = idx % 3;\n \n float sum = 0.0f;\n const float* w_row = vector_weight + o * vector_in;\n \n #pragma unroll 4\n for (int i = 0; i < vector_in; i++) {\n sum = fmaf(w_row[i], vector_feat[vector_offset + i * 3 + c], sum);\n }\n v_linear[o * 3 + c] = sum;\n }\n \n __syncthreads();\n \n // Apply gating to vector output\n for (int idx = tid; idx < total_v_out; idx += block_dim) {\n const int o = idx / 3;\n const int c = idx % 3;\n \n // Compute gate\n float gate_sum = gate_bias[o];\n const float* g_row = gate_weight + o * combined_dim;\n \n #pragma unroll 8\n for (int i = 0; i < combined_dim; i++) {\n gate_sum = fmaf(combined[i], g_row[i], gate_sum);\n }\n float gate = fast_sigmoid(gate_sum);\n \n v_out[v_out_offset + o * 3 + c] = gate * v_linear[o * 3 + c];\n }\n}\n\n// Host function\nstd::tuple<torch::Tensor, torch::Tensor> se3_forward_cuda(\n torch::Tensor scalar_feat,\n torch::Tensor vector_feat,\n torch::Tensor scalar_weight,\n torch::Tensor scalar_bias,\n torch::Tensor vector_weight,\n torch::Tensor gate_weight,\n torch::Tensor gate_bias\n) {\n const int batch_size = scalar_feat.size(0);\n const int num_nodes = scalar_feat.size(1);\n const int scalar_in = scalar_feat.size(2);\n const int vector_in = vector_feat.size(2);\n const int scalar_out = scalar_weight.size(0);\n const int vector_out = vector_weight.size(0);\n const int combined_dim = scalar_in + vector_in;\n \n const int total_bn = batch_size * num_nodes;\n const int block_size = 256; // Larger block for more parallelism\n const int grid_size = total_bn;\n \n // Shared memory: combined + v_linear\n const size_t smem_size = (combined_dim + vector_out * 3) * sizeof(float);\n \n // Allocate outputs\n auto s_out = torch::empty({batch_size, num_nodes, scalar_out}, scalar_feat.options());\n auto v_out = torch::empty({batch_size, num_nodes, vector_out, 3}, scalar_feat.options());\n \n se3_fused_kernel<<<grid_size, block_size, smem_size>>>(\n scalar_feat.data_ptr<float>(),\n vector_feat.data_ptr<float>(),\n scalar_weight.data_ptr<float>(),\n scalar_bias.data_ptr<float>(),\n vector_weight.data_ptr<float>(),\n gate_weight.data_ptr<float>(),\n gate_bias.data_ptr<float>(),\n s_out.data_ptr<float>(),\n v_out.data_ptr<float>(),\n batch_size, num_nodes, scalar_in, vector_in, scalar_out, vector_out, combined_dim\n );\n \n return std::make_tuple(s_out, v_out);\n}\n\"\"\"\n\ncpp_source = \"\"\"\nstd::tuple<torch::Tensor, torch::Tensor> se3_forward_cuda(\n torch::Tensor scalar_feat,\n torch::Tensor vector_feat,\n torch::Tensor scalar_weight,\n torch::Tensor scalar_bias,\n torch::Tensor vector_weight,\n torch::Tensor gate_weight,\n torch::Tensor gate_bias\n);\n\"\"\"\n\nse3_cuda = load_inline(\n name='se3_cuda_v10',\n cuda_sources=cuda_source,\n cpp_sources=cpp_source,\n functions=['se3_forward_cuda'],\n verbose=False,\n extra_cuda_cflags=['-O3', '--use_fast_math', '-Xptxas=-v']\n)\n\nclass ModelNew(nn.Module):\n def __init__(self, scalar_in, scalar_out, vector_in, vector_out):\n super().__init__()\n self.scalar_in = scalar_in\n self.scalar_out = scalar_out\n self.vector_in = vector_in\n self.vector_out = vector_out\n \n self.scalar_linear = nn.Linear(scalar_in + vector_in, scalar_out)\n self.vector_weight = nn.Parameter(torch.randn(vector_out, vector_in))\n nn.init.xavier_uniform_(self.vector_weight)\n self.vector_gate = nn.Linear(scalar_in + vector_in, vector_out)\n \n def forward(self, scalar_feat: torch.Tensor, vector_feat: torch.Tensor) -> tuple:\n scalar_feat = scalar_feat.contiguous().float()\n vector_feat = vector_feat.contiguous().float()\n \n scalar_weight = self.scalar_linear.weight.contiguous().float()\n scalar_bias = self.scalar_linear.bias.contiguous().float()\n vector_weight = self.vector_weight.contiguous().float()\n gate_weight = self.vector_gate.weight.contiguous().float()\n gate_bias = self.vector_gate.bias.contiguous().float()\n \n s_out, v_out = se3_cuda.se3_forward_cuda(\n scalar_feat, vector_feat,\n scalar_weight, scalar_bias,\n vector_weight, gate_weight, gate_bias\n )\n \n return s_out, v_out" }
result ← profile_kernel (ok)
okprofile_kernel profile_kernel PASSED: profiling complete. === Kernel Profile Summary === --- Kernel Breakdown (by GPU time) --- #1: aten::empty 22.0μs (37%) calls=1 #2: aten::to 14.0μs (24%) calls=1 #3: aten::empty 5.0μs (8%) calls=1 #4: aten::to 3.0μs (5%) calls=1 #5: aten::to 3.0μs (5%) calls=1 ... +4 more kernels --- Timing --- GPU time: 20.64 μs [↑0.4μs REGRESSED] --- Memory Bandwidth --- DRAM BW: 24.2/3350 GB/s (0.7%) read=24.2 write=0.0 GB/s Hit rates: L2=85.6% --- Compute Throughput --- Pipe util: FMA=3.2%, Tensor=0.1% --- Roofline Analysis --- Ridge point (FP32): 20.00 FLOPs/byte Classification: UNKNOWN --- Occupancy --- Achieved: 80.6% [↑37.7% ok] Eligible warps/cycle: 0.18 WARNING: <1 eligible warp/cycle = latency-bound, needs more parallelism Launch: regs/thread=32, smem/blk=1536B, block=256, grid=1024 --- Memory Access Quality --- Global ld coalescing: 17.38 sectors/req (17.4x wasted BW) --- Warp Stall Reasons (% of issue cycles) --- long_scoreboard 2236.4% #################### mio_throttle 557.9% #################### short_scoreboard 342.3% #################### --- Optimization Hints --- -> 2236% stalls: global memory latency (waiting for DRAM/L2). + sectors/req=17.4 -> uncoalesced global loads, restructure access pattern or use __ldg Try shared-memory tiling, prefetching, or reducing working set. -> Global load coalescing=17.4x (ideal=1.0) -> 17x wasted DRAM BW. Make per-warp accesses contiguous. -> Low eligible warps + low BW% + low compute% = LATENCY-BOUND. Need more parallelism (larger grid, more ILP, prefetching). --- Delta vs Previous Iteration --- GPU time: 20.29→20.64μs (↑0.35) REGRESSED Occupancy: 42.94→80.60% (↑37.66) ok Eligible warps/cyc: 0.12→0.18 (↑0.07) ok L2 hit%: 87.19→85.63% (↓1.57) REGRESSED
turn 11 · 1 tool call(s) · 349.8s turn · 20.9s LLM · tokens in=26,772 · out=2,161 · total=28,933 · 9,804 chars (click to expand)
turn 11349.8s turn · 20.9s LLM · 328.9s tools · tokens in=26,772 · out=2,161 · total=28,933
reasoning
Occupancy improved to 80.6%, but still having issues with memory coalescing and latency. The global load coalescing is 17.4x wasted bandwidth. Let me try a different approach - use warp-level parallelism and better data layout to improve coalescing. The problem is that the weight matrices are accessed in a strided manner (each thread accessing a different row). Let me try loading the combined vector into registers and using a different parallelization strategy. Also, I could use __ldg for read-only data to use the read-only cache.
assistantLet me try a different approach using warp-level parallelism and better cache utilization:
call → compile_kernel
callcompile_kernel { "kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\ncuda_source = \"\"\"\n#include <torch/extension.h>\n#include <cuda.h>\n#include <cuda_runtime.h>\n#include <cmath>\n\n// Optimized sigmoid\n__device__ __forceinline__ float fast_sigmoid(float x) {\n return 1.0f / (1.0f + expf(-x));\n}\n\n// Use __ldg for read-only cache\n__device__ __forceinline__ float ldg(const float* ptr) {\n return __ldg(ptr);\n}\n\n// Fused kernel optimized for coalescing and cache\n// Each warp handles one (b, n) pair, working on outputs cooperatively\n__global__ void se3_warp_kernel(\n const float* __restrict__ scalar_feat, // (B, N, scalar_in)\n const float* __restrict__ vector_feat, // (B, N, vector_in, 3)\n const float* __restrict__ scalar_weight, // (scalar_out, combined_dim)\n const float* __restrict__ scalar_bias, // (scalar_out,)\n const float* __restrict__ vector_weight, // (vector_out, vector_in)\n const float* __restrict__ gate_weight, // (vector_out, combined_dim)\n const float* __restrict__ gate_bias, // (vector_out,)\n float* __restrict__ s_out, // (B, N, scalar_out)\n float* __restrict__ v_out, // (B, N, vector_out, 3)\n int batch_size, int num_nodes, int scalar_in, int vector_in, \n int scalar_out, int vector_out, int combined_dim\n) {\n const int warp_size = 32;\n const int warp_id = threadIdx.x / warp_size;\n const int lane_id = threadIdx.x % warp_size;\n const int warps_per_block = blockDim.x / warp_size;\n const int global_warp_id = blockIdx.x * warps_per_block + warp_id;\n const int total_warps = batch_size * num_nodes;\n \n if (global_warp_id >= total_warps) return;\n \n const int b = global_warp_id / num_nodes;\n const int n = global_warp_id % num_nodes;\n \n // Input offsets\n const int scalar_offset = b * num_nodes * scalar_in + n * scalar_in;\n const int vector_offset = b * num_nodes * vector_in * 3 + n * vector_in * 3;\n \n // Output offsets\n const int s_out_offset = b * num_nodes * scalar_out + n * scalar_out;\n const int v_out_offset = b * num_nodes * vector_out * 3 + n * vector_out * 3;\n \n // Shared memory for combined features\n extern __shared__ float smem[];\n float* combined = smem; // combined_dim floats per warp\n \n // Each lane loads part of scalar features (coalesced across warp)\n for (int i = lane_id; i < scalar_in; i += warp_size) {\n combined[i] = scalar_feat[scalar_offset + i];\n }\n \n // Compute vector norms - each lane handles multiple vectors\n for (int v = lane_id; v < vector_in; v += warp_size) {\n float vx = vector_feat[vector_offset + v * 3 + 0];\n float vy = vector_feat[vector_offset + v * 3 + 1];\n float vz = vector_feat[vector_offset + v * 3 + 2];\n combined[scalar_in + v] = sqrtf(vx*vx + vy*vy + vz*vz);\n }\n \n __syncwarp();\n \n // Compute scalar linear output\n // Each lane handles a subset of output features\n for (int o = lane_id; o < scalar_out; o += warp_size) {\n float sum = scalar_bias[o];\n \n // Each lane reads a column of weight (coalesced within warp)\n for (int i = 0; i < combined_dim; i++) {\n sum = fmaf(combined[i], ldg(&scalar_weight[o * combined_dim + i]), sum);\n }\n s_out[s_out_offset + o] = sum;\n }\n \n // Compute vector linear and gating\n // Each lane handles multiple (output_idx, coord) pairs\n const int total_v_out = vector_out * 3;\n for (int idx = lane_id; idx < total_v_out; idx += warp_size) {\n const int o = idx / 3;\n const int c = idx % 3;\n \n // Vector linear: sum over input vectors\n float v_sum = 0.0f;\n for (int i = 0; i < vector_in; i++) {\n v_sum = fmaf(ldg(&vector_weight[o * vector_in + i]), \n vector_feat[vector_offset + i * 3 + c], v_sum);\n }\n \n // Compute gate\n float gate_sum = gate_bias[o];\n for (int i = 0; i < combined_dim; i++) {\n gate_sum = fmaf(combined[i], ldg(&gate_weight[o * combined_dim + i]), gate_sum);\n }\n float gate = fast_sigmoid(gate_sum);\n \n v_out[v_out_offset + o * 3 + c] = gate * v_sum;\n }\n}\n\n// Host function\nstd::tuple<torch::Tensor, torch::Tensor> se3_forward_cuda(\n torch::Tensor scalar_feat,\n torch::Tensor vector_feat,\n torch::Tensor scalar_weight,\n torch::Tensor scalar_bias,\n torch::Tensor vector_weight,\n torch::Tensor gate_weight,\n torch::Tensor gate_bias\n) {\n const int batch_size = scalar_feat.size(0);\n const int num_nodes = scalar_feat.size(1);\n const int scalar_in = scalar_feat.size(2);\n const int vector_in = vector_feat.size(2);\n const int scalar_out = scalar_weight.size(0);\n const int vector_out = vector_weight.size(0);\n const int combined_dim = scalar_in + vector_in;\n \n const int warp_size = 32;\n const int warps_per_block = 8; // 256 threads per block = 8 warps\n const int block_size = warps_per_block * warp_size;\n const int total_warps = batch_size * num_nodes;\n const int grid_size = (total_warps + warps_per_block - 1) / warps_per_block;\n \n // Shared memory: combined features per warp\n const size_t smem_size = combined_dim * sizeof(float);\n \n // Allocate outputs\n auto s_out = torch::empty({batch_size, num_nodes, scalar_out}, scalar_feat.options());\n auto v_out = torch::empty({batch_size, num_nodes, vector_out, 3}, scalar_feat.options());\n \n se3_warp_kernel<<<grid_size, block_size, smem_size>>>(\n scalar_feat.data_ptr<float>(),\n vector_feat.data_ptr<float>(),\n scalar_weight.data_ptr<float>(),\n scalar_bias.data_ptr<float>(),\n vector_weight.data_ptr<float>(),\n gate_weight.data_ptr<float>(),\n gate_bias.data_ptr<float>(),\n s_out.data_ptr<float>(),\n v_out.data_ptr<float>(),\n batch_size, num_nodes, scalar_in, vector_in, scalar_out, vector_out, combined_dim\n );\n \n return std::make_tuple(s_out, v_out);\n}\n\"\"\"\n\ncpp_source = \"\"\"\nstd::tuple<torch::Tensor, torch::Tensor> se3_forward_cuda(\n torch::Tensor scalar_feat,\n torch::Tensor vector_feat,\n torch::Tensor scalar_weight,\n torch::Tensor scalar_bias,\n torch::Tensor vector_weight,\n torch::Tensor gate_weight,\n torch::Tensor gate_bias\n);\n\"\"\"\n\nse3_cuda = load_inline(\n name='se3_cuda_v11',\n cuda_sources=cuda_source,\n cpp_sources=cpp_source,\n functions=['se3_forward_cuda'],\n verbose=False,\n extra_cuda_cflags=['-O3', '--use_fast_math', '-Xptxas=-v']\n)\n\nclass ModelNew(nn.Module):\n def __init__(self, scalar_in, scalar_out, vector_in, vector_out):\n super().__init__()\n self.scalar_in = scalar_in\n self.scalar_out = scalar_out\n self.vector_in = vector_in\n self.vector_out = vector_out\n \n self.scalar_linear = nn.Linear(scalar_in + vector_in, scalar_out)\n self.vector_weight = nn.Parameter(torch.randn(vector_out, vector_in))\n nn.init.xavier_uniform_(self.vector_weight)\n self.vector_gate = nn.Linear(scalar_in + vector_in, vector_out)\n \n def forward(self, scalar_feat: torch.Tensor, vector_feat: torch.Tensor) -> tuple:\n scalar_feat = scalar_feat.contiguous().float()\n vector_feat = vector_feat.contiguous().float()\n \n scalar_weight = self.scalar_linear.weight.contiguous().float()\n scalar_bias = self.scalar_linear.bias.contiguous().float()\n vector_weight = self.vector_weight.contiguous().float()\n gate_weight = self.vector_gate.weight.contiguous().float()\n gate_bias = self.vector_gate.bias.contiguous().float()\n \n s_out, v_out = se3_cuda.se3_forward_cuda(\n scalar_feat, vector_feat,\n scalar_weight, scalar_bias,\n vector_weight, gate_weight, gate_bias\n )\n \n return s_out, v_out" }
result ← compile_kernel (ok)
okcompile_kernel compile_kernel PASSED: kernel compiled without errors.
turn 12 · 1 tool call(s) · 382.0s turn · 18.0s LLM · tokens in=28,862 · out=2,123 · total=30,985 · 9,905 chars (click to expand)
turn 12382.0s turn · 18.0s LLM · 364.0s tools · tokens in=28,862 · out=2,123 · total=30,985
reasoning
The kernel is already correct and seems to be performing reasonably well. Let me check the correctness of this latest version and then consider if I should submit or try one more optimization. Looking at the profile from before: - GPU time: ~20μs - Memory coalescing still shows 17x wasted bandwidth - But the overall timing seems good Let me run correctness on this latest version first, then decide whether to submit or try one more optimization.
call → run_correctness
callrun_correctness { "kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\ncuda_source = \"\"\"\n#include <torch/extension.h>\n#include <cuda.h>\n#include <cuda_runtime.h>\n#include <cmath>\n\n// Optimized sigmoid\n__device__ __forceinline__ float fast_sigmoid(float x) {\n return 1.0f / (1.0f + expf(-x));\n}\n\n// Use __ldg for read-only cache\n__device__ __forceinline__ float ldg(const float* ptr) {\n return __ldg(ptr);\n}\n\n// Fused kernel optimized for coalescing and cache\n// Each warp handles one (b, n) pair, working on outputs cooperatively\n__global__ void se3_warp_kernel(\n const float* __restrict__ scalar_feat, // (B, N, scalar_in)\n const float* __restrict__ vector_feat, // (B, N, vector_in, 3)\n const float* __restrict__ scalar_weight, // (scalar_out, combined_dim)\n const float* __restrict__ scalar_bias, // (scalar_out,)\n const float* __restrict__ vector_weight, // (vector_out, vector_in)\n const float* __restrict__ gate_weight, // (vector_out, combined_dim)\n const float* __restrict__ gate_bias, // (vector_out,)\n float* __restrict__ s_out, // (B, N, scalar_out)\n float* __restrict__ v_out, // (B, N, vector_out, 3)\n int batch_size, int num_nodes, int scalar_in, int vector_in, \n int scalar_out, int vector_out, int combined_dim\n) {\n const int warp_size = 32;\n const int warp_id = threadIdx.x / warp_size;\n const int lane_id = threadIdx.x % warp_size;\n const int warps_per_block = blockDim.x / warp_size;\n const int global_warp_id = blockIdx.x * warps_per_block + warp_id;\n const int total_warps = batch_size * num_nodes;\n \n if (global_warp_id >= total_warps) return;\n \n const int b = global_warp_id / num_nodes;\n const int n = global_warp_id % num_nodes;\n \n // Input offsets\n const int scalar_offset = b * num_nodes * scalar_in + n * scalar_in;\n const int vector_offset = b * num_nodes * vector_in * 3 + n * vector_in * 3;\n \n // Output offsets\n const int s_out_offset = b * num_nodes * scalar_out + n * scalar_out;\n const int v_out_offset = b * num_nodes * vector_out * 3 + n * vector_out * 3;\n \n // Shared memory for combined features\n extern __shared__ float smem[];\n float* combined = smem; // combined_dim floats per warp\n \n // Each lane loads part of scalar features (coalesced across warp)\n for (int i = lane_id; i < scalar_in; i += warp_size) {\n combined[i] = scalar_feat[scalar_offset + i];\n }\n \n // Compute vector norms - each lane handles multiple vectors\n for (int v = lane_id; v < vector_in; v += warp_size) {\n float vx = vector_feat[vector_offset + v * 3 + 0];\n float vy = vector_feat[vector_offset + v * 3 + 1];\n float vz = vector_feat[vector_offset + v * 3 + 2];\n combined[scalar_in + v] = sqrtf(vx*vx + vy*vy + vz*vz);\n }\n \n __syncwarp();\n \n // Compute scalar linear output\n // Each lane handles a subset of output features\n for (int o = lane_id; o < scalar_out; o += warp_size) {\n float sum = scalar_bias[o];\n \n // Each lane reads a column of weight (coalesced within warp)\n for (int i = 0; i < combined_dim; i++) {\n sum = fmaf(combined[i], ldg(&scalar_weight[o * combined_dim + i]), sum);\n }\n s_out[s_out_offset + o] = sum;\n }\n \n // Compute vector linear and gating\n // Each lane handles multiple (output_idx, coord) pairs\n const int total_v_out = vector_out * 3;\n for (int idx = lane_id; idx < total_v_out; idx += warp_size) {\n const int o = idx / 3;\n const int c = idx % 3;\n \n // Vector linear: sum over input vectors\n float v_sum = 0.0f;\n for (int i = 0; i < vector_in; i++) {\n v_sum = fmaf(ldg(&vector_weight[o * vector_in + i]), \n vector_feat[vector_offset + i * 3 + c], v_sum);\n }\n \n // Compute gate\n float gate_sum = gate_bias[o];\n for (int i = 0; i < combined_dim; i++) {\n gate_sum = fmaf(combined[i], ldg(&gate_weight[o * combined_dim + i]), gate_sum);\n }\n float gate = fast_sigmoid(gate_sum);\n \n v_out[v_out_offset + o * 3 + c] = gate * v_sum;\n }\n}\n\n// Host function\nstd::tuple<torch::Tensor, torch::Tensor> se3_forward_cuda(\n torch::Tensor scalar_feat,\n torch::Tensor vector_feat,\n torch::Tensor scalar_weight,\n torch::Tensor scalar_bias,\n torch::Tensor vector_weight,\n torch::Tensor gate_weight,\n torch::Tensor gate_bias\n) {\n const int batch_size = scalar_feat.size(0);\n const int num_nodes = scalar_feat.size(1);\n const int scalar_in = scalar_feat.size(2);\n const int vector_in = vector_feat.size(2);\n const int scalar_out = scalar_weight.size(0);\n const int vector_out = vector_weight.size(0);\n const int combined_dim = scalar_in + vector_in;\n \n const int warp_size = 32;\n const int warps_per_block = 8; // 256 threads per block = 8 warps\n const int block_size = warps_per_block * warp_size;\n const int total_warps = batch_size * num_nodes;\n const int grid_size = (total_warps + warps_per_block - 1) / warps_per_block;\n \n // Shared memory: combined features per warp\n const size_t smem_size = combined_dim * sizeof(float);\n \n // Allocate outputs\n auto s_out = torch::empty({batch_size, num_nodes, scalar_out}, scalar_feat.options());\n auto v_out = torch::empty({batch_size, num_nodes, vector_out, 3}, scalar_feat.options());\n \n se3_warp_kernel<<<grid_size, block_size, smem_size>>>(\n scalar_feat.data_ptr<float>(),\n vector_feat.data_ptr<float>(),\n scalar_weight.data_ptr<float>(),\n scalar_bias.data_ptr<float>(),\n vector_weight.data_ptr<float>(),\n gate_weight.data_ptr<float>(),\n gate_bias.data_ptr<float>(),\n s_out.data_ptr<float>(),\n v_out.data_ptr<float>(),\n batch_size, num_nodes, scalar_in, vector_in, scalar_out, vector_out, combined_dim\n );\n \n return std::make_tuple(s_out, v_out);\n}\n\"\"\"\n\ncpp_source = \"\"\"\nstd::tuple<torch::Tensor, torch::Tensor> se3_forward_cuda(\n torch::Tensor scalar_feat,\n torch::Tensor vector_feat,\n torch::Tensor scalar_weight,\n torch::Tensor scalar_bias,\n torch::Tensor vector_weight,\n torch::Tensor gate_weight,\n torch::Tensor gate_bias\n);\n\"\"\"\n\nse3_cuda = load_inline(\n name='se3_cuda_v12',\n cuda_sources=cuda_source,\n cpp_sources=cpp_source,\n functions=['se3_forward_cuda'],\n verbose=False,\n extra_cuda_cflags=['-O3', '--use_fast_math', '-Xptxas=-v']\n)\n\nclass ModelNew(nn.Module):\n def __init__(self, scalar_in, scalar_out, vector_in, vector_out):\n super().__init__()\n self.scalar_in = scalar_in\n self.scalar_out = scalar_out\n self.vector_in = vector_in\n self.vector_out = vector_out\n \n self.scalar_linear = nn.Linear(scalar_in + vector_in, scalar_out)\n self.vector_weight = nn.Parameter(torch.randn(vector_out, vector_in))\n nn.init.xavier_uniform_(self.vector_weight)\n self.vector_gate = nn.Linear(scalar_in + vector_in, vector_out)\n \n def forward(self, scalar_feat: torch.Tensor, vector_feat: torch.Tensor) -> tuple:\n scalar_feat = scalar_feat.contiguous().float()\n vector_feat = vector_feat.contiguous().float()\n \n scalar_weight = self.scalar_linear.weight.contiguous().float()\n scalar_bias = self.scalar_linear.bias.contiguous().float()\n vector_weight = self.vector_weight.contiguous().float()\n gate_weight = self.vector_gate.weight.contiguous().float()\n gate_bias = self.vector_gate.bias.contiguous().float()\n \n s_out, v_out = se3_cuda.se3_forward_cuda(\n scalar_feat, vector_feat,\n scalar_weight, scalar_bias,\n vector_weight, gate_weight, gate_bias\n )\n \n return s_out, v_out" }
result ← run_correctness (fail)
failrun_correctness run_correctness FAILED: (0 / 3) trials did not all match. correctness_issue: Output mismatch max_difference: ['3.472298', '1.508341', '3.242343', '1.597288', '3.823638', '1.935500'] avg_difference: ['0.551678', '0.101511', '0.550287', '0.101203', '0.551363', '0.100641']
turn 13 · FINAL · 1 tool call(s) · 525.9s turn · 15.3s LLM · tokens in=31,047 · out=1,813 · total=32,860 · 8,645 chars (click to expand)
turn 13525.9s turn · 15.3s LLM · 510.6s tools · tokens in=31,047 · out=1,813 · total=32,860 · FINAL
reasoning
The warp-based kernel has correctness issues. Let me go back to the last working kernel (the fused kernel with 256 threads per block) and submit that one since it passed correctness and showed good performance improvement. Let me submit the working version.
assistantThe warp kernel has correctness issues. Let me submit the last working fused kernel which passed correctness and showed significant improvement:
call → submit_kernel
callsubmit_kernel { "kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\ncuda_source = \"\"\"\n#include <torch/extension.h>\n#include <cuda.h>\n#include <cuda_runtime.h>\n#include <cmath>\n\n// Optimized sigmoid\n__device__ __forceinline__ float fast_sigmoid(float x) {\n return 1.0f / (1.0f + expf(-x));\n}\n\n// Fused kernel with better parallelism\n__global__ void se3_fused_kernel(\n const float* __restrict__ scalar_feat,\n const float* __restrict__ vector_feat,\n const float* __restrict__ scalar_weight,\n const float* __restrict__ scalar_bias,\n const float* __restrict__ vector_weight,\n const float* __restrict__ gate_weight,\n const float* __restrict__ gate_bias,\n float* __restrict__ s_out,\n float* __restrict__ v_out,\n int batch_size, int num_nodes, int scalar_in, int vector_in, \n int scalar_out, int vector_out, int combined_dim\n) {\n const int bn_idx = blockIdx.x;\n const int total_bn = batch_size * num_nodes;\n if (bn_idx >= total_bn) return;\n \n const int b = bn_idx / num_nodes;\n const int n = bn_idx % num_nodes;\n const int tid = threadIdx.x;\n const int block_dim = blockDim.x;\n \n const int scalar_offset = b * num_nodes * scalar_in + n * scalar_in;\n const int vector_offset = b * num_nodes * vector_in * 3 + n * vector_in * 3;\n const int s_out_offset = b * num_nodes * scalar_out + n * scalar_out;\n const int v_out_offset = b * num_nodes * vector_out * 3 + n * vector_out * 3;\n \n extern __shared__ float smem[];\n float* combined = smem;\n float* v_linear = smem + combined_dim;\n \n for (int i = tid; i < scalar_in; i += block_dim) {\n combined[i] = scalar_feat[scalar_offset + i];\n }\n \n for (int v = tid; v < vector_in; v += block_dim) {\n const float* v_ptr = vector_feat + vector_offset + v * 3;\n float vx = v_ptr[0], vy = v_ptr[1], vz = v_ptr[2];\n combined[scalar_in + v] = sqrtf(vx*vx + vy*vy + vz*vz);\n }\n \n __syncthreads();\n \n for (int o = tid; o < scalar_out; o += block_dim) {\n float sum = scalar_bias[o];\n const float* w_row = scalar_weight + o * combined_dim;\n #pragma unroll 8\n for (int i = 0; i < combined_dim; i++) {\n sum = fmaf(combined[i], w_row[i], sum);\n }\n s_out[s_out_offset + o] = sum;\n }\n \n const int total_v_out = vector_out * 3;\n for (int idx = tid; idx < total_v_out; idx += block_dim) {\n const int o = idx / 3;\n const int c = idx % 3;\n float sum = 0.0f;\n const float* w_row = vector_weight + o * vector_in;\n #pragma unroll 4\n for (int i = 0; i < vector_in; i++) {\n sum = fmaf(w_row[i], vector_feat[vector_offset + i * 3 + c], sum);\n }\n v_linear[o * 3 + c] = sum;\n }\n \n __syncthreads();\n \n for (int idx = tid; idx < total_v_out; idx += block_dim) {\n const int o = idx / 3;\n const int c = idx % 3;\n float gate_sum = gate_bias[o];\n const float* g_row = gate_weight + o * combined_dim;\n #pragma unroll 8\n for (int i = 0; i < combined_dim; i++) {\n gate_sum = fmaf(combined[i], g_row[i], gate_sum);\n }\n float gate = fast_sigmoid(gate_sum);\n v_out[v_out_offset + o * 3 + c] = gate * v_linear[o * 3 + c];\n }\n}\n\nstd::tuple<torch::Tensor, torch::Tensor> se3_forward_cuda(\n torch::Tensor scalar_feat,\n torch::Tensor vector_feat,\n torch::Tensor scalar_weight,\n torch::Tensor scalar_bias,\n torch::Tensor vector_weight,\n torch::Tensor gate_weight,\n torch::Tensor gate_bias\n) {\n const int batch_size = scalar_feat.size(0);\n const int num_nodes = scalar_feat.size(1);\n const int scalar_in = scalar_feat.size(2);\n const int vector_in = vector_feat.size(2);\n const int scalar_out = scalar_weight.size(0);\n const int vector_out = vector_weight.size(0);\n const int combined_dim = scalar_in + vector_in;\n \n const int total_bn = batch_size * num_nodes;\n const int block_size = 256;\n const int grid_size = total_bn;\n const size_t smem_size = (combined_dim + vector_out * 3) * sizeof(float);\n \n auto s_out = torch::empty({batch_size, num_nodes, scalar_out}, scalar_feat.options());\n auto v_out = torch::empty({batch_size, num_nodes, vector_out, 3}, scalar_feat.options());\n \n se3_fused_kernel<<<grid_size, block_size, smem_size>>>(\n scalar_feat.data_ptr<float>(),\n vector_feat.data_ptr<float>(),\n scalar_weight.data_ptr<float>(),\n scalar_bias.data_ptr<float>(),\n vector_weight.data_ptr<float>(),\n gate_weight.data_ptr<float>(),\n gate_bias.data_ptr<float>(),\n s_out.data_ptr<float>(),\n v_out.data_ptr<float>(),\n batch_size, num_nodes, scalar_in, vector_in, scalar_out, vector_out, combined_dim\n );\n \n return std::make_tuple(s_out, v_out);\n}\n\"\"\"\n\ncpp_source = \"\"\"\nstd::tuple<torch::Tensor, torch::Tensor> se3_forward_cuda(\n torch::Tensor scalar_feat,\n torch::Tensor vector_feat,\n torch::Tensor scalar_weight,\n torch::Tensor scalar_bias,\n torch::Tensor vector_weight,\n torch::Tensor gate_weight,\n torch::Tensor gate_bias\n);\n\"\"\"\n\nse3_cuda = load_inline(\n name='se3_cuda_final',\n cuda_sources=cuda_source,\n cpp_sources=cpp_source,\n functions=['se3_forward_cuda'],\n verbose=False,\n extra_cuda_cflags=['-O3', '--use_fast_math']\n)\n\nclass ModelNew(nn.Module):\n def __init__(self, scalar_in, scalar_out, vector_in, vector_out):\n super().__init__()\n self.scalar_in = scalar_in\n self.scalar_out = scalar_out\n self.vector_in = vector_in\n self.vector_out = vector_out\n \n self.scalar_linear = nn.Linear(scalar_in + vector_in, scalar_out)\n self.vector_weight = nn.Parameter(torch.randn(vector_out, vector_in))\n nn.init.xavier_uniform_(self.vector_weight)\n self.vector_gate = nn.Linear(scalar_in + vector_in, vector_out)\n \n def forward(self, scalar_feat: torch.Tensor, vector_feat: torch.Tensor) -> tuple:\n scalar_feat = scalar_feat.contiguous().float()\n vector_feat = vector_feat.contiguous().float()\n \n scalar_weight = self.scalar_linear.weight.contiguous().float()\n scalar_bias = self.scalar_linear.bias.contiguous().float()\n vector_weight = self.vector_weight.contiguous().float()\n gate_weight = self.vector_gate.weight.contiguous().float()\n gate_bias = self.vector_gate.bias.contiguous().float()\n \n s_out, v_out = se3_cuda.se3_forward_cuda(\n scalar_feat, vector_feat,\n scalar_weight, scalar_bias,\n vector_weight, gate_weight, gate_bias\n )\n \n return s_out, v_out" }
result ← submit_kernel (ok)
oksubmit_kernel submit_kernel PASSED: (3 / 3) correctness trials all passed. Kernel runtime: 0.06 μs Runtime stats: mean=0.06μs median=?μs std=0.09μs Numerical precision: max_abs_err=7.15e-07 mean_abs_err=4.16e-08 max_rel_err=3.50e-02 Memory: 33.93 MB peak (ref: 34.55 MB, ratio: 0.9819x) Kernel launches: 9 (ref: 51, fusion ratio: 5.6667) SOL score: 0.0073
final submitted kernel (191 lines, 6,718 chars) — full source, untruncated
import torch
import torch.nn as nn
from torch.utils.cpp_extension import load_inline

cuda_source = """
#include <torch/extension.h>
#include <cuda.h>
#include <cuda_runtime.h>
#include <cmath>

// Optimized sigmoid
__device__ __forceinline__ float fast_sigmoid(float x) {
    return 1.0f / (1.0f + expf(-x));
}

// Fused kernel with better parallelism
__global__ void se3_fused_kernel(
    const float* __restrict__ scalar_feat,
    const float* __restrict__ vector_feat,
    const float* __restrict__ scalar_weight,
    const float* __restrict__ scalar_bias,
    const float* __restrict__ vector_weight,
    const float* __restrict__ gate_weight,
    const float* __restrict__ gate_bias,
    float* __restrict__ s_out,
    float* __restrict__ v_out,
    int batch_size, int num_nodes, int scalar_in, int vector_in, 
    int scalar_out, int vector_out, int combined_dim
) {
    const int bn_idx = blockIdx.x;
    const int total_bn = batch_size * num_nodes;
    if (bn_idx >= total_bn) return;
    
    const int b = bn_idx / num_nodes;
    const int n = bn_idx % num_nodes;
    const int tid = threadIdx.x;
    const int block_dim = blockDim.x;
    
    const int scalar_offset = b * num_nodes * scalar_in + n * scalar_in;
    const int vector_offset = b * num_nodes * vector_in * 3 + n * vector_in * 3;
    const int s_out_offset = b * num_nodes * scalar_out + n * scalar_out;
    const int v_out_offset = b * num_nodes * vector_out * 3 + n * vector_out * 3;
    
    extern __shared__ float smem[];
    float* combined = smem;
    float* v_linear = smem + combined_dim;
    
    for (int i = tid; i < scalar_in; i += block_dim) {
        combined[i] = scalar_feat[scalar_offset + i];
    }
    
    for (int v = tid; v < vector_in; v += block_dim) {
        const float* v_ptr = vector_feat + vector_offset + v * 3;
        float vx = v_ptr[0], vy = v_ptr[1], vz = v_ptr[2];
        combined[scalar_in + v] = sqrtf(vx*vx + vy*vy + vz*vz);
    }
    
    __syncthreads();
    
    for (int o = tid; o < scalar_out; o += block_dim) {
        float sum = scalar_bias[o];
        const float* w_row = scalar_weight + o * combined_dim;
        #pragma unroll 8
        for (int i = 0; i < combined_dim; i++) {
            sum = fmaf(combined[i], w_row[i], sum);
        }
        s_out[s_out_offset + o] = sum;
    }
    
    const int total_v_out = vector_out * 3;
    for (int idx = tid; idx < total_v_out; idx += block_dim) {
        const int o = idx / 3;
        const int c = idx % 3;
        float sum = 0.0f;
        const float* w_row = vector_weight + o * vector_in;
        #pragma unroll 4
        for (int i = 0; i < vector_in; i++) {
            sum = fmaf(w_row[i], vector_feat[vector_offset + i * 3 + c], sum);
        }
        v_linear[o * 3 + c] = sum;
    }
    
    __syncthreads();
    
    for (int idx = tid; idx < total_v_out; idx += block_dim) {
        const int o = idx / 3;
        const int c = idx % 3;
        float gate_sum = gate_bias[o];
        const float* g_row = gate_weight + o * combined_dim;
        #pragma unroll 8
        for (int i = 0; i < combined_dim; i++) {
            gate_sum = fmaf(combined[i], g_row[i], gate_sum);
        }
        float gate = fast_sigmoid(gate_sum);
        v_out[v_out_offset + o * 3 + c] = gate * v_linear[o * 3 + c];
    }
}

std::tuple<torch::Tensor, torch::Tensor> se3_forward_cuda(
    torch::Tensor scalar_feat,
    torch::Tensor vector_feat,
    torch::Tensor scalar_weight,
    torch::Tensor scalar_bias,
    torch::Tensor vector_weight,
    torch::Tensor gate_weight,
    torch::Tensor gate_bias
) {
    const int batch_size = scalar_feat.size(0);
    const int num_nodes = scalar_feat.size(1);
    const int scalar_in = scalar_feat.size(2);
    const int vector_in = vector_feat.size(2);
    const int scalar_out = scalar_weight.size(0);
    const int vector_out = vector_weight.size(0);
    const int combined_dim = scalar_in + vector_in;
    
    const int total_bn = batch_size * num_nodes;
    const int block_size = 256;
    const int grid_size = total_bn;
    const size_t smem_size = (combined_dim + vector_out * 3) * sizeof(float);
    
    auto s_out = torch::empty({batch_size, num_nodes, scalar_out}, scalar_feat.options());
    auto v_out = torch::empty({batch_size, num_nodes, vector_out, 3}, scalar_feat.options());
    
    se3_fused_kernel<<<grid_size, block_size, smem_size>>>(
        scalar_feat.data_ptr<float>(),
        vector_feat.data_ptr<float>(),
        scalar_weight.data_ptr<float>(),
        scalar_bias.data_ptr<float>(),
        vector_weight.data_ptr<float>(),
        gate_weight.data_ptr<float>(),
        gate_bias.data_ptr<float>(),
        s_out.data_ptr<float>(),
        v_out.data_ptr<float>(),
        batch_size, num_nodes, scalar_in, vector_in, scalar_out, vector_out, combined_dim
    );
    
    return std::make_tuple(s_out, v_out);
}
"""

cpp_source = """
std::tuple<torch::Tensor, torch::Tensor> se3_forward_cuda(
    torch::Tensor scalar_feat,
    torch::Tensor vector_feat,
    torch::Tensor scalar_weight,
    torch::Tensor scalar_bias,
    torch::Tensor vector_weight,
    torch::Tensor gate_weight,
    torch::Tensor gate_bias
);
"""

se3_cuda = load_inline(
    name='se3_cuda_final',
    cuda_sources=cuda_source,
    cpp_sources=cpp_source,
    functions=['se3_forward_cuda'],
    verbose=False,
    extra_cuda_cflags=['-O3', '--use_fast_math']
)

class ModelNew(nn.Module):
    def __init__(self, scalar_in, scalar_out, vector_in, vector_out):
        super().__init__()
        self.scalar_in = scalar_in
        self.scalar_out = scalar_out
        self.vector_in = vector_in
        self.vector_out = vector_out
        
        self.scalar_linear = nn.Linear(scalar_in + vector_in, scalar_out)
        self.vector_weight = nn.Parameter(torch.randn(vector_out, vector_in))
        nn.init.xavier_uniform_(self.vector_weight)
        self.vector_gate = nn.Linear(scalar_in + vector_in, vector_out)
    
    def forward(self, scalar_feat: torch.Tensor, vector_feat: torch.Tensor) -> tuple:
        scalar_feat = scalar_feat.contiguous().float()
        vector_feat = vector_feat.contiguous().float()
        
        scalar_weight = self.scalar_linear.weight.contiguous().float()
        scalar_bias = self.scalar_linear.bias.contiguous().float()
        vector_weight = self.vector_weight.contiguous().float()
        gate_weight = self.vector_gate.weight.contiguous().float()
        gate_bias = self.vector_gate.bias.contiguous().float()
        
        s_out, v_out = se3_cuda.se3_forward_cuda(
            scalar_feat, vector_feat,
            scalar_weight, scalar_bias,
            vector_weight, gate_weight, gate_bias
        )
        
        return s_out, v_out