FW-GLM-5-1 · popcorn · pop_l123_all_gpt
correct 5_FlowMatchingProbabilityFlowODE.py
model
FW-GLM-5-1
turns / max
15 / 15
tool calls
15
tokens (total)
278461
wall clock
4471.6s
truncated
no
backend
cuda fp32
variant
popcorn
runtime
1.54 μs
ref runtime
3.08 μs
speedup
2.00x
started
2026-05-11T18:42:22Z
timingkernelbench.timing
kernel runtime
1.54 μs
ref runtime
3.08 μs
speedup
2.00x
kernel mean / median / std
1.54 / — / 5.72e-04 μs
ref mean / median / std
3.08 / — / 0.03 μs
numerical precisioneval_kernel_against_ref
max abs error
2.38e-07
mean abs error
1.79e-08
max rel error
2.34e-06
mean rel error
4.92e-08
gpu memoryextended_metrics.measure_memory
kernel peak
33.76 MB
ref peak
33.78 MB
kernel / ref
1.00x
kernel launches / fusiontorch.profiler
kernel launches
2
ref launches
737
fusion ratio (ref / kernel)
368.50x
total cuda time
58 μs
SOL (speed-of-light)nsight_hardware_counters
SOL score (0–1)
1.000e-04
dram util %
0.0%
compute util %
0.0%
bottleneck
unknown
dominant pipe
None
arithmetic intensity
—
ridge point
20.00
roofline / occupancynsight_hardware_counters
dram bandwidth
0.28 GB/s
dram util %
0.0%
fp32 tflops
—
fp32 util %
—
fp16 tflops
—
occupancy %
12.5%
bottleneck
unknown
dominant pipe %
—
arithmetic intensity
—
ridge point
20.00
L1 hit %
—
L2 hit %
98.2%
ld sectors / req
21.26
st sectors / req
—
regs / thread
32
smem / block
3712 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
3386.3%
short_scoreboard
89.7%
reference PyTorch source (the prompt the agent sees)
import torch
import torch.nn as nn

# Default ModelNew is PyTorch-only. run_and_check: use check_kernel=False with backend=cuda
# until the candidate file contains a real CUDA kernel (see kernel_static_checker).


class Model(nn.Module):
    """
    **Fused probability-flow ODE integration** (flow-matching style) in one ``forward``.

    Models the ODE ``dx/dt = v_θ(x, t)`` on ``t ∈ [0, 1]`` with a learned velocity
    field. A **single fused pass** unrolls **fixed-step Euler** integration for
    ``num_steps`` substeps—typical for **real-time trajectory / action generation**
    where latency is dominated by repeated ``v_θ`` evaluations.

    This is the continuous-time analogue of a rectified-flow / conditional-flow
    sampler: one ``forward`` returns an approximate **x(1)** from **x(0)** without a
    Python loop across separate module calls (fusion target for the integrator +
    field).
    """

    def __init__(self, dim: int, num_steps: int):
        super().__init__()
        assert dim >= 1 and num_steps >= 1
        self.dim = dim
        self.num_steps = num_steps
        self.register_buffer("dt", torch.tensor(1.0 / float(num_steps)))

        self.velocity = nn.Sequential(
            nn.Linear(dim + 1, dim * 4),
            nn.SiLU(),
            nn.Linear(dim * 4, dim * 4),
            nn.SiLU(),
            nn.Linear(dim * 4, dim),
        )

    def forward(self, x0: torch.Tensor) -> torch.Tensor:
        """
        Args:
            x0: (B, dim) initial state at ``t = 0`` (e.g. noise or anchor trajectory).
        Returns:
            (B, dim) approximate state at ``t = 1`` after fused Euler integration.
        """
        B, d = x0.shape
        assert d == self.dim
        x = x0
        dt = self.dt.to(dtype=x0.dtype, device=x0.device)
        for k in range(self.num_steps):
            t = (float(k) + 0.5) / float(self.num_steps)
            t_b = torch.full((B, 1), t, device=x0.device, dtype=x0.dtype)
            inp = torch.cat([x, t_b], dim=-1)
            v = self.velocity(inp)
            x = x + dt * v
        return x


class ModelNew(nn.Module):
    """KernelBench candidate entry point; default delegates to ``Model``."""

    def __init__(self, dim: int, num_steps: int):
        super().__init__()
        self._impl = Model(dim, num_steps)

    def forward(self, x0: torch.Tensor) -> torch.Tensor:
        return self._impl(x0)


batch_size = 8
dim = 64
num_steps = 32


def get_inputs():
    return [torch.randn(popcorn_pri.jitter_int(batch_size), dim)]


def get_init_inputs():
    return [dim, num_steps]
turn 0178.9s turn · 6.4s LLM · 172.5s tools · tokens in=2,473 · out=403 · total=2,876
reasoning
Let me analyze this task. I need to replace the forward computation of a PyTorch model with a custom CUDA kernel. The model implements a fused probability-flow ODE integration using Euler method. Let me understand the model: 1. It takes `x0` of shape (B, dim) as input 2. It performs `num_steps` Euler integration steps 3. At each step k, it computes t = (k + 0.5) / num_steps 4. It concatenates x with t to form input to the velocity network 5. The velocity network is a 3-layer MLP: Linear(dim+1, dim*4) -> SiLU -> Linear(dim*4, dim*4) -> SiLU -> Linear(dim*4, dim) 6. It updates x = x + dt * v The key insight here is that we need to fuse the entire computation into a single kernel (or minimal kernels) to avoid Python loop overhead and enable kernel fusion. Let me think about the CUDA optimization strategy: 1. The velocity MLP needs to be computed `num_steps` times 2. Each MLP evaluation involves: - Concatenating x with t - First linear: (dim+1) -> (dim*4) - SiLU activation - Second linear: (dim*4) -> (dim*4) - SiLU activation - Third linear: (dim*4) -> dim 3. The final update: x = x + dt * v For optimal performance: - We could pre-load all the weights into shared memory or cache them in registers - Each thread block could handle one or more samples in the batch - We need to minimize global memory accesses Let me start by getting GPU specs and then writing a basic kernel.
assistantI'll start by understanding the GPU specs and then develop a custom CUDA kernel for this fused probability-flow ODE integration.
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) · 335.3s turn · 24.1s LLM · tokens in=2,745 · out=2,426 · total=5,171 · 14,157 chars (click to expand)
turn 1335.3s turn · 24.1s LLM · 311.2s tools · tokens in=2,745 · out=2,426 · total=5,171
reasoning
Now let me understand the problem better. The model does: 1. Euler integration for num_steps steps 2. At each step, computes velocity via an MLP with 3 linear layers and 2 SiLU activations 3. The MLP takes [x, t] as input where t = (k + 0.5) / num_steps for step k The MLP structure: - Input: dim + 1 - Layer 1: dim + 1 → dim * 4, SiLU - Layer 2: dim * 4 → dim * 4, SiLU - Layer 3: dim * 4 → dim Key insight: Since batch_size=8 and dim=64, the MLP sizes are: - Layer 1: 65 → 256 - Layer 2: 256 → 256 - Layer 3: 256 → 64 This is a relatively small network, and with batch_size=8, it's not a lot of work per forward pass. For the CUDA kernel, I need to: 1. Copy the weights from the PyTorch model 2. Implement the forward pass including the velocity network 3. Implement the Euler integration loop Let me write a first version:
assistantLet me write a CUDA kernel for this fused probability-flow ODE integration. The key is to implement the velocity network (3 linear layers with SiLU activations) and run Euler integration for num_steps.
call → compile_kernel
callcompile_kernel { "kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\n# Load and compile the CUDA kernel\ncuda_source = \"\"\"\n#include <torch/extension.h>\n#include <cuda.h>\n#include <cuda_runtime.h>\n#include <cmath>\n\n// SiLU activation: x * sigmoid(x)\n__device__ __forceinline__ float silu(float x) {\n return x * (1.0f / (1.0f + expf(-x)));\n}\n\n// Vectorized memory access helpers\n__device__ void load_vec4(const float* ptr, float4& val) {\n val = *reinterpret_cast<const float4*>(ptr);\n}\n\n__device__ void store_vec4(float* ptr, const float4& val) {\n *reinterpret_cast<float4*>(ptr) = val;\n}\n\n// Linear layer with SiLU: output = silu(input @ weight.T + bias)\ntemplate<int IN_DIM, int OUT_DIM>\n__device__ void linear_silu(\n const float* __restrict__ input,\n const float* __restrict__ weight,\n const float* __restrict__ bias,\n float* output,\n int tid\n) {\n if (tid < OUT_DIM) {\n float sum = bias[tid];\n for (int i = 0; i < IN_DIM; i++) {\n sum += input[i] * weight[tid * IN_DIM + i];\n }\n output[tid] = silu(sum);\n }\n}\n\n// Linear layer without activation: output = input @ weight.T + bias\ntemplate<int IN_DIM, int OUT_DIM>\n__device__ void linear(\n const float* __restrict__ input,\n const float* __restrict__ weight,\n const float* __restrict__ bias,\n float* output,\n int tid\n) {\n if (tid < OUT_DIM) {\n float sum = bias[tid];\n for (int i = 0; i < IN_DIM; i++) {\n sum += input[i] * weight[tid * IN_DIM + i];\n }\n output[tid] = sum;\n }\n}\n\n// Main kernel: fused ODE integration\n// Grid: batch_size blocks\n// Block: threads based on max hidden dim\n__global__ void fused_ode_kernel(\n const float* __restrict__ x0,\n const float* __restrict__ w1,\n const float* __restrict__ b1,\n const float* __restrict__ w2,\n const float* __restrict__ b2,\n const float* __restrict__ w3,\n const float* __restrict__ b3,\n float* __restrict__ x_out,\n int dim,\n int hidden_dim,\n int num_steps,\n int batch_size\n) {\n int batch_idx = blockIdx.x;\n int tid = threadIdx.x;\n \n if (batch_idx >= batch_size) return;\n \n // Shared memory for intermediate results\n extern __shared__ char smem[];\n float* s_input = reinterpret_cast<float*>(smem); // size: dim + 1\n float* s_hidden1 = s_input + dim + 1; // size: hidden_dim\n float* s_hidden2 = s_hidden1 + hidden_dim; // size: hidden_dim\n float* s_x = s_hidden2 + hidden_dim; // size: dim\n \n // Initialize x from x0\n if (tid < dim) {\n s_x[tid] = x0[batch_idx * dim + tid];\n }\n __syncthreads();\n \n float dt = 1.0f / float(num_steps);\n \n // Euler integration loop\n for (int step = 0; step < num_steps; step++) {\n float t = (float(step) + 0.5f) / float(num_steps);\n \n // Build input: [x, t]\n if (tid < dim) {\n s_input[tid] = s_x[tid];\n }\n if (tid == 0) {\n s_input[dim] = t;\n }\n __syncthreads();\n \n // Layer 1: (dim + 1) -> hidden_dim with SiLU\n linear_silu<dim+1, /*hidden_dim*/0>(\n s_input, w1, b1, s_hidden1, tid\n );\n // Use actual hidden_dim since template param is limited\n if (tid < hidden_dim) {\n float sum = b1[tid];\n for (int i = 0; i < dim + 1; i++) {\n sum += s_input[i] * w1[tid * (dim + 1) + i];\n }\n s_hidden1[tid] = silu(sum);\n }\n __syncthreads();\n \n // Layer 2: hidden_dim -> hidden_dim with SiLU\n if (tid < hidden_dim) {\n float sum = b2[tid];\n for (int i = 0; i < hidden_dim; i++) {\n sum += s_hidden1[i] * w2[tid * hidden_dim + i];\n }\n s_hidden2[tid] = silu(sum);\n }\n __syncthreads();\n \n // Layer 3: hidden_dim -> dim (no activation)\n if (tid < dim) {\n float sum = b3[tid];\n for (int i = 0; i < hidden_dim; i++) {\n sum += s_hidden2[i] * w3[tid * hidden_dim + i];\n }\n // v = sum, x = x + dt * v\n s_x[tid] = s_x[tid] + dt * sum;\n }\n __syncthreads();\n }\n \n // Write output\n if (tid < dim) {\n x_out[batch_idx * dim + tid] = s_x[tid];\n }\n}\n\n// Host function\ntorch::Tensor fused_ode_forward(\n torch::Tensor x0,\n torch::Tensor w1,\n torch::Tensor b1,\n torch::Tensor w2,\n torch::Tensor b2,\n torch::Tensor w3,\n torch::Tensor b3,\n int64_t num_steps\n) {\n TORCH_CHECK(x0.is_cuda(), \"x0 must be CUDA tensor\");\n TORCH_CHECK(x0.dim() == 2, \"x0 must be 2D\");\n \n int batch_size = x0.size(0);\n int dim = x0.size(1);\n int hidden_dim = w1.size(0);\n \n auto x_out = torch::empty_like(x0);\n \n // Shared memory: input (dim+1) + hidden1 + hidden2 + x\n int smem_size = (dim + 1 + hidden_dim * 2 + dim) * sizeof(float);\n \n int threads = (hidden_dim + 31) / 32 * 32; // Round up to warp size\n threads = max(threads, dim);\n threads = min(threads, 1024);\n \n fused_ode_kernel<<<batch_size, threads, smem_size>>>(\n x0.data_ptr<float>(),\n w1.data_ptr<float>(),\n b1.data_ptr<float>(),\n w2.data_ptr<float>(),\n b2.data_ptr<float>(),\n w3.data_ptr<float>(),\n b3.data_ptr<float>(),\n x_out.data_ptr<float>(),\n dim,\n hidden_dim,\n num_steps,\n batch_size\n );\n \n return x_out;\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor fused_ode_forward(\n torch::Tensor x0,\n torch::Tensor w1,\n torch::Tensor b1,\n torch::Tensor w2,\n torch::Tensor b2,\n torch::Tensor w3,\n torch::Tensor b3,\n int64_t num_steps\n);\n\"\"\"\n\n# Load the extension\nfused_ode_ext = load_inline(\n name='fused_ode_ext',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['fused_ode_forward'],\n extra_cuda_cflags=['-O3', '-use_fast_math'],\n verbose=False\n)\n\n\nclass ModelNew(nn.Module):\n def __init__(self, dim: int, num_steps: int):\n super().__init__()\n assert dim >= 1 and num_steps >= 1\n self.dim = dim\n self.num_steps = num_steps\n self.register_buffer(\"dt\", torch.tensor(1.0 / float(num_steps)))\n \n # Velocity network: same architecture as reference\n self.velocity = nn.Sequential(\n nn.Linear(dim + 1, dim * 4),\n nn.SiLU(),\n nn.Linear(dim * 4, dim * 4),\n nn.SiLU(),\n nn.Linear(dim * 4, dim),\n )\n self._init_weights()\n \n def _init_weights(self):\n # Same initialization as reference\n for m in self.velocity.modules():\n if isinstance(m, nn.Linear):\n nn.init.xavier_uniform_(m.weight)\n if m.bias is not None:\n nn.init.zeros_(m.bias)\n \n def forward(self, x0: torch.Tensor) -> torch.Tensor:\n B, d = x0.shape\n assert d == self.dim\n \n # Get weights\n layers = list(self.velocity.children())\n w1 = layers[0].weight\n b1 = layers[0].bias\n w2 = layers[3].weight\n b2 = layers[3].bias\n w3 = layers[6].weight\n b3 = layers[6].bias\n \n # Ensure contiguous\n w1 = w1.contiguous()\n b1 = b1.contiguous()\n w2 = w2.contiguous()\n b2 = b2.contiguous()\n w3 = w3.contiguous()\n b3 = b3.contiguous()\n x0 = x0.contiguous()\n \n return fused_ode_ext.fused_ode_forward(\n x0, w1, b1, w2, b2, w3, b3, self.num_steps\n )" }
result ← compile_kernel (fail)
failcompile_kernel compile_kernel FAILED: RuntimeError. RuntimeError: Error building extension 'fused_ode_ext': [1/3] /opt/conda/bin/x86_64-conda-linux-gnu-c++ -MMD -MF main.o.d -DTORCH_EXTENSION_NAME=fused_ode_ext -DTORCH_API_INCLUDE_EXTENSION_H -isystem /scratch/abaner/KernelBench/.venv/lib/python3.10/site-packages/torch/include -isystem /scratch/abaner/KernelBench/.venv/lib/python3.10/site-packages/torch/include/torch/csrc/api/include -isystem /usr/local/cuda/include -isystem /opt/conda/include/python3.10 -fPIC -std=c++17 -c /scratch/abaner/KernelBench/runs/pop_l123_all_gpt/popcorn/FW-GLM-5-1/level_3_problem_5_cache/k_31ba59d01ca9/fused_ode_ext/main.cpp -o main.o [2/3] /usr/local/cuda/bin/nvcc -MD -MF cuda.cuda.o.d -ccbin /opt/conda/bin/x86_64-conda-linux-gnu-cc -DTORCH_EXTENSION_NAME=fused_ode_ext -DTORCH_API_INCLUDE_EXTENSION_H -isystem /scratch/abaner/KernelBench/.venv/lib/python3.10/site-packages/torch/include -isystem /scratch/abaner/KernelBench/.venv/lib/python3.10/site-packages/torch/include/torch/csrc/api/include -isystem /usr/local/cuda/include -isystem /opt/conda/include/python3.10 -D__CUDA_NO_HALF_OPERATORS__ -D__CUDA_NO_HALF_CONVERSIONS__ -D__CUDA_NO_BFLOAT16_CONVERSIONS__ -D__CUDA_NO_HALF2_OPERATORS__ --expt-relaxed-constexpr -gencode=arch=compute_90,code=compute_90 -gencode=arch=compute_90,code=sm_90 --compiler-options '-fPIC' -O3 -use_fast_math -std=c++17 -c /scratch/abaner/KernelBench/runs/pop_l123_all_gpt/popcorn/FW-GLM-5-1/level_3_problem_5_cache/k_31ba59d01ca9/fused_ode_ext/cuda.cu -o cuda.cuda.o FAILED: [code=2] cuda.cuda.o /usr/local/cuda/bin/nvcc -MD -MF cuda.cuda.o.d -ccbin /opt/conda/bin/x86_64-conda-linux-gnu-cc -DTORCH_EXTENSION_NAME=fused_ode_ext -DTORCH_API_INCLUDE_EXTENSION_H -isystem /scratch/abaner/KernelBench/.venv/lib/python3.10/site-packages/torch/include -isystem /scratch/abaner/KernelBench/.venv/lib/python3.10/site-packages/torch/include/torch/csrc/api/include -isystem /usr/local/cuda/include -isystem /opt/conda/include/python3.10 -D__CUDA_NO_HALF_OPERATORS__ -D__CUDA_NO_HALF_CONVERSIONS__ -D__CUDA_NO_BFLOAT16_CONVERSIONS__ -D__CUDA_NO_HALF2_OPERATORS__ --expt-relaxed-constexpr -gencode=arch=compute_90,code=compute_90 -gencode=arch=compute_90,code=sm_90 --compiler-options '-fPIC' -O3 -use_fast_math -std=c++17 -c /scratch/abaner/KernelBench/runs/pop_l123_all_gpt/popcorn/FW-GLM-5-1/level_3_problem_5_cache/k_31ba59d01ca9/fused_ode_ext/cuda.cu -o cuda.cuda.o nvcc warning : incompatible redefinition for option 'compiler-bindir', the last value of this option was used /scratch/abaner/KernelBench/runs/pop_l123_all_gpt/popcorn/FW-GLM-5-1/level_3_problem_5_cache/k_31ba59d01ca9/fused_ode_ext/cuda.cu(111): error: expression must have a constant value linear_silu<dim+1, 0>( ^ /scratch/abaner/KernelBench/runs/pop_l123_all_gpt/popcorn/FW-GLM-5-1/level_3_problem_5_cache/k_31ba59d01ca9/fused_ode_ext/cuda.cu(111): note #2689-D: the value of parameter "dim" (declared at line 72) cannot be used as a constant linear_silu<dim+1, 0>( ^ /scratch/abaner/KernelBench/runs/pop_l123_all_gpt/popcorn/FW-GLM-5-1/level_3_problem_5_cache/k_31ba59d01ca9/fused_ode_ext/cuda.cu(111): error: no instance of function template "linear_silu" matches the argument list argument types are: (float *, const float *__restrict__, const float *__restrict__, float *, int) linear_silu<dim+1, 0>( ^ /scratch/abaner/KernelBench/runs/pop_l123_all_gpt/popcorn/FW-GLM-5-1/level_3_problem_5_cache/k_31ba59d01ca9/fused_ode_ext/cuda.cu(26): note #3323-D: substituting explicit template arguments "<<expression>, <expression>>" for function template "linear_silu" failed void linear_silu( ^ 2 errors detected in the compilation of "/scratch/abaner/KernelBench/runs/pop_l123_all_gpt/popcorn/FW-GLM-5-1/level_3_problem_5_cache/k_31ba59d01ca9/fused_ode_ext/cuda.cu". ninja: build stopped: subcommand failed.
turn 2 · 1 tool call(s) · 314.3s turn · 14.9s LLM · tokens in=6,200 · out=1,864 · total=8,064 · 8,069 chars (click to expand)
turn 2314.3s turn · 14.9s LLM · 299.4s tools · tokens in=6,200 · out=1,864 · total=8,064
reasoning
I need to fix the template issue. The dimension is a runtime parameter, not a compile-time constant. Let me rewrite the kernel without using templates for the dimensions, and instead use runtime parameters.
assistantLet me fix the kernel by removing the template approach and using runtime parameters instead:
call → compile_kernel
callcompile_kernel { "kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\n# Load and compile the CUDA kernel\ncuda_source = \"\"\"\n#include <torch/extension.h>\n#include <cuda.h>\n#include <cuda_runtime.h>\n#include <cmath>\n\n// SiLU activation: x * sigmoid(x)\n__device__ __forceinline__ float silu(float x) {\n return x * (1.0f / (1.0f + expf(-x)));\n}\n\n// Main kernel: fused ODE integration\n// Grid: batch_size blocks\n// Block: threads based on max hidden dim\n__global__ void fused_ode_kernel(\n const float* __restrict__ x0,\n const float* __restrict__ w1, // shape: (hidden_dim, dim+1)\n const float* __restrict__ b1, // shape: (hidden_dim,)\n const float* __restrict__ w2, // shape: (hidden_dim, hidden_dim)\n const float* __restrict__ b2, // shape: (hidden_dim,)\n const float* __restrict__ w3, // shape: (dim, hidden_dim)\n const float* __restrict__ b3, // shape: (dim,)\n float* __restrict__ x_out,\n int dim,\n int hidden_dim,\n int num_steps,\n int batch_size\n) {\n int batch_idx = blockIdx.x;\n int tid = threadIdx.x;\n \n if (batch_idx >= batch_size) return;\n \n // Shared memory for intermediate results\n extern __shared__ char smem[];\n float* s_input = reinterpret_cast<float*>(smem); // size: dim + 1\n float* s_hidden1 = s_input + dim + 1; // size: hidden_dim\n float* s_hidden2 = s_hidden1 + hidden_dim; // size: hidden_dim\n float* s_x = s_hidden2 + hidden_dim; // size: dim\n \n // Initialize x from x0\n if (tid < dim) {\n s_x[tid] = x0[batch_idx * dim + tid];\n }\n __syncthreads();\n \n float dt = 1.0f / float(num_steps);\n \n // Euler integration loop\n for (int step = 0; step < num_steps; step++) {\n float t = (float(step) + 0.5f) / float(num_steps);\n \n // Build input: [x, t]\n if (tid < dim) {\n s_input[tid] = s_x[tid];\n }\n if (tid == 0) {\n s_input[dim] = t;\n }\n __syncthreads();\n \n // Layer 1: (dim + 1) -> hidden_dim with SiLU\n if (tid < hidden_dim) {\n float sum = b1[tid];\n for (int i = 0; i < dim + 1; i++) {\n sum += s_input[i] * w1[tid * (dim + 1) + i];\n }\n s_hidden1[tid] = silu(sum);\n }\n __syncthreads();\n \n // Layer 2: hidden_dim -> hidden_dim with SiLU\n if (tid < hidden_dim) {\n float sum = b2[tid];\n for (int i = 0; i < hidden_dim; i++) {\n sum += s_hidden1[i] * w2[tid * hidden_dim + i];\n }\n s_hidden2[tid] = silu(sum);\n }\n __syncthreads();\n \n // Layer 3: hidden_dim -> dim (no activation)\n if (tid < dim) {\n float sum = b3[tid];\n for (int i = 0; i < hidden_dim; i++) {\n sum += s_hidden2[i] * w3[tid * hidden_dim + i];\n }\n // v = sum, x = x + dt * v\n s_x[tid] = s_x[tid] + dt * sum;\n }\n __syncthreads();\n }\n \n // Write output\n if (tid < dim) {\n x_out[batch_idx * dim + tid] = s_x[tid];\n }\n}\n\n// Host function\ntorch::Tensor fused_ode_forward(\n torch::Tensor x0,\n torch::Tensor w1,\n torch::Tensor b1,\n torch::Tensor w2,\n torch::Tensor b2,\n torch::Tensor w3,\n torch::Tensor b3,\n int64_t num_steps\n) {\n TORCH_CHECK(x0.is_cuda(), \"x0 must be CUDA tensor\");\n TORCH_CHECK(x0.dim() == 2, \"x0 must be 2D\");\n \n int batch_size = x0.size(0);\n int dim = x0.size(1);\n int hidden_dim = w1.size(0);\n \n auto x_out = torch::empty_like(x0);\n \n // Shared memory: input (dim+1) + hidden1 + hidden2 + x\n int smem_size = (dim + 1 + hidden_dim * 2 + dim) * sizeof(float);\n \n int threads = (hidden_dim + 31) / 32 * 32; // Round up to warp size\n threads = max(threads, dim);\n threads = min(threads, 1024);\n \n fused_ode_kernel<<<batch_size, threads, smem_size>>>(\n x0.data_ptr<float>(),\n w1.data_ptr<float>(),\n b1.data_ptr<float>(),\n w2.data_ptr<float>(),\n b2.data_ptr<float>(),\n w3.data_ptr<float>(),\n b3.data_ptr<float>(),\n x_out.data_ptr<float>(),\n dim,\n hidden_dim,\n num_steps,\n batch_size\n );\n \n return x_out;\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor fused_ode_forward(\n torch::Tensor x0,\n torch::Tensor w1,\n torch::Tensor b1,\n torch::Tensor w2,\n torch::Tensor b2,\n torch::Tensor w3,\n torch::Tensor b3,\n int64_t num_steps\n);\n\"\"\"\n\n# Load the extension\nfused_ode_ext = load_inline(\n name='fused_ode_ext',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['fused_ode_forward'],\n extra_cuda_cflags=['-O3', '-use_fast_math'],\n verbose=False\n)\n\n\nclass ModelNew(nn.Module):\n def __init__(self, dim: int, num_steps: int):\n super().__init__()\n assert dim >= 1 and num_steps >= 1\n self.dim = dim\n self.num_steps = num_steps\n self.register_buffer(\"dt\", torch.tensor(1.0 / float(num_steps)))\n \n # Velocity network: same architecture as reference\n self.velocity = nn.Sequential(\n nn.Linear(dim + 1, dim * 4),\n nn.SiLU(),\n nn.Linear(dim * 4, dim * 4),\n nn.SiLU(),\n nn.Linear(dim * 4, dim),\n )\n self._init_weights()\n \n def _init_weights(self):\n # Same initialization as reference\n for m in self.velocity.modules():\n if isinstance(m, nn.Linear):\n nn.init.xavier_uniform_(m.weight)\n if m.bias is not None:\n nn.init.zeros_(m.bias)\n \n def forward(self, x0: torch.Tensor) -> torch.Tensor:\n B, d = x0.shape\n assert d == self.dim\n \n # Get weights\n layers = list(self.velocity.children())\n w1 = layers[0].weight\n b1 = layers[0].bias\n w2 = layers[3].weight\n b2 = layers[3].bias\n w3 = layers[6].weight\n b3 = layers[6].bias\n \n # Ensure contiguous\n w1 = w1.contiguous()\n b1 = b1.contiguous()\n w2 = w2.contiguous()\n b2 = b2.contiguous()\n w3 = w3.contiguous()\n b3 = b3.contiguous()\n x0 = x0.contiguous()\n \n return fused_ode_ext.fused_ode_forward(\n x0, w1, b1, w2, b2, w3, b3, self.num_steps\n )" }
result ← compile_kernel (ok)
okcompile_kernel compile_kernel PASSED: kernel compiled without errors.
turn 3 · 1 tool call(s) · 333.4s turn · 15.8s LLM · tokens in=8,038 · out=1,828 · total=9,866 · 7,947 chars (click to expand)
turn 3333.4s turn · 15.8s LLM · 317.5s tools · tokens in=8,038 · out=1,828 · total=9,866
reasoning
The kernel compiled. Now let me run the correctness check.
assistantNow 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\n# Load and compile the CUDA kernel\ncuda_source = \"\"\"\n#include <torch/extension.h>\n#include <cuda.h>\n#include <cuda_runtime.h>\n#include <cmath>\n\n// SiLU activation: x * sigmoid(x)\n__device__ __forceinline__ float silu(float x) {\n return x * (1.0f / (1.0f + expf(-x)));\n}\n\n// Main kernel: fused ODE integration\n// Grid: batch_size blocks\n// Block: threads based on max hidden dim\n__global__ void fused_ode_kernel(\n const float* __restrict__ x0,\n const float* __restrict__ w1, // shape: (hidden_dim, dim+1)\n const float* __restrict__ b1, // shape: (hidden_dim,)\n const float* __restrict__ w2, // shape: (hidden_dim, hidden_dim)\n const float* __restrict__ b2, // shape: (hidden_dim,)\n const float* __restrict__ w3, // shape: (dim, hidden_dim)\n const float* __restrict__ b3, // shape: (dim,)\n float* __restrict__ x_out,\n int dim,\n int hidden_dim,\n int num_steps,\n int batch_size\n) {\n int batch_idx = blockIdx.x;\n int tid = threadIdx.x;\n \n if (batch_idx >= batch_size) return;\n \n // Shared memory for intermediate results\n extern __shared__ char smem[];\n float* s_input = reinterpret_cast<float*>(smem); // size: dim + 1\n float* s_hidden1 = s_input + dim + 1; // size: hidden_dim\n float* s_hidden2 = s_hidden1 + hidden_dim; // size: hidden_dim\n float* s_x = s_hidden2 + hidden_dim; // size: dim\n \n // Initialize x from x0\n if (tid < dim) {\n s_x[tid] = x0[batch_idx * dim + tid];\n }\n __syncthreads();\n \n float dt = 1.0f / float(num_steps);\n \n // Euler integration loop\n for (int step = 0; step < num_steps; step++) {\n float t = (float(step) + 0.5f) / float(num_steps);\n \n // Build input: [x, t]\n if (tid < dim) {\n s_input[tid] = s_x[tid];\n }\n if (tid == 0) {\n s_input[dim] = t;\n }\n __syncthreads();\n \n // Layer 1: (dim + 1) -> hidden_dim with SiLU\n if (tid < hidden_dim) {\n float sum = b1[tid];\n for (int i = 0; i < dim + 1; i++) {\n sum += s_input[i] * w1[tid * (dim + 1) + i];\n }\n s_hidden1[tid] = silu(sum);\n }\n __syncthreads();\n \n // Layer 2: hidden_dim -> hidden_dim with SiLU\n if (tid < hidden_dim) {\n float sum = b2[tid];\n for (int i = 0; i < hidden_dim; i++) {\n sum += s_hidden1[i] * w2[tid * hidden_dim + i];\n }\n s_hidden2[tid] = silu(sum);\n }\n __syncthreads();\n \n // Layer 3: hidden_dim -> dim (no activation)\n if (tid < dim) {\n float sum = b3[tid];\n for (int i = 0; i < hidden_dim; i++) {\n sum += s_hidden2[i] * w3[tid * hidden_dim + i];\n }\n // v = sum, x = x + dt * v\n s_x[tid] = s_x[tid] + dt * sum;\n }\n __syncthreads();\n }\n \n // Write output\n if (tid < dim) {\n x_out[batch_idx * dim + tid] = s_x[tid];\n }\n}\n\n// Host function\ntorch::Tensor fused_ode_forward(\n torch::Tensor x0,\n torch::Tensor w1,\n torch::Tensor b1,\n torch::Tensor w2,\n torch::Tensor b2,\n torch::Tensor w3,\n torch::Tensor b3,\n int64_t num_steps\n) {\n TORCH_CHECK(x0.is_cuda(), \"x0 must be CUDA tensor\");\n TORCH_CHECK(x0.dim() == 2, \"x0 must be 2D\");\n \n int batch_size = x0.size(0);\n int dim = x0.size(1);\n int hidden_dim = w1.size(0);\n \n auto x_out = torch::empty_like(x0);\n \n // Shared memory: input (dim+1) + hidden1 + hidden2 + x\n int smem_size = (dim + 1 + hidden_dim * 2 + dim) * sizeof(float);\n \n int threads = (hidden_dim + 31) / 32 * 32; // Round up to warp size\n threads = max(threads, dim);\n threads = min(threads, 1024);\n \n fused_ode_kernel<<<batch_size, threads, smem_size>>>(\n x0.data_ptr<float>(),\n w1.data_ptr<float>(),\n b1.data_ptr<float>(),\n w2.data_ptr<float>(),\n b2.data_ptr<float>(),\n w3.data_ptr<float>(),\n b3.data_ptr<float>(),\n x_out.data_ptr<float>(),\n dim,\n hidden_dim,\n num_steps,\n batch_size\n );\n \n return x_out;\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor fused_ode_forward(\n torch::Tensor x0,\n torch::Tensor w1,\n torch::Tensor b1,\n torch::Tensor w2,\n torch::Tensor b2,\n torch::Tensor w3,\n torch::Tensor b3,\n int64_t num_steps\n);\n\"\"\"\n\n# Load the extension\nfused_ode_ext = load_inline(\n name='fused_ode_ext',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['fused_ode_forward'],\n extra_cuda_cflags=['-O3', '-use_fast_math'],\n verbose=False\n)\n\n\nclass ModelNew(nn.Module):\n def __init__(self, dim: int, num_steps: int):\n super().__init__()\n assert dim >= 1 and num_steps >= 1\n self.dim = dim\n self.num_steps = num_steps\n self.register_buffer(\"dt\", torch.tensor(1.0 / float(num_steps)))\n \n # Velocity network: same architecture as reference\n self.velocity = nn.Sequential(\n nn.Linear(dim + 1, dim * 4),\n nn.SiLU(),\n nn.Linear(dim * 4, dim * 4),\n nn.SiLU(),\n nn.Linear(dim * 4, dim),\n )\n self._init_weights()\n \n def _init_weights(self):\n # Same initialization as reference\n for m in self.velocity.modules():\n if isinstance(m, nn.Linear):\n nn.init.xavier_uniform_(m.weight)\n if m.bias is not None:\n nn.init.zeros_(m.bias)\n \n def forward(self, x0: torch.Tensor) -> torch.Tensor:\n B, d = x0.shape\n assert d == self.dim\n \n # Get weights\n layers = list(self.velocity.children())\n w1 = layers[0].weight\n b1 = layers[0].bias\n w2 = layers[3].weight\n b2 = layers[3].bias\n w3 = layers[6].weight\n b3 = layers[6].bias\n \n # Ensure contiguous\n w1 = w1.contiguous()\n b1 = b1.contiguous()\n w2 = w2.contiguous()\n b2 = b2.contiguous()\n w3 = w3.contiguous()\n b3 = b3.contiguous()\n x0 = x0.contiguous()\n \n return fused_ode_ext.fused_ode_forward(\n x0, w1, b1, w2, b2, w3, b3, self.num_steps\n )" }
result ← run_correctness (fail)
failrun_correctness run_correctness FAILED: ? trials did not all match. runtime_error: 'SiLU' object has no attribute 'weight'
turn 4 · 1 tool call(s) · 639.9s turn · 18.0s LLM · tokens in=9,883 · out=1,954 · total=11,837 · 8,106 chars (click to expand)
turn 4639.9s turn · 18.0s LLM · 621.9s tools · tokens in=9,883 · out=1,954 · total=11,837
reasoning
The issue is that `nn.Sequential` with `nn.SiLU()` interleaves the Linear layers with activation modules. Let me fix the indexing: ``` nn.Sequential( nn.Linear(dim + 1, dim * 4), # 0 nn.SiLU(), # 1 nn.Linear(dim * 4, dim * 4), # 2 nn.SiLU(), # 3 nn.Linear(dim * 4, dim), # 4 ) ``` So the indices should be 0, 2, 4 for the Linear layers, and bias is also needed.
assistantThe issue is the indexing of layers in `nn.Sequential`. Let me fix that:
call → compile_kernel
callcompile_kernel { "kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\n# Load and compile the CUDA kernel\ncuda_source = \"\"\"\n#include <torch/extension.h>\n#include <cuda.h>\n#include <cuda_runtime.h>\n#include <cmath>\n\n// SiLU activation: x * sigmoid(x)\n__device__ __forceinline__ float silu(float x) {\n return x * (1.0f / (1.0f + expf(-x)));\n}\n\n// Main kernel: fused ODE integration\n// Grid: batch_size blocks\n// Block: threads based on max hidden dim\n__global__ void fused_ode_kernel(\n const float* __restrict__ x0,\n const float* __restrict__ w1, // shape: (hidden_dim, dim+1)\n const float* __restrict__ b1, // shape: (hidden_dim,)\n const float* __restrict__ w2, // shape: (hidden_dim, hidden_dim)\n const float* __restrict__ b2, // shape: (hidden_dim,)\n const float* __restrict__ w3, // shape: (dim, hidden_dim)\n const float* __restrict__ b3, // shape: (dim,)\n float* __restrict__ x_out,\n int dim,\n int hidden_dim,\n int num_steps,\n int batch_size\n) {\n int batch_idx = blockIdx.x;\n int tid = threadIdx.x;\n \n if (batch_idx >= batch_size) return;\n \n // Shared memory for intermediate results\n extern __shared__ char smem[];\n float* s_input = reinterpret_cast<float*>(smem); // size: dim + 1\n float* s_hidden1 = s_input + dim + 1; // size: hidden_dim\n float* s_hidden2 = s_hidden1 + hidden_dim; // size: hidden_dim\n float* s_x = s_hidden2 + hidden_dim; // size: dim\n \n // Initialize x from x0\n if (tid < dim) {\n s_x[tid] = x0[batch_idx * dim + tid];\n }\n __syncthreads();\n \n float dt = 1.0f / float(num_steps);\n \n // Euler integration loop\n for (int step = 0; step < num_steps; step++) {\n float t = (float(step) + 0.5f) / float(num_steps);\n \n // Build input: [x, t]\n if (tid < dim) {\n s_input[tid] = s_x[tid];\n }\n if (tid == 0) {\n s_input[dim] = t;\n }\n __syncthreads();\n \n // Layer 1: (dim + 1) -> hidden_dim with SiLU\n if (tid < hidden_dim) {\n float sum = b1[tid];\n for (int i = 0; i < dim + 1; i++) {\n sum += s_input[i] * w1[tid * (dim + 1) + i];\n }\n s_hidden1[tid] = silu(sum);\n }\n __syncthreads();\n \n // Layer 2: hidden_dim -> hidden_dim with SiLU\n if (tid < hidden_dim) {\n float sum = b2[tid];\n for (int i = 0; i < hidden_dim; i++) {\n sum += s_hidden1[i] * w2[tid * hidden_dim + i];\n }\n s_hidden2[tid] = silu(sum);\n }\n __syncthreads();\n \n // Layer 3: hidden_dim -> dim (no activation)\n if (tid < dim) {\n float sum = b3[tid];\n for (int i = 0; i < hidden_dim; i++) {\n sum += s_hidden2[i] * w3[tid * hidden_dim + i];\n }\n // v = sum, x = x + dt * v\n s_x[tid] = s_x[tid] + dt * sum;\n }\n __syncthreads();\n }\n \n // Write output\n if (tid < dim) {\n x_out[batch_idx * dim + tid] = s_x[tid];\n }\n}\n\n// Host function\ntorch::Tensor fused_ode_forward(\n torch::Tensor x0,\n torch::Tensor w1,\n torch::Tensor b1,\n torch::Tensor w2,\n torch::Tensor b2,\n torch::Tensor w3,\n torch::Tensor b3,\n int64_t num_steps\n) {\n TORCH_CHECK(x0.is_cuda(), \"x0 must be CUDA tensor\");\n TORCH_CHECK(x0.dim() == 2, \"x0 must be 2D\");\n \n int batch_size = x0.size(0);\n int dim = x0.size(1);\n int hidden_dim = w1.size(0);\n \n auto x_out = torch::empty_like(x0);\n \n // Shared memory: input (dim+1) + hidden1 + hidden2 + x\n int smem_size = (dim + 1 + hidden_dim * 2 + dim) * sizeof(float);\n \n int threads = (hidden_dim + 31) / 32 * 32; // Round up to warp size\n threads = max(threads, dim);\n threads = min(threads, 1024);\n \n fused_ode_kernel<<<batch_size, threads, smem_size>>>(\n x0.data_ptr<float>(),\n w1.data_ptr<float>(),\n b1.data_ptr<float>(),\n w2.data_ptr<float>(),\n b2.data_ptr<float>(),\n w3.data_ptr<float>(),\n b3.data_ptr<float>(),\n x_out.data_ptr<float>(),\n dim,\n hidden_dim,\n num_steps,\n batch_size\n );\n \n return x_out;\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor fused_ode_forward(\n torch::Tensor x0,\n torch::Tensor w1,\n torch::Tensor b1,\n torch::Tensor w2,\n torch::Tensor b2,\n torch::Tensor w3,\n torch::Tensor b3,\n int64_t num_steps\n);\n\"\"\"\n\n# Load the extension\nfused_ode_ext = load_inline(\n name='fused_ode_ext',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['fused_ode_forward'],\n extra_cuda_cflags=['-O3', '-use_fast_math'],\n verbose=False\n)\n\n\nclass ModelNew(nn.Module):\n def __init__(self, dim: int, num_steps: int):\n super().__init__()\n assert dim >= 1 and num_steps >= 1\n self.dim = dim\n self.num_steps = num_steps\n self.register_buffer(\"dt\", torch.tensor(1.0 / float(num_steps)))\n \n # Velocity network: same architecture as reference\n self.velocity = nn.Sequential(\n nn.Linear(dim + 1, dim * 4),\n nn.SiLU(),\n nn.Linear(dim * 4, dim * 4),\n nn.SiLU(),\n nn.Linear(dim * 4, dim),\n )\n \n def forward(self, x0: torch.Tensor) -> torch.Tensor:\n B, d = x0.shape\n assert d == self.dim\n \n # Sequential structure:\n # [0]: Linear(dim+1, dim*4)\n # [1]: SiLU\n # [2]: Linear(dim*4, dim*4)\n # [3]: SiLU\n # [4]: Linear(dim*4, dim)\n layers = list(self.velocity.children())\n w1 = layers[0].weight\n b1 = layers[0].bias\n w2 = layers[2].weight\n b2 = layers[2].bias\n w3 = layers[4].weight\n b3 = layers[4].bias\n \n # Ensure contiguous\n w1 = w1.contiguous()\n b1 = b1.contiguous()\n w2 = w2.contiguous()\n b2 = b2.contiguous()\n w3 = w3.contiguous()\n b3 = b3.contiguous()\n x0 = x0.contiguous()\n \n return fused_ode_ext.fused_ode_forward(\n x0, w1, b1, w2, b2, w3, b3, self.num_steps\n )" }
result ← compile_kernel (ok)
okcompile_kernel compile_kernel PASSED: kernel compiled without errors.
turn 5 · 1 tool call(s) · 292.2s turn · 15.1s LLM · tokens in=11,715 · out=1,816 · total=13,531 · 7,690 chars (click to expand)
turn 5292.2s turn · 15.1s LLM · 277.1s tools · tokens in=11,715 · out=1,816 · total=13,531
reasoning
Good, the indexing is now correct. 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\n# Load and compile the CUDA kernel\ncuda_source = \"\"\"\n#include <torch/extension.h>\n#include <cuda.h>\n#include <cuda_runtime.h>\n#include <cmath>\n\n// SiLU activation: x * sigmoid(x)\n__device__ __forceinline__ float silu(float x) {\n return x * (1.0f / (1.0f + expf(-x)));\n}\n\n// Main kernel: fused ODE integration\n// Grid: batch_size blocks\n// Block: threads based on max hidden dim\n__global__ void fused_ode_kernel(\n const float* __restrict__ x0,\n const float* __restrict__ w1, // shape: (hidden_dim, dim+1)\n const float* __restrict__ b1, // shape: (hidden_dim,)\n const float* __restrict__ w2, // shape: (hidden_dim, hidden_dim)\n const float* __restrict__ b2, // shape: (hidden_dim,)\n const float* __restrict__ w3, // shape: (dim, hidden_dim)\n const float* __restrict__ b3, // shape: (dim,)\n float* __restrict__ x_out,\n int dim,\n int hidden_dim,\n int num_steps,\n int batch_size\n) {\n int batch_idx = blockIdx.x;\n int tid = threadIdx.x;\n \n if (batch_idx >= batch_size) return;\n \n // Shared memory for intermediate results\n extern __shared__ char smem[];\n float* s_input = reinterpret_cast<float*>(smem); // size: dim + 1\n float* s_hidden1 = s_input + dim + 1; // size: hidden_dim\n float* s_hidden2 = s_hidden1 + hidden_dim; // size: hidden_dim\n float* s_x = s_hidden2 + hidden_dim; // size: dim\n \n // Initialize x from x0\n if (tid < dim) {\n s_x[tid] = x0[batch_idx * dim + tid];\n }\n __syncthreads();\n \n float dt = 1.0f / float(num_steps);\n \n // Euler integration loop\n for (int step = 0; step < num_steps; step++) {\n float t = (float(step) + 0.5f) / float(num_steps);\n \n // Build input: [x, t]\n if (tid < dim) {\n s_input[tid] = s_x[tid];\n }\n if (tid == 0) {\n s_input[dim] = t;\n }\n __syncthreads();\n \n // Layer 1: (dim + 1) -> hidden_dim with SiLU\n if (tid < hidden_dim) {\n float sum = b1[tid];\n for (int i = 0; i < dim + 1; i++) {\n sum += s_input[i] * w1[tid * (dim + 1) + i];\n }\n s_hidden1[tid] = silu(sum);\n }\n __syncthreads();\n \n // Layer 2: hidden_dim -> hidden_dim with SiLU\n if (tid < hidden_dim) {\n float sum = b2[tid];\n for (int i = 0; i < hidden_dim; i++) {\n sum += s_hidden1[i] * w2[tid * hidden_dim + i];\n }\n s_hidden2[tid] = silu(sum);\n }\n __syncthreads();\n \n // Layer 3: hidden_dim -> dim (no activation)\n if (tid < dim) {\n float sum = b3[tid];\n for (int i = 0; i < hidden_dim; i++) {\n sum += s_hidden2[i] * w3[tid * hidden_dim + i];\n }\n // v = sum, x = x + dt * v\n s_x[tid] = s_x[tid] + dt * sum;\n }\n __syncthreads();\n }\n \n // Write output\n if (tid < dim) {\n x_out[batch_idx * dim + tid] = s_x[tid];\n }\n}\n\n// Host function\ntorch::Tensor fused_ode_forward(\n torch::Tensor x0,\n torch::Tensor w1,\n torch::Tensor b1,\n torch::Tensor w2,\n torch::Tensor b2,\n torch::Tensor w3,\n torch::Tensor b3,\n int64_t num_steps\n) {\n TORCH_CHECK(x0.is_cuda(), \"x0 must be CUDA tensor\");\n TORCH_CHECK(x0.dim() == 2, \"x0 must be 2D\");\n \n int batch_size = x0.size(0);\n int dim = x0.size(1);\n int hidden_dim = w1.size(0);\n \n auto x_out = torch::empty_like(x0);\n \n // Shared memory: input (dim+1) + hidden1 + hidden2 + x\n int smem_size = (dim + 1 + hidden_dim * 2 + dim) * sizeof(float);\n \n int threads = (hidden_dim + 31) / 32 * 32; // Round up to warp size\n threads = max(threads, dim);\n threads = min(threads, 1024);\n \n fused_ode_kernel<<<batch_size, threads, smem_size>>>(\n x0.data_ptr<float>(),\n w1.data_ptr<float>(),\n b1.data_ptr<float>(),\n w2.data_ptr<float>(),\n b2.data_ptr<float>(),\n w3.data_ptr<float>(),\n b3.data_ptr<float>(),\n x_out.data_ptr<float>(),\n dim,\n hidden_dim,\n num_steps,\n batch_size\n );\n \n return x_out;\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor fused_ode_forward(\n torch::Tensor x0,\n torch::Tensor w1,\n torch::Tensor b1,\n torch::Tensor w2,\n torch::Tensor b2,\n torch::Tensor w3,\n torch::Tensor b3,\n int64_t num_steps\n);\n\"\"\"\n\n# Load the extension\nfused_ode_ext = load_inline(\n name='fused_ode_ext',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['fused_ode_forward'],\n extra_cuda_cflags=['-O3', '-use_fast_math'],\n verbose=False\n)\n\n\nclass ModelNew(nn.Module):\n def __init__(self, dim: int, num_steps: int):\n super().__init__()\n assert dim >= 1 and num_steps >= 1\n self.dim = dim\n self.num_steps = num_steps\n self.register_buffer(\"dt\", torch.tensor(1.0 / float(num_steps)))\n \n # Velocity network: same architecture as reference\n self.velocity = nn.Sequential(\n nn.Linear(dim + 1, dim * 4),\n nn.SiLU(),\n nn.Linear(dim * 4, dim * 4),\n nn.SiLU(),\n nn.Linear(dim * 4, dim),\n )\n \n def forward(self, x0: torch.Tensor) -> torch.Tensor:\n B, d = x0.shape\n assert d == self.dim\n \n # Sequential structure:\n # [0]: Linear(dim+1, dim*4)\n # [1]: SiLU\n # [2]: Linear(dim*4, dim*4)\n # [3]: SiLU\n # [4]: Linear(dim*4, dim)\n layers = list(self.velocity.children())\n w1 = layers[0].weight\n b1 = layers[0].bias\n w2 = layers[2].weight\n b2 = layers[2].bias\n w3 = layers[4].weight\n b3 = layers[4].bias\n \n # Ensure contiguous\n w1 = w1.contiguous()\n b1 = b1.contiguous()\n w2 = w2.contiguous()\n b2 = b2.contiguous()\n w3 = w3.contiguous()\n b3 = b3.contiguous()\n x0 = x0.contiguous()\n \n return fused_ode_ext.fused_ode_forward(\n x0, w1, b1, w2, b2, w3, b3, self.num_steps\n )" }
result ← run_correctness (ok)
okrun_correctness run_correctness PASSED: (3 / 3) trials all matched the reference. Numerical precision: max_abs_err=2.38e-07 mean_abs_err=1.79e-08 max_rel_err=2.34e-06
turn 6 · 1 tool call(s) · 502.3s turn · 15.0s LLM · tokens in=13,575 · out=1,837 · total=15,412 · 9,317 chars (click to expand)
turn 6502.3s turn · 15.0s LLM · 487.3s tools · tokens in=13,575 · out=1,837 · total=15,412
reasoning
Excellent! The kernel is correct. Now let me profile it to understand performance and identify optimization opportunities.
assistantThe kernel is correct. Let me profile it to understand the performance characteristics:
call → profile_kernel
callprofile_kernel { "kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\n# Load and compile the CUDA kernel\ncuda_source = \"\"\"\n#include <torch/extension.h>\n#include <cuda.h>\n#include <cuda_runtime.h>\n#include <cmath>\n\n// SiLU activation: x * sigmoid(x)\n__device__ __forceinline__ float silu(float x) {\n return x * (1.0f / (1.0f + expf(-x)));\n}\n\n// Main kernel: fused ODE integration\n// Grid: batch_size blocks\n// Block: threads based on max hidden dim\n__global__ void fused_ode_kernel(\n const float* __restrict__ x0,\n const float* __restrict__ w1, // shape: (hidden_dim, dim+1)\n const float* __restrict__ b1, // shape: (hidden_dim,)\n const float* __restrict__ w2, // shape: (hidden_dim, hidden_dim)\n const float* __restrict__ b2, // shape: (hidden_dim,)\n const float* __restrict__ w3, // shape: (dim, hidden_dim)\n const float* __restrict__ b3, // shape: (dim,)\n float* __restrict__ x_out,\n int dim,\n int hidden_dim,\n int num_steps,\n int batch_size\n) {\n int batch_idx = blockIdx.x;\n int tid = threadIdx.x;\n \n if (batch_idx >= batch_size) return;\n \n // Shared memory for intermediate results\n extern __shared__ char smem[];\n float* s_input = reinterpret_cast<float*>(smem); // size: dim + 1\n float* s_hidden1 = s_input + dim + 1; // size: hidden_dim\n float* s_hidden2 = s_hidden1 + hidden_dim; // size: hidden_dim\n float* s_x = s_hidden2 + hidden_dim; // size: dim\n \n // Initialize x from x0\n if (tid < dim) {\n s_x[tid] = x0[batch_idx * dim + tid];\n }\n __syncthreads();\n \n float dt = 1.0f / float(num_steps);\n \n // Euler integration loop\n for (int step = 0; step < num_steps; step++) {\n float t = (float(step) + 0.5f) / float(num_steps);\n \n // Build input: [x, t]\n if (tid < dim) {\n s_input[tid] = s_x[tid];\n }\n if (tid == 0) {\n s_input[dim] = t;\n }\n __syncthreads();\n \n // Layer 1: (dim + 1) -> hidden_dim with SiLU\n if (tid < hidden_dim) {\n float sum = b1[tid];\n for (int i = 0; i < dim + 1; i++) {\n sum += s_input[i] * w1[tid * (dim + 1) + i];\n }\n s_hidden1[tid] = silu(sum);\n }\n __syncthreads();\n \n // Layer 2: hidden_dim -> hidden_dim with SiLU\n if (tid < hidden_dim) {\n float sum = b2[tid];\n for (int i = 0; i < hidden_dim; i++) {\n sum += s_hidden1[i] * w2[tid * hidden_dim + i];\n }\n s_hidden2[tid] = silu(sum);\n }\n __syncthreads();\n \n // Layer 3: hidden_dim -> dim (no activation)\n if (tid < dim) {\n float sum = b3[tid];\n for (int i = 0; i < hidden_dim; i++) {\n sum += s_hidden2[i] * w3[tid * hidden_dim + i];\n }\n // v = sum, x = x + dt * v\n s_x[tid] = s_x[tid] + dt * sum;\n }\n __syncthreads();\n }\n \n // Write output\n if (tid < dim) {\n x_out[batch_idx * dim + tid] = s_x[tid];\n }\n}\n\n// Host function\ntorch::Tensor fused_ode_forward(\n torch::Tensor x0,\n torch::Tensor w1,\n torch::Tensor b1,\n torch::Tensor w2,\n torch::Tensor b2,\n torch::Tensor w3,\n torch::Tensor b3,\n int64_t num_steps\n) {\n TORCH_CHECK(x0.is_cuda(), \"x0 must be CUDA tensor\");\n TORCH_CHECK(x0.dim() == 2, \"x0 must be 2D\");\n \n int batch_size = x0.size(0);\n int dim = x0.size(1);\n int hidden_dim = w1.size(0);\n \n auto x_out = torch::empty_like(x0);\n \n // Shared memory: input (dim+1) + hidden1 + hidden2 + x\n int smem_size = (dim + 1 + hidden_dim * 2 + dim) * sizeof(float);\n \n int threads = (hidden_dim + 31) / 32 * 32; // Round up to warp size\n threads = max(threads, dim);\n threads = min(threads, 1024);\n \n fused_ode_kernel<<<batch_size, threads, smem_size>>>(\n x0.data_ptr<float>(),\n w1.data_ptr<float>(),\n b1.data_ptr<float>(),\n w2.data_ptr<float>(),\n b2.data_ptr<float>(),\n w3.data_ptr<float>(),\n b3.data_ptr<float>(),\n x_out.data_ptr<float>(),\n dim,\n hidden_dim,\n num_steps,\n batch_size\n );\n \n return x_out;\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor fused_ode_forward(\n torch::Tensor x0,\n torch::Tensor w1,\n torch::Tensor b1,\n torch::Tensor w2,\n torch::Tensor b2,\n torch::Tensor w3,\n torch::Tensor b3,\n int64_t num_steps\n);\n\"\"\"\n\n# Load the extension\nfused_ode_ext = load_inline(\n name='fused_ode_ext',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['fused_ode_forward'],\n extra_cuda_cflags=['-O3', '-use_fast_math'],\n verbose=False\n)\n\n\nclass ModelNew(nn.Module):\n def __init__(self, dim: int, num_steps: int):\n super().__init__()\n assert dim >= 1 and num_steps >= 1\n self.dim = dim\n self.num_steps = num_steps\n self.register_buffer(\"dt\", torch.tensor(1.0 / float(num_steps)))\n \n # Velocity network: same architecture as reference\n self.velocity = nn.Sequential(\n nn.Linear(dim + 1, dim * 4),\n nn.SiLU(),\n nn.Linear(dim * 4, dim * 4),\n nn.SiLU(),\n nn.Linear(dim * 4, dim),\n )\n \n def forward(self, x0: torch.Tensor) -> torch.Tensor:\n B, d = x0.shape\n assert d == self.dim\n \n # Sequential structure:\n # [0]: Linear(dim+1, dim*4)\n # [1]: SiLU\n # [2]: Linear(dim*4, dim*4)\n # [3]: SiLU\n # [4]: Linear(dim*4, dim)\n layers = list(self.velocity.children())\n w1 = layers[0].weight\n b1 = layers[0].bias\n w2 = layers[2].weight\n b2 = layers[2].bias\n w3 = layers[4].weight\n b3 = layers[4].bias\n \n # Ensure contiguous\n w1 = w1.contiguous()\n b1 = b1.contiguous()\n w2 = w2.contiguous()\n b2 = b2.contiguous()\n w3 = w3.contiguous()\n b3 = b3.contiguous()\n x0 = x0.contiguous()\n \n return fused_ode_ext.fused_ode_forward(\n x0, w1, b1, w2, b2, w3, b3, self.num_steps\n )" }
result ← profile_kernel (ok)
okprofile_kernel profile_kernel PASSED: profiling complete. === Kernel Profile Summary === --- Kernel Breakdown (by GPU time) --- #1: aten::empty_like 49.0μs (68%) calls=1 #2: aten::empty_strided 23.0μs (32%) calls=1 --- Timing --- GPU time: 1556.61 μs --- Memory Bandwidth --- DRAM BW: 0.3/3350 GB/s (0.0%) read=0.3 write=0.0 GB/s Hit rates: L2=104.0% --- Compute Throughput --- Pipe util: FMA=1.4%, Tensor=0.0% --- Roofline Analysis --- Ridge point (FP32): 20.00 FLOPs/byte Classification: UNKNOWN --- Occupancy --- Achieved: 12.5% Eligible warps/cycle: 0.03 WARNING: <1 eligible warp/cycle = latency-bound, needs more parallelism Launch: regs/thread=32, smem/blk=3712B, block=256, grid=8 --- Memory Access Quality --- Global ld coalescing: 31.84 sectors/req (31.8x wasted BW) --- Warp Stall Reasons (% of issue cycles) --- long_scoreboard 4416.5% #################### short_scoreboard 108.1% #################### --- Optimization Hints --- -> 4416% stalls: global memory latency (waiting for DRAM/L2). + sectors/req=31.8 -> uncoalesced global loads, restructure access pattern or use __ldg Try shared-memory tiling, prefetching, or reducing working set. -> Global load coalescing=31.8x (ideal=1.0) -> 32x wasted DRAM BW. Make per-warp accesses contiguous. -> Low occupancy (12%). Consider __launch_bounds__ or reducing register pressure. -> Low eligible warps + low BW% + low compute% = LATENCY-BOUND. Need more parallelism (larger grid, more ILP, prefetching).
turn 7 · 1 tool call(s) · 321.5s turn · 29.4s LLM · tokens in=15,871 · out=3,238 · total=19,109 · 13,329 chars (click to expand)
turn 7321.5s turn · 29.4s LLM · 292.1s tools · tokens in=15,871 · out=3,238 · total=19,109
reasoning
The profiling shows: 1. Very low occupancy (12.5%) - only 8 blocks with 256 threads each 2. Memory access is highly uncoalesced (31.8x wasted BW) 3. The kernel is latency-bound 4. Most time is spent in PyTorch operations (aten::empty_like, etc.) The issue is that the kernel is launched with only 8 blocks (batch_size=8), and each block has 256 threads. This gives low occupancy. The main issue is that the hidden_dim matrix-vector multiplication is done by having each thread compute one output element, but threads access weights in a strided pattern which is uncoalesced. Let me try a different approach: 1. Use more threads per block and parallelize across both batch and hidden dimensions 2. Use warp-level primitives for reduction or better access patterns Actually, looking at this more carefully, the problem is that the batch size is small (8), so we only launch 8 blocks. The hidden dimension is dim*4 = 256, so we have 256 threads per block. The main optimization opportunity is: 1. Improve memory coalescing by having threads in a warp access contiguous memory 2. Use warp-level tiling to share computation Let me try a warp-level approach where we parallelize within warps for the matrix-vector products.
assistantThe profiling shows the kernel is latency-bound with uncoalesced memory accesses. The main issues are: 1. Only 8 blocks (batch_size=8), each with 256 threads - low occupancy 2. Weight access pattern is strided (each thread reads one row of the weight matrix) 3. This leads to very poor memory coalescing (31.8x wasted BW) Let me rewrite the kernel with a warp-level tiling approach for better memory access patterns:
call → compile_kernel
callcompile_kernel { "kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\n# Load and compile the CUDA kernel\ncuda_source = \"\"\"\n#include <torch/extension.h>\n#include <cuda.h>\n#include <cuda_runtime.h>\n#include <cmath>\n\n// SiLU activation: x * sigmoid(x)\n__device__ __forceinline__ float silu(float x) {\n return x * (1.0f / (1.0f + expf(-x)));\n}\n\n// Warp-level matrix-vector multiply: each warp computes one output row\n// input: [IN_DIM], weight: [OUT_DIM * IN_DIM], bias: [OUT_DIM]\n// Each thread reads a portion of input and weight, then reduces within warp\ntemplate<int IN_DIM, int OUT_DIM>\n__device__ void warp_linear_silu(\n const float* __restrict__ input,\n const float* __restrict__ weight,\n const float* __restrict__ bias,\n float* output,\n int out_idx, // which output row this warp computes\n int lane_id\n) {\n float sum = 0.0f;\n \n // Strided access to input - each thread reads multiple elements\n for (int i = lane_id; i < IN_DIM; i += 32) {\n sum += input[i] * weight[out_idx * IN_DIM + i];\n }\n \n // Reduce within warp\n #pragma unroll\n for (int offset = 16; offset > 0; offset >>= 1) {\n sum += __shfl_down_sync(0xffffffff, sum, offset);\n }\n \n // Lane 0 adds bias and writes output\n if (lane_id == 0) {\n output[out_idx] = silu(sum + bias[out_idx]);\n }\n}\n\ntemplate<int IN_DIM, int OUT_DIM>\n__device__ void warp_linear(\n const float* __restrict__ input,\n const float* __restrict__ weight,\n const float* __restrict__ bias,\n float* output,\n int out_idx,\n int lane_id,\n bool apply_silu\n) {\n float sum = 0.0f;\n \n for (int i = lane_id; i < IN_DIM; i += 32) {\n sum += input[i] * weight[out_idx * IN_DIM + i];\n }\n \n #pragma unroll\n for (int offset = 16; offset > 0; offset >>= 1) {\n sum += __shfl_down_sync(0xffffffff, sum, offset);\n }\n \n if (lane_id == 0) {\n sum += bias[out_idx];\n output[out_idx] = apply_silu ? silu(sum) : sum;\n }\n}\n\n// Main kernel: fused ODE integration\n// Grid: (batch_size * num_warps_per_sample) blocks\n// Block: 32 threads (one warp)\n__global__ void fused_ode_kernel(\n const float* __restrict__ x0,\n const float* __restrict__ w1,\n const float* __restrict__ b1,\n const float* __restrict__ w2,\n const float* __restrict__ b2,\n const float* __restrict__ w3,\n const float* __restrict__ b3,\n float* __restrict__ x_out,\n int dim,\n int hidden_dim,\n int num_steps,\n int batch_size\n) {\n int lane_id = threadIdx.x;\n int warp_id = blockIdx.x;\n int batch_idx = warp_id / (hidden_dim / 32); // Each sample uses hidden_dim/32 warps\n int local_warp_id = warp_id % (hidden_dim / 32);\n \n if (batch_idx >= batch_size || lane_id >= 32) return;\n \n // Shared memory for this sample's data\n // We'll use global memory for x and intermediates, shared for tiling if needed\n // Actually, let's have each warp compute 32 output elements\n \n // Each warp computes 32 consecutive output elements\n int out_start = local_warp_id * 32;\n \n // Pointer to this sample's x in global memory\n // We need shared memory to hold x for the integration\n // Use a different approach: each block processes one batch sample\n // with multiple warps cooperating\n \n // Simplified: process one batch per block with multiple warps\n}\n\n// Alternative: one block per sample, multiple warps per block\n__global__ void fused_ode_kernel_v2(\n const float* __restrict__ x0,\n const float* __restrict__ w1,\n const float* __restrict__ b1,\n const float* __restrict__ w2,\n const float* __restrict__ b2,\n const float* __restrict__ w3,\n const float* __restrict__ b3,\n float* __restrict__ x_out,\n int dim,\n int hidden_dim,\n int num_steps,\n int batch_size\n) {\n int batch_idx = blockIdx.x;\n int lane_id = threadIdx.x & 31;\n int warp_id = threadIdx.x >> 5;\n int warps_per_block = blockDim.x >> 5;\n \n if (batch_idx >= batch_size) return;\n \n // Shared memory\n extern __shared__ char smem[];\n float* s_x = reinterpret_cast<float*>(smem); // dim\n float* s_input = s_x + dim; // dim + 1\n float* s_hidden1 = s_input + dim + 1; // hidden_dim\n float* s_hidden2 = s_hidden1 + hidden_dim; // hidden_dim\n \n // Initialize x from x0 (cooperative load)\n for (int i = threadIdx.x; i < dim; i += blockDim.x) {\n s_x[i] = x0[batch_idx * dim + i];\n }\n __syncthreads();\n \n float dt = 1.0f / float(num_steps);\n \n // Euler integration\n for (int step = 0; step < num_steps; step++) {\n float t = (float(step) + 0.5f) / float(num_steps);\n \n // Build input [x, t]\n for (int i = threadIdx.x; i < dim; i += blockDim.x) {\n s_input[i] = s_x[i];\n }\n if (threadIdx.x == 0) {\n s_input[dim] = t;\n }\n __syncthreads();\n \n // Layer 1: (dim+1) -> hidden_dim with SiLU\n // Each warp computes multiple outputs\n int outputs_per_warp = (hidden_dim + warps_per_block - 1) / warps_per_block;\n int my_out_start = warp_id * outputs_per_warp;\n int my_out_end = min(my_out_start + outputs_per_warp, hidden_dim);\n \n for (int out_idx = my_out_start + lane_id; out_idx < my_out_end; out_idx += 32) {\n float sum = b1[out_idx];\n for (int i = 0; i < dim + 1; i++) {\n sum += s_input[i] * w1[out_idx * (dim + 1) + i];\n }\n s_hidden1[out_idx] = silu(sum);\n }\n __syncthreads();\n \n // Layer 2: hidden_dim -> hidden_dim with SiLU\n outputs_per_warp = (hidden_dim + warps_per_block - 1) / warps_per_block;\n my_out_start = warp_id * outputs_per_warp;\n my_out_end = min(my_out_start + outputs_per_warp, hidden_dim);\n \n for (int out_idx = my_out_start + lane_id; out_idx < my_out_end; out_idx += 32) {\n float sum = b2[out_idx];\n for (int i = 0; i < hidden_dim; i++) {\n sum += s_hidden1[i] * w2[out_idx * hidden_dim + i];\n }\n s_hidden2[out_idx] = silu(sum);\n }\n __syncthreads();\n \n // Layer 3: hidden_dim -> dim (no activation)\n outputs_per_warp = (dim + warps_per_block - 1) / warps_per_block;\n my_out_start = warp_id * outputs_per_warp;\n my_out_end = min(my_out_start + outputs_per_warp, dim);\n \n for (int out_idx = my_out_start + lane_id; out_idx < my_out_end; out_idx += 32) {\n float sum = b3[out_idx];\n for (int i = 0; i < hidden_dim; i++) {\n sum += s_hidden2[i] * w3[out_idx * hidden_dim + i];\n }\n s_x[out_idx] = s_x[out_idx] + dt * sum;\n }\n __syncthreads();\n }\n \n // Write output\n for (int i = threadIdx.x; i < dim; i += blockDim.x) {\n x_out[batch_idx * dim + i] = s_x[i];\n }\n}\n\n// Host function\ntorch::Tensor fused_ode_forward(\n torch::Tensor x0,\n torch::Tensor w1,\n torch::Tensor b1,\n torch::Tensor w2,\n torch::Tensor b2,\n torch::Tensor w3,\n torch::Tensor b3,\n int64_t num_steps\n) {\n TORCH_CHECK(x0.is_cuda(), \"x0 must be CUDA tensor\");\n TORCH_CHECK(x0.dim() == 2, \"x0 must be 2D\");\n \n int batch_size = x0.size(0);\n int dim = x0.size(1);\n int hidden_dim = w1.size(0);\n \n auto x_out = torch::empty_like(x0);\n \n // Shared memory: x + input + hidden1 + hidden2\n int smem_size = (dim + dim + 1 + hidden_dim * 2) * sizeof(float);\n \n // Use 256 or 512 threads per block for better occupancy\n int threads = 256;\n if (hidden_dim <= 128) threads = 128;\n if (hidden_dim > 256) threads = 512;\n threads = min(threads, 1024);\n \n fused_ode_kernel_v2<<<batch_size, threads, smem_size>>>(\n x0.data_ptr<float>(),\n w1.data_ptr<float>(),\n b1.data_ptr<float>(),\n w2.data_ptr<float>(),\n b2.data_ptr<float>(),\n w3.data_ptr<float>(),\n b3.data_ptr<float>(),\n x_out.data_ptr<float>(),\n dim,\n hidden_dim,\n num_steps,\n batch_size\n );\n \n return x_out;\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor fused_ode_forward(\n torch::Tensor x0,\n torch::Tensor w1,\n torch::Tensor b1,\n torch::Tensor w2,\n torch::Tensor b2,\n torch::Tensor w3,\n torch::Tensor b3,\n int64_t num_steps\n);\n\"\"\"\n\n# Load the extension\nfused_ode_ext = load_inline(\n name='fused_ode_ext_v2',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['fused_ode_forward'],\n extra_cuda_cflags=['-O3', '-use_fast_math'],\n verbose=False\n)\n\n\nclass ModelNew(nn.Module):\n def __init__(self, dim: int, num_steps: int):\n super().__init__()\n assert dim >= 1 and num_steps >= 1\n self.dim = dim\n self.num_steps = num_steps\n self.register_buffer(\"dt\", torch.tensor(1.0 / float(num_steps)))\n \n # Velocity network: same architecture as reference\n self.velocity = nn.Sequential(\n nn.Linear(dim + 1, dim * 4),\n nn.SiLU(),\n nn.Linear(dim * 4, dim * 4),\n nn.SiLU(),\n nn.Linear(dim * 4, dim),\n )\n \n def forward(self, x0: torch.Tensor) -> torch.Tensor:\n B, d = x0.shape\n assert d == self.dim\n \n # Sequential structure:\n # [0]: Linear(dim+1, dim*4)\n # [1]: SiLU\n # [2]: Linear(dim*4, dim*4)\n # [3]: SiLU\n # [4]: Linear(dim*4, dim)\n layers = list(self.velocity.children())\n w1 = layers[0].weight\n b1 = layers[0].bias\n w2 = layers[2].weight\n b2 = layers[2].bias\n w3 = layers[4].weight\n b3 = layers[4].bias\n \n # Ensure contiguous\n w1 = w1.contiguous()\n b1 = b1.contiguous()\n w2 = w2.contiguous()\n b2 = b2.contiguous()\n w3 = w3.contiguous()\n b3 = b3.contiguous()\n x0 = x0.contiguous()\n \n return fused_ode_ext.fused_ode_forward(\n x0, w1, b1, w2, b2, w3, b3, self.num_steps\n )" }
result ← compile_kernel (ok)
okcompile_kernel compile_kernel PASSED: kernel compiled without errors.
turn 8 · 1 tool call(s) · 324.1s turn · 17.4s LLM · tokens in=18,843 · out=2,039 · total=20,882 · 8,570 chars (click to expand)
turn 8324.1s turn · 17.4s LLM · 306.7s tools · tokens in=18,843 · out=2,039 · total=20,882
reasoning
Let me check correctness again.
call → run_correctness
callrun_correctness { "kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\n# Load and compile the CUDA kernel\ncuda_source = \"\"\"\n#include <torch/extension.h>\n#include <cuda.h>\n#include <cuda_runtime.h>\n#include <cmath>\n\n// SiLU activation: x * sigmoid(x)\n__device__ __forceinline__ float silu(float x) {\n return x * (1.0f / (1.0f + expf(-x)));\n}\n\n// Alternative: one block per sample, multiple warps per block\n__global__ void fused_ode_kernel_v2(\n const float* __restrict__ x0,\n const float* __restrict__ w1,\n const float* __restrict__ b1,\n const float* __restrict__ w2,\n const float* __restrict__ b2,\n const float* __restrict__ w3,\n const float* __restrict__ b3,\n float* __restrict__ x_out,\n int dim,\n int hidden_dim,\n int num_steps,\n int batch_size\n) {\n int batch_idx = blockIdx.x;\n int lane_id = threadIdx.x & 31;\n int warp_id = threadIdx.x >> 5;\n int warps_per_block = blockDim.x >> 5;\n \n if (batch_idx >= batch_size) return;\n \n // Shared memory\n extern __shared__ char smem[];\n float* s_x = reinterpret_cast<float*>(smem); // dim\n float* s_input = s_x + dim; // dim + 1\n float* s_hidden1 = s_input + dim + 1; // hidden_dim\n float* s_hidden2 = s_hidden1 + hidden_dim; // hidden_dim\n \n // Initialize x from x0 (cooperative load)\n for (int i = threadIdx.x; i < dim; i += blockDim.x) {\n s_x[i] = x0[batch_idx * dim + i];\n }\n __syncthreads();\n \n float dt = 1.0f / float(num_steps);\n \n // Euler integration\n for (int step = 0; step < num_steps; step++) {\n float t = (float(step) + 0.5f) / float(num_steps);\n \n // Build input [x, t]\n for (int i = threadIdx.x; i < dim; i += blockDim.x) {\n s_input[i] = s_x[i];\n }\n if (threadIdx.x == 0) {\n s_input[dim] = t;\n }\n __syncthreads();\n \n // Layer 1: (dim+1) -> hidden_dim with SiLU\n // Each warp computes multiple outputs\n int outputs_per_warp = (hidden_dim + warps_per_block - 1) / warps_per_block;\n int my_out_start = warp_id * outputs_per_warp;\n int my_out_end = min(my_out_start + outputs_per_warp, hidden_dim);\n \n for (int out_idx = my_out_start + lane_id; out_idx < my_out_end; out_idx += 32) {\n float sum = b1[out_idx];\n for (int i = 0; i < dim + 1; i++) {\n sum += s_input[i] * w1[out_idx * (dim + 1) + i];\n }\n s_hidden1[out_idx] = silu(sum);\n }\n __syncthreads();\n \n // Layer 2: hidden_dim -> hidden_dim with SiLU\n outputs_per_warp = (hidden_dim + warps_per_block - 1) / warps_per_block;\n my_out_start = warp_id * outputs_per_warp;\n my_out_end = min(my_out_start + outputs_per_warp, hidden_dim);\n \n for (int out_idx = my_out_start + lane_id; out_idx < my_out_end; out_idx += 32) {\n float sum = b2[out_idx];\n for (int i = 0; i < hidden_dim; i++) {\n sum += s_hidden1[i] * w2[out_idx * hidden_dim + i];\n }\n s_hidden2[out_idx] = silu(sum);\n }\n __syncthreads();\n \n // Layer 3: hidden_dim -> dim (no activation)\n outputs_per_warp = (dim + warps_per_block - 1) / warps_per_block;\n my_out_start = warp_id * outputs_per_warp;\n my_out_end = min(my_out_start + outputs_per_warp, dim);\n \n for (int out_idx = my_out_start + lane_id; out_idx < my_out_end; out_idx += 32) {\n float sum = b3[out_idx];\n for (int i = 0; i < hidden_dim; i++) {\n sum += s_hidden2[i] * w3[out_idx * hidden_dim + i];\n }\n s_x[out_idx] = s_x[out_idx] + dt * sum;\n }\n __syncthreads();\n }\n \n // Write output\n for (int i = threadIdx.x; i < dim; i += blockDim.x) {\n x_out[batch_idx * dim + i] = s_x[i];\n }\n}\n\n// Host function\ntorch::Tensor fused_ode_forward(\n torch::Tensor x0,\n torch::Tensor w1,\n torch::Tensor b1,\n torch::Tensor w2,\n torch::Tensor b2,\n torch::Tensor w3,\n torch::Tensor b3,\n int64_t num_steps\n) {\n TORCH_CHECK(x0.is_cuda(), \"x0 must be CUDA tensor\");\n TORCH_CHECK(x0.dim() == 2, \"x0 must be 2D\");\n \n int batch_size = x0.size(0);\n int dim = x0.size(1);\n int hidden_dim = w1.size(0);\n \n auto x_out = torch::empty_like(x0);\n \n // Shared memory: x + input + hidden1 + hidden2\n int smem_size = (dim + dim + 1 + hidden_dim * 2) * sizeof(float);\n \n // Use 256 or 512 threads per block for better occupancy\n int threads = 256;\n if (hidden_dim <= 128) threads = 128;\n if (hidden_dim > 256) threads = 512;\n threads = min(threads, 1024);\n \n fused_ode_kernel_v2<<<batch_size, threads, smem_size>>>(\n x0.data_ptr<float>(),\n w1.data_ptr<float>(),\n b1.data_ptr<float>(),\n w2.data_ptr<float>(),\n b2.data_ptr<float>(),\n w3.data_ptr<float>(),\n b3.data_ptr<float>(),\n x_out.data_ptr<float>(),\n dim,\n hidden_dim,\n num_steps,\n batch_size\n );\n \n return x_out;\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor fused_ode_forward(\n torch::Tensor x0,\n torch::Tensor w1,\n torch::Tensor b1,\n torch::Tensor w2,\n torch::Tensor b2,\n torch::Tensor w3,\n torch::Tensor b3,\n int64_t num_steps\n);\n\"\"\"\n\n# Load the extension\nfused_ode_ext = load_inline(\n name='fused_ode_ext_v2',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['fused_ode_forward'],\n extra_cuda_cflags=['-O3', '-use_fast_math'],\n verbose=False\n)\n\n\nclass ModelNew(nn.Module):\n def __init__(self, dim: int, num_steps: int):\n super().__init__()\n assert dim >= 1 and num_steps >= 1\n self.dim = dim\n self.num_steps = num_steps\n self.register_buffer(\"dt\", torch.tensor(1.0 / float(num_steps)))\n \n # Velocity network: same architecture as reference\n self.velocity = nn.Sequential(\n nn.Linear(dim + 1, dim * 4),\n nn.SiLU(),\n nn.Linear(dim * 4, dim * 4),\n nn.SiLU(),\n nn.Linear(dim * 4, dim),\n )\n \n def forward(self, x0: torch.Tensor) -> torch.Tensor:\n B, d = x0.shape\n assert d == self.dim\n \n # Sequential structure:\n # [0]: Linear(dim+1, dim*4)\n # [1]: SiLU\n # [2]: Linear(dim*4, dim*4)\n # [3]: SiLU\n # [4]: Linear(dim*4, dim)\n layers = list(self.velocity.children())\n w1 = layers[0].weight\n b1 = layers[0].bias\n w2 = layers[2].weight\n b2 = layers[2].bias\n w3 = layers[4].weight\n b3 = layers[4].bias\n \n # Ensure contiguous\n w1 = w1.contiguous()\n b1 = b1.contiguous()\n w2 = w2.contiguous()\n b2 = b2.contiguous()\n w3 = w3.contiguous()\n b3 = b3.contiguous()\n x0 = x0.contiguous()\n \n return fused_ode_ext.fused_ode_forward(\n x0, w1, b1, w2, b2, w3, b3, self.num_steps\n )" }
result ← run_correctness (ok)
okrun_correctness run_correctness PASSED: (3 / 3) trials all matched the reference. Numerical precision: max_abs_err=2.38e-07 mean_abs_err=1.79e-08 max_rel_err=2.34e-06
turn 9 · 1 tool call(s) · 247.1s turn · 17.0s LLM · tokens in=20,933 · out=2,063 · total=22,996 · 10,385 chars (click to expand)
turn 9247.1s turn · 17.0s LLM · 230.1s tools · tokens in=20,933 · out=2,063 · total=22,996
reasoning
Good, correctness still passes. Let me profile this new version to see if it's better.
assistantGood, correctness still passes. Let me profile this version:
call → profile_kernel
callprofile_kernel { "kernel_code": "import torch\nimport torch.nn as nn\nfrom torch.utils.cpp_extension import load_inline\n\n# Load and compile the CUDA kernel\ncuda_source = \"\"\"\n#include <torch/extension.h>\n#include <cuda.h>\n#include <cuda_runtime.h>\n#include <cmath>\n\n// SiLU activation: x * sigmoid(x)\n__device__ __forceinline__ float silu(float x) {\n return x * (1.0f / (1.0f + expf(-x)));\n}\n\n// Alternative: one block per sample, multiple warps per block\n__global__ void fused_ode_kernel_v2(\n const float* __restrict__ x0,\n const float* __restrict__ w1,\n const float* __restrict__ b1,\n const float* __restrict__ w2,\n const float* __restrict__ b2,\n const float* __restrict__ w3,\n const float* __restrict__ b3,\n float* __restrict__ x_out,\n int dim,\n int hidden_dim,\n int num_steps,\n int batch_size\n) {\n int batch_idx = blockIdx.x;\n int lane_id = threadIdx.x & 31;\n int warp_id = threadIdx.x >> 5;\n int warps_per_block = blockDim.x >> 5;\n \n if (batch_idx >= batch_size) return;\n \n // Shared memory\n extern __shared__ char smem[];\n float* s_x = reinterpret_cast<float*>(smem); // dim\n float* s_input = s_x + dim; // dim + 1\n float* s_hidden1 = s_input + dim + 1; // hidden_dim\n float* s_hidden2 = s_hidden1 + hidden_dim; // hidden_dim\n \n // Initialize x from x0 (cooperative load)\n for (int i = threadIdx.x; i < dim; i += blockDim.x) {\n s_x[i] = x0[batch_idx * dim + i];\n }\n __syncthreads();\n \n float dt = 1.0f / float(num_steps);\n \n // Euler integration\n for (int step = 0; step < num_steps; step++) {\n float t = (float(step) + 0.5f) / float(num_steps);\n \n // Build input [x, t]\n for (int i = threadIdx.x; i < dim; i += blockDim.x) {\n s_input[i] = s_x[i];\n }\n if (threadIdx.x == 0) {\n s_input[dim] = t;\n }\n __syncthreads();\n \n // Layer 1: (dim+1) -> hidden_dim with SiLU\n // Each warp computes multiple outputs\n int outputs_per_warp = (hidden_dim + warps_per_block - 1) / warps_per_block;\n int my_out_start = warp_id * outputs_per_warp;\n int my_out_end = min(my_out_start + outputs_per_warp, hidden_dim);\n \n for (int out_idx = my_out_start + lane_id; out_idx < my_out_end; out_idx += 32) {\n float sum = b1[out_idx];\n for (int i = 0; i < dim + 1; i++) {\n sum += s_input[i] * w1[out_idx * (dim + 1) + i];\n }\n s_hidden1[out_idx] = silu(sum);\n }\n __syncthreads();\n \n // Layer 2: hidden_dim -> hidden_dim with SiLU\n outputs_per_warp = (hidden_dim + warps_per_block - 1) / warps_per_block;\n my_out_start = warp_id * outputs_per_warp;\n my_out_end = min(my_out_start + outputs_per_warp, hidden_dim);\n \n for (int out_idx = my_out_start + lane_id; out_idx < my_out_end; out_idx += 32) {\n float sum = b2[out_idx];\n for (int i = 0; i < hidden_dim; i++) {\n sum += s_hidden1[i] * w2[out_idx * hidden_dim + i];\n }\n s_hidden2[out_idx] = silu(sum);\n }\n __syncthreads();\n \n // Layer 3: hidden_dim -> dim (no activation)\n outputs_per_warp = (dim + warps_per_block - 1) / warps_per_block;\n my_out_start = warp_id * outputs_per_warp;\n my_out_end = min(my_out_start + outputs_per_warp, dim);\n \n for (int out_idx = my_out_start + lane_id; out_idx < my_out_end; out_idx += 32) {\n float sum = b3[out_idx];\n for (int i = 0; i < hidden_dim; i++) {\n sum += s_hidden2[i] * w3[out_idx * hidden_dim + i];\n }\n s_x[out_idx] = s_x[out_idx] + dt * sum;\n }\n __syncthreads();\n }\n \n // Write output\n for (int i = threadIdx.x; i < dim; i += blockDim.x) {\n x_out[batch_idx * dim + i] = s_x[i];\n }\n}\n\n// Host function\ntorch::Tensor fused_ode_forward(\n torch::Tensor x0,\n torch::Tensor w1,\n torch::Tensor b1,\n torch::Tensor w2,\n torch::Tensor b2,\n torch::Tensor w3,\n torch::Tensor b3,\n int64_t num_steps\n) {\n TORCH_CHECK(x0.is_cuda(), \"x0 must be CUDA tensor\");\n TORCH_CHECK(x0.dim() == 2, \"x0 must be 2D\");\n \n int batch_size = x0.size(0);\n int dim = x0.size(1);\n int hidden_dim = w1.size(0);\n \n auto x_out = torch::empty_like(x0);\n \n // Shared memory: x + input + hidden1 + hidden2\n int smem_size = (dim + dim + 1 + hidden_dim * 2) * sizeof(float);\n \n // Use 256 or 512 threads per block for better occupancy\n int threads = 256;\n if (hidden_dim <= 128) threads = 128;\n if (hidden_dim > 256) threads = 512;\n threads = min(threads, 1024);\n \n fused_ode_kernel_v2<<<batch_size, threads, smem_size>>>(\n x0.data_ptr<float>(),\n w1.data_ptr<float>(),\n b1.data_ptr<float>(),\n w2.data_ptr<float>(),\n b2.data_ptr<float>(),\n w3.data_ptr<float>(),\n b3.data_ptr<float>(),\n x_out.data_ptr<float>(),\n dim,\n hidden_dim,\n num_steps,\n batch_size\n );\n \n return x_out;\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor fused_ode_forward(\n torch::Tensor x0,\n torch::Tensor w1,\n torch::Tensor b1,\n torch::Tensor w2,\n torch::Tensor b2,\n torch::Tensor w3,\n torch::Tensor b3,\n int64_t num_steps\n);\n\"\"\"\n\n# Load the extension\nfused_ode_ext = load_inline(\n name='fused_ode_ext_v2',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['fused_ode_forward'],\n extra_cuda_cflags=['-O3', '-use_fast_math'],\n verbose=False\n)\n\n\nclass ModelNew(nn.Module):\n def __init__(self, dim: int, num_steps: int):\n super().__init__()\n assert dim >= 1 and num_steps >= 1\n self.dim = dim\n self.num_steps = num_steps\n self.register_buffer(\"dt\", torch.tensor(1.0 / float(num_steps)))\n \n # Velocity network: same architecture as reference\n self.velocity = nn.Sequential(\n nn.Linear(dim + 1, dim * 4),\n nn.SiLU(),\n nn.Linear(dim * 4, dim * 4),\n nn.SiLU(),\n nn.Linear(dim * 4, dim),\n )\n \n def forward(self, x0: torch.Tensor) -> torch.Tensor:\n B, d = x0.shape\n assert d == self.dim\n \n # Sequential structure:\n # [0]: Linear(dim+1, dim*4)\n # [1]: SiLU\n # [2]: Linear(dim*4, dim*4)\n # [3]: SiLU\n # [4]: Linear(dim*4, dim)\n layers = list(self.velocity.children())\n w1 = layers[0].weight\n b1 = layers[0].bias\n w2 = layers[2].weight\n b2 = layers[2].bias\n w3 = layers[4].weight\n b3 = layers[4].bias\n \n # Ensure contiguous\n w1 = w1.contiguous()\n b1 = b1.contiguous()\n w2 = w2.contiguous()\n b2 = b2.contiguous()\n w3 = w3.contiguous()\n b3 = b3.contiguous()\n x0 = x0.contiguous()\n \n return fused_ode_ext.fused_ode_forward(\n x0, w1, b1, w2, b2, w3, b3, self.num_steps\n )" }
result ← profile_kernel (ok)
okprofile_kernel profile_kernel PASSED: profiling complete. === Kernel Profile Summary === --- Kernel Breakdown (by GPU time) --- #1: aten::empty_like 74.0μs (70%) calls=1 #2: aten::empty_strided 32.0μs (30%) calls=1 --- Timing --- GPU time: 1537.98 μs [↓18.6μs ok] --- Memory Bandwidth --- DRAM BW: 0.3/3350 GB/s (0.0%) read=0.3 write=0.0 GB/s Hit rates: L2=96.9% --- Compute Throughput --- Pipe util: FMA=2.1%, Tensor=0.0% --- Roofline Analysis --- Ridge point (FP32): 20.00 FLOPs/byte Classification: UNKNOWN --- Occupancy --- Achieved: 12.5% Eligible warps/cycle: 0.05 WARNING: <1 eligible warp/cycle = latency-bound, needs more parallelism Launch: regs/thread=32, smem/blk=3712B, block=256, grid=8 --- Memory Access Quality --- Global ld coalescing: 21.26 sectors/req (21.3x wasted BW) --- Warp Stall Reasons (% of issue cycles) --- long_scoreboard 3386.6% #################### short_scoreboard 89.8% ################# --- Optimization Hints --- -> 3387% stalls: global memory latency (waiting for DRAM/L2). + sectors/req=21.3 -> uncoalesced global loads, restructure access pattern or use __ldg Try shared-memory tiling, prefetching, or reducing working set. -> Global load coalescing=21.3x (ideal=1.0) -> 21x wasted DRAM BW. Make per-warp accesses contiguous. -> Low occupancy (12%). Consider __launch_bounds__ or reducing register pressure. -> Low eligible warps + low BW% + low compute% = LATENCY-BOUND. Need more parallelism (larger grid, more ILP, prefetching). --- Delta vs Previous Iteration --- GPU time: 1556.61→1537.98μs (↓18.62) ok Eligible warps/cyc: 0.03→0.05 (↑0.02) ok Ld sectors/req: 31.84→21.26 (↓10.58) ok L2 hit%: 104.04→96.89% (↓7.15) REGRESSED
turn 10 · 1 tool call(s) · 305.6s turn · 36.3s LLM · tokens in=23,565 · out=3,690 · total=27,255 · 15,057 chars (click to expand)
turn 10305.6s turn · 36.3s LLM · 269.3s tools · tokens in=23,565 · out=3,690 · total=27,255
reasoning
The v2 kernel shows slightly better memory coalescing (21.3x vs 31.8x wasted BW), but still has very low occupancy (12.5%) and is latency-bound. The main issue is that we only have 8 blocks for 8 batch samples. Let me think about this more carefully. The weight access pattern is still uncoalesced because: - When thread i reads w1[out_idx * (dim+1) + i], threads in a warp read from different rows but consecutive columns - But the stride between rows (dim+1 = 65) is not contiguous For better coalescing, I should: 1. Have threads within a warp read contiguous addresses 2. This means each thread should compute a different output element, and all threads should read from the same row of weights Actually, the weight matrix is stored as [out_dim, in_dim] (PyTorch convention), so: - w1[row][col] = w1[row * (dim+1) + col] - If threads read w1[out_idx * (dim+1) + i] where out_idx varies by 32 (lane_id), we get strided access - But if we had threads read w1[row * (dim+1) + lane_id], we'd get contiguous access The issue is the inner loop iterates over input dimension i, not the output dimension. Let me think about a different approach. Actually, looking at this more carefully: - We have 8 blocks (batch_size=8), each with 256 threads (hidden_dim=256) - Each thread computes one output element - But the inner loop iterates over i in [0, dim+1), reading s_input[i] and w1[out_idx * (dim+1) + i] - For threads in a warp, out_idx differs by 32, so each thread reads from different rows of w1 The key insight is that the inner loop is serial - we iterate over the input dimension. During this iteration, we read one value from input and one from the weight row. The weight access is w1[out_idx * (dim+1) + i], which for threads in a warp: - out_idx differs by 32 (if we assign consecutive output elements to consecutive lanes) - i is the same for all threads in the iteration - So threads read from w1[out_idx*65 + i] where out_idx differs by 32 - The stride is 32*65 = 2080 elements between consecutive threads' accesses This is indeed strided. But wait - if we assign each warp to compute 32 consecutive outputs, and each lane computes one, then out_idx = my_out_start + lane_id, so threads in a warp compute outputs [my_out_start, my_out_start+32). Actually, looking at the code again: ```cpp for (int out_idx = my_out_start + lane_id; out_idx < my_out_end; out_idx += 32) { ``` So lane 0 computes out_idx = my_out_start, lane 1 computes my_out_start + 1, etc. This means consecutive lanes compute consecutive outputs! So out_idx differs by 1 between lanes, not by 32. Let me trace through: lane_id=0,1,2,...,31; out_idx = my_out_start + lane_id. - All lanes read w1[(my_out_start + lane_id) * 65 + i] - For lane k: address = (my_out_start + k) * 65 + i - Difference between lane k and k+1: 65 elements So consecutive lanes read from addresses that are 65 floats apart. Since each float is 4 bytes, that's 260 bytes. A cache line is 128 bytes (32 floats). So consecutive lanes access different cache lines. For coalesced access, we'd want consecutive lanes to read consecutive addresses. This would require the weight to be transposed to [in_dim, out_dim]. One option is to pre-transpose the weights on the host. But that adds overhead. Another approach is to use __ldg for read-only cache, which can help with some patterns. Let me try a different approach: use warp-wide reductions to compute the outputs more efficiently. Instead of each thread computing one output element, have all threads in a warp cooperate on computing multiple outputs. Actually, let me try a cleaner approach where threads read contiguous memory for weights. We can process the weight in a transposed manner by having all threads iterate together. Here's a better approach: For each output element, the computation is: output[out_idx] = sum over i of input[i] * weight[out_idx][i] + bias[out_idx] We can compute this as: - Thread k handles input elements i where i % 32 == k - Thread k reads input[i] and weight[...] - Then we warp-reduce to get the sum For coalesced weight access, we want threads to read weight[...][i] where i differs by 1 between consecutive threads. But with PyTorch's weight layout [out_dim, in_dim], weight[out_idx][i] is at address out_idx * in_dim + i. Hmm, let me think differently. Instead of reading one row of weights at a time, let's have threads cooperate to read multiple rows. Actually, for small batch sizes like 8, the real issue is that we have very few blocks, limiting occupancy. The GPU has 132 SMs on H100, but we're only using 8 blocks (1 block per sample). That's why occupancy is only 12.5%. Let me try increasing parallelism by processing multiple samples per block, or by splitting the work differently. Actually, wait - the profiling shows that with 8 blocks and 256 threads per block, we're at 12.5% occupancy. Let me check: H100 has 132 SMs, each can run multiple blocks. With shared memory per block being 3712 bytes, and each SM having 228KB, we can fit many blocks per SM. But the limiting factor is likely the number of warps. Actually, the occupancy formula: max warps per SM = 64 (for H100). With 8 blocks * 8 warps = 64 warps total. If the GPU has 132 SMs, that's 64 warps / 132 SMs = 0.48 warps per SM on average. But occupancy is measured as active warps / max warps, so we're getting 12.5% = 8/64 warps per SM. Wait, that's not right either. Let me recalculate: - 8 blocks, each with 256 threads = 8 warps per block - Total warps = 64 - H100 has 132 SMs - If blocks are distributed evenly, each SM gets 64/132 ≈ 0.5 warps - Max warps per SM = 64 - Occupancy ≈ 0.5/64 ≈ 0.8% But the profile shows 12.5% occupancy. Maybe the blocks are concentrated on fewer SMs. Anyway, the key insight is we have very low parallelism. We need to increase the grid size. One approach: process samples and ODE steps in parallel instead of sequentially. Instead of the loop over 32 steps, launch a kernel that processes all steps at once. But that requires storing intermediate states. Another approach: use the batch dimension more effectively. But with batch_size=8, that's limited. Actually, I wonder if the batch_size in the test is small. Let me check the test parameters: - batch_size = 8 - dim = 64 - num_steps = 32 - hidden_dim = dim * 4 = 256 With such a small batch size, the kernel is fundamentally limited by parallelism. Let me try a different approach: make the kernel work-efficient by processing multiple samples per block, or by processing the ODE steps more efficiently. Actually, let me try a different strategy. Since batch_size is small (8), let me use one block per sample but maximize thread utilization. For hidden_dim=256 and dim=64, we need: - Layer 1: 256 outputs - Layer 2: 256 outputs - Layer 3: 64 outputs With 256 threads, each thread computes 1 output for layers 1 and 2, and 1/4 outputs for layer 3. That seems reasonable. The real issue is the strided weight access. Let me try using __ldg to use the read-only cache, which can handle some strided patterns better.
assistantThe profiling still shows poor memory coalescing (21.3x wasted BW) and low occupancy (12.5%). The core issue is that with batch_size=8, we only have 8 blocks, which severely limits parallelism. Let me try a different approach: use `__ldg` for read-only cache on weights and try to improve the memory access pattern by having threads read contiguous weight elements:
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// SiLU activation: x * sigmoid(x)\n__device__ __forceinline__ float silu(float x) {\n return x * (1.0f / (1.0f + expf(-x)));\n}\n\n// Use __ldg for read-only cache on weights\n__device__ __forceinline__ float ldg(const float* ptr) {\n return __ldg(ptr);\n}\n\n// Main kernel: one block per sample\n__global__ void fused_ode_kernel_v3(\n const float* __restrict__ x0,\n const float* __restrict__ w1,\n const float* __restrict__ b1,\n const float* __restrict__ w2,\n const float* __restrict__ b2,\n const float* __restrict__ w3,\n const float* __restrict__ b3,\n float* __restrict__ x_out,\n int dim,\n int hidden_dim,\n int num_steps,\n int batch_size\n) {\n int batch_idx = blockIdx.x;\n int tid = threadIdx.x;\n int blockDim_x = blockDim.x;\n \n if (batch_idx >= batch_size) return;\n \n // Shared memory\n extern __shared__ char smem[];\n float* s_x = reinterpret_cast<float*>(smem);\n float* s_input = s_x + dim;\n float* s_hidden1 = s_input + dim + 1;\n float* s_hidden2 = s_hidden1 + hidden_dim;\n \n // Initialize x from x0 (cooperative load)\n for (int i = tid; i < dim; i += blockDim_x) {\n s_x[i] = x0[batch_idx * dim + i];\n }\n __syncthreads();\n \n const float dt = 1.0f / float(num_steps);\n \n // Precompute row strides for weights\n const int w1_stride = dim + 1;\n const int w2_stride = hidden_dim;\n const int w3_stride = hidden_dim;\n \n // Euler integration\n for (int step = 0; step < num_steps; step++) {\n const float t = (float(step) + 0.5f) / float(num_steps);\n \n // Build input [x, t]\n for (int i = tid; i < dim; i += blockDim_x) {\n s_input[i] = s_x[i];\n }\n if (tid == 0) {\n s_input[dim] = t;\n }\n __syncthreads();\n \n // Layer 1: (dim+1) -> hidden_dim with SiLU\n // Each thread computes one or more outputs\n for (int out_idx = tid; out_idx < hidden_dim; out_idx += blockDim_x) {\n float sum = ldg(&b1[out_idx]);\n // Unroll for better ILP\n #pragma unroll 4\n for (int i = 0; i < dim + 1; i++) {\n sum += s_input[i] * ldg(&w1[out_idx * w1_stride + i]);\n }\n s_hidden1[out_idx] = silu(sum);\n }\n __syncthreads();\n \n // Layer 2: hidden_dim -> hidden_dim with SiLU\n for (int out_idx = tid; out_idx < hidden_dim; out_idx += blockDim_x) {\n float sum = ldg(&b2[out_idx]);\n #pragma unroll 4\n for (int i = 0; i < hidden_dim; i++) {\n sum += s_hidden1[i] * ldg(&w2[out_idx * w2_stride + i]);\n }\n s_hidden2[out_idx] = silu(sum);\n }\n __syncthreads();\n \n // Layer 3: hidden_dim -> dim (no activation)\n for (int out_idx = tid; out_idx < dim; out_idx += blockDim_x) {\n float sum = ldg(&b3[out_idx]);\n #pragma unroll 4\n for (int i = 0; i < hidden_dim; i++) {\n sum += s_hidden2[i] * ldg(&w3[out_idx * w3_stride + i]);\n }\n s_x[out_idx] = s_x[out_idx] + dt * sum;\n }\n __syncthreads();\n }\n \n // Write output\n for (int i = tid; i < dim; i += blockDim_x) {\n x_out[batch_idx * dim + i] = s_x[i];\n }\n}\n\n// Host function\ntorch::Tensor fused_ode_forward(\n torch::Tensor x0,\n torch::Tensor w1,\n torch::Tensor b1,\n torch::Tensor w2,\n torch::Tensor b2,\n torch::Tensor w3,\n torch::Tensor b3,\n int64_t num_steps\n) {\n TORCH_CHECK(x0.is_cuda(), \"x0 must be CUDA tensor\");\n TORCH_CHECK(x0.dim() == 2, \"x0 must be 2D\");\n \n int batch_size = x0.size(0);\n int dim = x0.size(1);\n int hidden_dim = w1.size(0);\n \n auto x_out = torch::empty_like(x0);\n \n // Shared memory: x + input + hidden1 + hidden2\n int smem_size = (dim + dim + 1 + hidden_dim * 2) * sizeof(float);\n \n // Use enough threads to cover hidden_dim\n int threads = hidden_dim;\n threads = (threads + 31) / 32 * 32;\n threads = max(threads, 64);\n threads = min(threads, 1024);\n \n fused_ode_kernel_v3<<<batch_size, threads, smem_size>>>(\n x0.data_ptr<float>(),\n w1.data_ptr<float>(),\n b1.data_ptr<float>(),\n w2.data_ptr<float>(),\n b2.data_ptr<float>(),\n w3.data_ptr<float>(),\n b3.data_ptr<float>(),\n x_out.data_ptr<float>(),\n dim,\n hidden_dim,\n num_steps,\n batch_size\n );\n \n return x_out;\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor fused_ode_forward(\n torch::Tensor x0,\n torch::Tensor w1,\n torch::Tensor b1,\n torch::Tensor w2,\n torch::Tensor b2,\n torch::Tensor w3,\n torch::Tensor b3,\n int64_t num_steps\n);\n\"\"\"\n\nfused_ode_ext = load_inline(\n name='fused_ode_ext_v3',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['fused_ode_forward'],\n extra_cuda_cflags=['-O3', '-use_fast_math'],\n verbose=False\n)\n\n\nclass ModelNew(nn.Module):\n def __init__(self, dim: int, num_steps: int):\n super().__init__()\n assert dim >= 1 and num_steps >= 1\n self.dim = dim\n self.num_steps = num_steps\n self.register_buffer(\"dt\", torch.tensor(1.0 / float(num_steps)))\n \n self.velocity = nn.Sequential(\n nn.Linear(dim + 1, dim * 4),\n nn.SiLU(),\n nn.Linear(dim * 4, dim * 4),\n nn.SiLU(),\n nn.Linear(dim * 4, dim),\n )\n \n def forward(self, x0: torch.Tensor) -> torch.Tensor:\n B, d = x0.shape\n assert d == self.dim\n \n layers = list(self.velocity.children())\n w1 = layers[0].weight.contiguous()\n b1 = layers[0].bias.contiguous()\n w2 = layers[2].weight.contiguous()\n b2 = layers[2].bias.contiguous()\n w3 = layers[4].weight.contiguous()\n b3 = layers[4].bias.contiguous()\n x0 = x0.contiguous()\n \n return fused_ode_ext.fused_ode_forward(\n x0, w1, b1, w2, b2, w3, b3, self.num_steps\n )" }
result ← compile_kernel (ok)
okcompile_kernel compile_kernel PASSED: kernel compiled without errors.
turn 11 · 1 tool call(s) · 159.9s turn · 15.6s LLM · tokens in=25,450 · out=1,797 · total=27,247 · 7,633 chars (click to expand)
turn 11159.9s turn · 15.6s LLM · 144.2s tools · tokens in=25,450 · out=1,797 · total=27,247
reasoning
Let me check correctness and then profile.
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// SiLU activation: x * sigmoid(x)\n__device__ __forceinline__ float silu(float x) {\n return x * (1.0f / (1.0f + expf(-x)));\n}\n\n// Use __ldg for read-only cache on weights\n__device__ __forceinline__ float ldg(const float* ptr) {\n return __ldg(ptr);\n}\n\n// Main kernel: one block per sample\n__global__ void fused_ode_kernel_v3(\n const float* __restrict__ x0,\n const float* __restrict__ w1,\n const float* __restrict__ b1,\n const float* __restrict__ w2,\n const float* __restrict__ b2,\n const float* __restrict__ w3,\n const float* __restrict__ b3,\n float* __restrict__ x_out,\n int dim,\n int hidden_dim,\n int num_steps,\n int batch_size\n) {\n int batch_idx = blockIdx.x;\n int tid = threadIdx.x;\n int blockDim_x = blockDim.x;\n \n if (batch_idx >= batch_size) return;\n \n // Shared memory\n extern __shared__ char smem[];\n float* s_x = reinterpret_cast<float*>(smem);\n float* s_input = s_x + dim;\n float* s_hidden1 = s_input + dim + 1;\n float* s_hidden2 = s_hidden1 + hidden_dim;\n \n // Initialize x from x0 (cooperative load)\n for (int i = tid; i < dim; i += blockDim_x) {\n s_x[i] = x0[batch_idx * dim + i];\n }\n __syncthreads();\n \n const float dt = 1.0f / float(num_steps);\n \n // Precompute row strides for weights\n const int w1_stride = dim + 1;\n const int w2_stride = hidden_dim;\n const int w3_stride = hidden_dim;\n \n // Euler integration\n for (int step = 0; step < num_steps; step++) {\n const float t = (float(step) + 0.5f) / float(num_steps);\n \n // Build input [x, t]\n for (int i = tid; i < dim; i += blockDim_x) {\n s_input[i] = s_x[i];\n }\n if (tid == 0) {\n s_input[dim] = t;\n }\n __syncthreads();\n \n // Layer 1: (dim+1) -> hidden_dim with SiLU\n // Each thread computes one or more outputs\n for (int out_idx = tid; out_idx < hidden_dim; out_idx += blockDim_x) {\n float sum = ldg(&b1[out_idx]);\n // Unroll for better ILP\n #pragma unroll 4\n for (int i = 0; i < dim + 1; i++) {\n sum += s_input[i] * ldg(&w1[out_idx * w1_stride + i]);\n }\n s_hidden1[out_idx] = silu(sum);\n }\n __syncthreads();\n \n // Layer 2: hidden_dim -> hidden_dim with SiLU\n for (int out_idx = tid; out_idx < hidden_dim; out_idx += blockDim_x) {\n float sum = ldg(&b2[out_idx]);\n #pragma unroll 4\n for (int i = 0; i < hidden_dim; i++) {\n sum += s_hidden1[i] * ldg(&w2[out_idx * w2_stride + i]);\n }\n s_hidden2[out_idx] = silu(sum);\n }\n __syncthreads();\n \n // Layer 3: hidden_dim -> dim (no activation)\n for (int out_idx = tid; out_idx < dim; out_idx += blockDim_x) {\n float sum = ldg(&b3[out_idx]);\n #pragma unroll 4\n for (int i = 0; i < hidden_dim; i++) {\n sum += s_hidden2[i] * ldg(&w3[out_idx * w3_stride + i]);\n }\n s_x[out_idx] = s_x[out_idx] + dt * sum;\n }\n __syncthreads();\n }\n \n // Write output\n for (int i = tid; i < dim; i += blockDim_x) {\n x_out[batch_idx * dim + i] = s_x[i];\n }\n}\n\n// Host function\ntorch::Tensor fused_ode_forward(\n torch::Tensor x0,\n torch::Tensor w1,\n torch::Tensor b1,\n torch::Tensor w2,\n torch::Tensor b2,\n torch::Tensor w3,\n torch::Tensor b3,\n int64_t num_steps\n) {\n TORCH_CHECK(x0.is_cuda(), \"x0 must be CUDA tensor\");\n TORCH_CHECK(x0.dim() == 2, \"x0 must be 2D\");\n \n int batch_size = x0.size(0);\n int dim = x0.size(1);\n int hidden_dim = w1.size(0);\n \n auto x_out = torch::empty_like(x0);\n \n // Shared memory: x + input + hidden1 + hidden2\n int smem_size = (dim + dim + 1 + hidden_dim * 2) * sizeof(float);\n \n // Use enough threads to cover hidden_dim\n int threads = hidden_dim;\n threads = (threads + 31) / 32 * 32;\n threads = max(threads, 64);\n threads = min(threads, 1024);\n \n fused_ode_kernel_v3<<<batch_size, threads, smem_size>>>(\n x0.data_ptr<float>(),\n w1.data_ptr<float>(),\n b1.data_ptr<float>(),\n w2.data_ptr<float>(),\n b2.data_ptr<float>(),\n w3.data_ptr<float>(),\n b3.data_ptr<float>(),\n x_out.data_ptr<float>(),\n dim,\n hidden_dim,\n num_steps,\n batch_size\n );\n \n return x_out;\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor fused_ode_forward(\n torch::Tensor x0,\n torch::Tensor w1,\n torch::Tensor b1,\n torch::Tensor w2,\n torch::Tensor b2,\n torch::Tensor w3,\n torch::Tensor b3,\n int64_t num_steps\n);\n\"\"\"\n\nfused_ode_ext = load_inline(\n name='fused_ode_ext_v3',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['fused_ode_forward'],\n extra_cuda_cflags=['-O3', '-use_fast_math'],\n verbose=False\n)\n\n\nclass ModelNew(nn.Module):\n def __init__(self, dim: int, num_steps: int):\n super().__init__()\n assert dim >= 1 and num_steps >= 1\n self.dim = dim\n self.num_steps = num_steps\n self.register_buffer(\"dt\", torch.tensor(1.0 / float(num_steps)))\n \n self.velocity = nn.Sequential(\n nn.Linear(dim + 1, dim * 4),\n nn.SiLU(),\n nn.Linear(dim * 4, dim * 4),\n nn.SiLU(),\n nn.Linear(dim * 4, dim),\n )\n \n def forward(self, x0: torch.Tensor) -> torch.Tensor:\n B, d = x0.shape\n assert d == self.dim\n \n layers = list(self.velocity.children())\n w1 = layers[0].weight.contiguous()\n b1 = layers[0].bias.contiguous()\n w2 = layers[2].weight.contiguous()\n b2 = layers[2].bias.contiguous()\n w3 = layers[4].weight.contiguous()\n b3 = layers[4].bias.contiguous()\n x0 = x0.contiguous()\n \n return fused_ode_ext.fused_ode_forward(\n x0, w1, b1, w2, b2, w3, b3, self.num_steps\n )" }
result ← run_correctness (ok)
okrun_correctness run_correctness PASSED: (3 / 3) trials all matched the reference. Numerical precision: max_abs_err=2.38e-07 mean_abs_err=1.79e-08 max_rel_err=2.34e-06
turn 12 · 1 tool call(s) · 129.9s turn · 15.7s LLM · tokens in=27,328 · out=1,820 · total=29,148 · 9,328 chars (click to expand)
turn 12129.9s turn · 15.7s LLM · 114.1s tools · tokens in=27,328 · out=1,820 · total=29,148
reasoning
The kernel is correct. Let me profile this version to see if the __ldg cache helps with performance, then decide whether to submit or make further optimizations.
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// SiLU activation: x * sigmoid(x)\n__device__ __forceinline__ float silu(float x) {\n return x * (1.0f / (1.0f + expf(-x)));\n}\n\n// Use __ldg for read-only cache on weights\n__device__ __forceinline__ float ldg(const float* ptr) {\n return __ldg(ptr);\n}\n\n// Main kernel: one block per sample\n__global__ void fused_ode_kernel_v3(\n const float* __restrict__ x0,\n const float* __restrict__ w1,\n const float* __restrict__ b1,\n const float* __restrict__ w2,\n const float* __restrict__ b2,\n const float* __restrict__ w3,\n const float* __restrict__ b3,\n float* __restrict__ x_out,\n int dim,\n int hidden_dim,\n int num_steps,\n int batch_size\n) {\n int batch_idx = blockIdx.x;\n int tid = threadIdx.x;\n int blockDim_x = blockDim.x;\n \n if (batch_idx >= batch_size) return;\n \n // Shared memory\n extern __shared__ char smem[];\n float* s_x = reinterpret_cast<float*>(smem);\n float* s_input = s_x + dim;\n float* s_hidden1 = s_input + dim + 1;\n float* s_hidden2 = s_hidden1 + hidden_dim;\n \n // Initialize x from x0 (cooperative load)\n for (int i = tid; i < dim; i += blockDim_x) {\n s_x[i] = x0[batch_idx * dim + i];\n }\n __syncthreads();\n \n const float dt = 1.0f / float(num_steps);\n \n // Precompute row strides for weights\n const int w1_stride = dim + 1;\n const int w2_stride = hidden_dim;\n const int w3_stride = hidden_dim;\n \n // Euler integration\n for (int step = 0; step < num_steps; step++) {\n const float t = (float(step) + 0.5f) / float(num_steps);\n \n // Build input [x, t]\n for (int i = tid; i < dim; i += blockDim_x) {\n s_input[i] = s_x[i];\n }\n if (tid == 0) {\n s_input[dim] = t;\n }\n __syncthreads();\n \n // Layer 1: (dim+1) -> hidden_dim with SiLU\n // Each thread computes one or more outputs\n for (int out_idx = tid; out_idx < hidden_dim; out_idx += blockDim_x) {\n float sum = ldg(&b1[out_idx]);\n // Unroll for better ILP\n #pragma unroll 4\n for (int i = 0; i < dim + 1; i++) {\n sum += s_input[i] * ldg(&w1[out_idx * w1_stride + i]);\n }\n s_hidden1[out_idx] = silu(sum);\n }\n __syncthreads();\n \n // Layer 2: hidden_dim -> hidden_dim with SiLU\n for (int out_idx = tid; out_idx < hidden_dim; out_idx += blockDim_x) {\n float sum = ldg(&b2[out_idx]);\n #pragma unroll 4\n for (int i = 0; i < hidden_dim; i++) {\n sum += s_hidden1[i] * ldg(&w2[out_idx * w2_stride + i]);\n }\n s_hidden2[out_idx] = silu(sum);\n }\n __syncthreads();\n \n // Layer 3: hidden_dim -> dim (no activation)\n for (int out_idx = tid; out_idx < dim; out_idx += blockDim_x) {\n float sum = ldg(&b3[out_idx]);\n #pragma unroll 4\n for (int i = 0; i < hidden_dim; i++) {\n sum += s_hidden2[i] * ldg(&w3[out_idx * w3_stride + i]);\n }\n s_x[out_idx] = s_x[out_idx] + dt * sum;\n }\n __syncthreads();\n }\n \n // Write output\n for (int i = tid; i < dim; i += blockDim_x) {\n x_out[batch_idx * dim + i] = s_x[i];\n }\n}\n\n// Host function\ntorch::Tensor fused_ode_forward(\n torch::Tensor x0,\n torch::Tensor w1,\n torch::Tensor b1,\n torch::Tensor w2,\n torch::Tensor b2,\n torch::Tensor w3,\n torch::Tensor b3,\n int64_t num_steps\n) {\n TORCH_CHECK(x0.is_cuda(), \"x0 must be CUDA tensor\");\n TORCH_CHECK(x0.dim() == 2, \"x0 must be 2D\");\n \n int batch_size = x0.size(0);\n int dim = x0.size(1);\n int hidden_dim = w1.size(0);\n \n auto x_out = torch::empty_like(x0);\n \n // Shared memory: x + input + hidden1 + hidden2\n int smem_size = (dim + dim + 1 + hidden_dim * 2) * sizeof(float);\n \n // Use enough threads to cover hidden_dim\n int threads = hidden_dim;\n threads = (threads + 31) / 32 * 32;\n threads = max(threads, 64);\n threads = min(threads, 1024);\n \n fused_ode_kernel_v3<<<batch_size, threads, smem_size>>>(\n x0.data_ptr<float>(),\n w1.data_ptr<float>(),\n b1.data_ptr<float>(),\n w2.data_ptr<float>(),\n b2.data_ptr<float>(),\n w3.data_ptr<float>(),\n b3.data_ptr<float>(),\n x_out.data_ptr<float>(),\n dim,\n hidden_dim,\n num_steps,\n batch_size\n );\n \n return x_out;\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor fused_ode_forward(\n torch::Tensor x0,\n torch::Tensor w1,\n torch::Tensor b1,\n torch::Tensor w2,\n torch::Tensor b2,\n torch::Tensor w3,\n torch::Tensor b3,\n int64_t num_steps\n);\n\"\"\"\n\nfused_ode_ext = load_inline(\n name='fused_ode_ext_v3',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['fused_ode_forward'],\n extra_cuda_cflags=['-O3', '-use_fast_math'],\n verbose=False\n)\n\n\nclass ModelNew(nn.Module):\n def __init__(self, dim: int, num_steps: int):\n super().__init__()\n assert dim >= 1 and num_steps >= 1\n self.dim = dim\n self.num_steps = num_steps\n self.register_buffer(\"dt\", torch.tensor(1.0 / float(num_steps)))\n \n self.velocity = nn.Sequential(\n nn.Linear(dim + 1, dim * 4),\n nn.SiLU(),\n nn.Linear(dim * 4, dim * 4),\n nn.SiLU(),\n nn.Linear(dim * 4, dim),\n )\n \n def forward(self, x0: torch.Tensor) -> torch.Tensor:\n B, d = x0.shape\n assert d == self.dim\n \n layers = list(self.velocity.children())\n w1 = layers[0].weight.contiguous()\n b1 = layers[0].bias.contiguous()\n w2 = layers[2].weight.contiguous()\n b2 = layers[2].bias.contiguous()\n w3 = layers[4].weight.contiguous()\n b3 = layers[4].bias.contiguous()\n x0 = x0.contiguous()\n \n return fused_ode_ext.fused_ode_forward(\n x0, w1, b1, w2, b2, w3, b3, self.num_steps\n )" }
result ← profile_kernel (ok)
okprofile_kernel profile_kernel PASSED: profiling complete. === Kernel Profile Summary === --- Kernel Breakdown (by GPU time) --- #1: aten::empty_like 58.0μs (68%) calls=1 #2: aten::empty_strided 27.0μs (32%) calls=1 --- Timing --- GPU time: 1681.18 μs [↑143.2μs REGRESSED] --- Memory Bandwidth --- DRAM BW: 0.2/3350 GB/s (0.0%) read=0.2 write=0.0 GB/s Hit rates: L2=97.4% --- Compute Throughput --- Pipe util: FMA=2.9%, Tensor=0.0% --- Roofline Analysis --- Ridge point (FP32): 20.00 FLOPs/byte Classification: UNKNOWN --- Occupancy --- Achieved: 12.5% Eligible warps/cycle: 0.05 WARNING: <1 eligible warp/cycle = latency-bound, needs more parallelism Launch: regs/thread=30, smem/blk=3712B, block=256, grid=8 --- Memory Access Quality --- Global ld coalescing: 31.84 sectors/req (31.8x wasted BW) --- Warp Stall Reasons (% of issue cycles) --- long_scoreboard 2656.0% #################### short_scoreboard 9.8% # --- Optimization Hints --- -> 2656% stalls: global memory latency (waiting for DRAM/L2). + sectors/req=31.8 -> uncoalesced global loads, restructure access pattern or use __ldg Try shared-memory tiling, prefetching, or reducing working set. -> Global load coalescing=31.8x (ideal=1.0) -> 32x wasted DRAM BW. Make per-warp accesses contiguous. -> Low occupancy (12%). Consider __launch_bounds__ or reducing register pressure. -> Low eligible warps + low BW% + low compute% = LATENCY-BOUND. Need more parallelism (larger grid, more ILP, prefetching). --- Delta vs Previous Iteration --- GPU time: 1537.98→1681.18μs (↑143.20) REGRESSED Ld sectors/req: 21.26→31.84 (↑10.58) REGRESSED L2 hit%: 96.89→97.41% (↑0.52) ok
turn 13 · 1 tool call(s) · 17.9s turn · 17.9s LLM · tokens in=29,713 · out=2,001 · total=31,714 · 8,519 chars (click to expand)
turn 1317.9s turn · 17.9s LLM · 0.0s tools · tokens in=29,713 · out=2,001 · total=31,714
reasoning
The kernel is correct but performance isn't great due to low occupancy (only 8 blocks for batch_size=8). The kernel is latency-bound. Let me try one more optimization - using a grid-stride loop approach to process multiple batch samples per thread block, which would increase the grid size and improve occupancy. Or I could try using CUDA streams. Actually, given the constraints of the problem (batch_size=8, dim=64, num_steps=32), the small batch size fundamentally limits parallelism. The PyTorch reference also faces the same challenge, so a fused kernel should still provide speedup by eliminating Python loop overhead and kernel launch overhead. Let me check if the current kernel provides speedup vs the reference. The kernel is correct, so I should submit it and see if it's faster. But given the profiling shows it's still latency-bound with the same issues, maybe I should go back to my earlier v2 kernel which showed better coalescing (21.26 vs 31.84 sectors/req). Let me check the v2 version again - it showed better metrics. I should use that one for submission.
assistantLet me use the v2 kernel which showed better memory coalescing (21.26 vs 31.84 sectors/req):
call → static_check
callstatic_check { "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// SiLU activation: x * sigmoid(x)\n__device__ __forceinline__ float silu(float x) {\n return x * (1.0f / (1.0f + expf(-x)));\n}\n\n__global__ void fused_ode_kernel_v2(\n const float* __restrict__ x0,\n const float* __restrict__ w1,\n const float* __restrict__ b1,\n const float* __restrict__ w2,\n const float* __restrict__ b2,\n const float* __restrict__ w3,\n const float* __restrict__ b3,\n float* __restrict__ x_out,\n int dim,\n int hidden_dim,\n int num_steps,\n int batch_size\n) {\n int batch_idx = blockIdx.x;\n int lane_id = threadIdx.x & 31;\n int warp_id = threadIdx.x >> 5;\n int warps_per_block = blockDim.x >> 5;\n \n if (batch_idx >= batch_size) return;\n \n extern __shared__ char smem[];\n float* s_x = reinterpret_cast<float*>(smem);\n float* s_input = s_x + dim;\n float* s_hidden1 = s_input + dim + 1;\n float* s_hidden2 = s_hidden1 + hidden_dim;\n \n for (int i = threadIdx.x; i < dim; i += blockDim.x) {\n s_x[i] = x0[batch_idx * dim + i];\n }\n __syncthreads();\n \n float dt = 1.0f / float(num_steps);\n \n for (int step = 0; step < num_steps; step++) {\n float t = (float(step) + 0.5f) / float(num_steps);\n \n for (int i = threadIdx.x; i < dim; i += blockDim.x) {\n s_input[i] = s_x[i];\n }\n if (threadIdx.x == 0) {\n s_input[dim] = t;\n }\n __syncthreads();\n \n int outputs_per_warp = (hidden_dim + warps_per_block - 1) / warps_per_block;\n int my_out_start = warp_id * outputs_per_warp;\n int my_out_end = min(my_out_start + outputs_per_warp, hidden_dim);\n \n for (int out_idx = my_out_start + lane_id; out_idx < my_out_end; out_idx += 32) {\n float sum = b1[out_idx];\n for (int i = 0; i < dim + 1; i++) {\n sum += s_input[i] * w1[out_idx * (dim + 1) + i];\n }\n s_hidden1[out_idx] = silu(sum);\n }\n __syncthreads();\n \n outputs_per_warp = (hidden_dim + warps_per_block - 1) / warps_per_block;\n my_out_start = warp_id * outputs_per_warp;\n my_out_end = min(my_out_start + outputs_per_warp, hidden_dim);\n \n for (int out_idx = my_out_start + lane_id; out_idx < my_out_end; out_idx += 32) {\n float sum = b2[out_idx];\n for (int i = 0; i < hidden_dim; i++) {\n sum += s_hidden1[i] * w2[out_idx * hidden_dim + i];\n }\n s_hidden2[out_idx] = silu(sum);\n }\n __syncthreads();\n \n outputs_per_warp = (dim + warps_per_block - 1) / warps_per_block;\n my_out_start = warp_id * outputs_per_warp;\n my_out_end = min(my_out_start + outputs_per_warp, dim);\n \n for (int out_idx = my_out_start + lane_id; out_idx < my_out_end; out_idx += 32) {\n float sum = b3[out_idx];\n for (int i = 0; i < hidden_dim; i++) {\n sum += s_hidden2[i] * w3[out_idx * hidden_dim + i];\n }\n s_x[out_idx] = s_x[out_idx] + dt * sum;\n }\n __syncthreads();\n }\n \n for (int i = threadIdx.x; i < dim; i += blockDim.x) {\n x_out[batch_idx * dim + i] = s_x[i];\n }\n}\n\ntorch::Tensor fused_ode_forward(\n torch::Tensor x0,\n torch::Tensor w1,\n torch::Tensor b1,\n torch::Tensor w2,\n torch::Tensor b2,\n torch::Tensor w3,\n torch::Tensor b3,\n int64_t num_steps\n) {\n TORCH_CHECK(x0.is_cuda(), \"x0 must be CUDA tensor\");\n TORCH_CHECK(x0.dim() == 2, \"x0 must be 2D\");\n \n int batch_size = x0.size(0);\n int dim = x0.size(1);\n int hidden_dim = w1.size(0);\n \n auto x_out = torch::empty_like(x0);\n \n int smem_size = (dim + dim + 1 + hidden_dim * 2) * sizeof(float);\n \n int threads = 256;\n if (hidden_dim <= 128) threads = 128;\n if (hidden_dim > 256) threads = 512;\n threads = min(threads, 1024);\n \n fused_ode_kernel_v2<<<batch_size, threads, smem_size>>>(\n x0.data_ptr<float>(),\n w1.data_ptr<float>(),\n b1.data_ptr<float>(),\n w2.data_ptr<float>(),\n b2.data_ptr<float>(),\n w3.data_ptr<float>(),\n b3.data_ptr<float>(),\n x_out.data_ptr<float>(),\n dim,\n hidden_dim,\n num_steps,\n batch_size\n );\n \n return x_out;\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor fused_ode_forward(\n torch::Tensor x0,\n torch::Tensor w1,\n torch::Tensor b1,\n torch::Tensor w2,\n torch::Tensor b2,\n torch::Tensor w3,\n torch::Tensor b3,\n int64_t num_steps\n);\n\"\"\"\n\nfused_ode_ext = load_inline(\n name='fused_ode_ext_v2',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['fused_ode_forward'],\n extra_cuda_cflags=['-O3', '-use_fast_math'],\n verbose=False\n)\n\n\nclass ModelNew(nn.Module):\n def __init__(self, dim: int, num_steps: int):\n super().__init__()\n assert dim >= 1 and num_steps >= 1\n self.dim = dim\n self.num_steps = num_steps\n self.register_buffer(\"dt\", torch.tensor(1.0 / float(num_steps)))\n \n self.velocity = nn.Sequential(\n nn.Linear(dim + 1, dim * 4),\n nn.SiLU(),\n nn.Linear(dim * 4, dim * 4),\n nn.SiLU(),\n nn.Linear(dim * 4, dim),\n )\n \n def forward(self, x0: torch.Tensor) -> torch.Tensor:\n B, d = x0.shape\n assert d == self.dim\n \n layers = list(self.velocity.children())\n w1 = layers[0].weight.contiguous()\n b1 = layers[0].bias.contiguous()\n w2 = layers[2].weight.contiguous()\n b2 = layers[2].bias.contiguous()\n w3 = layers[4].weight.contiguous()\n b3 = layers[4].bias.contiguous()\n x0 = x0.contiguous()\n \n return fused_ode_ext.fused_ode_forward(\n x0, w1, b1, w2, b2, w3, b3, self.num_steps\n )" }
result ← static_check (ok)
okstatic_check static_check PASSED: no violations or warnings detected.
turn 14 · FINAL · 1 tool call(s) · 369.4s turn · 14.8s LLM · tokens in=31,585 · out=1,768 · total=33,353 · 7,685 chars (click to expand)
turn 14369.4s turn · 14.8s LLM · 354.6s tools · tokens in=31,585 · out=1,768 · total=33,353 · FINAL
reasoning
I need to submit my best kernel now. The v2 kernel showed better memory coalescing characteristics. Let me submit it.
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// SiLU activation: x * sigmoid(x)\n__device__ __forceinline__ float silu(float x) {\n return x * (1.0f / (1.0f + expf(-x)));\n}\n\n__global__ void fused_ode_kernel_v2(\n const float* __restrict__ x0,\n const float* __restrict__ w1,\n const float* __restrict__ b1,\n const float* __restrict__ w2,\n const float* __restrict__ b2,\n const float* __restrict__ w3,\n const float* __restrict__ b3,\n float* __restrict__ x_out,\n int dim,\n int hidden_dim,\n int num_steps,\n int batch_size\n) {\n int batch_idx = blockIdx.x;\n int lane_id = threadIdx.x & 31;\n int warp_id = threadIdx.x >> 5;\n int warps_per_block = blockDim.x >> 5;\n \n if (batch_idx >= batch_size) return;\n \n extern __shared__ char smem[];\n float* s_x = reinterpret_cast<float*>(smem);\n float* s_input = s_x + dim;\n float* s_hidden1 = s_input + dim + 1;\n float* s_hidden2 = s_hidden1 + hidden_dim;\n \n for (int i = threadIdx.x; i < dim; i += blockDim.x) {\n s_x[i] = x0[batch_idx * dim + i];\n }\n __syncthreads();\n \n float dt = 1.0f / float(num_steps);\n \n for (int step = 0; step < num_steps; step++) {\n float t = (float(step) + 0.5f) / float(num_steps);\n \n for (int i = threadIdx.x; i < dim; i += blockDim.x) {\n s_input[i] = s_x[i];\n }\n if (threadIdx.x == 0) {\n s_input[dim] = t;\n }\n __syncthreads();\n \n int outputs_per_warp = (hidden_dim + warps_per_block - 1) / warps_per_block;\n int my_out_start = warp_id * outputs_per_warp;\n int my_out_end = min(my_out_start + outputs_per_warp, hidden_dim);\n \n for (int out_idx = my_out_start + lane_id; out_idx < my_out_end; out_idx += 32) {\n float sum = b1[out_idx];\n for (int i = 0; i < dim + 1; i++) {\n sum += s_input[i] * w1[out_idx * (dim + 1) + i];\n }\n s_hidden1[out_idx] = silu(sum);\n }\n __syncthreads();\n \n outputs_per_warp = (hidden_dim + warps_per_block - 1) / warps_per_block;\n my_out_start = warp_id * outputs_per_warp;\n my_out_end = min(my_out_start + outputs_per_warp, hidden_dim);\n \n for (int out_idx = my_out_start + lane_id; out_idx < my_out_end; out_idx += 32) {\n float sum = b2[out_idx];\n for (int i = 0; i < hidden_dim; i++) {\n sum += s_hidden1[i] * w2[out_idx * hidden_dim + i];\n }\n s_hidden2[out_idx] = silu(sum);\n }\n __syncthreads();\n \n outputs_per_warp = (dim + warps_per_block - 1) / warps_per_block;\n my_out_start = warp_id * outputs_per_warp;\n my_out_end = min(my_out_start + outputs_per_warp, dim);\n \n for (int out_idx = my_out_start + lane_id; out_idx < my_out_end; out_idx += 32) {\n float sum = b3[out_idx];\n for (int i = 0; i < hidden_dim; i++) {\n sum += s_hidden2[i] * w3[out_idx * hidden_dim + i];\n }\n s_x[out_idx] = s_x[out_idx] + dt * sum;\n }\n __syncthreads();\n }\n \n for (int i = threadIdx.x; i < dim; i += blockDim.x) {\n x_out[batch_idx * dim + i] = s_x[i];\n }\n}\n\ntorch::Tensor fused_ode_forward(\n torch::Tensor x0,\n torch::Tensor w1,\n torch::Tensor b1,\n torch::Tensor w2,\n torch::Tensor b2,\n torch::Tensor w3,\n torch::Tensor b3,\n int64_t num_steps\n) {\n TORCH_CHECK(x0.is_cuda(), \"x0 must be CUDA tensor\");\n TORCH_CHECK(x0.dim() == 2, \"x0 must be 2D\");\n \n int batch_size = x0.size(0);\n int dim = x0.size(1);\n int hidden_dim = w1.size(0);\n \n auto x_out = torch::empty_like(x0);\n \n int smem_size = (dim + dim + 1 + hidden_dim * 2) * sizeof(float);\n \n int threads = 256;\n if (hidden_dim <= 128) threads = 128;\n if (hidden_dim > 256) threads = 512;\n threads = min(threads, 1024);\n \n fused_ode_kernel_v2<<<batch_size, threads, smem_size>>>(\n x0.data_ptr<float>(),\n w1.data_ptr<float>(),\n b1.data_ptr<float>(),\n w2.data_ptr<float>(),\n b2.data_ptr<float>(),\n w3.data_ptr<float>(),\n b3.data_ptr<float>(),\n x_out.data_ptr<float>(),\n dim,\n hidden_dim,\n num_steps,\n batch_size\n );\n \n return x_out;\n}\n\"\"\"\n\ncpp_source = \"\"\"\ntorch::Tensor fused_ode_forward(\n torch::Tensor x0,\n torch::Tensor w1,\n torch::Tensor b1,\n torch::Tensor w2,\n torch::Tensor b2,\n torch::Tensor w3,\n torch::Tensor b3,\n int64_t num_steps\n);\n\"\"\"\n\nfused_ode_ext = load_inline(\n name='fused_ode_ext_v2',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['fused_ode_forward'],\n extra_cuda_cflags=['-O3', '-use_fast_math'],\n verbose=False\n)\n\n\nclass ModelNew(nn.Module):\n def __init__(self, dim: int, num_steps: int):\n super().__init__()\n assert dim >= 1 and num_steps >= 1\n self.dim = dim\n self.num_steps = num_steps\n self.register_buffer(\"dt\", torch.tensor(1.0 / float(num_steps)))\n \n self.velocity = nn.Sequential(\n nn.Linear(dim + 1, dim * 4),\n nn.SiLU(),\n nn.Linear(dim * 4, dim * 4),\n nn.SiLU(),\n nn.Linear(dim * 4, dim),\n )\n \n def forward(self, x0: torch.Tensor) -> torch.Tensor:\n B, d = x0.shape\n assert d == self.dim\n \n layers = list(self.velocity.children())\n w1 = layers[0].weight.contiguous()\n b1 = layers[0].bias.contiguous()\n w2 = layers[2].weight.contiguous()\n b2 = layers[2].bias.contiguous()\n w3 = layers[4].weight.contiguous()\n b3 = layers[4].bias.contiguous()\n x0 = x0.contiguous()\n \n return fused_ode_ext.fused_ode_forward(\n x0, w1, b1, w2, b2, w3, b3, self.num_steps\n )" }
result ← submit_kernel (ok)
oksubmit_kernel submit_kernel PASSED: (3 / 3) correctness trials all passed. Kernel runtime: 1.54 μs Runtime stats: mean=1.54μs median=?μs std=0.00μs Numerical precision: max_abs_err=2.38e-07 mean_abs_err=1.79e-08 max_rel_err=2.34e-06 Memory: 33.76 MB peak (ref: 33.78 MB, ratio: 0.9994x) Kernel launches: 2 (ref: 737, fusion ratio: 368.5) SOL score: 0.0001
final submitted kernel (205 lines, 6,046 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>

// SiLU activation: x * sigmoid(x)
__device__ __forceinline__ float silu(float x) {
    return x * (1.0f / (1.0f + expf(-x)));
}

__global__ void fused_ode_kernel_v2(
    const float* __restrict__ x0,
    const float* __restrict__ w1,
    const float* __restrict__ b1,
    const float* __restrict__ w2,
    const float* __restrict__ b2,
    const float* __restrict__ w3,
    const float* __restrict__ b3,
    float* __restrict__ x_out,
    int dim,
    int hidden_dim,
    int num_steps,
    int batch_size
) {
    int batch_idx = blockIdx.x;
    int lane_id = threadIdx.x & 31;
    int warp_id = threadIdx.x >> 5;
    int warps_per_block = blockDim.x >> 5;
    
    if (batch_idx >= batch_size) return;
    
    extern __shared__ char smem[];
    float* s_x = reinterpret_cast<float*>(smem);
    float* s_input = s_x + dim;
    float* s_hidden1 = s_input + dim + 1;
    float* s_hidden2 = s_hidden1 + hidden_dim;
    
    for (int i = threadIdx.x; i < dim; i += blockDim.x) {
        s_x[i] = x0[batch_idx * dim + i];
    }
    __syncthreads();
    
    float dt = 1.0f / float(num_steps);
    
    for (int step = 0; step < num_steps; step++) {
        float t = (float(step) + 0.5f) / float(num_steps);
        
        for (int i = threadIdx.x; i < dim; i += blockDim.x) {
            s_input[i] = s_x[i];
        }
        if (threadIdx.x == 0) {
            s_input[dim] = t;
        }
        __syncthreads();
        
        int outputs_per_warp = (hidden_dim + warps_per_block - 1) / warps_per_block;
        int my_out_start = warp_id * outputs_per_warp;
        int my_out_end = min(my_out_start + outputs_per_warp, hidden_dim);
        
        for (int out_idx = my_out_start + lane_id; out_idx < my_out_end; out_idx += 32) {
            float sum = b1[out_idx];
            for (int i = 0; i < dim + 1; i++) {
                sum += s_input[i] * w1[out_idx * (dim + 1) + i];
            }
            s_hidden1[out_idx] = silu(sum);
        }
        __syncthreads();
        
        outputs_per_warp = (hidden_dim + warps_per_block - 1) / warps_per_block;
        my_out_start = warp_id * outputs_per_warp;
        my_out_end = min(my_out_start + outputs_per_warp, hidden_dim);
        
        for (int out_idx = my_out_start + lane_id; out_idx < my_out_end; out_idx += 32) {
            float sum = b2[out_idx];
            for (int i = 0; i < hidden_dim; i++) {
                sum += s_hidden1[i] * w2[out_idx * hidden_dim + i];
            }
            s_hidden2[out_idx] = silu(sum);
        }
        __syncthreads();
        
        outputs_per_warp = (dim + warps_per_block - 1) / warps_per_block;
        my_out_start = warp_id * outputs_per_warp;
        my_out_end = min(my_out_start + outputs_per_warp, dim);
        
        for (int out_idx = my_out_start + lane_id; out_idx < my_out_end; out_idx += 32) {
            float sum = b3[out_idx];
            for (int i = 0; i < hidden_dim; i++) {
                sum += s_hidden2[i] * w3[out_idx * hidden_dim + i];
            }
            s_x[out_idx] = s_x[out_idx] + dt * sum;
        }
        __syncthreads();
    }
    
    for (int i = threadIdx.x; i < dim; i += blockDim.x) {
        x_out[batch_idx * dim + i] = s_x[i];
    }
}

torch::Tensor fused_ode_forward(
    torch::Tensor x0,
    torch::Tensor w1,
    torch::Tensor b1,
    torch::Tensor w2,
    torch::Tensor b2,
    torch::Tensor w3,
    torch::Tensor b3,
    int64_t num_steps
) {
    TORCH_CHECK(x0.is_cuda(), "x0 must be CUDA tensor");
    TORCH_CHECK(x0.dim() == 2, "x0 must be 2D");
    
    int batch_size = x0.size(0);
    int dim = x0.size(1);
    int hidden_dim = w1.size(0);
    
    auto x_out = torch::empty_like(x0);
    
    int smem_size = (dim + dim + 1 + hidden_dim * 2) * sizeof(float);
    
    int threads = 256;
    if (hidden_dim <= 128) threads = 128;
    if (hidden_dim > 256) threads = 512;
    threads = min(threads, 1024);
    
    fused_ode_kernel_v2<<<batch_size, threads, smem_size>>>(
        x0.data_ptr<float>(),
        w1.data_ptr<float>(),
        b1.data_ptr<float>(),
        w2.data_ptr<float>(),
        b2.data_ptr<float>(),
        w3.data_ptr<float>(),
        b3.data_ptr<float>(),
        x_out.data_ptr<float>(),
        dim,
        hidden_dim,
        num_steps,
        batch_size
    );
    
    return x_out;
}
"""

cpp_source = """
torch::Tensor fused_ode_forward(
    torch::Tensor x0,
    torch::Tensor w1,
    torch::Tensor b1,
    torch::Tensor w2,
    torch::Tensor b2,
    torch::Tensor w3,
    torch::Tensor b3,
    int64_t num_steps
);
"""

fused_ode_ext = load_inline(
    name='fused_ode_ext_v2',
    cpp_sources=cpp_source,
    cuda_sources=cuda_source,
    functions=['fused_ode_forward'],
    extra_cuda_cflags=['-O3', '-use_fast_math'],
    verbose=False
)


class ModelNew(nn.Module):
    def __init__(self, dim: int, num_steps: int):
        super().__init__()
        assert dim >= 1 and num_steps >= 1
        self.dim = dim
        self.num_steps = num_steps
        self.register_buffer("dt", torch.tensor(1.0 / float(num_steps)))
        
        self.velocity = nn.Sequential(
            nn.Linear(dim + 1, dim * 4),
            nn.SiLU(),
            nn.Linear(dim * 4, dim * 4),
            nn.SiLU(),
            nn.Linear(dim * 4, dim),
        )
    
    def forward(self, x0: torch.Tensor) -> torch.Tensor:
        B, d = x0.shape
        assert d == self.dim
        
        layers = list(self.velocity.children())
        w1 = layers[0].weight.contiguous()
        b1 = layers[0].bias.contiguous()
        w2 = layers[2].weight.contiguous()
        b2 = layers[2].bias.contiguous()
        w3 = layers[4].weight.contiguous()
        b3 = layers[4].bias.contiguous()
        x0 = x0.contiguous()
        
        return fused_ode_ext.fused_ode_forward(
            x0, w1, b1, w2, b2, w3, b3, self.num_steps
        )