reasoning
reasoning (truncated 53961 chars): This task requires me to implement a custom CUDA kernel to replace the forward computation of the PyTorch model. The model implements a probability-flow ODE integration using Euler method with a learned velocity field.
Let me understand the model:
1. It takes an initial state `x0` of shape (B, dim)
2. It performs `num_steps` Euler integration steps
3. Each step:
- Computes time `t = (k + 0.5) / num_steps`
- Creates a tensor `t_b` of shape (B, 1) filled with `t`
- Concatenates `x` and `t_b` along the last dimension -> shape (B, dim+1)
- Passes through velocity network: Linear(dim+1, dim*4) -> SiLU -> Linear(dim*4, dim*4) -> SiLU -> Linear(dim*4, dim)
- Updates `x = x + dt * v`
4. Returns the final `x`
The velocity network is:
- Linear(dim+1, dim*4)
- SiLU activation
- Linear(dim*4, dim*4)
- SiLU activation
- Linear(dim*4, dim)
To implement this efficiently in CUDA, I need to:
1. Fuse all the operations into a single kernel
2. Avoid the Python loop overhead
3. Minimize memory transfers
Key challenges:
- The velocity network has three linear layers with SiLU activations
- Need to unroll the `num_steps` iterations
- Each step depends on the previous step's output
Optimization strategies:
1. Fuse all linear layers and activations into a single kernel per step, or better yet, fuse all steps
2. Use shared memory for intermediate results
3. Ensure coalesced memory access
Let me think about the data flow:
- Input: x0 of shape (B, dim)
- For each step:
- Input to velocity: [x, t] of shape (B, dim+1)
- Layer 1 output: (B, dim*4)
- Layer 2 output: (B, dim*4)
- Layer 3 output: (B, dim)
- Update: x = x + dt * v
I need to access the weights from the PyTorch model. The approach is:
1. Load the weights from the trained model
2. Use them in the CUDA kernel
Let me write the CUDA kernel. I'll need to:
1. Store the weights as constants or pass them as pointers
2. Implement matrix-vector multiplication for each linear layer
3. Implement SiLU activation (x * sigmoid(x))
4. Loop through the steps
Since batch_size=8, dim=64, num_steps=32:
- Each batch element is independent, so I can use one thread per batch element
- Each linear layer involves a matrix multiplication
For a batch of 8 elements with dimension 64:
- Layer 1: (dim+1) x (dim*4) = 65 x 256 matrix
- Layer 2: (dim*4) x (dim*4) = 256 x 256 matrix
- Layer 3: (dim*4) x dim = 256 x 64 matrix
The total computation per step is about 65*256 + 256*256 + 256*64 = 16640 + 65536 + 16384 = 98560 multiplications.
With 32 steps, that's about 3.15M operations per batch element, or 25.2M total.
Given the small batch size (8), I should probably have each thread handle one batch element and iterate through all operations.
Let me design the kernel:
- Grid: (B,) - one block per batch element? Or (1,) with threads for each batch element?
- Actually, with B=8, I could have one block with 8 threads (or more for parallelism within each element)
Better approach: Use thread blocks where each block handles a batch element, and threads within the block cooperate on the matrix-vector products.
But wait, with dim=64 and hidden_dim=256, the intermediate tensors are relatively small. I could:
1. Use one thread per batch element (8 threads total) - too few, poor GPU utilization
2. Use one warp per batch element (32 threads, 8 warps = 256 threads total for batch) - better
3. Use multiple warps per batch element for parallelization
Actually, let me think differently. The main computation is the linear layers. For each linear layer:
- For input size N and output size M, we compute output[i] = sum_j(W[i,j] * input[j]) + bias[i]
- This is a matrix-vector product
For the velocity network:
- Input: 65 elements (64 from x + 1 from t)
- Hidden: 256 elements
- Output: 64 elements
Let me use one thread block per batch element, with threads cooperating on the computation:
- Block size: 256 threads (one warp per 32 output elements, or spread differently)
- Each thread computes a portion of the output
For a matrix-vector product with output size M:
- Each thread computes one or more output elements
- Threads can load input cooperatively into shared memory
Let me write a simpler version first:
- One thread per batch element (B threads)
- Each thread serially computes all the linear layers and steps
This won't be optimal but will work. Then I can optimize.
Actually, with such small dimensions, the overhead of kernel launches and synchronization might dominate. Let me consider a different approach:
- Fuse everything into one kernel
- Use shared memory for intermediate results
- Parallelize across batch elements and computation within each batch element
Let me write the kernel:
```cpp
#include <cuda.h>
#include <cuda_runtime.h>
__device__ float silu(float x) {
return x * (1.0f / (1.0f + expf(-x)));
}
// Assumes weights are in global memory, passed as pointers
// Grid: (B, 1, 1), Block: (256, 1, 1)
// Each block handles one batch element
__global__ void flow_ode_kernel(
const float* __restrict__ x0,
float* __restrict__ x_out,
const float* __restrict__ w1, // (dim*4, dim+1)
const float* __restrict__ b1, // (dim*4,)
const float* __restrict__ w2, // (dim*4, dim*4)
const float* __restrict__ b2, // (dim*4,)
const float* __restrict__ w3, // (dim, dim*4)
const float* __restrict__ b3, // (dim,)
int dim,
int num_steps,
float dt
) {
int batch_idx = blockIdx.x;
int tid = threadIdx.x;
// Shared memory for intermediate results
extern __shared__ float shared[];
float* x = shared; // dim
float* hidden1 = x + dim; // dim*4
float* hidden2 = hidden1 + dim * 4; // dim*4
float* v = hidden2 + dim * 4; // dim
float* input = v + dim; // dim + 1
// Load x0 into shared memory
if (tid < dim) {
x[tid] = x0[batch_idx * dim + tid];
}
__syncthreads();
for (int step = 0; step < num_steps; step++) {
float t = (float(step) + 0.5f) / float(num_steps);
// Prepare input: [x, t]
if (tid < dim) {
input[tid] = x[tid];
}
if (tid == 0) {
input[dim] = t;
}
__syncthreads();
// Layer 1: Linear(dim+1, dim*4) + SiLU
for (int i = tid; i < dim * 4; i += blockDim.x) {
float sum = b1[i];
for (int j = 0; j < dim + 1; j++) {
sum += w1[i * (dim + 1) + j] * input[j];
}
hidden1[i] = silu(sum);
}
__syncthreads();
// Layer 2: Linear(dim*4, dim*4) + SiLU
for (int i = tid; i < dim * 4; i += blockDim.x) {
float sum = b2[i];
for (int j = 0; j < dim * 4; j++) {
sum += w2[i * dim * 4 + j] * hidden1[j];
}
hidden2[i] = silu(sum);
}
__syncthreads();
// Layer 3: Linear(dim*4, dim)
for (int i = tid; i < dim; i += blockDim.x) {
float sum = b3[i];
for (int j = 0; j < dim * 4; j++) {
sum += w3[i * dim * 4 + j] * hidden2[j];
}
v[i] = sum;
}
__syncthreads();
// Update: x = x + dt * v
if (tid < dim) {
x[tid] = x[tid] + dt * v[tid];
}
__syncthreads();
}
// Write result to global memory
if (tid < dim) {
x_out[batch_idx * dim + tid] = x[tid];
}
}
```
Wait, the shared memory size needs to be computed properly:
- x: dim = 64 floats
- hidden1: dim * 4 = 256 floats
- hidden2: dim * 4 = 256 floats
- v: dim = 64 floats
- input: dim + 1 = 65 floats
- Total: 64 + 256 + 256 + 64 + 65 = 705 floats = 2820 bytes
This fits easily in shared memory (typically 48KB or more).
Let me think about how to pass the weights. In PyTorch, I need to:
1. Extract weights from the velocity network
2. Pass them to the CUDA kernel
The velocity netwo
...[ omitted 53961 characters ]...
main kernel doesn't need it.
Let me also consider using `__launch_bounds__` to tell the compiler about the maximum block size:
```cpp
__global__ void __launch_bounds__(256) flow_ode_kernel(...)
```
This helps the compiler optimize register usage for the given block size.
Alright, let me update the kernel with these optimizations:
```cpp
__global__ void __launch_bounds__(256) flow_ode_kernel(
const float* __restrict__ x0,
float* __restrict__ x_out,
const float* __restrict__ w1,
const float* __restrict__ b1,
const float* __restrict__ w2,
const float* __restrict__ b2,
const float* __restrict__ w3,
const float* __restrict__ b3,
int dim,
int num_steps,
float dt
) {
const int batch_idx = blockIdx.x;
const int tid = threadIdx.x;
const int block_size = blockDim.x;
const int hidden_size = dim * 4;
const int input_size = dim + 1;
extern __shared__ float shared[];
float* x = shared;
float* hidden1 = x + dim;
float* hidden2 = hidden1 + hidden_size;
float* v = hidden2 + hidden_size;
float* input = v + dim;
for (int i = tid; i < dim; i += block_size) {
x[i] = __ldg(&x0[batch_idx * dim + i]);
}
__syncthreads();
for (int step = 0; step < num_steps; step++) {
const float t = (float(step) + 0.5f) / float(num_steps);
for (int i = tid; i < dim; i += block_size) {
input[i] = x[i];
}
if (tid == 0) input[dim] = t;
__syncthreads();
for (int i = tid; i < hidden_size; i += block_size) {
float sum = b1[i];
const float* w_row = w1 + i * input_size;
for (int j = 0; j < input_size; j++) {
sum += __ldg(&w_row[j]) * input[j];
}
hidden1[i] = silu(sum);
}
__syncthreads();
for (int i = tid; i < hidden_size; i += block_size) {
float sum = b2[i];
const float* w_row = w2 + i * hidden_size;
for (int j = 0; j < hidden_size; j++) {
sum += __ldg(&w_row[j]) * hidden1[j];
}
hidden2[i] = silu(sum);
}
__syncthreads();
for (int i = tid; i < dim; i += block_size) {
float sum = b3[i];
const float* w_row = w3 + i * hidden_size;
for (int j = 0; j < hidden_size; j++) {
sum += __ldg(&w_row[j]) * hidden2[j];
}
v[i] = sum;
}
__syncthreads();
for (int i = tid; i < dim; i += block_size) {
x[i] = fmaf(dt, v[i], x[i]);
}
__syncthreads();
}
for (int i = tid; i < dim; i += block_size) {
x_out[batch_idx * dim + i] = x[i];
}
}
```
I added `__ldg` for reading from `x0` initially, and for reading weights. I also pre-computed the row pointer `w_row` to reduce address computation overhead.
Let me finalize and submit.
One more thing: I should check if the bias vectors need `__ldg`. They're small and accessed once per output element, so caching them shouldn't make a big difference. But for consistency, I'll add it:
```cpp
float sum = __ldg(&b1[i]);
```
Alright, final version:
```python
import torch
import torch.nn as nn
from torch.utils.cpp_extension import load_inline
cuda_source = r"""
#include <cuda.h>
#include <cuda_runtime.h>
__device__ __forceinline__ float silu(float x) {
return x / (1.0f + expf(-x));
}
__global__ void __launch_bounds__(256) flow_ode_kernel(
const float* __restrict__ x0,
float* __restrict__ x_out,
const float* __restrict__ w1,
const float* __restrict__ b1,
const float* __restrict__ w2,
const float* __restrict__ b2,
const float* __restrict__ w3,
const float* __restrict__ b3,
int dim,
int num_steps,
float dt
) {
const int batch_idx = blockIdx.x;
const int tid = threadIdx.x;
const int block_size = blockDim.x;
const int hidden_size = dim * 4;
const int input_size = dim + 1;
extern __shared__ float shared[];
float* x = shared;
float* hidden1 = x + dim;
float* hidden2 = hidden1 + hidden_size;
float* v = hidden2 + hidden_size;
float* input = v + dim;
for (int i = tid; i < dim; i += block_size) {
x[i] = __ldg(&x0[batch_idx * dim + i]);
}
__syncthreads();
for (int step = 0; step < num_steps; step++) {
const float t = (float(step) + 0.5f) / float(num_steps);
for (int i = tid; i < dim; i += block_size) {
input[i] = x[i];
}
if (tid == 0) input[dim] = t;
__syncthreads();
for (int i = tid; i < hidden_size; i += block_size) {
float sum = __ldg(&b1[i]);
for (int j = 0; j < input_size; j++) {
sum += __ldg(&w1[i * input_size + j]) * input[j];
}
hidden1[i] = silu(sum);
}
__syncthreads();
for (int i = tid; i < hidden_size; i += block_size) {
float sum = __ldg(&b2[i]);
for (int j = 0; j < hidden_size; j++) {
sum += __ldg(&w2[i * hidden_size + j]) * hidden1[j];
}
hidden2[i] = silu(sum);
}
__syncthreads();
for (int i = tid; i < dim; i += block_size) {
float sum = __ldg(&b3[i]);
for (int j = 0; j < hidden_size; j++) {
sum += __ldg(&w3[i * hidden_size + j]) * hidden2[j];
}
v[i] = sum;
}
__syncthreads();
for (int i = tid; i < dim; i += block_size) {
x[i] = fmaf(dt, v[i], x[i]);
}
__syncthreads();
}
for (int i = tid; i < dim; i += block_size) {
x_out[batch_idx * dim + i] = x[i];
}
}
torch::Tensor flow_ode_cuda(
torch::Tensor x0,
torch::Tensor w1, torch::Tensor b1,
torch::Tensor w2, torch::Tensor b2,
torch::Tensor w3, torch::Tensor b3,
int dim, int num_steps, float dt
) {
const int B = x0.size(0);
auto x_out = torch::empty_like(x0);
const int threads = 256;
const int shared_mem = (11 * dim + 1) * sizeof(float);
flow_ode_kernel<<<B, threads, shared_mem>>>(
x0.data_ptr<float>(),
x_out.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>(),
dim, num_steps, dt
);
return x_out;
}
"""
flow_ode_module = load_inline(
name='flow_ode',
cpp_sources=['torch::Tensor flow_ode_cuda(torch::Tensor x0, torch::Tensor w1, torch::Tensor b1, torch::Tensor w2, torch::Tensor b2, torch::Tensor w3, torch::Tensor b3, int dim, int num_steps, float dt);'],
cuda_sources=[cuda_source],
functions=['flow_ode_cuda'],
extra_cuda_cflags=['-O3', '-use_fast_math'],
verbose=False
)
class ModelNew(nn.Module):
def __init__(self, dim: int, num_steps: int):
super().__init__()
self.dim = dim
self.num_steps = 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),
)
self.register_buffer("dt", torch.tensor(1.0 / float(num_steps)))
def forward(self, x0: torch.Tensor) -> torch.Tensor:
B, d = x0.shape
assert d == self.dim
w1 = self.velocity[0].weight
b1 = self.velocity[0].bias
w2 = self.velocity[3].weight
b2 = self.velocity[3].bias
w3 = self.velocity[6].weight
b3 = self.velocity[6].bias
return flow_ode_module.flow_ode_cuda(
x0, w1, b1, w2, b2, w3, b3,
self.dim, self.num_steps, self.dt.item()
)
```
This is my final version. 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 = r\"\"\"\n#include <cuda.h>\n#include <cuda_runtime.h>\n\n__device__ __forceinline__ float silu(float x) {\n return x / (1.0f + expf(-x));\n}\n\n__global__ void __launch_bounds__(256) flow_ode_kernel(\n const float* __restrict__ x0,\n float* __restrict__ x_out,\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 int dim,\n int num_steps,\n float dt\n) {\n const int batch_idx = blockIdx.x;\n const int tid = threadIdx.x;\n const int block_size = blockDim.x;\n const int hidden_size = dim * 4;\n const int input_size = dim + 1;\n \n extern __shared__ float shared[];\n float* x = shared;\n float* hidden1 = x + dim;\n float* hidden2 = hidden1 + hidden_size;\n float* v = hidden2 + hidden_size;\n float* input = v + dim;\n \n for (int i = tid; i < dim; i += block_size) {\n x[i] = __ldg(&x0[batch_idx * dim + i]);\n }\n __syncthreads();\n \n for (int step = 0; step < num_steps; step++) {\n const float t = (float(step) + 0.5f) / float(num_steps);\n \n for (int i = tid; i < dim; i += block_size) {\n input[i] = x[i];\n }\n if (tid == 0) input[dim] = t;\n __syncthreads();\n \n for (int i = tid; i < hidden_size; i += block_size) {\n float sum = __ldg(&b1[i]);\n for (int j = 0; j < input_size; j++) {\n sum += __ldg(&w1[i * input_size + j]) * input[j];\n }\n hidden1[i] = silu(sum);\n }\n __syncthreads();\n \n for (int i = tid; i < hidden_size; i += block_size) {\n float sum = __ldg(&b2[i]);\n for (int j = 0; j < hidden_size; j++) {\n sum += __ldg(&w2[i * hidden_size + j]) * hidden1[j];\n }\n hidden2[i] = silu(sum);\n }\n __syncthreads();\n \n for (int i = tid; i < dim; i += block_size) {\n float sum = __ldg(&b3[i]);\n for (int j = 0; j < hidden_size; j++) {\n sum += __ldg(&w3[i * hidden_size + j]) * hidden2[j];\n }\n v[i] = sum;\n }\n __syncthreads();\n \n for (int i = tid; i < dim; i += block_size) {\n x[i] = fmaf(dt, v[i], x[i]);\n }\n __syncthreads();\n }\n \n for (int i = tid; i < dim; i += block_size) {\n x_out[batch_idx * dim + i] = x[i];\n }\n}\n\ntorch::Tensor flow_ode_cuda(\n torch::Tensor x0,\n torch::Tensor w1, torch::Tensor b1,\n torch::Tensor w2, torch::Tensor b2,\n torch::Tensor w3, torch::Tensor b3,\n int dim, int num_steps, float dt\n) {\n const int B = x0.size(0);\n auto x_out = torch::empty_like(x0);\n \n const int threads = 256;\n const int shared_mem = (11 * dim + 1) * sizeof(float);\n \n flow_ode_kernel<<<B, threads, shared_mem>>>(\n x0.data_ptr<float>(),\n x_out.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 dim, num_steps, dt\n );\n \n return x_out;\n}\n\"\"\"\n\nflow_ode_module = load_inline(\n name='flow_ode',\n cpp_sources=['torch::Tensor flow_ode_cuda(torch::Tensor x0, torch::Tensor w1, torch::Tensor b1, torch::Tensor w2, torch::Tensor b2, torch::Tensor w3, torch::Tensor b3, int dim, int num_steps, float dt);'],\n cuda_sources=[cuda_source],\n functions=['flow_ode_cuda'],\n extra_cuda_cflags=['-O3', '-use_fast_math'],\n verbose=False\n)\n\nclass ModelNew(nn.Module):\n def __init__(self, dim: int, num_steps: int):\n super().__init__()\n self.dim = dim\n self.num_steps = 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 self.register_buffer(\"dt\", torch.tensor(1.0 / float(num_steps)))\n \n def forward(self, x0: torch.Tensor) -> torch.Tensor:\n B, d = x0.shape\n assert d == self.dim\n \n w1 = self.velocity[0].weight\n b1 = self.velocity[0].bias\n w2 = self.velocity[3].weight\n b2 = self.velocity[3].bias\n w3 = self.velocity[6].weight\n b3 = self.velocity[6].bias\n \n return flow_ode_module.flow_ode_cuda(\n x0, w1, b1, w2, b2, w3, b3,\n self.dim, self.num_steps, self.dt.item()\n )"
}