reasoning
reasoning (truncated 43839 chars): Let me understand the task:
1. I need to replace a PyTorch model that implements a stack of planar normalizing flow layers
2. Each layer applies: f(z) = z + u * tanh(w^T z + b)
3. There's also a log-determinant-Jacobian correction
4. The `_constrain_u` function ensures invertibility
Let me analyze the forward pass step by step:
For each flow layer i:
1. Get w, u, b parameters
2. Constrain u to ensure w^T u >= -1
3. Compute linear = z @ w + b (B,)
4. Compute h = tanh(linear)
5. Compute h_prime = 1.0 - h^2
6. Update z = z + u * h (broadcasting u to (B, dim) and h to (B, 1))
7. Compute psi = h_prime * w (h_prime is (B, 1) and w is (dim,))
8. Compute log_det = log(|1 + psi @ u|)
9. Accumulate sum_log_det
Let me write a custom CUDA kernel for this:
```python
import torch
import torch.nn as nn
import torch.nn.functional as F
from torch.utils.cpp_extension import load_inline
# Define CUDA kernel
cuda_source = """
#include <torch/extension.h>
#include <cuda.h>
#include <cuda_runtime.h>
#include <cmath>
__global__ void planar_flow_forward_kernel(
const float* z_in,
const float* w,
const float* u,
const float* b,
float* z_out,
float* sum_log_det,
int batch_size,
int dim,
int num_flows
) {
int batch_idx = blockIdx.x * blockDim.x + threadIdx.x;
if (batch_idx >= batch_size) return;
// Load z into shared memory or registers
// For each sample in batch, we need to apply all flows
float z_local[32]; // Assuming dim <= 32
for (int d = 0; d < dim; d++) {
z_local[d] = z_in[batch_idx * dim + d];
}
float log_det_sum = 0.0f;
for (int flow = 0; flow < num_flows; flow++) {
// Get parameters for this flow
const float* w_flow = w + flow * dim;
const float* u_flow = u + flow * dim;
float b_flow = b[flow];
// Compute w^T u for constraint
float wtu = 0.0f;
for (int d = 0; d < dim; d++) {
wtu += w_flow[d] * u_flow[d];
}
// Constrain u: m = -1 + softplus(wtu), u_hat = u + (m - wtu) * w / ||w||^2
float softplus_wtu = logf(1.0f + expf(wtu));
float m = -1.0f + softplus_wtu;
float w_norm_sq = 0.0f;
for (int d = 0; d < dim; d++) {
w_norm_sq += w_flow[d] * w_flow[d];
}
// Compute u_hat
float u_hat[32];
for (int d = 0; d < dim; d++) {
u_hat[d] = u_flow[d] + (m - wtu) * w_flow[d] / w_norm_sq;
}
// Compute linear = z^T w + b
float linear = b_flow;
for (int d = 0; d < dim; d++) {
linear += z_local[d] * w_flow[d];
}
// Compute h = tanh(linear)
float h = tanhf(linear);
// Compute h_prime = 1 - h^2
float h_prime = 1.0f - h * h;
// Update z = z + u_hat * h
for (int d = 0; d < dim; d++) {
z_local[d] += u_hat[d] * h;
}
// Compute psi @ u_hat
float psi_u = 0.0f;
for (int d = 0; d < dim; d++) {
psi_u += h_prime * w_flow[d] * u_hat[d];
}
// Compute log_det = log(|1 + psi @ u_hat|)
float det = 1.0f + psi_u;
log_det_sum += logf(fabsf(det) + 1e-8f);
}
// Write output
for (int d = 0; d < dim; d++) {
z_out[batch_idx * dim + d] = z_local[d];
}
sum_log_det[batch_idx] = log_det_sum;
}
torch::Tensor planar_flow_forward_cuda(
torch::Tensor z,
torch::Tensor w_flat,
torch::Tensor u_flat,
torch::Tensor b_flat,
int num_flows
) {
int batch_size = z.size(0);
int dim = z.size(1);
auto z_out = torch::empty_like(z);
auto sum_log_det = torch::zeros({batch_size}, z.options());
const int block_size = 256;
const int num_blocks = (batch_size + block_size - 1) / block_size;
planar_flow_forward_kernel<<<num_blocks, block_size>>>(
z.data_ptr<float>(),
w_flat.data_ptr<float>(),
u_flat.data_ptr<float>(),
b_flat.data_ptr<float>(),
z_out.data_ptr<float>(),
sum_log_det.data_ptr<float>(),
batch_size,
dim,
num_flows
);
return torch::cat({z_out, sum_log_det.unsqueeze(1)}, 1);
}
"""
cpp_source = """
torch::Tensor planar_flow_forward_cuda(
torch::Tensor z,
torch::Tensor w_flat,
torch::Tensor u_flat,
torch::Tensor b_flat,
int num_flows);
"""
# Load the extension
planar_flow_ext = load_inline(
name='planar_flow_ext',
cpp_sources=cpp_source,
cuda_sources=cuda_source,
functions=['planar_flow_forward_cuda'],
extra_cuda_cflags=['-O3'],
verbose=False
)
class ModelNew(nn.Module):
def __init__(self, dim, num_flows):
super().__init__()
self.dim = dim
self.num_flows = num_flows
self.w = nn.ParameterList([nn.Parameter(torch.randn(dim)) for _ in range(num_flows)])
self.u = nn.ParameterList([nn.Parameter(torch.randn(dim)) for _ in range(num_flows)])
self.b = nn.ParameterList([nn.Parameter(torch.zeros(1)) for _ in range(num_flows)])
def forward(self, z: torch.Tensor) -> tuple:
# Flatten parameters
w_flat = torch.stack([self.w[i] for i in range(self.num_flows)]).flatten()
u_flat = torch.stack([self.u[i] for i in range(self.num_flows)]).flatten()
b_flat = torch.stack([self.b[i] for i in range(self.num_flows)]).flatten()
result = planar_flow_ext.planar_flow_forward_cuda(z, w_flat, u_flat, b_flat, self.num_flows)
z_out = result[:, :-1]
sum_log_det = result[:, -1]
return z_out, sum_log_det
```
Wait, there are several issues:
1. The kernel assumes dim <= 32 and uses local arrays which might not work for arbitrary dimensions
2. The constrain_u computation uses the original u_flow but needs u_hat
Let me reconsider the approach. The dimension is 32 according to the reference, so we can use local arrays, but we should make it more general.
Actually, let me trace through the reference implementation more carefully:
```python
def _constrain_u(self, w, u):
"""Ensure invertibility: w^T u >= -1."""
wtu = (w * u).sum()
m = -1 + F.softplus(wtu)
u_hat = u + (m - wtu) * w / (w ** 2).sum()
return u_hat
```
So:
- wtu = sum(w * u)
- m = -1 + log(1 + exp(wtu)) (softplus)
- u_hat = u + (m - wtu) * w / sum(w^2)
Then in forward:
```python
linear = z @ w + b # (B,)
h = torch.tanh(linear)
h_prime = 1.0 - h ** 2
z = z + u.unsqueeze(0) * h.unsqueeze(-1) # u_hat, not u
psi = h_prime.unsqueeze(-1) * w.unsqueeze(0) # (B, dim)
log_det = torch.log(torch.abs(1.0 + psi @ u) + 1e-8) # u_hat
```
So psi = h_prime * w (element-wise multiplication with broadcasting), and psi @ u_hat is the dot product.
Let me rewrite the kernel more carefully:
```cpp
__global__ void planar_flow_forward_kernel(
const float* z_in,
const float* w,
const float* u,
const float* b,
float* z_out,
float* sum_log_det,
int batch_size,
int dim,
int num_flows
) {
int batch_idx = blockIdx.x * blockDim.x + threadIdx.x;
if (batch_idx >= batch_size) return;
// Each thread processes one sample
// We'll use shared memory for parameters
extern __shared__ float shared_params[];
float* z_local = shared_params; // We need dim * num_flows * 2 for w and u, plus num_flows for b
// Actually, let's use registers for z_local and load params from global memory
float z_local[32]; // assuming dim <= 32
for (int d = 0; d < dim; d++) {
z_local[d] = z_in[batch_idx * dim + d];
}
float log_det_sum = 0.0f;
for (int flow = 0; flow < num_flows; flow++) {
const float* w_flow = w + flow * dim;
const float* u_flow = u + flow * dim;
float b_flow = b[flow];
// Constrain u
float wtu = 0.0f;
float w_norm_sq = 0.0f;
...[ omitted 43839 characters ]...
ses `1e-8f` as the epsilon in the log, which matches the original. But I should check if there are any other numerical differences.
The main operations are:
- `logf(1.0f + expf(wtu))` for softplus - this might have slight numerical differences from `torch.nn.functional.softplus`
- `tanhf(linear)` for tanh - should be the same
- `logf(fabsf(det) + 1e-8f)` for the log determinant - should be the same
For `softplus`, PyTorch uses a numerically stable implementation:
```python
def softplus(input, beta=1, threshold=20):
return (1/beta) * log(1 + exp(beta * input))
```
And for large values, it uses a linear approximation to avoid overflow. My implementation uses:
```cpp
if (x > 20.0f) {
return x;
}
return logf(1.0f + expf(x));
```
This should match PyTorch's behavior.
For `tanh`, CUDA's `tanhf` should be accurate enough for fp32.
For `log`, CUDA's `logf` should be accurate enough.
I think the implementation is correct. Let me submit.
Actually, I want to also verify that the dimensions are handled correctly. In the kernel:
```cpp
const int batch_idx = blockIdx.x * blockDim.x + threadIdx.x;
```
This computes the batch index for each thread. If batch_size is 1024 and block_size is 256, then:
- blockIdx.x ranges from 0 to 3
- threadIdx.x ranges from 0 to 255
- batch_idx ranges from 0 to 1023
This covers all batch elements.
For the shared memory:
```cpp
const int shared_mem_size = (num_flows * dim * 2 + num_flows) * sizeof(float);
```
For num_flows=8 and dim=32:
- shared_mem_size = (8 * 32 * 2 + 8) * 4 = (512 + 8) * 4 = 2080 bytes
This is well within the 48KB limit for shared memory per block.
For loading parameters into shared memory:
```cpp
for (int i = tid; i < total_params; i += block_size) {
...
}
```
With tid ranging from 0 to 255 and total_params = 520, the first 255 iterations cover indices 0-254, the second set covers 256-510 (with tid=0 to 254), and the third set covers 511-519 (with tid=0 to 8).
Wait, let me trace through more carefully. With block_size = 256 and total_params = 520:
- tid=0: loads i=0, 256, 512 (but 512 >= 520, so only 0, 256)
- tid=1: loads i=1, 257, 513 (but 513 >= 520, so only 1, 257)
- ...
- tid=263: loads i=263, 519 (but 263 >= 256, wait, tid only goes up to 255)
Actually, I need to be more careful. Let me trace through again:
- For tid=0: i=0, then i=256, then i=512 (>= 520, stop). So tid=0 loads indices 0 and 256.
- For tid=1: i=1, then i=257, then i=513 (>= 520, stop). So tid=1 loads indices 1 and 257.
- ...
- For tid=263: wait, tid can only be 0 to 255.
Let me recalculate. With tid from 0 to 255 and stride of 256:
- Iteration 1: tid=0 loads i=0, tid=1 loads i=1, ..., tid=255 loads i=255
- Iteration 2: tid=0 loads i=256, tid=1 loads i=257, ..., tid=255 loads i=511 (but wait, 511 < 520)
- Iteration 3: tid=0 loads i=512 (but 512 >= 520, stop)
Actually, let me be more precise. The loop is:
```cpp
for (int i = tid; i < total_params; i += block_size) {
...
}
```
For tid=0: i goes 0, 256, 512. At i=512, i >= 520, so the loop condition `i < total_params` is false. So tid=0 only loads i=0 and i=256.
For tid=1: i goes 1, 257, 513. At i=513, i >= 520. So tid=1 loads i=1 and i=257.
...
For tid=263: But tid can only go up to 255 (block_size=256). So tid=263 doesn't exist.
Let me think again. total_params = 520. block_size = 256.
- tid=0: loads 0, 256 (2 iterations)
- tid=1: loads 1, 257 (2 iterations)
- ...
- tid=263: tid can only be 0 to 255.
So for tid from 0 to 255:
- tid=0 loads 0, 256
- tid=1 loads 1, 257
- ...
- tid=263 doesn't exist
- tid=264 doesn't exist
- ...
- tid=255 loads 255, 511 (but 511 < 520, so it loads both)
Wait, for tid=255: i goes 255, then i=255+256=511. At i=511, i < 520, so it loads 511. Then i=511+256=767 >= 520, so it stops.
So tid=255 loads i=255 and i=511.
What about tid=256? It doesn't exist because threadIdx.x only goes up to blockDim.x - 1 = 255.
So indices from 0 to 511 are covered, but what about indices 512 to 519?
Let me check: total_params = 520.
- tid=0: 0, 256
- tid=1: 1, 257
- ...
- tid=255: 255, 511
So indices 0 to 255 and 256 to 511 are covered. But indices 512 to 519 are not covered!
I have a bug. Let me fix it:
```cpp
for (int i = tid; i < total_params; i += block_size) {
...
}
```
With total_params = 520 and block_size = 256:
- The loop should cover indices 0 to 519.
- With stride 256, each thread handles indices tid, tid+256, tid+512, ...
- For tid=0: 0, 256, 512 (512 < 520, so it loads), then 768 (>= 520, stop)
- For tid=1: 1, 257, 513, then 769 (stop)
- ...
- For tid=7: 7, 263, 519, then 775 (stop)
- ...
- For tid=8: 8, 264, 520 (520 >= 520, stop at 520 because the condition is i < total_params)
Wait, let me re-check. The condition is `i < total_params`, which is `i < 520`.
- For tid=7: i=7 (loads), i=263 (loads), i=519 (519 < 520, loads). Then i=775 (>= 520, stop). So tid=7 loads 7, 263, 519.
- For tid=8: i=8 (loads), i=264 (loads), i=520 (520 >= 520, stop). So tid=8 loads 8, 264.
So indices 512 to 519 are loaded by tid=0 to tid=7.
Let me verify:
- tid=0 loads 0, 256, 512 (512 < 520, so loads)
- tid=1 loads 1, 257, 513
- ...
- tid=7 loads 7, 263, 519
- tid=8 loads 8, 264 (520 >= 520, stop)
So all indices from 0 to 519 are covered. My original code is correct!
Actually wait, I made an error earlier. Let me recalculate once more:
- total_params = num_flows * dim * 2 + num_flows = 8 * 32 * 2 + 8 = 512 + 8 = 520.
So:
- tid=0: i goes 0, 256, 512. All are < 520. So tid=0 loads 0, 256, 512. ✓
- tid=1: i goes 1, 257, 513. All are < 520. So tid=1 loads 1, 257, 513. ✓
- ...
- tid=7: i goes 7, 263, 519. All are < 520. So tid=7 loads 7, 263, 519. ✓
- tid=8: i goes 8, 264, 520. 520 is not < 520, so tid=8 loads 8, 264 only. ✓
- ...
- tid=255: i goes 255, 511, 767. 511 < 520, 767 >= 520. So tid=255 loads 255, 511. ✓
All indices 0 to 519 are covered. Great, the code is correct.
Now let me verify the shared memory layout:
- Indices 0 to 255 (total_w = 8 * 32 = 256): w parameters
- Indices 256 to 511 (total_u = 8 * 32 = 256): u parameters
- Indices 512 to 519 (total_b = 8): b parameters
In the loading code:
```cpp
if (i < total_w) {
shared_mem[i] = w[i];
} else if (i < total_w + total_u) {
shared_mem[i] = u[i - total_w];
} else {
shared_mem[i] = b[i - total_w - total_u];
}
```
- For i in [0, 256): shared_mem[i] = w[i] ✓
- For i in [256, 512): shared_mem[i] = u[i - 256] ✓
- For i in [512, 520): shared_mem[i] = b[i - 512] ✓
All good!
Let me submit the final implementation.
One more check: I should make sure the kernel compiles. Let me check for any syntax errors:
1. `extern __shared__ float shared_mem[];` - correct syntax for dynamic shared memory.
2. `__syncthreads();` - correct barrier.
3. `logf`, `expf`, `tanhf`, `fabsf` - correct single-precision math functions.
I think the implementation is ready. Let me submit.
Wait, I just realized I need to handle the case where the input tensor might not be float32. The problem says fp32 precision, so I'll assume it's always float32. But to be safe, I could add a type check in Python.
Actually, let me also handle the case where the input is not contiguous. I already call `z.contiguous()` in Python, which should handle this.
Alright, I'm confident the implementation is correct. Let me write the final code and submit.
Oh, one more thing. I noticed that in the original code, the parameters are nn.ParameterList, which is a list of parameters. When I stack them, I need to make sure the order is correct.
```python
self.w = nn.ParameterList([nn.Parameter(torch.randn(dim)) for _ in range(num_flows)])
```
So `self.w[0]`, `self.w[1]`, ..., `self.w[num_flows-1]` are the parameters for each flow.
When I stack them:
```python
w_flat = torch.stack(list(self.w)).contiguous()
```
This gives a tensor of shape `(num_flows, dim)`, where `w_flat[0]` is `self.w[0]`, etc.
In the kernel, I access `w + flow * dim`, which gives the parameters for flow `flow`. This is correct.
Alright, final submission:
call → submit_kernel
callsubmit_kernel
{
"kernel_code": "import torch\nimport torch.nn as nn\nimport torch.nn.functional as F\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__device__ __forceinline__ float softplus_stable(float x) {\n if (x > 20.0f) {\n return x;\n }\n return logf(1.0f + expf(x));\n}\n\n__global__ void planar_flow_forward_kernel(\n const float* __restrict__ z_in,\n const float* __restrict__ w,\n const float* __restrict__ u,\n const float* __restrict__ b,\n float* __restrict__ z_out,\n float* __restrict__ sum_log_det,\n int batch_size,\n int dim,\n int num_flows\n) {\n extern __shared__ float shared_mem[];\n \n const int tid = threadIdx.x;\n const int block_size = blockDim.x;\n const int batch_idx = blockIdx.x * block_size + tid;\n \n const int total_w = num_flows * dim;\n const int total_u = num_flows * dim;\n const int total_b = num_flows;\n const int total_params = total_w + total_u + total_b;\n \n // Cooperatively load parameters into shared memory\n for (int i = tid; i < total_params; i += block_size) {\n if (i < total_w) {\n shared_mem[i] = w[i];\n } else if (i < total_w + total_u) {\n shared_mem[i] = u[i - total_w];\n } else {\n shared_mem[i] = b[i - total_w - total_u];\n }\n }\n \n __syncthreads();\n \n if (batch_idx >= batch_size) return;\n \n const float* w_shared = shared_mem;\n const float* u_shared = shared_mem + total_w;\n const float* b_shared = shared_mem + total_w + total_u;\n \n float log_det_sum = 0.0f;\n \n // Load z into z_out (will be updated in place)\n for (int d = 0; d < dim; d++) {\n z_out[batch_idx * dim + d] = z_in[batch_idx * dim + d];\n }\n \n for (int flow = 0; flow < num_flows; flow++) {\n const float* w_flow = w_shared + flow * dim;\n const float* u_flow = u_shared + flow * dim;\n const float b_flow = b_shared[flow];\n \n // Compute wtu, w_norm_sq, and linear in one pass\n float wtu = 0.0f;\n float w_norm_sq = 0.0f;\n float linear = b_flow;\n \n for (int d = 0; d < dim; d++) {\n float z_val = z_out[batch_idx * dim + d];\n float w_d = w_flow[d];\n float u_d = u_flow[d];\n wtu += w_d * u_d;\n w_norm_sq += w_d * w_d;\n linear += z_val * w_d;\n }\n \n // Constrain u: m = -1 + softplus(wtu), scale = (m - wtu) / ||w||^2\n float m = -1.0f + softplus_stable(wtu);\n float scale = (m - wtu) / w_norm_sq;\n \n // Compute h = tanh(linear) and h_prime = 1 - h^2\n float h = tanhf(linear);\n float h_prime = 1.0f - h * h;\n \n // Update z and compute psi @ u_hat in one pass\n float psi_u = 0.0f;\n for (int d = 0; d < dim; d++) {\n float z_val = z_out[batch_idx * dim + d];\n float u_hat_d = u_flow[d] + scale * w_flow[d];\n z_out[batch_idx * dim + d] = z_val + u_hat_d * h;\n psi_u += h_prime * w_flow[d] * u_hat_d;\n }\n \n // Compute log determinant: log(|1 + psi @ u_hat|)\n float det = 1.0f + psi_u;\n log_det_sum += logf(fabsf(det) + 1e-8f);\n }\n \n sum_log_det[batch_idx] = log_det_sum;\n}\n\nstd::vector<torch::Tensor> planar_flow_forward_cuda(\n torch::Tensor z,\n torch::Tensor w_flat,\n torch::Tensor u_flat,\n torch::Tensor b_flat,\n int num_flows\n) {\n const int batch_size = z.size(0);\n const int dim = z.size(1);\n \n auto z_out = torch::empty_like(z);\n auto sum_log_det = torch::zeros({batch_size}, z.options());\n \n const int block_size = 256;\n const int num_blocks = (batch_size + block_size - 1) / block_size;\n \n const int shared_mem_size = (num_flows * dim * 2 + num_flows) * sizeof(float);\n \n planar_flow_forward_kernel<<<num_blocks, block_size, shared_mem_size>>>(\n z.data_ptr<float>(),\n w_flat.data_ptr<float>(),\n u_flat.data_ptr<float>(),\n b_flat.data_ptr<float>(),\n z_out.data_ptr<float>(),\n sum_log_det.data_ptr<float>(),\n batch_size,\n dim,\n num_flows\n );\n \n return {z_out, sum_log_det};\n}\n\"\"\"\n\ncpp_source = \"\"\"\nstd::vector<torch::Tensor> planar_flow_forward_cuda(\n torch::Tensor z,\n torch::Tensor w_flat,\n torch::Tensor u_flat,\n torch::Tensor b_flat,\n int num_flows);\n\"\"\"\n\nplanar_flow_ext = load_inline(\n name='planar_flow_ext_v2',\n cpp_sources=cpp_source,\n cuda_sources=cuda_source,\n functions=['planar_flow_forward_cuda'],\n extra_cuda_cflags=['-O3'],\n verbose=False\n)\n\n\nclass ModelNew(nn.Module):\n \"\"\"\n Stack of planar normalizing flow layers with custom CUDA kernel.\n Each layer applies the invertible transform f(z) = z + u * tanh(w^T z + b),\n with a log-determinant-Jacobian correction.\n \"\"\"\n\n def __init__(self, dim, num_flows):\n super().__init__()\n self.dim = dim\n self.num_flows = num_flows\n self.w = nn.ParameterList([nn.Parameter(torch.randn(dim)) for _ in range(num_flows)])\n self.u = nn.ParameterList([nn.Parameter(torch.randn(dim)) for _ in range(num_flows)])\n self.b = nn.ParameterList([nn.Parameter(torch.zeros(1)) for _ in range(num_flows)])\n\n def forward(self, z: torch.Tensor) -> tuple:\n \"\"\"\n Args:\n z: (B, dim) - samples from base distribution\n Returns:\n (z_out, sum_log_det):\n z_out: (B, dim) - transformed samples\n sum_log_det: (B,) - total log |det df/dz|\n \"\"\"\n # Flatten parameters for CUDA kernel\n w_flat = torch.stack(list(self.w)).contiguous()\n u_flat = torch.stack(list(self.u)).contiguous()\n b_flat = torch.stack([b.squeeze() for b in self.b]).contiguous()\n \n z_out, sum_log_det = planar_flow_ext.planar_flow_forward_cuda(\n z.contiguous(), w_flat, u_flat, b_flat, self.num_flows\n )\n \n return z_out, sum_log_det"
}