Let me understand the task: 1. The reference model has a fixed mask `_MASK` of shape (D=44,) with boolean values 2. The forward pass: - Takes input `x` of shape (B=18, D=44) - Expands the mask to shape (B, D) - Gets row 0 expanded to shape (B, D) - Returns `torch.where(m, row0, x)` - i.e., where mask is True, use row0 values, otherwise use x values So essentially, for columns where the mask is True, we broadcast row 0's value to all rows. For columns where mask is False, we keep the original values. This is a fairly simple operation. Let me think about how to optimize it: 1. The mask is fixed and known at compile time - we could potentially hardcode it 2. The operation is element-wise with a condition 3. Memory access pattern: for each element, we read from x (possibly row 0), and write to output Let me write a CUDA kernel that: 1. Each thread handles one element 2. Reads the mask value for its column 3. If mask is True, reads from row 0, column j 4. Otherwise reads from x[b, j] 5. Writes to output[b, j] Let me first get the GPU specs to understand the hardware. Actually, let me start by writing a simple kernel and see if it works and how it performs. ```python import torch import torch.nn as nn from torch.utils.cpp_extension import load_inline from kernelbench.distributed_collectives import default_device B = 18 D = 44 # Fixed mask (not all True, not all False) _MASK = torch.tensor( [1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1], dtype=torch.bool, ) cuda_source = """ #include <torch/extension.h> #include <cuda.h> #include <cuda_runtime.h> __global__ void broadcast_masked_kernel(const float* __restrict__ x, float* __restrict__ out, const bool* __restrict__ mask, int B, int D) { int idx = blockIdx.x * blockDim.x + threadIdx.x; int total = B * D; if (idx < total) { int b = idx / D; int j = idx % D; if (mask[j]) { out[idx] = x[j]; // x[0, j] } else { out[idx] = x[idx]; // x[b, j] } } } torch::Tensor broadcast_masked_cuda(torch::Tensor x, torch::Tensor mask) { int B = x.size(0); int D = x.size(1); auto out = torch::empty_like(x); int total = B * D; int threads = 256; int blocks = (total + threads - 1) / threads; broadcast_masked_kernel<<<blocks, threads>>>( x.data_ptr<float>(), out.data_ptr<float>(), mask.data_ptr<bool>(), B, D ); return out; } """ cpp_source = """ torch::Tensor broadcast_masked_cuda(torch::Tensor x, torch::Tensor mask); """ broadcast_module = load_inline( name='broadcast_masked', cpp_sources=cpp_source, cuda_sources=cuda_source, functions=['broadcast_masked_cuda'], verbose=True ) class ModelNew(nn.Module): def __init__(self): super().__init__() self.register_buffer("row_mask", _MASK.clone(), persistent=False) def forward(self, x: torch.Tensor) -> torch.Tensor: m = self.row_mask.to(device=x.device) return broadcast_module.broadcast_masked_cuda(x, m) ``` Wait, let me think about this more carefully. The problem is very small - B=18, D=44, so total elements = 18 * 44 = 792. This is a very small kernel! With only 792 elements, a single warp (32 threads) would need 25 warps, or about 1-2 blocks depending on block size. The overhead of kernel launch might dominate. Let me think about optimizations: 1. Since the mask is fixed and small (44 elements), we could load it into shared memory or even constant memory 2. We could even encode the mask in the kernel itself since it's fixed Actually, since the mask is fixed and known at compile time, I could encode it directly in the kernel. Let me think about how to do this efficiently. The mask is: [1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1] That's 44 values. I could use a bitset to encode this more efficiently. Let me count: - 44 bits = 44 / 32 = 1.375, so we need 2 32-bit integers Actually, let me just proceed with a simpler approach first - using the mask as a tensor. Let me compile and test. Actually, let me get GPU specs first to understand what we're working with.

Now let me write my custom CUDA kernel. The key operation is: 1. For each element (b, j), if mask[j] is True, output x[0, j], else output x[b, j] This is essentially: `output[b, j] = mask[j] ? x[0, j] : x[b, j]` I can write a simple kernel that handles this efficiently. The mask is fixed and small (44 elements), so I can pass it as a kernel argument or use constant memory. Let me write the kernel: ```python import torch import torch.nn as nn from torch.utils.cpp_extension import load_inline from kernelbench.distributed_collectives import default_device B = 18 D = 44 _MASK = torch.tensor( [1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1], dtype=torch.bool, ) cuda_source = """ __global__ void broadcast_mask_kernel(const float* x, float* out, const bool* mask, int B, int D) { int idx = blockIdx.x * blockDim.x + threadIdx.x; int total = B * D; if (idx < total) { int b = idx / D; int j = idx % D; if (mask[j]) { out[idx] = x[j]; // x[0, j] is at position j } else { out[idx] = x[idx]; // x[b, j] } } } torch::Tensor broadcast_mask_cuda(torch::Tensor x, torch::Tensor mask) { int B = x.size(0); int D = x.size(1); auto out = torch::empty_like(x); int total = B * D; int threads = 256; int blocks = (total + threads - 1) / threads; broadcast_mask_kernel<<<blocks, threads>>>( x.data_ptr<float>(), out.data_ptr<float>(), mask.data_ptr<bool>(), B, D ); return out; } """ cpp_source = "torch::Tensor broadcast_mask_cuda(torch::Tensor x, torch::Tensor mask);" cuda_module = load_inline( name='broadcast_mask', cpp_sources=cpp_source, cuda_sources=cuda_source, functions=['broadcast_mask_cuda'], verbose=True, ) class ModelNew(nn.Module): def __init__(self): super().__init__() self.register_buffer("row_mask", _MASK.clone(), persistent=False) def forward(self, x: torch.Tensor) -> torch.Tensor: return cuda_module.broadcast_mask_cuda(x, self.row_mask.to(device=x.device)) ``` Wait, there's an issue - the mask is a bool tensor. Let me check if CUDA bool works properly. It should, but I might need to use `bool*` or cast properly. Actually, looking at the reference more carefully: - `row0 = x[0:1].expand(B, D)` - this broadcasts row 0 to shape (B, D) - `torch.where(m, row0, x)` - where mask is True, use row0, else use x So the operation is correct. Let me compile and test.

Great, the kernel compiles. Now let me check correctness.

There's a syntax error in the forward method - I have two `-> torch.Tensor` annotations. Let me fix that.

The kernel is correct. Now let me try to optimize it for better performance. Current kernel: - Simple 1D grid with 256 threads per block - Total elements: B * D = 18 * 44 = 792 - With 256 threads, we need only 4 blocks - Each thread does: load mask[j], branch, load x[j] or x[idx], store out[idx] Potential optimizations: 1. The data is very small (792 elements), so overhead dominates 2. Could use constant memory for the mask since it's fixed 3. Could use shared memory for mask 4. Could increase thread count to maximize occupancy But given the very small size (792 elements), most optimizations won't help much. Let me try a few things: 1. Use __ldg for read-only cache on x[0] row (first D elements) 2. Use a constant memory or compile-time mask 3. Better memory access patterns Actually, let me think about this more carefully. The mask is small (44 elements). I could: - Load it into shared memory or registers - Use constant memory for it Also, since we're accessing x[0, j] for all rows when mask[j] is true, and x[0] is only 44 elements, this is a repeated read pattern. Let me try optimizing with shared memory for the mask and better memory access. Actually, given the small size, let me just ensure we're using good memory access patterns and minimal branching. Let me also use vectorized loads if possible. Let me try a version that loads mask into shared memory and uses coalesced access patterns.

Now let me test correctness of this optimized version.

There's a typo in my code - I wrote `def __init__(init)` instead of `def __init__(self)`. Let me fix that.

Good, this also works. Let me try a different approach - since D=44 is very small and evenly divisible, I could potentially use a simpler approach. Also, let me think about the memory access pattern. For B=18, D=44, the total is only 792 elements. A single warp (32 threads) can process this in 25 iterations. Or a single block of 256 threads can process this in ~4 iterations. The issue is the "modulo" operation for `j = i % D` - modulo is expensive on GPUs. Since D is a compile-time constant, the compiler might optimize it, but let me try using integer division instead. Actually, let me try another optimization: use vectorized loads/stores with float4. Since D=44 is not a multiple of 4, this might be tricky. Actually, for this small problem size, the kernel launch overhead might dominate. Let me try a different approach - using a single thread block with enough threads, and see if that helps. Let me also try using constants in the kernel itself to avoid any memory reads for the mask.

Let me run correctness check on this version.

The kernel is working correctly with constant memory for the mask. Let me run a static check to make sure there are no issues before submitting.

The kernel is correct, passes static check, and uses constant memory to embed the mask for faster access. Let me submit it.