{
  "strategic_intent": "Researching the reference implementation, checking the GPU environment, and understanding the benchmark and verification scripts.",
  "title": "Research & Baseline Establishment",
  "summary": "We are beginning the W4A16 GEMM optimization task. First, we need to inspect the existing files: reference.py, check.py, benchmark.py, and PROMPT.txt. We also need to query the available GPU (architecture, SM count, CUDA version) to design our high-performance Triton or PyTorch/CUDA C++ kernel properly."
}

{
  "start_line": 1,
  "file_path": "reference.py",
  "end_line": 200
}

{
  "start_line": 1,
  "file_path": "PROMPT.txt",
  "end_line": 200
}

{
  "end_line": 200,
  "start_line": 1,
  "file_path": "check.py"
}

{
  "file_path": "benchmark.py",
  "end_line": 200,
  "start_line": 1
}

{
  "end_line": 200,
  "file_path": "shapes.py",
  "start_line": 1
}

{
  "end_line": 200,
  "file_path": "problem.yaml",
  "start_line": 1
}

{
  "command": "nvidia-smi && uv run python -c \"import torch; print(torch.__version__); print(torch.cuda.get_device_name(0)); print(torch.cuda.get_device_properties(0))\"",
  "description": "Get details about the GPU hardware, CUDA version, PyTorch version, and device capabilities."
}

{
  "description": "Check the installed Triton version.",
  "command": "uv run python -c \"import triton; print(triton.__version__)\""
}

{
  "command": "uv pip list",
  "description": "List installed packages in the workspace virtual environment."
}

{
  "file_path": "sota.py",
  "end_line": 200,
  "start_line": 1
}

{
  "content": "<6155 chars \u2014 see below>",
  "file_path": "solution.py"
}

import torch
import torch.nn as nn
import triton
import triton.language as tl

GROUP_SIZE = 128

@triton.autotune(
    configs=[
        triton.Config({'BLOCK_SIZE_M': 16, 'BLOCK_SIZE_N': 256, 'BLOCK_SIZE_K': 128, 'num_stages': 4, 'num_warps': 4}),
        triton.Config({'BLOCK_SIZE_M': 32, 'BLOCK_SIZE_N': 128, 'BLOCK_SIZE_K': 128, 'num_stages': 4, 'num_warps': 4}),
        triton.Config({'BLOCK_SIZE_M': 64, 'BLOCK_SIZE_N': 128, 'BLOCK_SIZE_K': 128, 'num_stages': 4, 'num_warps': 4}),
        triton.Config({'BLOCK_SIZE_M': 128, 'BLOCK_SIZE_N': 128, 'BLOCK_SIZE_K': 128, 'num_stages': 4, 'num_warps': 8}),
        triton.Config({'BLOCK_SIZE_M': 64, 'BLOCK_SIZE_N': 64, 'BLOCK_SIZE_K': 128, 'num_stages': 4, 'num_warps': 4}),
        triton.Config({'BLOCK_SIZE_M': 16, 'BLOCK_SIZE_N': 128, 'BLOCK_SIZE_K': 128, 'num_stages': 4, 'num_warps': 4}),
    ],
    key=['M', 'N', 'K'],
)
@triton.jit
def w4a16_gemm_kernel(
    x_ptr, w_ptr, scales_ptr, zeros_ptr, out_ptr,
    M, N, K,
    stride_xm, stride_xk,
    stride_wk, stride_wn,
    stride_sm, stride_sn,
    stride_zm, stride_zn,
    stride_om, stride_on,
    BLOCK_SIZE_M: tl.constexpr,
    BLOCK_SIZE_N: tl.constexpr,
    BLOCK_SIZE_K: tl.constexpr,
    GROUP_SIZE: tl.constexpr,
):
    pid = tl.program_id(0)
    num_pid_m = tl.cdiv(M, BLOCK_SIZE_M)
    num_pid_n = tl.cdiv(N, BLOCK_SIZE_N)
    
    # 2D Grid with Program ID grouping/swizzling for L2 cache reuse
    num_pid_in_group = 8
    group_id = pid // (num_pid_in_group * num_pid_n)
    first_pid_m = group_id * num_pid_in_group
    group_size_m = min(num_pid_m - first_pid_m, num_pid_in_group)
    pid_m = first_pid_m + (pid % group_size_m)
    pid_n = (pid % (group_size_m * num_pid_n)) // group_size_m

    offs_am = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
    offs_bn = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
    
    BLOCK_SIZE_K_half = BLOCK_SIZE_K // 2
    offs_k_half = tl.arange(0, BLOCK_SIZE_K_half)
    offs_b_k = tl.arange(0, BLOCK_SIZE_K_half)
    
    a_mask = offs_am[:, None] < M
    b_mask = offs_bn[None, :] < N
    
    accumulator = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)
    
    for k_curr in range(0, K, BLOCK_SIZE_K):
        # Even and Odd input pointers
        a_even_ptrs = x_ptr + (offs_am[:, None] * stride_xm + (k_curr + 2 * offs_k_half)[None, :] * stride_xk)
        a_odd_ptrs = x_ptr + (offs_am[:, None] * stride_xm + (k_curr + 2 * offs_k_half + 1)[None, :] * stride_xk)
        
        a_even = tl.load(a_even_ptrs, mask=a_mask & ((k_curr + 2 * offs_k_half)[None, :] < K), other=0.0)
        a_odd = tl.load(a_odd_ptrs, mask=a_mask & ((k_curr + 2 * offs_k_half + 1)[None, :] < K), other=0.0)
        
        # Load packed weights
        b_ptrs = w_ptr + ((k_curr // 2 + offs_b_k[:, None]) * stride_wk + offs_bn[None, :] * stride_wn)
        b_packed = tl.load(b_ptrs, mask=b_mask & ((k_curr // 2 + offs_b_k[:, None]) < (K // 2)), other=0)
        
        # Unpack even/odd
        b_even_uint8 = b_packed & 0xF
        b_odd_uint8 = (b_packed >> 4) & 0xF
        
        # Load scale and zero for current group
        k_group = k_curr // GROUP_SIZE
        scale_ptrs = scales_ptr + (k_group * stride_sm + offs_bn * stride_sn)
        zero_ptrs = zeros_ptr + (k_group * stride_zm + offs_zn * stride_zn)
        
        scale = tl.load(scale_ptrs, mask=offs_bn < N, other=0.0)
        zero = tl.load(zero_ptrs, mask=offs_bn < N, other=0.0)
        
        # Dequantize to bfloat16
        w_even = (b_even_uint8.to(tl.bfloat16) - zero[None, :]) * scale[None, :]
        w_odd = (b_odd_uint8.to(tl.bfloat16) - zero[None, :]) * scale[None, :]
        
        # Dot products
        accumulator += tl.dot(a_even, w_even)
        accumulator += tl.dot(a_odd, w_odd)
        
    # Write to output
    c = accumulator.to(tl.bfloat16)
    offs_om = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
    offs_on = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
    out_ptrs = out_ptr + (offs_om[:, None] *

... (2155 more chars)

{
  "command": "uv run check.py",
  "description": "Run correctness verification on the custom Triton kernel."
}

{
  "allow_multiple": false,
  "file_path": "solution.py",
  "instruction": "Use BLOCK_SIZE_K // 2 directly in tl.arange so that it is recognized as a constexpr.",
  "new_string": "<96 chars \u2014 see below>",
  "old_string": "<138 chars \u2014 see below>"
}

    offs_k_half = tl.arange(0, BLOCK_SIZE_K // 2)
    offs_b_k = tl.arange(0, BLOCK_SIZE_K // 2)

    BLOCK_SIZE_K_half = BLOCK_SIZE_K // 2
    offs_k_half = tl.arange(0, BLOCK_SIZE_K_half)
    offs_b_k = tl.arange(0, BLOCK_SIZE_K_half)

{
  "command": "uv run check.py",
  "description": "Run correctness verification again."
}

{
  "file_path": "test_simple.py",
  "content": "<764 chars \u2014 see below>"
}

import torch
import reference
import solution

device = torch.device("cuda:0")
M, N, K = 1, 12288, 4096

print("Initializing reference model...")
ref_model = reference.Model(M, N, K).to(device).eval()

print("Initializing solution model...")
sol_model = solution.Model(M, N, K).to(device).eval()

print("Loading state dict...")
sol_model.load_state_dict(ref_model.state_dict(), strict=True)

print("Getting inputs...")
inputs = [t.to(device) for t in reference.get_inputs()]

print("Running reference forward...")
ref_out = ref_model(*inputs)
print("Reference forward done.")

print("Running solution forward...")
sol_out = sol_model(*inputs)
print("Solution forward done.")

diff = (ref_out - sol_out).abs().max()
print(f"Max absolute difference: {diff.item()}")

{
  "description": "Run the simple debug script.",
  "command": "uv run test_simple.py"
}

{
  "instruction": "Correct the variable name `offs_zn` to `offs_bn` in the zero pointer calculation.",
  "file_path": "solution.py",
  "new_string": "        zero_ptrs = zeros_ptr + (k_group * stride_zm + offs_bn * stride_zn)",
  "allow_multiple": false,
  "old_string": "        zero_ptrs = zeros_ptr + (k_group * stride_zm + offs_zn * stride_zn)"
}

{
  "description": "Run the simple debug script again.",
  "command": "uv run test_simple.py"
}

{
  "content": "<896 chars \u2014 see below>",
  "file_path": "triton_vec_add.py"
}

import torch
import triton
import triton.language as tl

@triton.jit
def add_kernel(x_ptr, y_ptr, output_ptr, n_elements, BLOCK_SIZE: tl.constexpr):
    pid = tl.program_id(axis=0)
    block_start = pid * BLOCK_SIZE
    offsets = block_start + tl.arange(0, BLOCK_SIZE)
    mask = offsets < n_elements
    x = tl.load(x_ptr + offsets, mask=mask)
    y = tl.load(y_ptr + offsets, mask=mask)
    output = x + y
    tl.store(output_ptr + offsets, output, mask=mask)

def add(x: torch.Tensor, y: torch.Tensor):
    output = torch.empty_like(x)
    assert x.is_cuda and y.is_cuda and output.is_cuda
    n_elements = output.numel()
    grid = lambda meta: (triton.cdiv(n_elements, meta['BLOCK_SIZE']),)
    add_kernel[grid](x, y, output, n_elements, BLOCK_SIZE=1024)
    return output

x = torch.rand(10000, device='cuda')
y = torch.rand(10000, device='cuda')
res = add(x, y)
print("SUCCESS!", res[:5])

{
  "description": "Run the simple vector add test script.",
  "command": "uv run triton_vec_add.py"
}

{
  "content": "<5303 chars \u2014 see below>",
  "file_path": "solution.py"
}

import torch
import torch.nn as nn
import triton
import triton.language as tl

GROUP_SIZE = 128

@triton.jit
def w4a16_gemm_kernel(
    x_ptr, w_ptr, scales_ptr, zeros_ptr, out_ptr,
    M, N, K,
    stride_xm, stride_xk,
    stride_wk, stride_wn,
    stride_sm, stride_sn,
    stride_zm, stride_zn,
    stride_om, stride_on,
    BLOCK_SIZE_M: tl.constexpr,
    BLOCK_SIZE_N: tl.constexpr,
    BLOCK_SIZE_K: tl.constexpr,
    GROUP_SIZE: tl.constexpr,
):
    pid = tl.program_id(0)
    num_pid_m = tl.cdiv(M, BLOCK_SIZE_M)
    num_pid_n = tl.cdiv(N, BLOCK_SIZE_N)
    
    # 2D Grid with Program ID grouping/swizzling for L2 cache reuse
    num_pid_in_group = 8
    group_id = pid // (num_pid_in_group * num_pid_n)
    first_pid_m = group_id * num_pid_in_group
    group_size_m = min(num_pid_m - first_pid_m, num_pid_in_group)
    pid_m = first_pid_m + (pid % group_size_m)
    pid_n = (pid % (group_size_m * num_pid_n)) // group_size_m

    offs_am = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
    offs_bn = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
    
    offs_k_half = tl.arange(0, BLOCK_SIZE_K // 2)
    offs_b_k = tl.arange(0, BLOCK_SIZE_K // 2)
    
    a_mask = offs_am[:, None] < M
    b_mask = offs_bn[None, :] < N
    
    accumulator = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)
    
    for k_curr in range(0, K, BLOCK_SIZE_K):
        # Even and Odd input pointers
        a_even_ptrs = x_ptr + (offs_am[:, None] * stride_xm + (k_curr + 2 * offs_k_half)[None, :] * stride_xk)
        a_odd_ptrs = x_ptr + (offs_am[:, None] * stride_xm + (k_curr + 2 * offs_k_half + 1)[None, :] * stride_xk)
        
        a_even = tl.load(a_even_ptrs, mask=a_mask & ((k_curr + 2 * offs_k_half)[None, :] < K), other=0.0)
        a_odd = tl.load(a_odd_ptrs, mask=a_mask & ((k_curr + 2 * offs_k_half + 1)[None, :] < K), other=0.0)
        
        # Load packed weights
        b_ptrs = w_ptr + ((k_curr // 2 + offs_b_k[:, None]) * stride_wk + offs_bn[None, :] * stride_wn)
        b_packed = tl.load(b_ptrs, mask=b_mask & ((k_curr // 2 + offs_b_k[:, None]) < (K // 2)), other=0)
        
        # Unpack even/odd
        b_even_uint8 = b_packed & 0xF
        b_odd_uint8 = (b_packed >> 4) & 0xF
        
        # Load scale and zero for current group
        k_group = k_curr // GROUP_SIZE
        scale_ptrs = scales_ptr + (k_group * stride_sm + offs_bn * stride_sn)
        zero_ptrs = zeros_ptr + (k_group * stride_zm + offs_bn * stride_zn)
        
        scale = tl.load(scale_ptrs, mask=offs_bn < N, other=0.0)
        zero = tl.load(zero_ptrs, mask=offs_bn < N, other=0.0)
        
        # Dequantize to bfloat16
        w_even = (b_even_uint8.to(tl.bfloat16) - zero[None, :]) * scale[None, :]
        w_odd = (b_odd_uint8.to(tl.bfloat16) - zero[None, :]) * scale[None, :]
        
        # Dot products
        accumulator += tl.dot(a_even, w_even)
        accumulator += tl.dot(a_odd, w_odd)
        
    # Write to output
    c = accumulator.to(tl.bfloat16)
    offs_om = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
    offs_on = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
    out_ptrs = out_ptr + (offs_om[:, None] * stride_om + offs_on[None, :] * stride_on)
    out_mask = (offs_om[:, None] < M) & (offs_on[None, :] < N)
    tl.store(out_ptrs, c, mask=out_mask)


class Model(nn.Module):
    def __init__(self, M: int, N: int, K: int, group_size: int = GROUP_SIZE):
        super().__init__()
        assert K % group_size == 0, "K must be divisible by group_size"
        assert K % 2 == 0, "K must be even (int4 packing)"
        self.M, self.N, self.K = M, N, K
        self.group_size = group_size
        n_groups = K // group_size

        # Register buffers so load_state_dict works
        self.register_buffer("w_q", torch.empty((K // 2, N), dtype=torch.uint8))
        self.register_buffer("scales", torch.empty((n_groups, N), dtype=torch.bfloat16))
        self.register_buffer("zeros", torch.empty((n_groups, N), dtype=torch.bfloat

... (1303 more chars)

{
  "command": "uv run test_simple.py",
  "description": "Run the simple debug script with fixed config."
}

{
  "content": "<5335 chars \u2014 see below>",
  "file_path": "solution.py"
}

import torch
import torch.nn as nn
import triton
import triton.language as tl

GROUP_SIZE = 128

@triton.jit
def w4a16_gemm_kernel(
    x_ptr, w_ptr, scales_ptr, zeros_ptr, out_ptr,
    M, N,
    stride_xm, stride_xk,
    stride_wk, stride_wn,
    stride_sm, stride_sn,
    stride_zm, stride_zn,
    stride_om, stride_on,
    BLOCK_SIZE_M: tl.constexpr,
    BLOCK_SIZE_N: tl.constexpr,
    BLOCK_SIZE_K: tl.constexpr,
    GROUP_SIZE: tl.constexpr,
    K: tl.constexpr,
):
    pid = tl.program_id(0)
    num_pid_m = tl.cdiv(M, BLOCK_SIZE_M)
    num_pid_n = tl.cdiv(N, BLOCK_SIZE_N)
    
    # 2D Grid with Program ID grouping/swizzling for L2 cache reuse
    num_pid_in_group = 8
    group_id = pid // (num_pid_in_group * num_pid_n)
    first_pid_m = group_id * num_pid_in_group
    group_size_m = min(num_pid_m - first_pid_m, num_pid_in_group)
    pid_m = first_pid_m + (pid % group_size_m)
    pid_n = (pid % (group_size_m * num_pid_n)) // group_size_m

    offs_am = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
    offs_bn = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
    
    offs_k_half = tl.arange(0, BLOCK_SIZE_K // 2)
    offs_b_k = tl.arange(0, BLOCK_SIZE_K // 2)
    
    a_mask = offs_am[:, None] < M
    b_mask = offs_bn[None, :] < N
    
    accumulator = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)
    
    for k_curr in range(0, K, BLOCK_SIZE_K):
        # Even and Odd input pointers
        a_even_ptrs = x_ptr + (offs_am[:, None] * stride_xm + (k_curr + 2 * offs_k_half)[None, :] * stride_xk)
        a_odd_ptrs = x_ptr + (offs_am[:, None] * stride_xm + (k_curr + 2 * offs_k_half + 1)[None, :] * stride_xk)
        
        a_even = tl.load(a_even_ptrs, mask=a_mask & ((k_curr + 2 * offs_k_half)[None, :] < K), other=0.0)
        a_odd = tl.load(a_odd_ptrs, mask=a_mask & ((k_curr + 2 * offs_k_half + 1)[None, :] < K), other=0.0)
        
        # Load packed weights
        b_ptrs = w_ptr + ((k_curr // 2 + offs_b_k[:, None]) * stride_wk + offs_bn[None, :] * stride_wn)
        b_packed = tl.load(b_ptrs, mask=b_mask & ((k_curr // 2 + offs_b_k[:, None]) < (K // 2)), other=0)
        
        # Unpack even/odd
        b_even_uint8 = b_packed & 0xF
        b_odd_uint8 = (b_packed >> 4) & 0xF
        
        # Load scale and zero for current group
        k_group = k_curr // GROUP_SIZE
        scale_ptrs = scales_ptr + (k_group * stride_sm + offs_bn * stride_sn)
        zero_ptrs = zeros_ptr + (k_group * stride_zm + offs_bn * stride_zn)
        
        scale = tl.load(scale_ptrs, mask=offs_bn < N, other=0.0)
        zero = tl.load(zero_ptrs, mask=offs_bn < N, other=0.0)
        
        # Dequantize to bfloat16
        w_even = (b_even_uint8.to(tl.bfloat16) - zero[None, :]) * scale[None, :]
        w_odd = (b_odd_uint8.to(tl.bfloat16) - zero[None, :]) * scale[None, :]
        
        # Dot products
        accumulator += tl.dot(a_even, w_even)
        accumulator += tl.dot(a_odd, w_odd)
        
    # Write to output
    c = accumulator.to(tl.bfloat16)
    offs_om = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
    offs_on = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
    out_ptrs = out_ptr + (offs_om[:, None] * stride_om + offs_on[None, :] * stride_on)
    out_mask = (offs_om[:, None] < M) & (offs_on[None, :] < N)
    tl.store(out_ptrs, c, mask=out_mask)


class Model(nn.Module):
    def __init__(self, M: int, N: int, K: int, group_size: int = GROUP_SIZE):
        super().__init__()
        assert K % group_size == 0, "K must be divisible by group_size"
        assert K % 2 == 0, "K must be even (int4 packing)"
        self.M, self.N, self.K = M, N, K
        self.group_size = group_size
        n_groups = K // group_size

        # Register buffers so load_state_dict works
        self.register_buffer("w_q", torch.empty((K // 2, N), dtype=torch.uint8))
        self.register_buffer("scales", torch.empty((n_groups, N), dtype=torch.bfloat16))
        self.register_buffer("zeros", torch.empty((n_groups, N), 

... (1335 more chars)

{
  "description": "Run the simple debug script with constexpr K.",
  "command": "uv run test_simple.py"
}

{
  "command": "uv run check.py",
  "description": "Run the full correctness check across all shapes and seeds."
}

{
  "description": "Run performance benchmarks across all shapes with baselines.",
  "command": "KBH_BENCHMARK_BASELINES=1 uv run benchmark.py"
}

{
  "strategic_intent": "Re-integrating autotuner with constexpr K and benchmarking performance.",
  "title": "Autotuning & Performance Tuning",
  "summary": "By identifying that K must be a constexpr in the Triton kernel signature, we solved the compilation hang. Now we will re-enable the Triton autotuner to select the best tile sizes (BLOCK_SIZE_M, BLOCK_SIZE_N, BLOCK_SIZE_K, num_stages, num_warps) for each M, N, K shape. This will automatically improve performance, especially for larger M shapes (like M=256) where our hardcoded block sizes were suboptimal."
}

{
  "file_path": "solution.py",
  "content": "<5918 chars \u2014 see below>"
}

import torch
import torch.nn as nn
import triton
import triton.language as tl

GROUP_SIZE = 128

@triton.autotune(
    configs=[
        triton.Config({'BLOCK_SIZE_M': 16, 'BLOCK_SIZE_N': 128, 'BLOCK_SIZE_K': 128, 'num_stages': 4, 'num_warps': 4}),
        triton.Config({'BLOCK_SIZE_M': 16, 'BLOCK_SIZE_N': 256, 'BLOCK_SIZE_K': 128, 'num_stages': 4, 'num_warps': 4}),
        triton.Config({'BLOCK_SIZE_M': 32, 'BLOCK_SIZE_N': 128, 'BLOCK_SIZE_K': 128, 'num_stages': 4, 'num_warps': 4}),
        triton.Config({'BLOCK_SIZE_M': 64, 'BLOCK_SIZE_N': 128, 'BLOCK_SIZE_K': 128, 'num_stages': 4, 'num_warps': 4}),
        triton.Config({'BLOCK_SIZE_M': 128, 'BLOCK_SIZE_N': 128, 'BLOCK_SIZE_K': 128, 'num_stages': 4, 'num_warps': 8}),
        triton.Config({'BLOCK_SIZE_M': 64, 'BLOCK_SIZE_N': 64, 'BLOCK_SIZE_K': 128, 'num_stages': 4, 'num_warps': 4}),
        triton.Config({'BLOCK_SIZE_M': 32, 'BLOCK_SIZE_N': 256, 'BLOCK_SIZE_K': 128, 'num_stages': 4, 'num_warps': 8}),
    ],
    key=['M', 'N'],
)
@triton.jit
def w4a16_gemm_kernel(
    x_ptr, w_ptr, scales_ptr, zeros_ptr, out_ptr,
    M, N,
    stride_xm, stride_xk,
    stride_wk, stride_wn,
    stride_sm, stride_sn,
    stride_zm, stride_zn,
    stride_om, stride_on,
    BLOCK_SIZE_M: tl.constexpr,
    BLOCK_SIZE_N: tl.constexpr,
    BLOCK_SIZE_K: tl.constexpr,
    GROUP_SIZE: tl.constexpr,
    K: tl.constexpr,
):
    pid = tl.program_id(0)
    num_pid_m = tl.cdiv(M, BLOCK_SIZE_M)
    num_pid_n = tl.cdiv(N, BLOCK_SIZE_N)
    
    # 2D Grid with Program ID grouping/swizzling for L2 cache reuse
    num_pid_in_group = 8
    group_id = pid // (num_pid_in_group * num_pid_n)
    first_pid_m = group_id * num_pid_in_group
    group_size_m = min(num_pid_m - first_pid_m, num_pid_in_group)
    pid_m = first_pid_m + (pid % group_size_m)
    pid_n = (pid % (group_size_m * num_pid_n)) // group_size_m

    offs_am = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
    offs_bn = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
    
    offs_k_half = tl.arange(0, BLOCK_SIZE_K // 2)
    offs_b_k = tl.arange(0, BLOCK_SIZE_K // 2)
    
    a_mask = offs_am[:, None] < M
    b_mask = offs_bn[None, :] < N
    
    accumulator = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)
    
    for k_curr in range(0, K, BLOCK_SIZE_K):
        # Even and Odd input pointers
        a_even_ptrs = x_ptr + (offs_am[:, None] * stride_xm + (k_curr + 2 * offs_k_half)[None, :] * stride_xk)
        a_odd_ptrs = x_ptr + (offs_am[:, None] * stride_xm + (k_curr + 2 * offs_k_half + 1)[None, :] * stride_xk)
        
        a_even = tl.load(a_even_ptrs, mask=a_mask & ((k_curr + 2 * offs_k_half)[None, :] < K), other=0.0)
        a_odd = tl.load(a_odd_ptrs, mask=a_mask & ((k_curr + 2 * offs_k_half + 1)[None, :] < K), other=0.0)
        
        # Load packed weights
        b_ptrs = w_ptr + ((k_curr // 2 + offs_b_k[:, None]) * stride_wk + offs_bn[None, :] * stride_wn)
        b_packed = tl.load(b_ptrs, mask=b_mask & ((k_curr // 2 + offs_b_k[:, None]) < (K // 2)), other=0)
        
        # Unpack even/odd
        b_even_uint8 = b_packed & 0xF
        b_odd_uint8 = (b_packed >> 4) & 0xF
        
        # Load scale and zero for current group
        k_group = k_curr // GROUP_SIZE
        scale_ptrs = scales_ptr + (k_group * stride_sm + offs_bn * stride_sn)
        zero_ptrs = zeros_ptr + (k_group * stride_zm + offs_bn * stride_zn)
        
        scale = tl.load(scale_ptrs, mask=offs_bn < N, other=0.0)
        zero = tl.load(zero_ptrs, mask=offs_bn < N, other=0.0)
        
        # Dequantize to bfloat16
        w_even = (b_even_uint8.to(tl.bfloat16) - zero[None, :]) * scale[None, :]
        w_odd = (b_odd_uint8.to(tl.bfloat16) - zero[None, :]) * scale[None, :]
        
        # Dot products
        accumulator += tl.dot(a_even, w_even)
        accumulator += tl.dot(a_odd, w_odd)
        
    # Write to output
    c = accumulator.to(tl.bfloat16)
    offs_om = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
    offs_on = pid

... (1918 more chars)

{
  "description": "Run the simple debug script with autotuning.",
  "command": "uv run test_simple.py"
}

{
  "file_path": "solution.py",
  "content": "<5896 chars \u2014 see below>"
}

import torch
import torch.nn as nn
import triton
import triton.language as tl

GROUP_SIZE = 128

@triton.jit
def w4a16_gemm_kernel(
    x_ptr, w_ptr, scales_ptr, zeros_ptr, out_ptr,
    M, N,
    stride_xm, stride_xk,
    stride_wk, stride_wn,
    stride_sm, stride_sn,
    stride_zm, stride_zn,
    stride_om, stride_on,
    BLOCK_SIZE_M: tl.constexpr,
    BLOCK_SIZE_N: tl.constexpr,
    BLOCK_SIZE_K: tl.constexpr,
    GROUP_SIZE: tl.constexpr,
    K: tl.constexpr,
):
    pid = tl.program_id(0)
    num_pid_m = tl.cdiv(M, BLOCK_SIZE_M)
    num_pid_n = tl.cdiv(N, BLOCK_SIZE_N)
    
    # 2D Grid with Program ID grouping/swizzling for L2 cache reuse
    num_pid_in_group = 8
    group_id = pid // (num_pid_in_group * num_pid_n)
    first_pid_m = group_id * num_pid_in_group
    group_size_m = min(num_pid_m - first_pid_m, num_pid_in_group)
    pid_m = first_pid_m + (pid % group_size_m)
    pid_n = (pid % (group_size_m * num_pid_n)) // group_size_m

    offs_am = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
    offs_bn = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
    
    offs_k_half = tl.arange(0, BLOCK_SIZE_K // 2)
    offs_b_k = tl.arange(0, BLOCK_SIZE_K // 2)
    
    a_mask = offs_am[:, None] < M
    b_mask = offs_bn[None, :] < N
    
    accumulator = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)
    
    for k_curr in range(0, K, BLOCK_SIZE_K):
        # Even and Odd input pointers
        a_even_ptrs = x_ptr + (offs_am[:, None] * stride_xm + (k_curr + 2 * offs_k_half)[None, :] * stride_xk)
        a_odd_ptrs = x_ptr + (offs_am[:, None] * stride_xm + (k_curr + 2 * offs_k_half + 1)[None, :] * stride_xk)
        
        a_even = tl.load(a_even_ptrs, mask=a_mask & ((k_curr + 2 * offs_k_half)[None, :] < K), other=0.0)
        a_odd = tl.load(a_odd_ptrs, mask=a_mask & ((k_curr + 2 * offs_k_half + 1)[None, :] < K), other=0.0)
        
        # Load packed weights
        b_ptrs = w_ptr + ((k_curr // 2 + offs_b_k[:, None]) * stride_wk + offs_bn[None, :] * stride_wn)
        b_packed = tl.load(b_ptrs, mask=b_mask & ((k_curr // 2 + offs_b_k[:, None]) < (K // 2)), other=0)
        
        # Unpack even/odd
        b_even_uint8 = b_packed & 0xF
        b_odd_uint8 = (b_packed >> 4) & 0xF
        
        # Load scale and zero for current group
        k_group = k_curr // GROUP_SIZE
        scale_ptrs = scales_ptr + (k_group * stride_sm + offs_bn * stride_sn)
        zero_ptrs = zeros_ptr + (k_group * stride_zm + offs_bn * stride_zn)
        
        scale = tl.load(scale_ptrs, mask=offs_bn < N, other=0.0)
        zero = tl.load(zero_ptrs, mask=offs_bn < N, other=0.0)
        
        # Dequantize to bfloat16
        w_even = (b_even_uint8.to(tl.bfloat16) - zero[None, :]) * scale[None, :]
        w_odd = (b_odd_uint8.to(tl.bfloat16) - zero[None, :]) * scale[None, :]
        
        # Dot products
        accumulator += tl.dot(a_even, w_even)
        accumulator += tl.dot(a_odd, w_odd)
        
    # Write to output
    c = accumulator.to(tl.bfloat16)
    offs_om = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
    offs_on = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
    out_ptrs = out_ptr + (offs_om[:, None] * stride_om + offs_on[None, :] * stride_on)
    out_mask = (offs_om[:, None] < M) & (offs_on[None, :] < N)
    tl.store(out_ptrs, c, mask=out_mask)


class Model(nn.Module):
    def __init__(self, M: int, N: int, K: int, group_size: int = GROUP_SIZE):
        super().__init__()
        assert K % group_size == 0, "K must be divisible by group_size"
        assert K % 2 == 0, "K must be even (int4 packing)"
        self.M, self.N, self.K = M, N, K
        self.group_size = group_size
        n_groups = K // group_size

        # Register buffers so load_state_dict works
        self.register_buffer("w_q", torch.empty((K // 2, N), dtype=torch.uint8))
        self.register_buffer("scales", torch.empty((n_groups, N), dtype=torch.bfloat16))
        self.register_buffer("zeros", torch.empty((n_groups, N), 

... (1896 more chars)

{
  "description": "Verify correctness with the manual dispatcher.",
  "command": "uv run check.py"
}

{
  "command": "KBH_BENCHMARK_BASELINES=1 uv run benchmark.py",
  "description": "Run performance benchmark with manual dispatcher."
}

{
  "content": "<9200 chars \u2014 see below>",
  "file_path": "solution.py"
}

import torch
import torch.nn as nn
import triton
import triton.language as tl

GROUP_SIZE = 128

@triton.jit
def w4a16_gemv_kernel(
    x_ptr, w_ptr, scales_ptr, zeros_ptr, out_ptr,
    N,
    stride_xk,
    stride_wk, stride_wn,
    stride_sm, stride_sn,
    stride_zm, stride_zn,
    stride_on,
    BLOCK_SIZE_N: tl.constexpr,
    BLOCK_SIZE_K: tl.constexpr,
    GROUP_SIZE: tl.constexpr,
    K: tl.constexpr,
):
    pid_n = tl.program_id(0)
    
    offs_bn = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
    b_mask = offs_bn < N
    
    accumulator = tl.zeros((BLOCK_SIZE_N,), dtype=tl.float32)
    
    BLOCK_SIZE_K_half = BLOCK_SIZE_K // 2
    offs_k_half = tl.arange(0, BLOCK_SIZE_K_half)
    offs_b_k = tl.arange(0, BLOCK_SIZE_K_half)
    
    for k_curr in range(0, K, BLOCK_SIZE_K):
        # Load x_even and x_odd as 1D vectors
        x_even_ptrs = x_ptr + (k_curr + 2 * offs_k_half) * stride_xk
        x_odd_ptrs = x_ptr + (k_curr + 2 * offs_k_half + 1) * stride_xk
        
        x_even = tl.load(x_even_ptrs, mask=(k_curr + 2 * offs_k_half) < K, other=0.0)
        x_odd = tl.load(x_odd_ptrs, mask=(k_curr + 2 * offs_k_half + 1) < K, other=0.0)
        
        # Load packed weights
        b_ptrs = w_ptr + ((k_curr // 2 + offs_b_k[:, None]) * stride_wk + offs_bn[None, :] * stride_wn)
        b_packed = tl.load(b_ptrs, mask=b_mask[None, :] & ((k_curr // 2 + offs_b_k[:, None]) < (K // 2)), other=0)
        
        # Unpack even/odd
        b_even_uint8 = b_packed & 0xF
        b_odd_uint8 = (b_packed >> 4) & 0xF
        
        # Load scale and zero for current group
        k_group = k_curr // GROUP_SIZE
        scale_ptrs = scales_ptr + (k_group * stride_sm + offs_bn * stride_sn)
        zero_ptrs = zeros_ptr + (k_group * stride_zm + offs_bn * stride_zn)
        
        scale = tl.load(scale_ptrs, mask=b_mask, other=0.0)
        zero = tl.load(zero_ptrs, mask=b_mask, other=0.0)
        
        # Dequantize to bfloat16
        w_even = (b_even_uint8.to(tl.bfloat16) - zero[None, :]) * scale[None, :]
        w_odd = (b_odd_uint8.to(tl.bfloat16) - zero[None, :]) * scale[None, :]
        
        # Element-wise multiply and accumulate
        prod_even = x_even[:, None] * w_even
        prod_odd = x_odd[:, None] * w_odd
        
        # Sum along columns to get N outputs
        accumulator += tl.sum((prod_even + prod_odd).to(tl.float32), axis=0)
        
    # Write to output vector
    out_ptrs = out_ptr + offs_bn * stride_on
    tl.store(out_ptrs, accumulator.to(tl.bfloat16), mask=b_mask)


@triton.jit
def w4a16_gemm_kernel(
    x_ptr, w_ptr, scales_ptr, zeros_ptr, out_ptr,
    M, N,
    stride_xm, stride_xk,
    stride_wk, stride_wn,
    stride_sm, stride_sn,
    stride_zm, stride_zn,
    stride_om, stride_on,
    BLOCK_SIZE_M: tl.constexpr,
    BLOCK_SIZE_N: tl.constexpr,
    BLOCK_SIZE_K: tl.constexpr,
    GROUP_SIZE: tl.constexpr,
    K: tl.constexpr,
):
    pid = tl.program_id(0)
    num_pid_m = tl.cdiv(M, BLOCK_SIZE_M)
    num_pid_n = tl.cdiv(N, BLOCK_SIZE_N)
    
    # 2D Grid with Program ID grouping/swizzling for L2 cache reuse
    num_pid_in_group = 8
    group_id = pid // (num_pid_in_group * num_pid_n)
    first_pid_m = group_id * num_pid_in_group
    group_size_m = min(num_pid_m - first_pid_m, num_pid_in_group)
    pid_m = first_pid_m + (pid % group_size_m)
    pid_n = (pid % (group_size_m * num_pid_n)) // group_size_m

    offs_am = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
    offs_bn = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
    
    offs_k_half = tl.arange(0, BLOCK_SIZE_K // 2)
    offs_b_k = tl.arange(0, BLOCK_SIZE_K // 2)
    
    a_mask = offs_am[:, None] < M
    b_mask = offs_bn[None, :] < N
    
    accumulator = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)
    
    for k_curr in range(0, K, BLOCK_SIZE_K):
        # Even and Odd input pointers
        a_even_ptrs = x_ptr + (offs_am[:, None] * stride_xm + (k_curr + 2 * offs_k_half)[None, :] * stride_xk)
        a_odd

... (5200 more chars)

{
  "description": "Verify correctness of the specialized GEMV path.",
  "command": "uv run check.py"
}

{
  "instruction": "Use BLOCK_SIZE_K // 2 directly in tl.arange for w4a16_gemv_kernel.",
  "new_string": "<96 chars \u2014 see below>",
  "file_path": "solution.py",
  "old_string": "<138 chars \u2014 see below>",
  "allow_multiple": false
}

    offs_k_half = tl.arange(0, BLOCK_SIZE_K // 2)
    offs_b_k = tl.arange(0, BLOCK_SIZE_K // 2)

    BLOCK_SIZE_K_half = BLOCK_SIZE_K // 2
    offs_k_half = tl.arange(0, BLOCK_SIZE_K_half)
    offs_b_k = tl.arange(0, BLOCK_SIZE_K_half)

{
  "description": "Verify correctness with the updated GEMV kernel.",
  "command": "uv run check.py"
}

{
  "description": "Benchmark performance of GEMV and GEMM paths.",
  "command": "KBH_BENCHMARK_BASELINES=1 uv run benchmark.py"
}

{
  "content": "<6334 chars \u2014 see below>",
  "file_path": "solution.py"
}

import torch
import torch.nn as nn
import triton
import triton.language as tl

GROUP_SIZE = 128

@triton.jit
def w4a16_gemm_kernel(
    x_ptr, w_ptr, scales_ptr, zeros_ptr, out_ptr,
    M, N,
    stride_xm, stride_xk,
    stride_wk, stride_wn,
    stride_sm, stride_sn,
    stride_zm, stride_zn,
    stride_om, stride_on,
    BLOCK_SIZE_M: tl.constexpr,
    BLOCK_SIZE_N: tl.constexpr,
    BLOCK_SIZE_K: tl.constexpr,
    GROUP_SIZE: tl.constexpr,
    K: tl.constexpr,
):
    pid = tl.program_id(0)
    num_pid_m = tl.cdiv(M, BLOCK_SIZE_M)
    num_pid_n = tl.cdiv(N, BLOCK_SIZE_N)
    
    # 2D Grid with Program ID grouping/swizzling for L2 cache reuse
    num_pid_in_group = 8
    group_id = pid // (num_pid_in_group * num_pid_n)
    first_pid_m = group_id * num_pid_in_group
    group_size_m = min(num_pid_m - first_pid_m, num_pid_in_group)
    pid_m = first_pid_m + (pid % group_size_m)
    pid_n = (pid % (group_size_m * num_pid_n)) // group_size_m

    offs_am = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
    offs_bn = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
    
    offs_k_half = tl.arange(0, BLOCK_SIZE_K // 2)
    offs_b_k = tl.arange(0, BLOCK_SIZE_K // 2)
    
    a_mask = offs_am[:, None] < M
    b_mask = offs_bn[None, :] < N
    
    accumulator = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)
    
    for k_curr in range(0, K, BLOCK_SIZE_K):
        # Even and Odd input pointers
        a_even_ptrs = x_ptr + (offs_am[:, None] * stride_xm + (k_curr + 2 * offs_k_half)[None, :] * stride_xk)
        a_odd_ptrs = x_ptr + (offs_am[:, None] * stride_xm + (k_curr + 2 * offs_k_half + 1)[None, :] * stride_xk)
        
        a_even = tl.load(a_even_ptrs, mask=a_mask & ((k_curr + 2 * offs_k_half)[None, :] < K), other=0.0)
        a_odd = tl.load(a_odd_ptrs, mask=a_mask & ((k_curr + 2 * offs_k_half + 1)[None, :] < K), other=0.0)
        
        # Load packed weights
        b_ptrs = w_ptr + ((k_curr // 2 + offs_b_k[:, None]) * stride_wk + offs_bn[None, :] * stride_wn)
        b_packed = tl.load(b_ptrs, mask=b_mask & ((k_curr // 2 + offs_b_k[:, None]) < (K // 2)), other=0)
        
        # Unpack even/odd
        b_even_uint8 = b_packed & 0xF
        b_odd_uint8 = (b_packed >> 4) & 0xF
        
        # Load scale and zero for current group
        k_group = k_curr // GROUP_SIZE
        scale_ptrs = scales_ptr + (k_group * stride_sm + offs_bn * stride_sn)
        zero_ptrs = zeros_ptr + (k_group * stride_zm + offs_bn * stride_zn)
        
        scale = tl.load(scale_ptrs, mask=offs_bn < N, other=0.0)
        zero = tl.load(zero_ptrs, mask=offs_bn < N, other=0.0)
        
        # Dequantize to bfloat16
        w_even = (b_even_uint8.to(tl.bfloat16) - zero[None, :]) * scale[None, :]
        w_odd = (b_odd_uint8.to(tl.bfloat16) - zero[None, :]) * scale[None, :]
        
        # Dot products
        accumulator += tl.dot(a_even, w_even)
        accumulator += tl.dot(a_odd, w_odd)
        
    # Write to output
    c = accumulator.to(tl.bfloat16)
    offs_om = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
    offs_on = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
    out_ptrs = out_ptr + (offs_om[:, None] * stride_om + offs_on[None, :] * stride_on)
    out_mask = (offs_om[:, None] < M) & (offs_on[None, :] < N)
    tl.store(out_ptrs, c, mask=out_mask)


class Model(nn.Module):
    def __init__(self, M: int, N: int, K: int, group_size: int = GROUP_SIZE):
        super().__init__()
        assert K % group_size == 0, "K must be divisible by group_size"
        assert K % 2 == 0, "K must be even (int4 packing)"
        self.M, self.N, self.K = M, N, K
        self.group_size = group_size
        n_groups = K // group_size

        # Register buffers so load_state_dict works
        self.register_buffer("w_q", torch.empty((K // 2, N), dtype=torch.uint8))
        self.register_buffer("scales", torch.empty((n_groups, N), dtype=torch.bfloat16))
        self.register_buffer("zeros", torch.empty((n_groups, N), 

... (2334 more chars)

{
  "file_path": "optimize_configs.py",
  "content": "<4481 chars \u2014 see below>"
}

import torch
import reference
import solution
import shapes
import time

device = torch.device("cuda:0")

# All shapes to optimize
SHAPES = shapes.SHAPES

# Hyperparameter space to explore
BLOCK_SIZE_M_OPTS = [16, 32, 64, 128]
BLOCK_SIZE_N_OPTS = [64, 128, 256]
BLOCK_SIZE_K_OPTS = [64, 128, 256]
NUM_WARPS_OPTS = [4, 8]
NUM_STAGES_OPTS = [2, 3, 4, 5]

print("Starting grid search for optimal configurations...")

best_configs = {}

for idx, shape in enumerate(SHAPES):
    M, N, K = shape["M"], shape["N"], shape["K"]
    print(f"\n==================================================")
    print(f"Optimizing Shape {idx}: M={M}, N={N}, K={K}")
    print(f"==================================================")
    
    # Initialize reference and solution models for this shape
    reference.M = M
    reference.N = N
    reference.K = K
    init_args = reference.get_init_inputs()
    ref_model = reference.Model(*init_args).to(device).eval()
    sol_model = solution.Model(*init_args).to(device).eval()
    sol_model.load_state_dict(ref_model.state_dict(), strict=True)
    
    inputs = [t.to(device) for t in reference.get_inputs()]
    x = inputs[0]
    
    # Warmup and baseline
    with torch.no_grad():
        ref_out = ref_model(x)
        # Check standard default forward runs
        _ = sol_model(x)
        
    best_ms = float('inf')
    best_cfg = None
    
    # Grid search
    count = 0
    for BM in BLOCK_SIZE_M_OPTS:
        if BM < 16:
            continue
        for BN in BLOCK_SIZE_N_OPTS:
            for BK in BLOCK_SIZE_K_OPTS:
                # Group size along K is 128, so BK should be a multiple of group size
                # or group size should be a multiple of BK. To be aligned with GROUP_SIZE (128),
                # BK must be either 128 or 256. If BK is 64, we need scales to be aligned.
                # Since we use k_group = k_curr // 128, BK=64 also works as long as BK is divisor of 128.
                # So BK of 64, 128, 256 are all perfectly valid.
                for warps in NUM_WARPS_OPTS:
                    for stages in NUM_STAGES_OPTS:
                        cfg = {
                            'BLOCK_SIZE_M': BM,
                            'BLOCK_SIZE_N': BN,
                            'BLOCK_SIZE_K': BK,
                            'num_warps': warps,
                            'num_stages': stages
                        }
                        
                        try:
                            # Warmup
                            with torch.no_grad():
                                sol_out = sol_model(x, config_override=cfg)
                                # Basic correctness check
                                if not torch.allclose(ref_out, sol_out, atol=0.10, rtol=0.10):
                                    continue
                                    
                            # Time it
                            start_evt = torch.cuda.Event(enable_timing=True)
                            end_evt = torch.cuda.Event(enable_timing=True)
                            
                            # Warmup
                            for _ in range(5):
                                _ = sol_model(x, config_override=cfg)
                            
                            torch.cuda.synchronize()
                            start_evt.record()
                            for _ in range(50):
                                _ = sol_model(x, config_override=cfg)
                            end_evt.record()
                            torch.cuda.synchronize()
                            
                            ms = start_evt.elapsed_time(end_evt) / 50.0
                            count += 1
                            
                            if ms < best_ms:
                                best_ms = ms
                                best_cfg = cfg
                                print(f"  New Best: {cfg} -> {ms:.4f} ms")
                        except Exception as e:
     

... (481 more chars)

{
  "description": "Run the configuration optimizer script.",
  "command": "uv run optimize_configs.py"
}

{
  "content": "<6822 chars \u2014 see below>",
  "file_path": "solution.py"
}

import torch
import torch.nn as nn
import triton
import triton.language as tl

GROUP_SIZE = 128

@triton.jit
def w4a16_gemm_kernel(
    x_ptr, w_ptr, scales_ptr, zeros_ptr, out_ptr,
    M, N,
    stride_xm, stride_xk,
    stride_wk, stride_wn,
    stride_sm, stride_sn,
    stride_zm, stride_zn,
    stride_om, stride_on,
    BLOCK_SIZE_M: tl.constexpr,
    BLOCK_SIZE_N: tl.constexpr,
    BLOCK_SIZE_K: tl.constexpr,
    GROUP_SIZE: tl.constexpr,
    K: tl.constexpr,
):
    pid = tl.program_id(0)
    num_pid_m = tl.cdiv(M, BLOCK_SIZE_M)
    num_pid_n = tl.cdiv(N, BLOCK_SIZE_N)
    
    # 2D Grid with Program ID grouping/swizzling for L2 cache reuse
    num_pid_in_group = 8
    group_id = pid // (num_pid_in_group * num_pid_n)
    first_pid_m = group_id * num_pid_in_group
    group_size_m = min(num_pid_m - first_pid_m, num_pid_in_group)
    pid_m = first_pid_m + (pid % group_size_m)
    pid_n = (pid % (group_size_m * num_pid_n)) // group_size_m

    offs_am = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
    offs_bn = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
    
    offs_k_half = tl.arange(0, BLOCK_SIZE_K // 2)
    offs_b_k = tl.arange(0, BLOCK_SIZE_K // 2)
    
    a_mask = offs_am[:, None] < M
    b_mask = offs_bn[None, :] < N
    
    accumulator = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)
    
    for k_curr in range(0, K, BLOCK_SIZE_K):
        # Even and Odd input pointers
        a_even_ptrs = x_ptr + (offs_am[:, None] * stride_xm + (k_curr + 2 * offs_k_half)[None, :] * stride_xk)
        a_odd_ptrs = x_ptr + (offs_am[:, None] * stride_xm + (k_curr + 2 * offs_k_half + 1)[None, :] * stride_xk)
        
        a_even = tl.load(a_even_ptrs, mask=a_mask & ((k_curr + 2 * offs_k_half)[None, :] < K), other=0.0)
        a_odd = tl.load(a_odd_ptrs, mask=a_mask & ((k_curr + 2 * offs_k_half + 1)[None, :] < K), other=0.0)
        
        # Load packed weights
        b_ptrs = w_ptr + ((k_curr // 2 + offs_b_k[:, None]) * stride_wk + offs_bn[None, :] * stride_wn)
        b_packed = tl.load(b_ptrs, mask=b_mask & ((k_curr // 2 + offs_b_k[:, None]) < (K // 2)), other=0)
        
        # Unpack even/odd
        b_even_uint8 = b_packed & 0xF
        b_odd_uint8 = (b_packed >> 4) & 0xF
        
        # Load scale and zero for current group
        k_group = k_curr // GROUP_SIZE
        scale_ptrs = scales_ptr + (k_group * stride_sm + offs_bn * stride_sn)
        zero_ptrs = zeros_ptr + (k_group * stride_zm + offs_bn * stride_zn)
        
        scale = tl.load(scale_ptrs, mask=offs_bn < N, other=0.0)
        zero = tl.load(zero_ptrs, mask=offs_bn < N, other=0.0)
        
        # Dequantize to bfloat16
        w_even = (b_even_uint8.to(tl.bfloat16) - zero[None, :]) * scale[None, :]
        w_odd = (b_odd_uint8.to(tl.bfloat16) - zero[None, :]) * scale[None, :]
        
        # Dot products
        accumulator += tl.dot(a_even, w_even)
        accumulator += tl.dot(a_odd, w_odd)
        
    # Write to output
    c = accumulator.to(tl.bfloat16)
    offs_om = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
    offs_on = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
    out_ptrs = out_ptr + (offs_om[:, None] * stride_om + offs_on[None, :] * stride_on)
    out_mask = (offs_om[:, None] < M) & (offs_on[None, :] < N)
    tl.store(out_ptrs, c, mask=out_mask)


class Model(nn.Module):
    def __init__(self, M: int, N: int, K: int, group_size: int = GROUP_SIZE):
        super().__init__()
        assert K % group_size == 0, "K must be divisible by group_size"
        assert K % 2 == 0, "K must be even (int4 packing)"
        self.M, self.N, self.K = M, N, K
        self.group_size = group_size
        n_groups = K // group_size

        # Register buffers so load_state_dict works
        self.register_buffer("w_q", torch.empty((K // 2, N), dtype=torch.uint8))
        self.register_buffer("scales", torch.empty((n_groups, N), dtype=torch.bfloat16))
        self.register_buffer("zeros", torch.empty((n_groups, N), 

... (2822 more chars)

{
  "description": "Verify correctness with hand-tuned optimal configs.",
  "command": "uv run check.py"
}

{
  "command": "KBH_BENCHMARK_BASELINES=1 uv run benchmark.py",
  "description": "Run the benchmark to measure our final performance results."
}

{
  "file_path": "solution.py",
  "content": "<6926 chars \u2014 see below>"
}

import torch
import torch.nn as nn
import triton
import triton.language as tl

GROUP_SIZE = 128

@triton.jit
def w4a16_gemm_kernel(
    x_ptr, w_ptr, scales_ptr, zeros_ptr, out_ptr,
    M, N,
    stride_xm, stride_xk,
    stride_wk, stride_wn,
    stride_sm, stride_sn,
    stride_zm, stride_zn,
    stride_om, stride_on,
    BLOCK_SIZE_M: tl.constexpr,
    BLOCK_SIZE_N: tl.constexpr,
    BLOCK_SIZE_K: tl.constexpr,
    GROUP_SIZE: tl.constexpr,
    K: tl.constexpr,
):
    pid = tl.program_id(0)
    num_pid_m = tl.cdiv(M, BLOCK_SIZE_M)
    num_pid_n = tl.cdiv(N, BLOCK_SIZE_N)
    
    # 2D Grid with Program ID grouping/swizzling for L2 cache reuse
    num_pid_in_group = 8
    group_id = pid // (num_pid_in_group * num_pid_n)
    first_pid_m = group_id * num_pid_in_group
    group_size_m = min(num_pid_m - first_pid_m, num_pid_in_group)
    pid_m = first_pid_m + (pid % group_size_m)
    pid_n = (pid % (group_size_m * num_pid_n)) // group_size_m

    offs_am = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
    offs_bn = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
    
    offs_k_half = tl.arange(0, BLOCK_SIZE_K // 2)
    offs_b_k = tl.arange(0, BLOCK_SIZE_K // 2)
    
    a_mask = offs_am[:, None] < M
    b_mask = offs_bn[None, :] < N
    
    # Hoist invariant pointer offsets outside the loop
    a_base_even_ptrs = x_ptr + (offs_am[:, None] * stride_xm + (2 * offs_k_half)[None, :] * stride_xk)
    a_base_odd_ptrs = x_ptr + (offs_am[:, None] * stride_xm + (2 * offs_k_half + 1)[None, :] * stride_xk)
    
    b_base_ptrs = w_ptr + (offs_b_k[:, None] * stride_wk + offs_bn[None, :] * stride_wn)
    
    scale_base_ptrs = scales_ptr + offs_bn * stride_sn
    zero_base_ptrs = zeros_ptr + offs_bn * stride_zn
    
    accumulator = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)
    
    for k_curr in range(0, K, BLOCK_SIZE_K):
        # Even and Odd input pointers
        a_even = tl.load(a_base_even_ptrs + k_curr * stride_xk, mask=a_mask & ((k_curr + 2 * offs_k_half)[None, :] < K), other=0.0)
        a_odd = tl.load(a_base_odd_ptrs + k_curr * stride_xk, mask=a_mask & ((k_curr + 2 * offs_k_half + 1)[None, :] < K), other=0.0)
        
        # Load packed weights
        b_packed = tl.load(b_base_ptrs + (k_curr // 2) * stride_wk, mask=b_mask & ((k_curr // 2 + offs_b_k[:, None]) < (K // 2)), other=0)
        
        # Unpack even/odd
        b_even_uint8 = b_packed & 0xF
        b_odd_uint8 = (b_packed >> 4) & 0xF
        
        # Load scale and zero for current group
        k_group = k_curr // GROUP_SIZE
        scale = tl.load(scale_base_ptrs + k_group * stride_sm, mask=b_mask, other=0.0)
        zero = tl.load(zero_base_ptrs + k_group * stride_zm, mask=b_mask, other=0.0)
        
        # Dequantize to bfloat16
        w_even = (b_even_uint8.to(tl.bfloat16) - zero[None, :]) * scale[None, :]
        w_odd = (b_odd_uint8.to(tl.bfloat16) - zero[None, :]) * scale[None, :]
        
        # Dot products
        accumulator += tl.dot(a_even, w_even)
        accumulator += tl.dot(a_odd, w_odd)
        
    # Write to output
    c = accumulator.to(tl.bfloat16)
    offs_om = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
    offs_on = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
    out_ptrs = out_ptr + (offs_om[:, None] * stride_om + offs_on[None, :] * stride_on)
    out_mask = (offs_om[:, None] < M) & (offs_on[None, :] < N)
    tl.store(out_ptrs, c, mask=out_mask)


class Model(nn.Module):
    def __init__(self, M: int, N: int, K: int, group_size: int = GROUP_SIZE):
        super().__init__()
        assert K % group_size == 0, "K must be divisible by group_size"
        assert K % 2 == 0, "K must be even (int4 packing)"
        self.M, self.N, self.K = M, N, K
        self.group_size = group_size
        n_groups = K // group_size

        # Register buffers so load_state_dict works
        self.register_buffer("w_q", torch.empty((K // 2, N), dtype=torch.uint8))
        self.register_buffer("scales", torch.empty

... (2926 more chars)

{
  "command": "uv run check.py",
  "description": "Verify correctness of loop-hoisted Triton kernel."
}

{
  "content": "<6963 chars \u2014 see below>",
  "file_path": "solution.py"
}

import torch
import torch.nn as nn
import triton
import triton.language as tl

GROUP_SIZE = 128

@triton.jit
def w4a16_gemm_kernel(
    x_ptr, w_ptr, scales_ptr, zeros_ptr, out_ptr,
    M, N,
    stride_xm, stride_xk,
    stride_wk, stride_wn,
    stride_sm, stride_sn,
    stride_zm, stride_zn,
    stride_om, stride_on,
    BLOCK_SIZE_M: tl.constexpr,
    BLOCK_SIZE_N: tl.constexpr,
    BLOCK_SIZE_K: tl.constexpr,
    GROUP_SIZE: tl.constexpr,
    K: tl.constexpr,
):
    pid = tl.program_id(0)
    num_pid_m = tl.cdiv(M, BLOCK_SIZE_M)
    num_pid_n = tl.cdiv(N, BLOCK_SIZE_N)
    
    # 2D Grid with Program ID grouping/swizzling for L2 cache reuse
    num_pid_in_group = 8
    group_id = pid // (num_pid_in_group * num_pid_n)
    first_pid_m = group_id * num_pid_in_group
    group_size_m = min(num_pid_m - first_pid_m, num_pid_in_group)
    pid_m = first_pid_m + (pid % group_size_m)
    pid_n = (pid % (group_size_m * num_pid_n)) // group_size_m

    offs_am = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
    offs_bn = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
    
    offs_k_half = tl.arange(0, BLOCK_SIZE_K // 2)
    offs_b_k = tl.arange(0, BLOCK_SIZE_K // 2)
    
    a_mask = offs_am[:, None] < M
    b_mask = offs_bn[None, :] < N
    b_col_mask = offs_bn < N
    
    # Hoist invariant pointer offsets outside the loop
    a_base_even_ptrs = x_ptr + (offs_am[:, None] * stride_xm + (2 * offs_k_half)[None, :] * stride_xk)
    a_base_odd_ptrs = x_ptr + (offs_am[:, None] * stride_xm + (2 * offs_k_half + 1)[None, :] * stride_xk)
    
    b_base_ptrs = w_ptr + (offs_b_k[:, None] * stride_wk + offs_bn[None, :] * stride_wn)
    
    scale_base_ptrs = scales_ptr + offs_bn * stride_sn
    zero_base_ptrs = zeros_ptr + offs_bn * stride_zn
    
    accumulator = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)
    
    for k_curr in range(0, K, BLOCK_SIZE_K):
        # Even and Odd input pointers
        a_even = tl.load(a_base_even_ptrs + k_curr * stride_xk, mask=a_mask & ((k_curr + 2 * offs_k_half)[None, :] < K), other=0.0)
        a_odd = tl.load(a_base_odd_ptrs + k_curr * stride_xk, mask=a_mask & ((k_curr + 2 * offs_k_half + 1)[None, :] < K), other=0.0)
        
        # Load packed weights
        b_packed = tl.load(b_base_ptrs + (k_curr // 2) * stride_wk, mask=b_mask & ((k_curr // 2 + offs_b_k[:, None]) < (K // 2)), other=0)
        
        # Unpack even/odd
        b_even_uint8 = b_packed & 0xF
        b_odd_uint8 = (b_packed >> 4) & 0xF
        
        # Load scale and zero for current group
        k_group = k_curr // GROUP_SIZE
        scale = tl.load(scale_base_ptrs + k_group * stride_sm, mask=b_col_mask, other=0.0)
        zero = tl.load(zero_base_ptrs + k_group * stride_zm, mask=b_col_mask, other=0.0)
        
        # Dequantize to bfloat16
        w_even = (b_even_uint8.to(tl.bfloat16) - zero[None, :]) * scale[None, :]
        w_odd = (b_odd_uint8.to(tl.bfloat16) - zero[None, :]) * scale[None, :]
        
        # Dot products
        accumulator += tl.dot(a_even, w_even)
        accumulator += tl.dot(a_odd, w_odd)
        
    # Write to output
    c = accumulator.to(tl.bfloat16)
    offs_om = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
    offs_on = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
    out_ptrs = out_ptr + (offs_om[:, None] * stride_om + offs_on[None, :] * stride_on)
    out_mask = (offs_om[:, None] < M) & (offs_on[None, :] < N)
    tl.store(out_ptrs, c, mask=out_mask)


class Model(nn.Module):
    def __init__(self, M: int, N: int, K: int, group_size: int = GROUP_SIZE):
        super().__init__()
        assert K % group_size == 0, "K must be divisible by group_size"
        assert K % 2 == 0, "K must be even (int4 packing)"
        self.M, self.N, self.K = M, N, K
        self.group_size = group_size
        n_groups = K // group_size

        # Register buffers so load_state_dict works
        self.register_buffer("w_q", torch.empty((K // 2, N), dtype=torch.uint8))
        self.

... (2963 more chars)

{
  "description": "Verify correctness of loop-hoisted kernel with 1D masks.",
  "command": "uv run check.py"
}

{
  "description": "Benchmark the performance of our loop-hoisted optimized kernel.",
  "command": "KBH_BENCHMARK_BASELINES=1 uv run benchmark.py"
}

{
  "description": "Re-optimize configurations for the loop-hoisted kernel.",
  "command": "uv run optimize_configs.py"
}

{
  "content": "<6963 chars \u2014 see below>",
  "file_path": "solution.py"
}

import torch
import torch.nn as nn
import triton
import triton.language as tl

GROUP_SIZE = 128

@triton.jit
def w4a16_gemm_kernel(
    x_ptr, w_ptr, scales_ptr, zeros_ptr, out_ptr,
    M, N,
    stride_xm, stride_xk,
    stride_wk, stride_wn,
    stride_sm, stride_sn,
    stride_zm, stride_zn,
    stride_om, stride_on,
    BLOCK_SIZE_M: tl.constexpr,
    BLOCK_SIZE_N: tl.constexpr,
    BLOCK_SIZE_K: tl.constexpr,
    GROUP_SIZE: tl.constexpr,
    K: tl.constexpr,
):
    pid = tl.program_id(0)
    num_pid_m = tl.cdiv(M, BLOCK_SIZE_M)
    num_pid_n = tl.cdiv(N, BLOCK_SIZE_N)
    
    # 2D Grid with Program ID grouping/swizzling for L2 cache reuse
    num_pid_in_group = 8
    group_id = pid // (num_pid_in_group * num_pid_n)
    first_pid_m = group_id * num_pid_in_group
    group_size_m = min(num_pid_m - first_pid_m, num_pid_in_group)
    pid_m = first_pid_m + (pid % group_size_m)
    pid_n = (pid % (group_size_m * num_pid_n)) // group_size_m

    offs_am = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
    offs_bn = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
    
    offs_k_half = tl.arange(0, BLOCK_SIZE_K // 2)
    offs_b_k = tl.arange(0, BLOCK_SIZE_K // 2)
    
    a_mask = offs_am[:, None] < M
    b_mask = offs_bn[None, :] < N
    b_col_mask = offs_bn < N
    
    # Hoist invariant pointer offsets outside the loop
    a_base_even_ptrs = x_ptr + (offs_am[:, None] * stride_xm + (2 * offs_k_half)[None, :] * stride_xk)
    a_base_odd_ptrs = x_ptr + (offs_am[:, None] * stride_xm + (2 * offs_k_half + 1)[None, :] * stride_xk)
    
    b_base_ptrs = w_ptr + (offs_b_k[:, None] * stride_wk + offs_bn[None, :] * stride_wn)
    
    scale_base_ptrs = scales_ptr + offs_bn * stride_sn
    zero_base_ptrs = zeros_ptr + offs_bn * stride_zn
    
    accumulator = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)
    
    for k_curr in range(0, K, BLOCK_SIZE_K):
        # Even and Odd input pointers
        a_even = tl.load(a_base_even_ptrs + k_curr * stride_xk, mask=a_mask & ((k_curr + 2 * offs_k_half)[None, :] < K), other=0.0)
        a_odd = tl.load(a_base_odd_ptrs + k_curr * stride_xk, mask=a_mask & ((k_curr + 2 * offs_k_half + 1)[None, :] < K), other=0.0)
        
        # Load packed weights
        b_packed = tl.load(b_base_ptrs + (k_curr // 2) * stride_wk, mask=b_mask & ((k_curr // 2 + offs_b_k[:, None]) < (K // 2)), other=0)
        
        # Unpack even/odd
        b_even_uint8 = b_packed & 0xF
        b_odd_uint8 = (b_packed >> 4) & 0xF
        
        # Load scale and zero for current group
        k_group = k_curr // GROUP_SIZE
        scale = tl.load(scale_base_ptrs + k_group * stride_sm, mask=b_col_mask, other=0.0)
        zero = tl.load(zero_base_ptrs + k_group * stride_zm, mask=b_col_mask, other=0.0)
        
        # Dequantize to bfloat16
        w_even = (b_even_uint8.to(tl.bfloat16) - zero[None, :]) * scale[None, :]
        w_odd = (b_odd_uint8.to(tl.bfloat16) - zero[None, :]) * scale[None, :]
        
        # Dot products
        accumulator += tl.dot(a_even, w_even)
        accumulator += tl.dot(a_odd, w_odd)
        
    # Write to output
    c = accumulator.to(tl.bfloat16)
    offs_om = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
    offs_on = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
    out_ptrs = out_ptr + (offs_om[:, None] * stride_om + offs_on[None, :] * stride_on)
    out_mask = (offs_om[:, None] < M) & (offs_on[None, :] < N)
    tl.store(out_ptrs, c, mask=out_mask)


class Model(nn.Module):
    def __init__(self, M: int, N: int, K: int, group_size: int = GROUP_SIZE):
        super().__init__()
        assert K % group_size == 0, "K must be divisible by group_size"
        assert K % 2 == 0, "K must be even (int4 packing)"
        self.M, self.N, self.K = M, N, K
        self.group_size = group_size
        n_groups = K // group_size

        # Register buffers so load_state_dict works
        self.register_buffer("w_q", torch.empty((K // 2, N), dtype=torch.uint8))
        self.

... (2963 more chars)

{
  "description": "Verify correctness with absolute fastest configs.",
  "command": "uv run check.py"
}

{
  "command": "KBH_BENCHMARK_BASELINES=1 uv run benchmark.py",
  "description": "Benchmark final performance of the customized, loop-hoisted Triton kernel."
}

{
  "description": "Clean up temporary scratch files.",
  "command": "rm -f test_simple.py triton_vec_add.py optimize_configs.py"
}

{
  "description": "Final verification check.",
  "command": "uv run check.py"
}

{
  "strategic_intent": "Task successfully completed. Preparing the final response.",
  "title": "Task Completed",
  "summary": "We have successfully implemented and thoroughly verified a high-performance, fused weight-only int4 quantized GEMM (W4A16) in solution.py. The implementation uses a highly optimized Triton kernel with hoisted pointer arithmetic, 1D mask-driven dequantization, and custom program ID swizzling. We systematically tuned the block sizes, warp counts, and pipeline stages for each specific input shape (including decode and prefill workloads). The kernel is 100% correct, pass

... (269 more chars)