./kernelbenchhardv3runsdroid · custom:GLM-5.1-[Z.AI-Coding-Plan]-0
droid / custom:GLM-5.1-[Z.AI-Coding-Plan]-0 session: cf1bd39f-82e1-4237-a45a-6ef43b1615dc cwd: /tmp/KernelBench-Hard-zai-droid/problems/07_w4a16_gemm
INCOMPLETE SESSION. hit wall-clock budget (SIGTERM). The transcript below is usable but may be missing the agent's final tool calls or summary. Don't score this run as a clean failure or success.
harness
droid
model
custom:GLM-5.1-[Z.AI-Coding-Plan]-0
turns
38
tools called
0
events
40
input toks
93,501
output toks
76,054
cache hit
3,839,168
solution.py
benchmark.log
check.log
result.json
"""Fused W4A16 GEMM kernel using Triton.

AWQ/GPTQ-style asymmetric int4 with per-group bf16 scales and zero-points.
Fuses unpack + dequant + matmul in a single pass.
"""
from __future__ import annotations

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


# ---------------------------------------------------------------------------
# GEMV kernel for M=1 (decode / memory-bound), autotuned
# ---------------------------------------------------------------------------
@triton.autotune(
    configs=[
        triton.Config({'BLOCK_N': 32, 'BLOCK_K': 32}, num_warps=4),
        triton.Config({'BLOCK_N': 32, 'BLOCK_K': 64}, num_warps=4),
        triton.Config({'BLOCK_N': 32, 'BLOCK_K': 128}, num_warps=4),
        triton.Config({'BLOCK_N': 64, 'BLOCK_K': 32}, num_warps=4),
        triton.Config({'BLOCK_N': 64, 'BLOCK_K': 64}, num_warps=4),
        triton.Config({'BLOCK_N': 64, 'BLOCK_K': 128}, num_warps=4),
        triton.Config({'BLOCK_N': 128, 'BLOCK_K': 32}, num_warps=4),
        triton.Config({'BLOCK_N': 128, 'BLOCK_K': 64}, num_warps=4),
        triton.Config({'BLOCK_N': 128, 'BLOCK_K': 128}, num_warps=4),
        triton.Config({'BLOCK_N': 64, 'BLOCK_K': 32}, num_warps=8),
        triton.Config({'BLOCK_N': 64, 'BLOCK_K': 64}, num_warps=8),
        triton.Config({'BLOCK_N': 128, 'BLOCK_K': 64}, num_warps=8),
        triton.Config({'BLOCK_N': 128, 'BLOCK_K': 128}, num_warps=8),
        triton.Config({'BLOCK_N': 256, 'BLOCK_K': 128}, num_warps=8),
    ],
    key=['N', 'K'],
)
@triton.jit
def _w4a16_gemv_kernel(
    X_ptr,
    WQ_ptr,
    S_ptr,
    Z_ptr,
    Out_ptr,
    N: tl.constexpr,
    K: tl.constexpr,
    GROUP_SIZE: tl.constexpr,
    BLOCK_N: tl.constexpr,
    BLOCK_K: tl.constexpr,
):
    pid = tl.program_id(0)
    off_n = pid * BLOCK_N + tl.arange(0, BLOCK_N)
    mask_n = off_n < N

    acc = tl.zeros((BLOCK_N,), dtype=tl.float32)

    num_k_blocks = K // BLOCK_K
    for kb in range(num_k_blocks):
        off_k = kb * BLOCK_K + tl.arange(0, BLOCK_K)

        x_vals = tl.load(X_ptr + off_k, mask=off_k < K, other=0.0).to(tl.float32)

        off_kh = off_k // 2
        nibble = off_k % 2

        wq_ptrs = WQ_ptr + off_kh[:, None] * N + off_n[None, :]
        wq_vals = tl.load(wq_ptrs, mask=(off_kh[:, None] < K // 2) & mask_n[None, :], other=0)
        lo = wq_vals & 0xF
        hi = (wq_vals >> 4) & 0xF
        unpacked = tl.where(nibble[:, None] == 0, lo, hi).to(tl.float32)

        off_g = off_k // GROUP_SIZE
        s_ptrs = S_ptr + off_g[:, None] * N + off_n[None, :]
        z_ptrs = Z_ptr + off_g[:, None] * N + off_n[None, :]
        s_vals = tl.load(s_ptrs, mask=(off_g[:, None] < K // GROUP_SIZE) & mask_n[None, :], other=0.0).to(tl.float32)
        z_vals = tl.load(z_ptrs, mask=(off_g[:, None] < K // GROUP_SIZE) & mask_n[None, :], other=0.0).to(tl.float32)

        w_deq = (unpacked - z_vals) * s_vals
        acc += tl.sum(x_vals[:, None] * w_deq, axis=0)

    tl.store(Out_ptr + off_n, acc.to(tl.bfloat16), mask=mask_n)


# ---------------------------------------------------------------------------
# Batched GEMV: 1D grid over (M, N_tiles). Each program handles one row.
# ---------------------------------------------------------------------------
@triton.jit
def _w4a16_batched_gemv_kernel(
    X_ptr,
    WQ_ptr,
    S_ptr,
    Z_ptr,
    Out_ptr,
    N: tl.constexpr,
    K: tl.constexpr,
    GROUP_SIZE: tl.constexpr,
    N_TILES: tl.constexpr,
    BLOCK_N: tl.constexpr,
    BLOCK_K: tl.constexpr,
):
    pid = tl.program_id(0)
    m = pid // N_TILES
    nt = pid % N_TILES

    off_n = nt * BLOCK_N + tl.arange(0, BLOCK_N)
    mask_n = off_n < N

    acc = tl.zeros((BLOCK_N,), dtype=tl.float32)

    num_k_blocks = K // BLOCK_K
    for kb in range(num_k_blocks):
        off_k = kb * BLOCK_K + tl.arange(0, BLOCK_K)

        x_ptrs = X_ptr + m * K + off_k
        x_vals = tl.load(x_ptrs, mask=off_k < K, other=0.0).to(tl.float32)

        off_kh = off_k // 2
        nibble = off_k % 2

        wq_ptrs = WQ_ptr + off_kh[:, None] * N + off_n[None, :]
        wq_vals = tl.load(wq_ptrs, mask=(off_kh[:, None] < K // 2) & mask_n[None, :], other=0)
        lo = wq_vals & 0xF
        hi = (wq_vals >> 4) & 0xF
        unpacked = tl.where(nibble[:, None] == 0, lo, hi).to(tl.float32)

        off_g = off_k // GROUP_SIZE
        s_ptrs = S_ptr + off_g[:, None] * N + off_n[None, :]
        z_ptrs = Z_ptr + off_g[:, None] * N + off_n[None, :]
        s_vals = tl.load(s_ptrs, mask=(off_g[:, None] < K // GROUP_SIZE) & mask_n[None, :], other=0.0).to(tl.float32)
        z_vals = tl.load(z_ptrs, mask=(off_g[:, None] < K // GROUP_SIZE) & mask_n[None, :], other=0.0).to(tl.float32)

        w_deq = (unpacked - z_vals) * s_vals
        acc += tl.sum(x_vals[:, None] * w_deq, axis=0)

    tl.store(Out_ptr + m * N + off_n, acc.to(tl.bfloat16), mask=mask_n)


# ---------------------------------------------------------------------------
# GEMM kernel using tl.dot for tensor cores, autotuned
# ---------------------------------------------------------------------------
@triton.autotune(
    configs=[
        triton.Config({'BLOCK_M': 16, 'BLOCK_N': 32, 'BLOCK_K': 64}, num_stages=2, num_warps=2),
        triton.Config({'BLOCK_M': 16, 'BLOCK_N': 64, 'BLOCK_K': 64}, num_stages=2, num_warps=2),
        triton.Config({'BLOCK_M': 32, 'BLOCK_N': 32, 'BLOCK_K': 64}, num_stages=2, num_warps=4),
        triton.Config({'BLOCK_M': 32, 'BLOCK_N': 64, 'BLOCK_K': 64}, num_stages=2, num_warps=4),
        triton.Config({'BLOCK_M': 32, 'BLOCK_N': 64, 'BLOCK_K': 128}, num_stages=2, num_warps=4),
        triton.Config({'BLOCK_M': 64, 'BLOCK_N': 64, 'BLOCK_K': 64}, num_stages=2, num_warps=4),
        triton.Config({'BLOCK_M': 64, 'BLOCK_N': 128, 'BLOCK_K': 64}, num_stages=2, num_warps=8),
        triton.Config({'BLOCK_M': 128, 'BLOCK_N': 64, 'BLOCK_K': 64}, num_stages=2, num_warps=8),
        triton.Config({'BLOCK_M': 64, 'BLOCK_N': 64, 'BLOCK_K': 128}, num_stages=3, num_warps=4),
        triton.Config({'BLOCK_M': 128, 'BLOCK_N': 128, 'BLOCK_K': 64}, num_stages=2, num_warps=8),
        triton.Config({'BLOCK_M': 32, 'BLOCK_N': 128, 'BLOCK_K': 128}, num_stages=3, num_warps=4),
        triton.Config({'BLOCK_M': 64, 'BLOCK_N': 128, 'BLOCK_K': 128}, num_stages=3, num_warps=8),
        triton.Config({'BLOCK_M': 128, 'BLOCK_N': 64, 'BLOCK_K': 128}, num_stages=3, num_warps=8),
        triton.Config({'BLOCK_M': 128, 'BLOCK_N': 128, 'BLOCK_K': 128}, num_stages=3, num_warps=8),
    ],
    key=['M_total', 'N', 'K'],
)
@triton.jit
def _w4a16_gemm_kernel(
    X_ptr,
    WQ_ptr,
    S_ptr,
    Z_ptr,
    Out_ptr,
    M_total: tl.constexpr,
    N: tl.constexpr,
    K: tl.constexpr,
    GROUP_SIZE: tl.constexpr,
    BLOCK_M: tl.constexpr,
    BLOCK_N: tl.constexpr,
    BLOCK_K: tl.constexpr,
):
    pid_m = tl.program_id(0)
    pid_n = tl.program_id(1)
    off_m = pid_m * BLOCK_M + tl.arange(0, BLOCK_M)
    off_n = pid_n * BLOCK_N + tl.arange(0, BLOCK_N)
    mask_m = off_m < M_total
    mask_n = off_n < N

    acc = tl.zeros((BLOCK_M, BLOCK_N), dtype=tl.float32)

    num_k_blocks = K // BLOCK_K
    for kb in range(num_k_blocks):
        off_k = kb * BLOCK_K + tl.arange(0, BLOCK_K)

        x_ptrs = X_ptr + off_m[:, None] * K + off_k[None, :]
        x_vals = tl.load(x_ptrs, mask=mask_m[:, None] & (off_k[None, :] < K), other=0.0)

        off_kh = off_k // 2
        nibble = off_k % 2

        wq_ptrs = WQ_ptr + off_kh[:, None] * N + off_n[None, :]
        wq_vals = tl.load(wq_ptrs, mask=(off_kh[:, None] < K // 2) & mask_n[None, :], other=0)
        lo = wq_vals & 0xF
        hi = (wq_vals >> 4) & 0xF
        unpacked = tl.where(nibble[:, None] == 0, lo, hi).to(tl.float32)

        off_g = off_k // GROUP_SIZE
        s_ptrs = S_ptr + off_g[:, None] * N + off_n[None, :]
        z_ptrs = Z_ptr + off_g[:, None] * N + off_n[None, :]
        s_vals = tl.load(s_ptrs, mask=(off_g[:, None] < K // GROUP_SIZE) & mask_n[None, :], other=0.0).to(tl.float32)
        z_vals = tl.load(z_ptrs, mask=(off_g[:, None] < K // GROUP_SIZE) & mask_n[None, :], other=0.0).to(tl.float32)

        w_deq = (unpacked - z_vals) * s_vals
        w_bf = w_deq.to(tl.bfloat16)

        acc = tl.dot(x_vals, w_bf, acc=acc)

    out_ptrs = Out_ptr + off_m[:, None] * N + off_n[None, :]
    tl.store(out_ptrs, acc.to(tl.bfloat16), mask=mask_m[:, None] & mask_n[None, :])


def _w4a16_forward(x, w_q, scales, zeros, K, group_size):
    M_val = x.shape[0]
    N_val = w_q.shape[1]
    out = torch.empty((M_val, N_val), dtype=torch.bfloat16, device=x.device)

    if M_val == 1:
        # GEMV for M=1 decode
        grid = lambda META: (triton.cdiv(N_val, META['BLOCK_N']),)
        _w4a16_gemv_kernel[grid](
            x, w_q, scales, zeros, out,
            N=N_val, K=K, GROUP_SIZE=group_size,
        )
    else:
        # GEMM with tensor cores for M > 16
        grid = lambda META: (
            triton.cdiv(M_val, META['BLOCK_M']),
            triton.cdiv(N_val, META['BLOCK_N']),
        )
        _w4a16_gemm_kernel[grid](
            x, w_q, scales, zeros, out,
            M_total=M_val, N=N_val, K=K, GROUP_SIZE=group_size,
        )

    return out


class Model(nn.Module):
    """W4A16 GEMM with fused Triton kernel."""

    def __init__(self, M: int, N: int, K: int, group_size: int = 128):
        super().__init__()
        self.M, self.N, self.K = M, N, K
        self.group_size = group_size
        n_groups = K // group_size
        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.bfloat16))

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        return _w4a16_forward(x, self.w_q, self.scales, self.zeros, self.K, self.group_size)


M = 1
N = 12288
K = 4096


def get_inputs():
    x = torch.randn(M, K, dtype=torch.bfloat16)
    return [x]


def get_init_inputs():
    return [M, N, K]
shape=0 variant=eager tflops=0.126 gbps=33.533 ms=0.798
shape=0 variant=compiled tflops=0.612 gbps=162.717 ms=0.165
shape=0 variant=solution tflops=1.051 gbps=279.382 ms=0.096
shape=0 solution_peak_fraction=0.1552
shape=1 variant=eager tflops=4.010 gbps=34.594 ms=0.803
shape=1 variant=compiled tflops=18.681 gbps=161.149 ms=0.172
shape=1 variant=solution tflops=20.527 gbps=177.070 ms=0.157
shape=1 solution_peak_fraction=0.0984
shape=2 variant=eager tflops=29.750 gbps=40.552 ms=0.866
shape=2 variant=compiled tflops=107.668 gbps=146.765 ms=0.239
shape=2 variant=solution tflops=70.968 gbps=96.737 ms=0.363
shape=2 solution_peak_fraction=0.0537
shape=3 variant=eager tflops=0.167 gbps=44.561 ms=0.200
shape=3 variant=compiled tflops=0.433 gbps=115.211 ms=0.078
shape=3 variant=solution tflops=0.381 gbps=101.469 ms=0.088
shape=3 solution_peak_fraction=0.0564
shape=4 variant=eager tflops=1.985 gbps=33.584 ms=0.946
shape=4 variant=compiled tflops=9.651 gbps=163.248 ms=0.195
shape=4 variant=solution tflops=11.042 gbps=186.777 ms=0.170
shape=4 solution_peak_fraction=0.1038
peak_fraction: 0.0863
RESULT: LOW
PASS
{
    "problem": "07_w4a16_gemm",
    "harness": "droid",
    "model": "custom:GLM-5.1-[Z.AI-Coding-Plan]-0",
    "reasoning_effort": "",
    "has_solution": true,
    "correct": true,
    "peak_fraction": 0.0863,
    "elapsed_seconds": 2700,
    "harness_exit_code": 124,
    "session_complete": false,
    "usage": {"input_tokens": 93501, "output_tokens": 76054, "cache_read_tokens": 3839168, "cache_creation_tokens": 0, "reasoning_tokens": 0, "total_cost_usd": null}
}

timeline (40 events)

system — init
session start cwd=/tmp/KernelBench-Hard-zai-droid/problems/07_w4a16_gemm model=custom:GLM-5.1-[Z.AI-Coding-Plan]-0 effort=none tools=31
user
I need you to write a weight-only int4 quantized GEMM (W4A16) for the RTX PRO 6000 (SM120 Blackwell, GDDR7, 1.8 TB/s). The reference implementation is in reference.py and your kernel goes in solution.py. You can make whatever mess you want in this directory — scratch files, intermediate kernels, build artifacts, profiling traces — but the final answer has to be in solution.py with the same Model, get_inputs, and get_init_inputs interface as reference.py. The scheme is AWQ/GPTQ-style asymmetric int4 with explicit zero-points and per-group bf16 scales. Inputs are x of shape (M, K) bf16, w_q of shape (K // 2, N) uint8 (two int4 weights packed per byte, low nibble = even-K row, high nibble = odd-K row), scales of shape (K // 128, N) bf16, and zeros of shape (K // 128, N) bf16. Group size is 128 along K. Dequant per group is w_bf[k, n] = (unpack(w_q)[k, n] - zeros[k // 128, n]) * scales[k // 128, n], and the output is (M, N) bf16. Correctness tolerance is 0.10 abs/rel — group-quant adds noise on top of bf16 accumulator slop. The shapes you have to handle are M=1 N=12288 K=4096 (decode, memory-bound on the int4 weight read), M=32 N=12288 K=4096 (small prefill, mixed regime), M=256 N=12288 K=4096 (larger prefill, approaching compute-bound), M=1 N=4096 K=4096 (decode, square), and M=16 N=14336 K=4096 (speculative-decode-ish). This needs to be a real custom kernel that fuses unpack and GEMM in the same pass — a separate dequant-then-matmul wastes the entire bandwidth advantage of int4. Don't import or call bitsandbytes.functional.dequantize_4bit, bitsandbytes.functional.gemv_4bit, marlin_kernel.gemm, or torch.nn.functional.linear. Try CUTLASS mixed-input GEMM (the intended path), Triton with a fused dequant epilogue, CUDA C++ via load_inline, or inline PTX — your call. Anything you're uncertain about, look up PTX docs, clone CUTLASS or Marlin or bitsandbytes or other reference repos, read library headers, and investigate. Your flywheel is implement, profile (ncu, nsys, torch.profiler — whatever's useful) and time it with benchmark.py, verify correctness by running `python check.py` and reading the output, then iterate. Don't substitute your own one-off correctness snippets for check.py — it iterates over every shape, your spot-check almost certainly won't. If `python check.py` hasn't printed PASS, you're not done. Take as long as you need to actually push the number up.
assistant
Let me check the environment and available tools first.
assistant
Let me check Triton's capabilities and see what other solutions in this repo look like for reference:
assistant
Now let me build the Triton kernel. The strategy: - For M=1 (decode): Use a GEMV-style kernel where each program handles a subset of output columns, streams through K in chunks, unpacks int4 weights on the fly, dequantizes, and accumulates the dot product. - For M>1 (prefill): Use a blocked GEMM kernel with fused dequant. Let me first test a simple Triton approach:
assistant
The GEMM kernel is too large for shared memory. Let me reduce block sizes and fix the approach. The issue is the GEMM kernel with BLOCK_K=128 creates too many large buffers. Let me restructure:
assistant
Wait, I left a placeholder in the GEMM kernel. Since I'm using the per-row GEMV approach for now, let me remove the broken GEMM kernel and just test the GEMV approach first:
assistant
Correctness passes. Now let's benchmark:
assistant
The result is LOW (0.0202 peak fraction). The M=1 decode case is the best at 0.168 (302 GB/s out of 1800 GB/s). The per-row GEMV approach is terrible for M>1. I need to: 1. For M=1: Optimize the GEMV kernel for more bandwidth 2. For M>1: Implement a proper tiled GEMM with tl.dot Let me now build a proper GEMM kernel. The key insight is to use tl.dot with proper tiling. Let me think about this more carefully. For the GEMM kernel, I need to: - Tile M and N - Walk through K in tiles - For each K tile, load x tiles, load/unpack/dequant weight tiles, and use tl.dot The trick is that tl.dot requires the inner dimension (K) to be at least 16 for tensor cores, and the data types must be compatible (bf16 x bf16 -> fp32). Let me redesign with smaller block sizes:
assistant
The problem is in the store pointer shape mismatch. The `off_m` is BLOCK_M=32 and `off_n` is BLOCK_N=64, so `off_m[:, None] * N + off_n[:, None]` doesn't work when shapes don't match. I need `off_n[None, :]`. Let me fix:
assistant
Now let's benchmark:
assistant
Still LOW at 0.0306. The big improvement is in shape 2 (M=256) which now uses the tiled GEMM and gets 27 TFLOPS. But the decode shapes (M=1) are only ~276 GB/s. Let me analyze the bottleneck: For M=1 decode, the roofline is memory-bound. Peak bandwidth is 1800 GB/s, and we're getting ~276 GB/s (~15%). The GEMV kernel loads a full (BLOCK_K, BLOCK_N) tile of weights per K-block. With BLOCK_K=128, BLOCK_N=64, that's 128*64 = 8192 elements per K step, with 32 K-steps = 262K loads per program. With 192 programs (12288/64), total weight loads = 50M. The packed weight matrix is 2048*12288 = 25M bytes, and we're reading each element once, so it's optimal in terms of reads. The issue is probably low GPU occupancy. With BLOCK_N=64, we only have 12288/64 = 192 programs. Let me increase parallelism and try different block sizes:
assistant
Let me rethink the approach. The key issues: 1. M=1 decode: 276 GB/s is only 15% of peak (1800 GB/s). Need more memory-level parallelism. 2. M>1 small: Per-row GEMV is slow - need a proper tiled approach. 3. M=256 GEMM: 27 TFLOPS - need to push higher. Let me think about how to better use the GEMV kernel for decode. The GEMV kernel loads (BLOCK_K, BLOCK_N) weight tiles which is 128*64 = 8KB of uint8. This is reasonable. The issue is the GEMV is compute-limited by the element-wise multiply. Let me try using tl.dot even for the GEMV case by reshaping. Actually, the key insight is that for the GEMV, each program should use more threads to saturate memory bandwidth. Let me try a different GEMV approach with more programs (smaller BLOCK_N) and also try to use tl.dot by treating it as a (1, BLOCK_K) x (BLOCK_K, BLOCK_N) matmul. Let me try a new approach with a 2D grid for GEMV (split both N and K across programs):
assistant
Can't index with `[0]` in Triton. Let me use `tl.view` or reshape instead:
assistant
Correctness passes. Let me benchmark:
assistant
Much worse! The split-K approach is hurting because of atomic_add contention on bf16. And the per-row GEMV with tl.dot is also slower. Let me go back to the simpler approach that was faster and focus on improving it. The best previous result was 0.0306 peak_fraction with the simple GEMV. The key observations: 1. M=1 decode: ~276 GB/s is the best I got - need more bandwidth 2. M=32 and M=16: per-row GEMV is slow 3. M=256: GEMM with tl.dot gives 27 TFLOPS Let me focus on: making the per-row GEMV use tl.dot properly (it should be (1, BK) x (BK, BN)), and using larger BLOCK_N for the decode case. Also, I should try the per-row approach with a batched kernel that handles all rows in one 2D grid. The key issue with the per-row GEMV was that row_idx was a constexpr which meant a separate compilation for each row. Let me use a proper 2D GEMM grid even for small M values. Let me take a fundamentally different approach: always use the tiled GEMM kernel but with BLOCK_M=M when M is small.
assistant
Big improvement! Peak fraction went from 0.0306 to 0.0864. The autotuned GEMM is much better: - Shape 1 (M=32): 20.8 TFLOPS (was 1.7) - Shape 2 (M=256): 72.8 TFLOPS (was 27) - Shape 4 (M=16): 11.0 TFLOPS (was 2.0) - Shape 3 (M=1): 0.37 TFLOPS, 98 GB/s (was 0.44, 117 GB/s - slightly worse) - Shape 0 (M=1): 1.04 TFLOPS, 278 GB/s (same as before) The decode shapes (M=1) are still the bottleneck for the geomean. Let me see what the autotune picked and try to improve the GEMV kernel. For M=1 decode, the bandwidth limit is 1800 GB/s and we're at 278 GB/s (15%). The main issue is that the GEMV kernel doesn't use tensor cores efficiently. Let me try using tl.dot in the GEMV kernel with BLOCK_K aligned to 16 (minimum for tensor cores). Also, I should try much larger BLOCK_N to reduce overhead.
assistant
Slightly worse at 0.0853 (was 0.0864). The new configs didn't help much. Let me analyze what's happening: 1. Shape 0 (M=1, N=12288, K=4096): 284 GB/s, 0.158 peak fraction 2. Shape 3 (M=1, N=4096, K=4096): 90 GB/s, 0.050 peak fraction - this is the small-N decode The decode case for small N is very slow. For shape 3, the bytes formula is: M*K*2 + (K/2)*N + (K/128)*N*2 + (K/128)*N*2 + M*N*2 = 1*4096*2 + 2048*4096 + 32*4096*2 + 32*4096*2 + 1*4096*2 = 8192 + 8388608 + 262144 + 262144 + 8192 = ~8.9 MB. At 1800 GB/s peak, the minimum time should be ~5 µs. We're at 99 µs. The kernel launch overhead and low occupancy are killing us. Let me think about what we can do for the M=1 case. The key optimization is to maximize the number of active warps per SM. With BLOCK_N=64 and N=12288, we get 192 programs. With 188 SMs, that's barely 1 per SM. With N=4096, we get 64 programs - very few. Let me try a different approach for M=1: use a smaller BLOCK_N to get more programs, and also use num_warps=4 or 8 for more memory-level parallelism. Actually, wait - I should try using the GEMM kernel (with tl.dot) even for M=1, by treating it as a (1, BLOCK_K) x (BLOCK_K, BLOCK_N) matmul with BLOCK_M=1. But BLOCK_M=1 might not work well with tensor cores (minimum is usually 16). Let me try a different approach: for the GEMV kernel, make it so multiple programs work on the same N tile but different K tiles, and then use atomic_add. Or just try increasing BLOCK_N significantly. Actually, let me step back and think about what a good bandwidth number would look like. For the large decode case (shape 0): - Total bytes: M*K*2 + (K/2)*N + 2*(K/128)*N*2 + M*N*2 = 8192 + 25165824 + 786432 + 24576 = ~26 MB - Peak: 1800 GB/s → minimum time: ~14.5 µs - We're at 94 µs, so 15.4% efficiency The main bottleneck is probably: 1. Each program loads BLOCK_K * BLOCK_N weights (128 * 64 = 8KB) per K-block, and iterates over K/BLOCK_K = 32 blocks 2. Each program loads a total of 256KB of weights across all K blocks 3. With 192 programs, total weight traffic = 49.5 MB, but the actual weight matrix is only 25 MB 4. So each weight element is loaded exactly once - good The issue is likely low occupancy. With BLOCK_N=64, each program needs BLOCK_K * BLOCK_N = 128*64 = 8192 registers just for the weight tile, plus similar for the scale/zero tiles. That's a lot of registers per thread. Let me try smaller BLOCK_K to reduce register pressure and increase occupancy:
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Wait, `num_warps` isn't a kwarg to the kernel call in Triton. Let me add it to the kernel decorator or use a different approach. Let me actually use autotune for the GEMV too:
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Let me take a completely different approach. Instead of trying to hand-tune, let me write a clean version that uses autotuning for the GEMV as well, and also optimizes the weight loading pattern. The key insight for M=1 decode is to maximize the bandwidth utilization by having many programs each doing a small amount of work. Let me also try a fundamentally different approach: precompute the dequantized weights in a separate pass but using shared memory within the kernel, or use a smarter loading pattern. Actually, let me think about this differently. The problem says the regime is "memory" (memory-bound). The roofline formula says bytes = M*K*2 + (K/2)*N + (K/128)*N*2 + (K/128)*N*2 + M*N*2. For shape 0 (M=1, N=12288, K=4096): - x: 8KB - w_q: 25.2 MB - scales: 786 KB - zeros: 786 KB - out: 24 KB - Total: ~26.8 MB At 1800 GB/s peak, the roofline time is ~14.9 µs, which means 0.536 TFLOPS at the roofline. Our solution gets 1.068 TFLOPS at 284 GB/s. That's 284/1800 = 15.8% of bandwidth. For shape 3 (M=1, N=4096, K=4096): - w_q: 8.4 MB - scales: 262 KB - zeros: 262 KB - Total: ~8.9 MB At 1800 GB/s, roofline time is ~5 µs → 0.336 TFLOPS roofline TFLOPS. We get 0.338 TFLOPS - basically at the roofline! Wait, that means shape 3 is already near-optimal. Let me re-check: shape 3 peak_fraction is 0.050 based on bandwidth. So 90 GB/s / 1800 GB/s = 5%. That seems low... Actually looking at the bytes formula more carefully for shape 3: M*K*2 + (K/2)*N + (K/128)*N*2 + (K/128)*N*2 + M*N*2 = 1*4096*2 + 2048*4096 + 32*4096*2 + 32*4096*2 + 1*4096*2 = 8192 + 8388608 + 262144 + 262144 + 8192 = 8,929,280 bytes ≈ 8.9 MB. At 90 GB/s and 8.9 MB, time = 8.9/90 = 0.099 ms = 99 µs. At peak 1800 GB/s, time = 8.9/1800 = 4.9 µs = 0.005 ms. So we're 20x slower than peak. The issue is definitely kernel launch overhead and low occupancy for the small-N decode case. Let me try a completely different approach - using CUDA C++ with torch.utils.cpp_extension.load_inline for maximum control:
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0.0875, slightly better. Shape 3 improved from 90 to 104 GB/s. The autotuning is helping a bit. The fundamental problem is the GEMV bandwidth. Let me try a different strategy. For M=1 decode, the most important thing is maximizing DRAM bandwidth utilization. The key is: 1. Enough concurrent programs to fill all SMs 2. Enough memory-level parallelism (outstanding loads) per program Let me try to understand what the compiled PyTorch version is doing that gets 160 GB/s. It's doing the full dequant-then-matmul (which is much more memory traffic) but getting 160 GB/s. Our fused version should be much faster since it reads less data. The compiled version benefits from cuBLAS's highly optimized matmul. Wait - the compiled version reads the full dequantized weight matrix (K*N*2 bytes) which is much larger, but it still achieves higher effective throughput because cuBLAS has extremely optimized GEMV kernels with software pipelining. For our fused kernel, the bottleneck is likely the element-wise multiply and sum in the GEMV. Each step does: load 128x64 uint8, unpack to 128x64 float32, load 128x64 scales/zeros, dequantize, multiply with x, reduce. This is a lot of computation per memory load. Let me try a different data layout - instead of loading (BLOCK_K, BLOCK_N) tiles where the K dimension varies, I should load in a pattern that maximizes coalesced access. Currently w_q is row-major (K//2, N), so loading w_q[off_kh, off_n] with off_kh varying across threads is actually accessing different rows - not coalesced! The memory access pattern is the issue. Let me think about this: - w_q has shape (K//2, N) in row-major - When we load w_q[off_kh[:, None], off_n[None, :]], the inner dimension (contiguous) is N - Each thread loads w_q[off_kh[thread_k], off_n[thread_n]] - For a fixed thread_n, different thread_k values access different rows = different cache lines - This is strided access, bad for coalescing The solution is to reorganize so threads in a warp access contiguous memory. This means we should have the K dimension as the "inner" dimension in our load pattern, or we should transpose the iteration order. Actually, in Triton, `tl.load` handles this automatically through vectorization. The pointer layout `WQ_ptr + off_kh[:, None] * N + off_n[None, :]` means for each row (fixed off_kh), the off_n values are contiguous. So loads within a row are coalesced. The issue is that we're loading multiple rows at once. Let me try a different approach: load the weights in smaller K blocks but with larger N blocks, so each load is more coalesced. Or even better, restructure the kernel so the inner loop is over N (for each K chunk, iterate over N blocks) instead of over K (for each N block, iterate over K). Actually, let me try something simpler: use a much larger BLOCK_N to maximize coalescing and fewer programs with more work per program:
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Good, correctness is fine. Let me run the full benchmark:
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0.0872. Shape 0 got a slight improvement (0.161 peak fraction, 290 GB/s). The autotuning with larger BLOCK_N configs didn't help much. The decode shapes are fundamentally limited by the GEMV approach. Let me try a completely different approach for M=1: instead of using Triton, use a CUDA kernel via torch.utils.cpp_extension.load_inline. This gives us much more control over memory access patterns, vector loads, etc.
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Let me try an approach where I write a CUDA C++ kernel using load_inline that does vectorized loads (uint4/ushort for coalesced access) and shared memory:
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That file is a mess. Let me clean it up and write the final solution:
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Now let me try a CUDA C++ kernel for the M=1 case via load_inline. This should give much better performance for the memory-bound decode case:
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The issue is with the `data_ptr<bf16>()` call - the `__nv_bfloat16` type isn't directly supported as a template parameter for `data_ptr`. Let me fix this:
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The CUDA kernel is much slower than Triton! 0.135 ms vs 0.047 ms for Triton (shape 0). The warp-per-tile approach with TILE_N=4 only uses 12288/4 = 3072 warps, or 96 blocks. That's about 0.5 blocks per SM. Very low occupancy. Let me try a different approach: each thread handles one output column (maximum parallelism), but use vectorized loads for better memory throughput:
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Even slower - 0.196 ms vs 0.047 ms for Triton. The per-thread approach has terrible memory access patterns (stride N between consecutive K reads). The Triton kernel's approach of loading contiguous N tiles is actually much better. Let me go back to the Triton approach and try to improve it further. The Triton GEMV is already at ~280 GB/s. The key issue is that for the overall benchmark, the geometric mean is dragged down by shapes 2 and 3. Let me reconsider the approach. Instead of trying to squeeze more out of the GEMV, let me focus on making ALL shapes use the tiled GEMM with tl.dot, which should improve shapes 1, 2, 4 while keeping the M=1 decode competitive. The problem is that BLOCK_M=1 doesn't work with tl.dot on tensor cores. Wait - let me check if the Triton kernel actually uses tensor cores for the GEMM. The tl.dot with bf16 inputs should use tensor cores. Let me verify by checking the achieved TFLOPS. For shape 2 (M=256, N=12288, K=4096): 72.8 TFLOPS. The peak bf16 TFLOPS for RTX PRO 6000 should be very high (let me check the hardware spec):
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OK, so peak bf16 is 200 TFLOPS. Our GEMM achieves 72.8 TFLOPS which is 36.4% of peak - decent for a first attempt but there's room for improvement. The benchmark scores by peak bandwidth: - Shape 0 (M=1, N=12288): 290 GB/s / 1800 = 0.161 - Shape 1 (M=32, N=12288): 180 GB/s / 1800 = 0.100 - Shape 2 (M=256, N=12288): 99 GB/s / 1800 = 0.055 - Shape 3 (M=1, N=4096): 104 GB/s / 1800 = 0.058 - Shape 4 (M=16, N=14336): 190 GB/s / 1800 = 0.105 Geomean ≈ 0.087 To get to 0.1, I need to improve all shapes by about 15%. Let me focus on the lowest scores: - Shape 2 (M=256): 99 GB/s → needs ~120+ GB/s - Shape 3 (M=1, N=4096): 104 GB/s → needs ~130+ GB/s For shape 2, the issue is that the GEMM reads the weight matrix multiple times (once per M tile). With only 2 M tiles (256/128), the redundancy is 2x. But even with perfect caching (L2), the first pass would bring weights into cache and the second would hit. But Triton doesn't guarantee L2 behavior. Let me try a different GEMM strategy for shape 2: use a larger BLOCK_M (like 256) so there's only one M tile, eliminating redundancy. But this might not compile due to register pressure. Actually, let me try another approach: for all shapes, use the GEMV kernel (one row at a time) but launch all rows in parallel. This way each row reads the weight matrix independently. For M rows, we launch M * ceil(N/BN) programs. Each program handles one row and one N-tile. This maximizes parallelism and has no weight redundancy. But for M=256, N=12288, BN=64: 256 * 192 = 49152 programs. With 188 SMs, that's 261 programs per SM. The issue is that each program reads the full weight row for its K-tiles. But since different programs for different M rows read the same weights, L2 cache should help. Wait, but in the GEMV kernel, each program iterates over ALL K (loading the full weight column for its N tile). For M=256, there are 256 programs per N tile, all reading the same weight data. If they run concurrently, the L2 can't help (they read at the same time). If they run sequentially (pinned to the same SM), then L2 helps. Let me try this approach and see:
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Worse overall (0.0623 vs 0.0875). The batched GEMV is much worse for M=32 (0.028 vs 0.100) and M=16 (0.051 vs 0.105). Shape 0 and 3 improved slightly. The batched GEMV doesn't use tensor cores, so for M>1 it's inherently slower than the tiled GEMM. Let me go back to the best approach (autotuned GEMV for M=1, autotuned GEMM for M>1) and try to optimize further:
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Now let me think about what's fundamentally limiting the performance. Let me look at the reference compiled (torch.compile) performance and compare: - Shape 0 compiled: 160 GB/s (0.339 peak fraction) - Shape 0 solution: 290 GB/s (0.161 peak fraction) - actually BETTER than compiled! Wait, our solution is getting 290 GB/s vs compiled at 160 GB/s. That's great! The compiled version does full dequant+matmul which reads 2x more data. Our fused kernel reads the packed int4 directly, saving half the weight bandwidth. So we should be ~2x faster on decode, which is what we see. The benchmark result says `RESULT: LOW` because the peak_fraction (geomean) is 0.087, which is less than 0.1. But this is a tough benchmark. Let me check what "LOW" actually means in the benchmark: Looking at the benchmark code: `print(f"RESULT: {'OK' if gmean >= 0.1 else 'LOW'}")`. So 0.1 is the threshold. We're at 0.087 - need to improve by ~15%. The main drags are shapes 2 and 3: - Shape 2 (M=256): 99 GB/s → need ~115 GB/s - Shape 3 (M=1, N=4096): ~104 GB/s → need ~120 GB/s For shape 2, the GEMM kernel is at 72.8 TFLOPS. The bottleneck is that the weight matrix is read multiple times. With BLOCK_M=128, there are 2 M tiles and 96 N tiles. Each M tile reads all weights independently. But with swizzle/pipeline, Triton should cache weights in shared memory across N tiles... but actually each program has its own (M-tile, N-tile) and reads a different slice of weights. Let me try using a much larger BLOCK_M (256) for shape 2 to eliminate M-tile redundancy: Actually, the autotuner should be trying BLOCK_M=128 already. With M=256 and BLOCK_M=128, there are only 2 M-tiles. The redundancy is 2x for weight reads. If BLOCK_M=256, there's 1 M-tile and 0 redundancy. But BLOCK_M=256, BLOCK_N=64, BLOCK_K=64 would require 256*64 registers for the accumulator alone (256*64*4 bytes = 64KB). That's way too much. Let me try a different approach: use the GEMV kernel for M=256 but launch it as a batch over all 256 rows:
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Right, Triton JIT functions must be in files. Let me try a different approach. Let me look at what score we actually need and try to optimize the weakest shapes. The current scores are: - Shape 0 (M=1, N=12288): ~0.16 peak fraction - Shape 1 (M=32, N=12288): ~0.10 - Shape 2 (M=256, N=12288): ~0.055 - Shape 3 (M=1, N=4096): ~0.055 - Shape 4 (M=16, N=14336): ~0.10 Geomean ≈ 0.087 To reach 0.1, I need to improve all shapes proportionally by 0.1/0.087 ≈ 15%. Or I can focus on improving the weakest shapes (2 and 3) which drag the geomean down the most. For shape 2 (M=256), the GEMM kernel achieves 72.8 TFLOPS but only 99 GB/s effective. The bytes formula gives 33.4 MB. At 99 GB/s, time = 337 µs. The GEMM kernel is reading the weight matrix and scales/zeros multiple times due to the M tiling. For shape 3 (M=1, N=4096), the GEMV gets 104 GB/s with only 8.9 MB to transfer. The issue is low occupancy: only 64 programs with BN=64. Let me try a key optimization: for the GEMV kernel, load the x vector into shared memory first, then reuse it across all N tiles. This doesn't help Triton directly, but I can try smaller BLOCK_N to increase parallelism. Actually, let me try to just get the score above 0.1 by optimizing the overall kernel. One key thing I notice: the problem regime is "memory" which means peak_fraction is measured against bandwidth, not TFLOPS. For the GEMM shapes (M>1), we're actually reading much more data than the bytes_formula suggests because of weight redundancy. Let me try to use the GEMV approach for M<=32 (where M is small enough that tensor cores don't help much anyway) and the GEMM approach for M>32. But the current approach already does this! Let me just focus on tuning the GEMV kernel for better bandwidth on M=1. Actually, let me reconsider the problem. The bytes_formula counts: - x: M*K*2 bytes (read once) - w_q: (K/2)*N bytes (should be read once for optimal) - scales: (K/128)*N*2 bytes - zeros: (K/128)*N*2 bytes - out: M*N*2 bytes (write once) For M=256 shape 2: - x: 2 MB - w_q: 25 MB - scales: 786 KB - zeros: 786 KB - out: 6 MB - Total: ~34.6 MB But our GEMM kernel reads the weight matrix for each M-tile. With 2 M-tiles, it reads 50 MB of weights. The L2 cache might mitigate some of this, but Triton kernels typically don't benefit much from L2. The fundamental issue is that the roofline model assumes optimal data access, but our tiled GEMM reads weights redundantly. For the decode shapes (M=1), this isn't an issue since there's only one "tile" in M. Let me try using the GEMV approach for ALL shapes. For M=256, this means launching 256 * 192 = 49152 programs. Each program handles one (row, N-tile) pair and reads the full weight column for its N-tile. Since different programs for the same N-tile but different rows read the same weights, the L2 cache should help. With 188 SMs, each SM handles ~261 programs, and within each SM, programs sharing an N-tile would hit in L2. Let me implement this as a file-based kernel:
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Good improvement! Shape 0 went from 0.16 to 0.21 (375 GB/s!), Shape 1 from 0.10 to 0.12, Shape 3 from 0.058 to 0.076. But shape 4 dropped from 0.10 to 0.051 because the batched GEMV is worse for M=16 than the autotuned GEMM. Let me fix shape 4 by using the GEMM kernel for M=16:
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Hmm, shape 0 went back to 0.156 (was 0.209). The autotune must have selected a different config. The problem is that removing the M<=16 batched GEMV path also removed the batched GEMV kernel's cache effect. Wait, I see what happened: shape 0 (M=1) uses the `_w4a16_gemv_kernel`, and shape 3 (M=1) also uses it. The batched GEMV was only for M<=16. But the shape 0 score changed because... hmm, that shouldn't have changed. Unless the autotune cache was affected. Let me re-run to get a stable result:
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OK, the earlier shape 0 improvement (0.209) was from the previous version that had the batched GEMV. Let me try the version that gave the best results before and also keep the batched GEMV for M<=16 but also allow the GEMM autotuned version: Actually, looking back at the results more carefully: - With batched GEMV for M<=16: shape 0 = 0.209, shape 4 = 0.051, geomean = 0.089 - Without batched GEMV: shape 0 = 0.160, shape 4 = 0.104, geomean = 0.088 The batched GEMV helped shape 0 dramatically but hurt shape 4. The difference in shape 0 is suspicious - why would the GEMV kernel perform differently? Let me check... Oh, I see - when I had the batched GEMV for M<=16, the `_w4a16_batched_gemv_kernel` was compiled for shape 1 (M=32) too (M<=16 is wrong, I had M<=16 check but shapes 1 is M=32). Let me re-check... No wait, M<=16 would only trigger for M=1 and M=16. Shape 0 is M=1. Actually the M==1 check runs first! The batched GEMV only triggers for 1 < M <= 16, which is only shape 4 (M=16). So shape 0 should not be affected. Unless the Triton cache had a stale entry. Let me try the hybrid approach again with a clean cache:
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The batched GEMV hurts shape 4 (0.050 vs 0.104). The previous 0.209 result for shape 0 must have been a fluke or cache issue. Let me go back to the simpler version without the batched GEMV and focus on optimizing the main kernels. Let me try a different approach entirely. The key insight is that for the memory-bound regime (M=1), the GEMV is limited by bandwidth. For the compute-bound regime (M=256), the GEMM is limited by how fast we can stream weights. The bottleneck for ALL shapes is weight reading. One idea: pre-load the dequantized weights into the L2 cache using a prefetch kernel, then do the matmul. But this is complex in Triton. Another idea: for the GEMM, use the batched GEMV approach but group programs so that programs working on the same N-tile but different M rows are scheduled on the same SM, enabling L2 cache reuse of the weight tile. Actually, Triton's 2D grid already does something similar. The issue is that for shape 2 (M=256, N=12288), the 2D grid has (2, 96) = 192 programs. With 188 SMs, most SMs get 1 program. Each program reads a (BLOCK_K, BLOCK_N) tile of weights per K step. With BLOCK_K=64, BLOCK_N=64, each tile is 64*64 = 4096 bytes. Over 64 K steps, each program reads 256 KB of weights. Two M-tile programs reading the same N-tile read the same weights, so with L2 caching, the second should hit. But the L2 cache on RTX PRO 6000 is probably large enough to hold at least one K-tile across all N-tiles. The total weight for one K-block is (K//2) * N = 2048 * 12288 = 25 MB for the full row. The L2 cache is probably 6-12 MB on this GPU, so it can't hold even one full K-row. OK, let me try a completely different approach. Let me try to improve the GEMM kernel by increasing the K block size to reduce the number of weight loads:
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Now let me add more aggressive GEMM configs with larger BLOCK_K and num_stages for better pipelining:
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0.0868. The new configs didn't help shape 2 (70.8 TFLOPS, was 72.8). Shape 2 is now slightly worse. Let me take a step back and think about what's fundamentally limiting performance. The key metrics: 1. **Shape 0 (M=1, N=12288)**: 287 GB/s. We need ~360 GB/s for 0.20 peak fraction. 2. **Shape 1 (M=32, N=12288)**: 179 GB/s. Tensor core GEMM is doing 20.8 TFLOPS. 3. **Shape 2 (M=256, N=12288)**: 97 GB/s. GEMM at 70.8 TFLOPS but only 97 GB/s effective. 4. **Shape 3 (M=1, N=4096)**: 101 GB/s. Low N = low parallelism. 5. **Shape 4 (M=16, N=14336)**: 186 GB/s. GEMM at 11 TFLOPS. For the geomean to reach 0.1, I need: (0.16 * 0.10 * 0.055 * 0.056 * 0.10)^(1/5) * factor >= 0.1. Current = 0.087. Need 15% improvement overall. The weakest links are shapes 2 and 3. Let me focus on shape 3 first (M=1, N=4096) since it's a decode case where I have more control. For shape 3, N=4096. With BLOCK_N=64, only 64 programs. With BLOCK_N=32, 128 programs. With BLOCK_N=128, 32 programs. The issue is too few programs for 188 SMs. The autotuner should find the best BLOCK_N. Let me check what it selects by adding a print: Actually, let me try to manually tune the GEMV for the M=1 N=4096 case:
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Let me try a different approach. Instead of autotuning the GEMV, let me write a specific non-autotuned GEMV kernel and test various configurations manually to find the optimal one: