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Grouped GEMM + Quant (SM100)#

This is an experimental API and subject to change.

Legacy dense-only API note: This page documents the older dense-only grouped quant API. For new integrations, prefer the unified Grouped GEMM + Quant (Unified) page.

Overview#

Grouped GEMM + Quant fusion: A contiguous grouped block-scaled GEMM with output quantization on NVIDIA Blackwell GPUs (SM100+), designed for MoE (Mixture of Experts) workloads. Implemented with CUTLASS/CUTE. Groups are contiguous in the M dimension and described by padded_offsets (cumulative aligned end offsets). Used for FC2 (forward down-projection) and dFC1 (backward FC1 GEMMs).

This kernel performs:

  1. Block-scaled grouped GEMM: Low-precision GEMM (FP4, FP8) with per-block scale factors across multiple expert groups

  2. Per-row gating: Multiplies output by per-row gating probability

  3. Optional quantized output: Produces row and column scale factors for downstream quantization

Shapes#

  • Inputs

    • A: contiguous activation tensor across all groups, shape (valid_m, K, 1)

    • B: weight tensor across all groups, shape (N, K, L)

    • SFA: scale factor tensor for A, shape (32, 4, ceil(valid_m/128), 4, ceil(ceil(K/sf_vec_size)/4), 1)

    • SFB: scale factor tensor for B, shape (32, 4, ceil(N/128), 4, ceil(ceil(K/sf_vec_size)/4), L)

    • padded_offsets: cumulative sum of aligned group M sizes, shape (L,). valid_m = padded_offsets[-1]

    • alpha: per-group scaling factors, shape (L,)

    • prob: per-row gating probabilities, shape (valid_m, 1, 1). Required.

    • norm_const: normalization constant for FP8 quantization, shape (1,)

  • Outputs

    • D: row-quantized output, shape (valid_m, N, 1)

    • D_col: column-quantized output, shape (valid_m, N, 1)

    • SFD_row: row scale factors (when SFD outputs are enabled, i.e. FP8 inputs), shape (32, 4, ceil(valid_m/128), 4, ceil(ceil(N/sf_vec_size)/4), 1)

    • SFD_col: column scale factors (when SFD outputs are enabled, i.e. FP8 inputs), shape (32, 4, ceil(N/128), 4, ceil(ceil(valid_m/sf_vec_size)/4), 1)

    • amax: per-group amax (when d_dtype is bf16/float16), shape (L, 1)

Equations#

Step 1: Block-scaled grouped GEMM (per group g with rows m in [padded_offsets[g-1], padded_offsets[g])):

\( \text{ref}[m, n] = \alpha_g \sum_{k} \text{dequantize}(A[m, k], \text{SFA}) \cdot \text{dequantize}(B[n, k, g], \text{SFB}) \)

Step 2: Per-row gating:

\( D[m, n] = \text{prob}[m] \cdot \text{ref}[m, n] \)

Step 3: Optional output quantization (when SFD outputs are generated):

Let \(\text{rcp_max} = 1 / q_{\max}\), where \(q_{\max}\) is the maximum representable value of the output data type (e.g., 448 for FP8 E4M3, 57344 for FP8 E5M2).

\( \text{SFD_row}[m, n] = \text{norm_const} \cdot \max_{k \in \text{block}} |D[m, k]| \cdot \text{rcp_max} \)

\( D_{\text{quantized}}[m, n] = D[m, n] \cdot \frac{\text{norm_const}}{\text{SFD_row}[m, n]} \)

Diagram#

 A (valid_m×K×1)    B (N×K×L)           padded_offsets
 SFA                SFB                      |
   |                 |                       |
   |    +------------+                       |
   |    |                                    |
   v    v                                    v
  Dequantize → Grouped GEMM (per group ranges) → Select B[:,:,group_idx]
                    |
                    | × alpha[group_idx]
                    v
               ref (valid_m×N×1)
                    |
                    | × prob
                    v
               D (valid_m×N×1)
                    |
         +----------+-----------+
         |                      |
         v                      v
    Row Quantize           Col Quantize
         |                      |
         v                      v
    D_row, SFD_row        D_col, SFD_col

API Usage#

High-level Wrapper#

from cudnn import grouped_gemm_quant_wrapper_sm100
from cuda.bindings import driver as cuda

stream = cuda.CUstream(torch.cuda.current_stream().cuda_stream)

outputs = grouped_gemm_quant_wrapper_sm100(
    a_tensor=a,
    b_tensor=b,
    sfa_tensor=sfa,
    sfb_tensor=sfb,
    padded_offsets=padded_offsets,
    alpha_tensor=alpha,
    norm_const_tensor=norm_const,  # Required when SFD outputs are enabled (FP8 inputs)
    prob_tensor=prob,
    acc_dtype=torch.float32,
    c_dtype=torch.bfloat16,
    d_dtype=torch.bfloat16,
    cd_major="n",
    mma_tiler_mn=(256, 256),
    cluster_shape_mn=(2, 1),
    sf_vec_size=16,
    vector_f32=False,
    m_aligned=256,
    discrete_col_sfd=False,
    current_stream=stream,
)

# dictionary access:
d = outputs["d_tensor"]             # row-quantized output
d_col = outputs["d_col_tensor"]     # column-quantized output
amax = outputs["amax_tensor"]       # per-group amax (when d_dtype is bf16/float16)
sfd_row = outputs["sfd_row_tensor"] # row scale factors (when SFD outputs are enabled, FP8 inputs)
sfd_col = outputs["sfd_col_tensor"] # column scale factors (when SFD outputs are enabled, FP8 inputs)

# or tuple unpacking:
d, d_col, amax, sfd_row, sfd_col = outputs

Class API#

from cudnn import GroupedGemmQuantSm100
from cuda.bindings import driver as cuda

stream = cuda.CUstream(torch.cuda.current_stream().cuda_stream)

api = GroupedGemmQuantSm100(
    sample_a=a,
    sample_b=b,
    sample_d=d,
    sample_sfa=sfa,
    sample_sfb=sfb,
    sample_padded_offsets=padded_offsets,
    sample_alpha=alpha,
    sample_d_col=d_col,
    # Optional quantization outputs
    sample_sfd_row=sfd_row,        # Required when SFD outputs are enabled
    sample_sfd_col=sfd_col,        # Required when SFD outputs are enabled
    sample_amax=amax,              # Required for bf16 output with FP4 input
    sample_norm_const=norm_const,  # Required when SFD outputs are enabled
    sample_prob=prob,              # Per-row gating probabilities (required)
    # Configuration
    acc_dtype=torch.float32,
    mma_tiler_mn=(256, 256),
    cluster_shape_mn=(2, 1),
    sf_vec_size=16,
    vector_f32=False,
    m_aligned=256,
    discrete_col_sfd=False,
)
assert api.check_support()
api.compile()
api.execute(
    a_tensor=a,
    b_tensor=b,
    d_tensor=d,
    sfa_tensor=sfa,
    sfb_tensor=sfb,
    padded_offsets=padded_offsets,
    alpha_tensor=alpha,
    d_col_tensor=d_col,
    sfd_row_tensor=sfd_row,
    sfd_col_tensor=sfd_col,
    amax_tensor=amax,
    norm_const_tensor=norm_const,
    prob_tensor=prob,
    current_stream=stream,
)

Parameters#

Input/Output Tensors#

  • Input tensor A: a_tensor (wrapper) or sample_a, a_tensor (class)

    • Shape: (valid_m, K, 1)

    • Stride: (K, 1, valid_m·K) – must be K-major

    • Dtype (ab_dtype): {float4_e2m1fn_x2, uint8, float8_e4m3fn, float8_e5m2}

      • uint8 is interpreted as packed FP4 (two FP4 values per byte)

  • Input tensor B: b_tensor (wrapper) or sample_b, b_tensor (class)

    • Shape: (N, K, L) where L = num_groups

    • Stride: (K, 1, N·K) – must be K-major

    • Dtype (ab_dtype): Must match A

  • Output tensor D: d_tensor (class) or returned in wrapper dict

    • Shape: (valid_m, N, 1)

    • Stride: (N, 1, valid_m·N) – must be N-major

    • Dtype (d_dtype): {float16, bfloat16, float32} for FP4 inputs; {float16, bfloat16, float8_e4m3fn, float8_e5m2, float4_e2m1fn_x2} otherwise

  • Output tensor D_col: d_col_tensor (class) or returned in wrapper dict

    • Shape: (valid_m, N, 1)

    • Stride: (N, 1, valid_m·N) – must match D (N-major)

    • Dtype: Must match D

  • Input tensor prob: prob_tensor (wrapper) or sample_prob (class)

    • Shape: (valid_m, 1, 1)

    • Dtype: float32

    • Required: the kernel unconditionally multiplies output by per-row gating probability. Pass a tensor of ones when no gating is needed.

  • Scale factor tensors

    • SFA (A scale factor): sfa_tensor (wrapper) or sample_sfa, sfa_tensor (class)

      • Shape: (32, 4, ceil(valid_m/128), 4, ceil(ceil(K/sf_vec_size)/4), 1)

      • Dtype (sf_dtype): {float8_e8m0fnu, float8_e4m3fn}

    • SFB (B scale factor): sfb_tensor (wrapper) or sample_sfb, sfb_tensor (class)

      • Shape: (32, 4, ceil(N/128), 4, ceil(ceil(K/sf_vec_size)/4), L)

      • Dtype: Must match SFA

    • SFD_row (D row scale factor, optional): sfd_row_tensor (wrapper) or sample_sfd_row, sfd_row_tensor (class)

      • Shape: (32, 4, ceil(valid_m/128), 4, ceil(ceil(N/sf_vec_size)/4), 1)

      • Dtype: Must match SFA

      • Required when: SFD outputs are enabled (FP8 inputs)

    • SFD_col (D column scale factor, optional): sfd_col_tensor (wrapper) or sample_sfd_col, sfd_col_tensor (class)

      • Shape: (32, 4, ceil(N/128), 4, ceil(ceil(valid_m/sf_vec_size)/4), 1)

      • Dtype: Must match SFA

      • Required when: SFD outputs are enabled (FP8 inputs)

  • Group offsets

    • padded_offsets: Cumulative sum of aligned group M sizes

      • Shape: (L,) where L = num_groups

      • Dtype: int32

      • padded_offsets[-1] equals valid_m; each offset is a multiple of m_aligned

  • Scaling tensors

    • alpha: Per-group scaling factors

      • Shape: (L,) where L = num_groups

      • Dtype: float32

    • amax (optional): Per-group max absolute values

      • Shape: (L, 1)

      • Dtype: float32

      • Required when: d_dtype ∈ {bfloat16, float16}

    • norm_const (optional): Normalization constant for FP8 quantization

      • Shape: (1,)

      • Dtype: float32

      • Required when: sfd_row_tensor/sfd_col_tensor are provided (FP8 inputs)

Common Parameters#

  • acc_dtype: torch.dtype

    • Accumulator dtype. Must be torch.float32

  • mma_tiler_mn: Tuple[int, int]

    • Kernel tile size (TILE_M, TILE_N). Default: (256, 256)

    • TILE_M ∈ {128, 256}

    • TILE_N = 256

  • cluster_shape_mn: Tuple[int, int] | None

    • Thread Block cluster shape (CLUSTER_M, CLUSTER_N)

    • Constraints: positive powers of 2, both ≤ 4, CLUSTER_M × CLUSTER_N ≤ 16

    • Default: (2, 1) when TILE_M=256, (1, 1) otherwise

  • sf_vec_size: int

    • Scale factor vector size (number of elements per scale factor)

    • Allowed values: {16, 32}. Default: 16

  • vector_f32: bool

    • Enable packed f32 operations for improved performance

    • Default: False

  • m_aligned: int

    • Internal constant equal to FIX_PAD_SIZE (256); cannot be changed (the implementation raises ValueError for any other value)

    • Must be divisible by mma_tiler_mn[0]

  • discrete_col_sfd: bool

    • If True, generate discrete column scale factors grouped by expert tiles

    • Only applies when sfd_row_tensor, sfd_col_tensor, and norm_const_tensor are provided

    • Default: False

  • CUDA stream (current_stream in class API, current_stream in wrapper)

Wrapper-specific Parameters: grouped_gemm_quant_wrapper_sm100#

  • c_dtype: torch.dtype: Internal C tensor data type (not user-visible). Default: torch.bfloat16

  • d_dtype: torch.dtype: Output D tensor data type. Default: torch.bfloat16

  • cd_major: str: Major dimension for D tensors. Must be "n" (only N-major layout is supported). Default: "n"

Wrapper Return Values#

Returns a TupleDict - a dictionary-like object that also supports tuple unpacking and integer indexing.

Dictionary keys (also the tuple unpacking order):

  • d_tensor: Row-quantized output

  • d_col_tensor: Column-quantized output

  • amax_tensor: Per-group amax (when d_dtype ∈ {bfloat16, float16})

  • sfd_row_tensor: Row scale factors (when SFD outputs are enabled)

  • sfd_col_tensor: Column scale factors (when SFD outputs are enabled)

Class-specific Parameters#

GroupedGemmQuantSm100 (constructor)#

  • sample_a, sample_b, sample_d, sample_sfa, sample_sfb, sample_padded_offsets, sample_alpha, sample_d_col, sample_sfd_row, sample_sfd_col, sample_amax, sample_norm_const, sample_prob – see Input/Output tensors

    • Note: sample_sfd_row, sample_sfd_col, sample_norm_const must be all None or all not None

GroupedGemmQuantSm100.execute#

  • a_tensor, b_tensor, d_tensor, sfa_tensor, sfb_tensor, padded_offsets, alpha_tensor, d_col_tensor, sfd_row_tensor, sfd_col_tensor, amax_tensor, norm_const_tensor, prob_tensor – see Input/Output tensors. Must have same layout as sample tensors provided in constructor.

Support Surface and Constraints#

Layouts and Strides#

  • A must be K-major (contiguous along K dimension)

  • B must be K-major (contiguous along K dimension)

  • D and D_col must be N-major (contiguous along N dimension)

  • All tensors must be 16-byte aligned along the contiguous dimension

Data Types#

Input/Weight Types (ab_dtype)#

Format

ab_dtype

sf_dtype

sf_vec_size

d_dtype

MXFP8

float8_e4m3fn or float8_e5m2

float8_e8m0fnu

32

{float16, bfloat16, float8_e4m3fn, float8_e5m2, float4_e2m1fn_x2}

NVF4

float4_e2m1fn_x2 or uint8

{float8_e4m3fn, float8_e8m0fnu}

{16, 32}

{float16, bfloat16, float32}

Additional Type Constraints#

  • A and B must have the same dtype

  • SFA, SFB, SFD_row, and SFD_col must have the same dtype

  • D and D_col must have the same dtype

  • acc_dtype must be float32

  • sf_dtype=float8_e4m3fn is incompatible with sf_vec_size=32

  • FP8 ab_dtype is incompatible with sf_vec_size=16

  • FP4 ab_dtype with sf_vec_size=16 and d_dtype=float32 is not supported

  • FP4 ab_dtype requires c_dtype ∈ {float16, bfloat16}

Scale Factor Output Requirements#

  • When sfd_row_tensor/sfd_col_tensor are provided (FP8 inputs):

    • sfd_row_tensor, sfd_col_tensor, and norm_const_tensor are all required

    • These must be provided together (all None or all not None)

  • When d_dtype ∈ {bfloat16, float16}:

    • amax_tensor is required for tracking per-group max values

Tiling and Cluster#

  • mma_tiler_mn[0] = 256 enables 2-CTA instructions automatically (use_2cta_instrs=True)

  • When use_2cta_instrs=True: cluster_shape_mn[0] must be divisible by 2

  • m_aligned must be divisible by mma_tiler_mn[0] to prevent tiles from spanning multiple groups

Shapes and Divisibility#

  • padded_offsets length L is the expert count and must be <= 1024

  • Each group’s M dimension is aligned to m_aligned

  • valid_m = padded_offsets[-1] determines the actual tensor M dimension

  • Scale factor tensor shapes follow the MMA atom tiling pattern: (32, 4, ceil(dim/128), 4, ceil(K_groups/4), L)

Environment#

  • Requires CUDA with SM100+ compute capability (Blackwell GPUs)

Usage Examples#

For usage examples, see test cases in test/python/fe_api/test_grouped_gemm_quant.py + test/python/fe_api/test_grouped_gemm_quant_utils.py