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Grouped GEMM + SwiGLU (SM100)

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This is an experimental API and subject to change.

Legacy contiguous-only API note: This page documents the older contiguous-only SwiGLU API. For new integrations, prefer the unified Grouped GEMM + GLU API, which covers dense and discrete weight layouts.

JAX support

cudnn.grouped_gemm_swiglu_wrapper_sm100 accepts Torch tensors and canonical MXFP8 JAX arrays or tracers. Torch execution is unchanged; JAX dispatches to cudnn.jax.grouped_gemm_swiglu, eagerly or under jax.jit, with XLA-owned buffers and stream ordering. cudnn.torch.grouped_gemm_swiglu remains an alias to the same wrapper and inherits its dispatch. Direct API-class construction with JAX samples remains unsupported.

Wrapper signatures and defaults are unchanged. JAX wrapper calls must set sf_vec_size=32 and an explicit FP8 d_dtype. The direct cudnn.jax API retains its MXFP8 defaults. See the JAX execution contract below.

Overview

Grouped GEMM + SwiGLU fusion: A contiguous grouped block-scaled GEMM fused with a SwiGLU epilogue 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).

This kernel performs:

  1. Block-scaled grouped GEMM: Low-precision GEMM (FP4, FP8) with per-block scale factors across multiple expert groups
  2. SwiGLU activation: Fused activation applied to the GEMM output
  3. Optional quantized output: Produces row and column scale factors for downstream quantization

Shapes

Equations

  • 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)
    • norm_const: normalization constant for FP8 quantization, shape (1,)
  • Outputs
    • C: intermediate GEMM result, shape (valid_m, N, 1)
    • D: row-quantized SwiGLU output, shape (valid_m, N/2, 1)
    • D_col: column-quantized SwiGLU output, shape (valid_m, N/2, 1)
    • SFD_row: row scale factors (when d_dtype is FP8), shape (32, 4, ceil(valid_m/128), 4, ceil(ceil((N/2)/sf_vec_size)/4), 1)
    • SFD_col: column scale factors (when d_dtype is FP8), shape (32, 4, ceil((N/2)/128), 4, ceil(ceil(valid_m/sf_vec_size)/4), 1)
    • amax: per-group amax (when d_dtype is bf16/fp16), shape (L, 1)

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

C[m,n]=αg∑kdequantize(A[m,k],SFA)⋅dequantize(B[n,k,g],SFB)C[m, n] = \alpha_g \sum_{k} \text{dequantize}(A[m, k], \text{SFA}) \cdot \text{dequantize}(B[n, k, g], \text{SFB})

Step 2: SwiGLU epilogue (performed by pairing 32-column blocks along N):

Let block size G = 32. For each pair of consecutive 32-wide column blocks:

  • Input block: X_b = C[:, 2·b·G : 2·b·G + G]
  • Gate block: G_b = C[:, 2·b·G + G : 2·b·G + 2·G]
D[:,bG:(b+1)G]=prob⋅Xb⋅swish(Gb),swish(x)=x⋅σ(x)D[:, bG:(b+1)G] = \text{prob} \cdot X_b \cdot \text{swish}(G_b), \quad \text{swish}(x) = x \cdot \sigma(x)

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

SFD_row[m,n]=norm_const⋅max⁡k∈block∣D[m,k]∣⋅rcp_max\text{SFD\_row}[m, n] = \text{norm\_const} \cdot \max_{k \in \text{block}} |D[m, k]| \cdot \text{rcp\_max} Dquantized[m,n]=D[m,n]⋅norm_constSFD_row[m,n]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
               C (valid_m×N×1)
                    |
                    | Pair 32-col blocks: [X0|G0|X1|G1|...]
                    |     X_b × swish(G_b)
                    v
                    | × prob
                    v
               D (valid_m×N/2×1)
                    |
         +----------+-----------+
         |                      |
         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_swiglu_wrapper_sm100
from cuda.bindings import driver as cuda
stream = cuda.CUstream(torch.cuda.current_stream().cuda_stream)
outputs = grouped_gemm_swiglu_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=32,
    vector_f32=False,
    m_aligned=256,
    discrete_col_sfd=False,
    current_stream=stream,
)
# dictionary access:
c = outputs["c_tensor"] # intermediate GEMM result
d = outputs["d_tensor"] # row-quantized SwiGLU output
d_col = outputs["d_col_tensor"] # column-quantized SwiGLU output
amax = outputs["amax_tensor"] # per-group amax (when d_dtype is bf16)
sfd_row = outputs["sfd_row_tensor"] # row scale factors (when d_dtype is FP8)
sfd_col = outputs["sfd_col_tensor"] # column scale factors (when d_dtype is FP8)
# or tuple unpacking:
c, d, d_col, amax, sfd_row, sfd_col = outputs

Class API

from cudnn import GroupedGemmSwigluSm100
from cuda.bindings import driver as cuda
stream = cuda.CUstream(torch.cuda.current_stream().cuda_stream)
api = GroupedGemmSwigluSm100(
    sample_a=a,
    sample_b=b,
    sample_c=c,
    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,              # Optional gating probabilities
    # Configuration
    acc_dtype=torch.float32,
    mma_tiler_mn=(256, 256),
    cluster_shape_mn=(2, 1),
    sf_vec_size=32,
    vector_f32=False,
    m_aligned=256,
    discrete_col_sfd=False,
)
assert api.check_support()
api.compile()
api.execute(
    a_tensor=a,
    b_tensor=b,
    c_tensor=c,
    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 C: c_tensor (class) or returned in wrapper dict

    • Shape: (valid_m, N, 1)
    • Stride: (N, 1, valid_m·N) – must be N-major
    • Dtype (c_dtype): {float16, bfloat16} for FP4 inputs; {float32, float16, bfloat16, float8_e4m3fn, float8_e5m2, float4_e2m1fn_x2} otherwise

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

    • Shape: (valid_m, N/2, 1)
    • Stride: (N/2, 1, valid_m·N/2) – must be N-major
    • Dtype (d_dtype): {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/2, 1)
    • Stride: (N/2, 1, valid_m·N/2) – must match D (N-major)
    • Dtype: Must match D

  • 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/2)/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/2)/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
    • prob (optional): Per-row gating probabilities
      • Shape: (valid_m, 1, 1)
      • 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 ∈ {64, 128, 256}
    • TILE_N ∈ {128, 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

    • Alignment requirement for group M dimension
    • Must equal FIX_PAD_SIZE (256) and be divisible by mma_tiler_mn[0]
    • Default: 256

  • 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_swiglu_wrapper_sm100

  • c_dtype: torch.dtype: Intermediate C tensor data type. Default: torch.bfloat16
  • d_dtype: torch.dtype: Output D tensor data type. Default: torch.bfloat16
  • cd_major: str: Major dimension for C and 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):

  • c_tensor: Intermediate GEMM result
  • d_tensor: Row-quantized SwiGLU output
  • d_col_tensor: Column-quantized SwiGLU 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

GroupedGemmSwigluSm100 (constructor)

  • sample_a, sample_b, sample_c, 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

GroupedGemmSwigluSm100.execute

  • a_tensor, b_tensor, c_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 and B must be K-major (contiguous along K dimension)
  • C, D, and D_col must be N-major (contiguous along N dimension)
  • All tensors must be 16-byte aligned along the contiguous dimension

Canonical layouts (additive)

Each input is also accepted in its natural row-major form. Canonical inputs compile at their own rank and bind directly, with no per-call host-side views; the pre-permuted kernel-facing forms above keep working unchanged:

  • A: (valid_m, K) row-major
  • B: (L, N, K) C-contiguous
  • SFA/SFB: any dense C-contiguous buffer with the MMA-tiled element count, e.g. flat 1-D or the physical (L, ceil(mn/128), ceil(ceil(K/sf_vec_size)/4), 32, 4, 4) allocation — no .view().permute() gymnastics required. The kernel rebuilds the MMA-tiled SF layouts from the GEMM shapes and reads only the base pointer.
  • prob: (valid_m,), float32 or bfloat16
  • alpha_tensor remains required; pass explicit per-group scaling factors.

Flat SF buffers must already contain the packed MMA-tiled scale bytes in physical order. Ordinary row-major logical scales need packing before this API is called.

These layouts are also used by the JAX execution path below. Unified GLU/dGLU APIs are separate.

When A is canonical (2-D), the wrapper returns natural-shaped outputs: c (valid_m, N), d/d_col (valid_m, N/2) row-major, and sfd_row/sfd_col as C-contiguous physical (1, ceil(mn/128), rest, 32, 4, 4) buffers.

JAX execution

cudnn.jax.grouped_gemm_swiglu runs the contiguous-weight MXFP8 fusion through cudnn.jax.call, eagerly or under jax.jit. All operands are ordinary JAX arrays managed by XLA. Torch callers use cudnn.torch.grouped_gemm_swiglu or the existing top-level wrapper name. Both paths return TupleDict with the same key order and tuple-unpacking behavior. The JAX path registers this output type as a JAX pytree.

Use canonical A (m,k), B (experts,n,k), and prob (m,) (fp32 or bf16). Scale factors are E8M0 arrays, or uint8 bit patterns, containing the packed MMA-tiled physical bytes; physical 6-D and flat buffers are accepted. Pass explicit fp32 alpha (experts,), norm_const (1,), and int32 padded_offsets (experts,). Offsets must be nondecreasing multiples of 256 in [0,m]; m must be a positive multiple of 256. These device values are the caller’s responsibility.

Forward returns c_tensor (m,n), d_tensor/d_col_tensor (m,n/2), physical sfd_row_tensor/sfd_col_tensor, and amax_tensor=None.

The JAX API fixes scale-vector size to 32 and defaults d_dtype to FP8 e4m3. It requires explicit probability and normalization arrays. Mixed Torch/JAX operands are rejected. Torch-specific streams, output buffers, accumulation/layout options, and epilogues are not JAX parameters. The optional JAX configuration is c_dtype, d_dtype, mma_tiler_mn, and cluster_shape_mn. Configuration arguments must be static under jax.jit:

import jax
from cudnn.jax import grouped_gemm_swiglu
compiled = jax.jit(grouped_gemm_swiglu)
result = compiled(**jax_inputs)

The existing wrapper also works under jax.jit:

from functools import partial
import cudnn
import ml_dtypes
compiled = jax.jit(partial(
    cudnn.grouped_gemm_swiglu_wrapper_sm100,
    sf_vec_size=32,
    d_dtype=ml_dtypes.float8_e4m3fn,
))
result = compiled(**jax_inputs)

On the wrapper’s JAX path, unsupported options raise ValueError: non-FP32 accumulation, non-n output layout, scale-vector size other than 32, vector_f32=True, non-default m_aligned, discrete_col_sfd=True, and caller streams.

The Torch alias preserves the existing wrapper signature, including its dtype and scale-vector defaults. For example, select MXFP8 explicitly:

from cudnn.torch import grouped_gemm_swiglu
import torch
result = grouped_gemm_swiglu(**torch_inputs, d_dtype=torch.float8_e4m3fn, sf_vec_size=32)

This initial bridge supports FP8 e4m3/e5m2 A/B and FP8 D, with E8M0 block scales of vector size 32. Packed FP4, BF16 D, bias, and discrete-column SF layout are outside its contract. Outputs are initialized to zero (raw zero bytes for SF) to define untouched padding; backward dprob also requires initialization for atomic accumulation. CUDA graph compatibility uses the standard CuTeDSL JAX bridge. This API supplies the fused backward operation explicitly; it does not register an automatic jax.grad rule. Full TE training integration is separate validation.

Data Types

Input/Weight Types (ab_dtype)

Formatab_dtypesf_dtypesf_vec_sized_dtype
MXFP8float8_e4m3fn or float8_e5m2float8_e8m0fnu32{float16, bfloat16, float8_e4m3fn, float8_e5m2}
NVF4float4_e2m1fn_x2 or uint8{float8_e4m3fn, float8_e8m0fnu}{16, 32}{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
  • FP4 ab_dtype with sf_vec_size=16 and d_dtype=float32 is not supported
  • FP8 ab_dtype with mma_tiler_mn[1]=128 and FP8 d_dtype is not supported
  • FP4 ab_dtype is not compatible with FP8 c_dtype

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

  • N must be divisible by 64 (two consecutive 32-column blocks for SwiGLU pairing)
  • 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/grouped_gemm/test_grouped_gemm_swiglu.py + test/python/fe_api/grouped_gemm/test_grouped_gemm_swiglu_utils.py