fast_trimul

Fused Triangle Multiplicative Update (AlphaFold2 / AlphaFold3 family) on CUTLASS CuTe DSL kernels — a drop-in nn.Module for the structural-biology stacks. Hardware Agnostic library!

Works with OpenFold, OpenFold-3, Boltz, Chai, and Protenix.

At a glance

*This runs the real OpenFold-3 code with fast_trimul patched in — the exact one-line swap from the Quickstart, with a ready-to-run quickstart_lightning example included. Speed — the graphed fast kernel beats the stock (native) trunk at every N:

Memory — but graphed's peak VRAM is higher:

Why more memory? Each CUDA graph reserves its own buffers (not reused across layers), so activation memory reads 0 GB but resurfaces as higher peak VRAM — the speed-for-memory trade-off.

Big memory win, per op: the kernel itself keeps near-zero scratch memory and uses ~2.2–2.4× less peak VRAM than the plain layer (10.1 vs 22–24 GB at N=2048), letting it fold ~1.4× longer sequences before running out — the higher VRAM above is only from graphing all 8 trunk layers at once (memory figures ↓).

Small, hackable kernels: written in Python-level CuTe DSL (not thousands of lines of C++/CUDA), so tuning a tile or porting to a new GPU is a quick edit, not a rewrite.

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Table of Contents

• Why fast_trimul?
• Quickstart: accelerate OpenFold-3 in one line
• Install
• Quick start
• Swap into a real model (whole-trunk example)
• Gradients (training)
• Benchmark
• Benchmark results
• Architecture
• API
• Limitations
• Roadmap
• Contributing
• Related Resources
• Built With
• Contact
• Citation
• License

Why fast_trimul?

Output matches the standard module within tiny rounding (about $6 \times 10^{-6}$ in half-precision). Verified by loading trained weights and comparing outputs across OpenFold, OpenFold-3, Boltz-1, Protenix, and an AF3/Chai-style reference (with detailed evaluations in reports/results/ and figures below.

Uses roughly half the GPU memory with almost zero scratch data at any sequence length $N$, cutting memory usage by 2.2–2.4× at $N=2048$ and fitting ~1.4× longer sequences before running out of memory while reaching up to 39 TFLOP/s.Fastest on short sequences, running 4.5–6.8× quicker than the plain layer at $N=8$ and remaining the fastest up to $N=128$. At small sizes, most execution time goes to launching tiny GPU steps; recording them into a single CUDA graph eliminates this overhead. This directly benefits real-world workloads like large-scale screening, peptides, and repeated refinement passes.

Runs anywhere without crashing by using a fast CUTLASS kernel when supported and gracefully falling back to a plain PyTorch version for unusual shapes or data types. Supporting new hardware like TPUs or Intel GPUs requires only a small add-on rather than a rewrite. Works at any sequence length as a direct drop-in replacement with no whole-model compilation step needed.

Quickstart: accelerate OpenFold-3 in one line

One line — patch_openfold3() — swaps OpenFold-3's TriMul for the fast kernel before you build the model. This exact script is verified on an NVIDIA A100 — both Lightning AI and Google Colab:

uv pip install --system openfold3 fast_trimul "cuda-python<13"

import fast_trimul
fast_trimul.patch_openfold3()          # <-- That is it!! OpenFold-3 now runs on the fast kernel.

# build and run OpenFold-3 exactly as you always would:
import torch
from openfold3.core.model.latent.pairformer import PairFormerStack

model = PairFormerStack(c_s=384, c_z=128, no_blocks=8, c_hidden_pair_bias=32, no_heads_pair_bias=4,
                        c_hidden_mul=128, c_hidden_pair_att=32, no_heads_pair=4,
                        transition_type="swiglu", transition_n=4, pair_dropout=0.25,
                        fuse_projection_weights=False, blocks_per_ckpt=None, inf=1e9).cuda().eval()

N = 64
s = torch.randn(1, N, 384, device="cuda")
z = torch.randn(1, N, N, 128, device="cuda")
with torch.no_grad():
    _, out_z = model(s, z, torch.ones(1, N, device="cuda"), torch.ones(1, N, N, device="cuda"))
print("OpenFold-3 running on fast_trimul ->", tuple(out_z.shape))    # (1, 256, 256, 128)

Same one-liner for the other stacks: patch_openfold(), patch_boltz(), patch_protenix(). Ready-to-run copies are in quickstart/ — one for Lightning AI (the snippet above) and one for Google Colab (adds a tiny fake-scipy shim so OpenFold-3 imports without Colab's numpy quirk; the patch_openfold3() integration is identical).

Prefer no global patch?

Use the module directly (FastTriangleMultiplication, see Quick start), and use @accelerate / with accelerated("cuda"): to pin which backend runs your own code (they control cuda-vs-torch selection, not the swap).

Run the shipped benchmark on your own GPU for numbers — see Benchmark below, and read Limitations for where torch.compile is the better choice.

Install

pip install fast_trimul          # or: uv pip install fast_trimul

Or install the latest straight from GitHub (no PyPI release needed — pure-Python package, so there's no compile step):

pip install git+https://github.com/tiagomonteiro0715/fast_trimul

Requires a CUDA GPU, torch, nvidia-cutlass-dsl, and cuda-python. Kernels JIT-compile on first use (one-time cost, then cached in-process).

Driver note: cuda-python must match your CUDA driver (it can be newer than the runtime, never older). If nvidia-smi shows CUDA 12.x (e.g. driver 570), pin the CUDA-12 line — otherwise you get cudaErrorInsufficientDriver (35):

pip install "cuda-python<13"

fast_trimul pins cuda-python<13 by default (most drivers are still CUDA 12.x); override it if your driver is CUDA 13+.

Troubleshooting the first run (kernels JIT-compile then):

• JIT/build errors (missing nvcc or CUDA headers): set CUDA_HOME to your CUDA toolkit so the compiler and headers are found.
• Slow or failing first-shape autotune: set FAST_TRIMUL_AUTOTUNE=0 to skip GEMM autotuning (uses a safe default config).

Quick start

On Google Colab (Runtime → Change runtime type → GPU), install first:

!pip install -q uv
!uv pip install fast_trimul

Then use it:

import torch
from fast_trimul import FastTriangleMultiplication

module = FastTriangleMultiplication(d_z=128, d_c=128, mode="outgoing").cuda()
z = torch.randn(1, 256, 256, 128, device="cuda")          # (B, N, N, d_z)
mask = torch.ones(1, 256, 256, device="cuda")             # optional (B, N, N)
out = module(z, mask=mask)                                 # same dtype as z

For fastest inference at a fixed shape, capture a CUDA graph once — this removes the per-launch overhead of the internal kernels, which dominates the runtime at small N:

module.graphed(z, mask)      # capture once at this shape (inference only)
out = module(z, mask=mask)   # subsequent calls replay the graph

Low-level functional API (FlashAttention style):

from fast_trimul import functional
out = functional.triangle_multiplication(z, module._impl, mask=mask)

Load pretrained weights from a target library — one call, pick the source (names are remapped, and fused a/b projections are split, for you):

module.load_weights(ref.state_dict(), source="openfold")   # or: openfold3 / protenix / boltz / chai

The five named helpers (load_openfold_state_dict, …) still work as thin aliases. These target modules apply their residual (+ z) outside the triangle block, so build with residual=False when matching their output exactly:

module = FastTriangleMultiplication(d_z=128, d_c=128, mode="outgoing", residual=False).cuda()

Pick or force a backend (default is "auto" — fastest available, then torch):

from fast_trimul import list_backends
list_backends()                                            # e.g. ['torch', 'cuda']
FastTriangleMultiplication(d_z=128, backend="cuda")        # force the fast path (still falls back)
FastTriangleMultiplication(d_z=128, backend="torch")       # force the portable reference

Opt in explicitly, without any global monkeypatching (safe under strict runtime policies) — @accelerate on a function, or the scoped accelerated():

from fast_trimul import accelerate, accelerated

@accelerate                    # runs this function with the accelerated backend
def infer(z): ...

with accelerated("cuda"):      # scoped: reverts on exit, never leaks
    out = model(z)

One-line correctness check — build your library's TriMul, then:

import fast_trimul
fast_trimul.verify("openfold", my_openfold_trimul)         # -> True if outputs match (fp16 tol)

verify stays a one-liner even when a library changes its API, because you pass the reference module and only the (registered) name-remap is library-specific.

Swap into a real model (whole-trunk example)

Drop fast_trimul into a library's trunk by replacing its TriMul class with a thin adapter, then capturing a CUDA graph per layer. Verified end-to-end on the OpenFold-3 Pairformer trunk (A100).

import torch
import openfold3.core.model.latent.base_blocks as blocks
from openfold3.core.model.latent.pairformer import PairFormerStack
from fast_trimul import FastTriangleMultiplication

# 1) a thin adapter: match the library's constructor, swallow its extra forward kwargs,
#    and use residual=False (the block adds the residual itself).
class FastTriMul(FastTriangleMultiplication):
    def __init__(self, c_z, c_hidden=None, *args, **kw):
        super().__init__(d_z=c_z, d_c=c_hidden or c_z, mode="outgoing", residual=False)
    def forward(self, z, mask=None, **kw):
        return super().forward(z, mask=mask)

# 2) patch the library's TriMul classes BEFORE building the model
blocks.TriangleMultiplicationOutgoing = FastTriMul
blocks.TriangleMultiplicationIncoming = FastTriMul
blocks.FusedTriangleMultiplicationOutgoing = FastTriMul
blocks.FusedTriangleMultiplicationIncoming = FastTriMul

model = PairFormerStack(c_s=384, c_z=128, no_blocks=8, ...).cuda().eval()

# 3) capture a CUDA graph for each swapped-in layer (fixed shape, inference only)
dummy_z = torch.randn(1, N, N, 128, device="cuda")
dummy_mask = torch.ones(1, N, N, device="cuda")
for m in model.modules():
    if isinstance(m, FastTriangleMultiplication):
        m.graphed(dummy_z, dummy_mask)

# ... now run model(s, z, single_mask, pair_mask) as usual ...

Install for this example (note the CUDA-12 driver pin — see Install):

uv pip install --system openfold3 fast_trimul "cuda-python<13"

Whole-trunk results (OpenFold-3 Pairformer, 8 blocks)

Full forward of the Pairformer trunk, random weights + inputs, 100 timed passes. Measured on NVIDIA A100-SXM4-40GB (Lightning AI). Latency in ms (lower is better), peak VRAM in GB; bold = fastest at that N.

Reading it honestly — when to use each:

• graphed is fastest at every N (1.15–1.35× over native) with near-deterministic latency, but reserves memory — one CUDA graph per layer, so peak VRAM grows to ~1.9× native at N=512. Use it when you're latency-bound and have VRAM headroom.
• eager matches native's memory (~equal), and is faster than native only at larger N (256+); at small N it's slower than native, because the un-graphed fused kernel is launch-bound across the trunk's ~16 TriMul layers.
• So: graphed for latency, eager for large-N at native-level memory. The whole-trunk win here is speed (graphed), not memory — the per-op memory advantage doesn't stack across many graphed layers.

Gradients (training)

The forward runs the fused fp16 kernel; the backward is a correct torch recompute (correct, not yet fast), so gradients flow and you can train / fine-tune with it. Do not call .graphed() for training — graphs are inference only. Verified on A100:

import torch
from fast_trimul import FastTriangleMultiplication

trimul = FastTriangleMultiplication(d_z=128, d_c=128, mode="outgoing").cuda()
z = torch.randn(1, 64, 64, 128, device="cuda", requires_grad=True)   # N a multiple of 8
out = trimul(z, mask=torch.ones(1, 64, 64, device="cuda"))
out.sum().backward()                                                 # gradients recomputed through the kernel
assert z.grad is not None and torch.isfinite(z.grad).all()           # input grads flow
assert all(p.grad is not None for p in trimul.parameters())          # parameter grads flow

Benchmark

The package ships a benchmark that measures machine ceilings (memory bandwidth, fp16 tensor-core peak, launch floor), a per-iteration median timer, achieved TFLOP/s, peak memory, and a size sweep. It reports fast_trimul both un-graphed and graphed, next to torch.compile and an eager reference, so you can compare on your own hardware:

!pip install -q uv
!uv pip install fast_trimul

from fast_trimul.benchmark import run_benchmark
run_benchmark()              # or: run_benchmark(head_size=384, sweep=(128, 256, 512))

Or from a shell:

python -m fast_trimul.benchmark

It reports these variants:

• fast no-graph — the kernel, fp16, un-graphed (shows the launch-overhead cost),
• fast +graph — the same kernel with a captured CUDA graph (.graphed()),
• compile — torch.compile(mode="reduce-overhead") and default mode,
• torch eager — the eager reference.

Use CUDA events + synchronize() (as the shipped benchmark does) so timing reflects when the GPU finishes the work, not when the launch is queued. Warm up (or call .graphed()) before timing to exclude the one-time JIT/autotune cost.

Benchmark results

Speed (latency) and peak-memory scaling for a single Triangle-Multiplicative Update across five stacks, plus the OpenFold-3 Pairformer whole-trunk (8 blocks). fast_trimul is the vermilion line; an ✕ marks where a baseline ran out of memory. Single-op runs on an NVIDIA A100-SXM4-80GB (PyTorch 2.13 / CUDA 13.0, B=1, d_z=d_c=128, TF32 on so the fp32 baselines are fair, medians of 30 timed / 5 warmup runs); the whole-trunk on an A100-40GB, 100 passes.

Full tables live in reports/results/, one-click reproduction notebooks in reports/colab_reproduce/, and the figures are regenerated by reports/plot_results.py.

Boltz-1

Chai / AF3

OpenFold (AF2)

OpenFold-3

Protenix

Whole-trunk — OpenFold-3 Pairformer (8 blocks)

cuda ungraphed = un-graphed fused kernel; graphed = with a captured CUDA graph; native = the library's stock trunk.

Why the baselines OOM: their temporary activations grow quadratically-to-cubically with N, so by N=3072 they no longer fit the 80 GB card (fragmentation also blocks a contiguous alloc); torch.compile shrinks but doesn't remove those buffers. fast_trimul keeps activations on-chip (SRAM), so its extra activation memory stays 0 GB and it still fits at N=3584.

Architecture

The library is a small stable front-end over a registry of interchangeable backends. CUDA is one backend; a pure-torch backend is the universal fallback. Adding new hardware or a new library is a plug-in (one decorated class/function), not a core edit.

The kernels are written in Python-level CuTe DSL, not thousands of lines of C++/CUDA — so the whole kernel codebase stays small and readable, and tuning a tile size, adding a fused epilogue, or porting to a new GPU is a quick edit instead of a rewrite.

  front-end   @accelerate  accelerated()  verify()          # stable, tiny
      │
  guard        contiguous · dtype · align · int64 strides   # NormalizedInput
      │
  dispatch     pick backend, then FALL BACK: cuda -> torch  # never crashes on a bad shape
      │
  backends     cuda_cute (CUTLASS)   torch_ref (portable)   # + future: xla/tpu, xpu/intel

Everything the architecture adds — registries, guard, dispatch, decorators — is O(1) overhead; only the op itself scales with N. The CUDA kernels (_kernels.py) are untouched.

Adding a new backend

from fast_trimul.core.registry import backend

@backend("mybackend", dtypes={torch.float16}, min_align=8)
class MyBackend:
    def __init__(self, caps): self.caps = caps
    def execute(self, inp, params): ...   # inp.tensor is guarded (contiguous, right dtype)

That one file makes backend="mybackend" selectable and slots it into the fallback chain — no changes to the dispatcher or the module.

API

• fast_trimul.FastTriangleMultiplication(d_z, d_c=None, mode="outgoing", residual=True, backend="auto") — the module. forward(z, mask=None), .graphed(z, mask=None), .load_weights(state_dict, source=...) (plus the named aliases .load_openfold_state_dict / .load_openfold3_state_dict / .load_protenix_state_dict / .load_boltz_state_dict).
• fast_trimul.accelerate / fast_trimul.accelerated(backend="auto") — explicit opt-in decorator / scoped context manager.
• fast_trimul.verify(source, reference, ...) — one-line correctness check against a reference module.
• fast_trimul.list_backends() — backends registered on this machine.
• fast_trimul.functional.triangle_multiplication(z, params, mask=None) — low-level functional call.
• fast_trimul.core.registry.{backend, weights_for} — decorators to register a new backend or library weight-map.

Limitations (read before relying on it)

• torch.compile(mode="reduce-overhead") is competitive and often faster above small N. On an A100 it is frequently faster per call in the mid-range and, on several stacks, uses similar peak memory. These kernels are not yet epilogue-fused (future work), so the reasons to prefer this are drop-in-ness and robustness, not raw latency: reduce-overhead needs static shapes and recompiles per sequence length (awkward for variable-length inputs) and can break on some models, whereas this is a plain nn.Module that works on any shape with no compilation step. Benchmark both on your workload.
• Don't wrap a patched model in torch.compile. After patch_openfold3() the TriMul runs a JIT-compiled CUTLASS kernel that torch.compile can't trace through — use one or the other. For launch-overhead reduction, use .graphed() instead.
• First call is slow: JIT compile + GEMM autotune. On the first forward at a new shape, the GEMM configs are auto-tuned (one-time, cached). Disable with the env var FAST_TRIMUL_AUTOTUNE=0. Warm up (or call .graphed()) before timing.
• fp16 only. bf16/fp32 inputs are cast to fp16 and back; keep the module in fp16 (do not call .float()/.bfloat16() on it).
• Pretrained weights need name remapping. Each library names its projections/norms differently, so a strict checkpoint load will not line up. Automated for the common stacks via load_weights(sd, source=...): openfold (OpenFold/AF2), openfold3 (separate or fused variant), protenix, boltz, and chai (Boltz/Chai/AF3 fuse the a/b projections). Other stacks: supply a @weights_for remap.
• Mask semantics are approximate. The mask is applied to the pair tensor in and out; validate against each library's exact masking before production use.
• Backward is correct but not fast (torch recompute), so it helps inference more than training throughput.
• The CUDA kernel is Ampere (sm80) tested; fp16 only. On other hardware, or for bf16/fp32, or non-multiple-of-8 N, the dispatcher falls back to the pure-torch backend (correct, slower). Hopper/Blackwell + fp8 are future work.
• Building a module needs a CUDA GPU + CUTLASS (the fused kernel weights live in a CUTLASS module). import fast_trimul itself is lazy and does not require CUTLASS until you construct FastTriangleMultiplication.

Roadmap

• Epilogue fusion / megakernel: fuse post-GEMM norms + activations.
• Multi-arc support: H100/H200 (FP8/FP16 paths), B200 (NVFP4/FP4, Gen 2 Transformer Engine).
• Fused backward kernel (transposed operands) to remove autograd memory overhead.

Contributing

Contributions, bug reports, and benchmark numbers from your own hardware are welcome!

• Found a bug, a shape that falls back unexpectedly, or a stack whose weights don't remap? Open an issue, or reach out at monteiro.t@northeastern.edu.
• Added a new backend or a @weights_for map for another library? Send a pull request — a new backend or weight-map is one decorated class/function and needs no changes to the core (see Architecture → Adding a new backend).
• Enjoyed it? Star the repository — it helps others find the project.

Related Resources

• The Math Behind Artificial Intelligence — a guide to AI's mathematical foundations from an engineering perspective.
• My FreeCodeCamp Articles — tutorials and deep dives on AI and programming.
• Signal Processing Guide — companion resource on signal processing.

Built With

• Python — the front-end, dispatcher, backends, and integrations.
• NVIDIA CUTLASS CuTe DSL — the fused GEMM / kernel core, written in Python-level CuTe DSL so the kernels stay clean, editable, and easy to re-tune for new GPU generations.
• PyTorch — tensors, autograd, and CUDA-graph capture.
• cuda-python — the driver bindings the kernels launch through.
• uv — fast Python package installer used throughout the docs.

Contact

Tiago Monteiro

• Email: monteiro.t@northeastern.edu
• GitHub: @tiagomonteiro0715
• FreeCodeCamp: Author Profile

Citation

If you use fast_trimul in research, please cite it:

@software{monteiro_fast_trimul,
  author = {Monteiro, Tiago},
  title  = {fast_trimul: Fused Triangle Multiplicative Update on CUTLASS CuTe DSL kernels},
  year   = {2026},
  url    = {https://github.com/tiagomonteiro0715/fast_trimul}
}

License

Apache License 2.0 (this project) — see LICENSE. The GEMM core is derived from NVIDIA CUTLASS — specifically the CuTe DSL Ampere dense-GEMM example tensorop_gemm.py — and is licensed under BSD 3-Clause — see NOTICE.

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