FoldAttention

FoldAttention: Declared-Reference Softmax for Fast Decode and Deterministic Backward
Sriman Achanta
Paper: https://arxiv.org/abs/2609.33410

FoldAttention declares softmax's reference before execution. Final weights make decode contributions additive, while a shared integer grid makes the backward deterministic without serializing its reductions.

Usage

Install FoldAttention from PyPI:

pip install fold-attention

Install the CUDA 13 dependencies with the cu13 extra:

pip install "fold-attention[cu13]"

FoldAttention requires Python 3.12 or newer and an NVIDIA SM90 GPU.

Code usage

Training

fold_attn_func follows FlashAttention's (batch, seqlen, heads, head_dim) layout. Keys and values may use fewer heads for GQA or MQA.

from fold_attention import fold_attn_func

out = fold_attn_func(q, k, v, causal=True)
out.backward(dout)

The forward uses FlashAttention-4. The FoldAttention backward produces bit-identical gradients across repeated runs, batching, and variable-length packing.

For packed self-attention, pass (total_tokens, heads, head_dim) tensors and a CUDA int32 cumulative-length vector:

from fold_attention import fold_attn_varlen_func

out = fold_attn_varlen_func(q, k, v, cu_seqlens, causal=True)

Decode

FoldKVCache owns one layer's paged cache. prefill runs FlashAttention-4 and writes the cache. fold_attn_with_kvcache optionally appends one token per request, then attends over the updated cache.

from fold_attention import FoldKVCache, fold_attn_with_kvcache

cache = FoldKVCache(
    batch=batch_size,
    n_heads=n_heads,
    n_kv_heads=n_kv_heads,
    head_dim=head_dim,
    max_len=max_len,
    depth=16,
)

prompt_out = cache.prefill(q, k, v, cu_seqlens)
step_out = fold_attn_with_kvcache(q_step, cache, k_step, v_step)

Set depth=None for dense decode. A finite depth cuts low-weight keys while retaining their normalization mass. Set v8=True to store values in two E4M3 planes.

Benchmarks

Decode speed and accuracy

Latency against FP32-relative error on seven real-model generations. Each FoldAttention curve sweeps the decode depth.

Deterministic backward

Causal backward throughput across MHA and GQA shapes. The rows below each panel report FoldAttention throughput relative to the fastest deterministic and nondeterministic kernel.

The benchmark suite and measurement protocol are documented in benchmarks/README.md.

License

FoldAttention is released under the Apache License 2.0.