ATFlash: Per-RoPE-Wavelength Attention Windows for Compute/Memory-Efficient LLM Inference

The attention score with rotary position embeddings (RoPE) decomposes exactly into a sum over its 2D-rotation frequency pairs, and each pair's wavelength limits how far it can discriminate position. Aligned with this structure, we propose the per-RoPE-wavelength distance window: it prunes the query--key inner-product terms beyond a wavelength-proportional distance. Unlike a sliding window, every key remains reachable, at least through the low-frequency pairs. The reduction rate is input-independent, with a closed form logarithmic in the sequence length N, in contrast to dynamic-sparse methods like MInference. Such token-level selection is orthogonal to our frequency-level pruning. The window can therefore be applied on top of those methods. On Qwen2.5-0.5B and Llama-3.2-3B, the window prunes 37--48% of the query--key inner-product terms within each model's native context length. Relative to full attention, the top-1 match rate stays at 96--98% and the mean output-distribution KL at the 10^{-3}-nat level on LongBench-v2 contexts. We examine absolute scores on long-context benchmarks such as RULER, OpenAI-MRCR, LongCodeQA, and \inftyBench: they are broadly preserved. We implement the window as a slice of the query--key contraction axis, leaving the online-softmax recurrences untouched, and port it with minimal diffs into the released FlashAttention-4 prefill and FlashInfer decode. On RTX PRO 6000 with Llama, both ports outpace stock with gains growing with context length, up to 1.29\times at 128K. End to end on Qwen2.5-7B-1M, with 57% of the inner-product terms pruned, the speedup reaches 1.31\times at a 1M-token context.