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 ∞Bench: 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× at 128K. End to end on Qwen2.5-7B-1M, with 57% of the inner-product terms pruned, the speedup reaches 1.31× at a 1M-token context.
Long contexts have become standard in pretrained LLMs, yet they remain expensive to run: prefill compute grows quadratically with sequence length, and every decode step re-reads a key-value cache that grows linearly with it. Sparse attention cuts these costs by attending only to a relevant subset of past tokens, but selecting that subset is itself expensive. We present SpotAttention, a lightweight selector that attaches to a frozen pretrained transformer and learns by KL distillation to estimate its attention distribution. The selector picks the top-K keys each query attends to, and because its estimate is a calibrated distribution, a dual top-p rule reads the per-query, per-layer budget directly from it. Across Qwen3 (dense, 4B-32B) and Qwen3.5 (hybrid linear/full attention, 4B-9B), SpotAttention matches dense accuracy at contexts up to 128K tokens, eight times the training length. Decode at L=128K runs 3.9x faster than FlashAttention and 1.8x faster than Twilight, the strongest training-free baseline. Quantizing the selector's K-cache to INT4 or FP4 microscale shrinks it 3.5x at no accuracy cost.
Rotary Position Embedding (RoPE) is widely adopted in Transformers to encode positional information, yet standard implementations enforce a uniform frequency schedule and scaling across all attention heads. Using simplified retrieval tasks and length generalization scenarios, we show -- both empirically and theoretically -- that heads with different functional roles require distinct frequency ranges and attention scaling factors to operate effectively. Ignoring this structure leads to suboptimal utilization of embedding dimensions and degraded performance, particularly under long-context settings. To address these limitations, we propose AdaRoPE, which equips each attention head with learnable rotation frequencies and attention scaling factors. Pretrained LLMs with AdaRoPE consistently outperform existing RoPE variants, including partial RoPE and NoPE baselines. For context extension, we further show that uniform frequency and attention scaling, used in methods such as YaRN, are suboptimal. By applying head-specific scaling, AdaRoPE enables better context extension while better preserving short-context performance in both the extrapolation setting and the long-context continued pretraining setting. These results highlight the importance of optimizing rotary position embedding at the level of individual attention heads.
Rotary Position Embeddings (RoPE) make attention scores position-relative but leave the value pathway position-blind: the message sent by a value token is the same regardless of its distance from the query. We propose RoVE, a parameter-free modification that makes values position-sensitive by rotating them simultaneously with keys, and show that it turns RoPE attention into attentive convolution. This new perspective unifies several independent formulations of the same operation across computer vision, robotics, and modern LLM architectures. Trained 124M and 354M GPT-2 models show consistent empirical gains over RoPE on few-shot in-context learning, out-of-distribution perplexity, and long-context retrieval, with the clearest improvements on tasks that require long-range aggregation.
Alejandro García-Castellanos, Maurice Weiler, Erik J Bekkers