A value-of-information router that measures, for each query, how decisively the top-k cut was made, and doubles the kept set for the queries where that gap is smallest is proposed; the rule is backbone-agnostic and stacks with existing block-scoring methods such as Quest.
Abstract
Block-sparse attention scales long-context language models by replacing the O(N^2) softmax with a per-query top-k selection over key blocks. This cutoff is myopic: when the k-th and (k+1)-th blocks are nearly tied in score, the selector commits without spending extra budget, and a dropped block carrying answer evidence is unrecoverable downstream. We propose a value-of-information router that measures, for each query, how decisively the top-k cut was made, and doubles the kept set for the queries where that gap is smallest; the rule is backbone-agnostic and stacks with existing block-scoring methods such as Quest. On LongBench-v2 medium at n=215 (the entire dataset subset), router-on-Quest reaches paired recall 0.75 vs. top-k 0.47 -- +28 pp over the SSA-style baseline (McNemar p<0.01) -- and lands within 2 pp of dense on RULER NIAH multikey at the same context. The lift reproduces on four models from three architectures (Qwen2.5, Mistral-Nemo, Qwen3.6). At 128K, the router preserves 0.81 and 0.89 of dense accuracy on Qwen2.5-7B-1M and Qwen3.6 (vs. SSA-style top-k at 0.09 on the former) while the fused selection-plus-kernel pipeline runs at 0.62x and 0.80x dense wall time.
Results motivate CertKV, a training-free compressor that reserves one tail-summary slot per head and allocates the rest by value dispersion, which is top-two in seven of nine LongBench-v2 settings, remains in the leading compressed tier on 128K RULER, and realizes a ten-fold cache budget in a packed Llama prototype.
Long-context LLM inference is bottlenecked by quadratic attention computation and growing KV-cache costs. Existing sparse attention and KV-compression methods typically decide which tokens or heads to preserve from runtime attention scores, observation windows, calibration prompts, or learned gates, making head diagnosis input-dependent and costly to deploy. We propose Autonomy-of-Heads (AoH), a data-free method that identifies retrieval and streaming heads from the spectral geometry of query-key projections. AoH defines the kernel attention operator $M_h = W_K^{h\top}W_Q^h$ and uses its effective-rank as a weight-space measure of head function: concentrated spectra indicate a small number of dominant query-key matching directions and are associated with retrieval heads, whereas diffuse spectra indicate the absence of a dominant global matching direction and are associated with streaming heads. We further derive an efficient $d_\text{head}$-dimensional computation that avoids constructing the full $d_\text{model}\times d_\text{model}$ matrix. We conducted extensive experiments across models demonstrating that at 50\% sparsity, AoH retains 96.5\% of Full Attention performance on average while reducing prefill and decode latency by up to 41.4\% and 66.0\%, respectively, and KV-cache memory by 50.0\% at 256K tokens.
YeHan Yang, Junyuan Shang, Yang Li et al.· 0 citations
The results suggest that simple pruning-inspired orderings can provide useful fixed sparse supports for PEFT, especially when combined with low-rank adapters.
Ivan D. Ilin, Philip Zmushko, Peter Richtárik· arXiv.org· 0 citations
Token-level sparse attention, as implemented by DeepSeek Sparse Attention (DSA) in production systems, makes the downstream attention efficient but shifts the bottleneck to the indexer that feeds it. To select the top-k tokens for each query, the indexer must still score every preceding token, incurring a cost of O(L^2) per layer for a sequence of length L. We observe that this per-query scan is largely redundant: nearby queries select highly overlapping top-k tokens, and the indexer scores are long-tailed along the key axis. We exploit these properties in PIVOT, Proxy Indexing Via One full-prefix Traversal, a training-free, drop-in replacement for the DSA indexer that shares one prefix scan across a group of nearby queries. PIVOT aggregates a group into a single proxy query, performs one shared full-prefix scan to obtain a candidate set, and then selects a top-k for each query from that set. Two variants trade speed for fidelity: PIVOT-Reuse shares the proxy top-k across the group for maximum speed, whereas PIVOT-Refine re-scores the candidate set with the indexer of each query and then selects an individual top-k, matching the dense indexer at a small additional cost. A single algorithm covers both inference phases, differing only in how groups are formed: fixed-size groups of consecutive queries in prefill, and the queries decoded together in one multi-token prediction (MTP) step in decode. On DeepSeek-V3.2 and GLM-5.1 across LongBench and RULER, PIVOT matches the accuracy of the dense DSA indexer while accelerating it by up to 4x and reducing end-to-end latency by up to 1.6x at long context.
F-WANDA is introduced, a drop-in modification of WANDA that reallocates the per-row keep budget across output neurons in proportion to the empirical Fisher information of the pre-activation, placing F-WANDA on the Pareto frontier of quality versus pruning cost for sustainable LLM compression.
This work provides a new method for fine-tuning models with sparse attention that works for any KV cache policy, runs on a moderate hardware budget, and allows the model to co-adapt with the policy, often outperforming models trained with exact attention (sequence parallelism).
Matthias W. Seeger, Zeyu Zhang, Vihang Patil et al.· 0 citations
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