Attention-Mass Condensation for Sparse Decoding

Long-context decoding is increasingly limited by KV-cache memory traffic since each generated token attends over a cache whose size grows linearly with context length. Existing sparse decoding methods reduce this cost by selecting subsets of tokens or pages, but are designed for softmax attention, whose dense tails make any truncation discard nonzero probability mass. In contrast, $α$-entmax produces exact zeros, turning sparse decoding from dense-tail approximation into support recovery: if the selected candidates contain the entmax support, sparse decoding remains exact. While recent entmax kernels enable efficient training, they do not address the autoregressive decoding bottleneck, where dense inference still streams the full KV cache before sparsity is known. In this work, we introduce EntmaxKV, an entmax-native sparse decoding framework that exploits sparsity before KV pages are loaded. EntmaxKV combines query-aware page scoring, support-aware candidate selection, and sparse entmax attention. We analyze truncation error through the dropped probability mass $δ$, showing that output error is controlled by $δ$ and vanishes when the entmax support is recovered. We further introduce a Gaussian-aware entmax selector that estimates the entmax threshold from lightweight page statistics, adapting the selected budget to the score distribution. Empirically, EntmaxKV drops less probability mass, retains more support tokens, and achieves lower output error than softmax-based sparse decoding at matched KV budgets. On long-context and language modeling benchmarks, it closely matches full-cache entmax while using a small fraction of the KV cache, achieving up to $3.36\times$ (softmax) and $5.43\times$ (entmax) speedup over full attention baselines at 1M context length. Code available at: https://github.com/deep-spin/entmaxkv.

Long-context prefill remains expensive because full/GQA layers still score the historical sequence, even in hybrid models with local, sparse, linear, or recurrent components. We study how much dense attention is needed to preserve task-level behavior under explicit support granularity and top-k budgets. We introduce an attention-mass top-k oracle for existing GQA checkpoints: for each layer and query position, it computes dense attention, selects head-averaged token support, and recomputes attention only on that support. The oracle is a diagnostic reference, not a deployable accelerator, and separates sparse-budget feasibility from indexer error and runtime realization effects. On Qwen-family retrieval-heavy evaluations, the longest per-query oracle rows stay within 1 point of dense, and a Qwen3.5-9B RULER-style sweep from 4K to 100K stays within 0.48 points. Guided by the oracle, we derive a head-collapsed auxiliary indexer trained by KL distillation from dense attention-mass distributions while keeping the backbone frozen. With separately distilled Qwen3.5-0.8B and Qwen3.5-9B indexers, the reported 16K/32K validation macro gaps are +2.04 and +1.13 points, treated as quality preservation rather than improvement; fused selection-block-shared support can introduce a larger realization gap. Preliminary single-card TTFT measurements show distilled-indexer sparse serving speedups of 1.71x for Qwen3.5-0.8B on NPU and 1.93x for Qwen3.5-9B on GPU against its dense FlashAttention-2 baseline. Additional random-init stress rows reach 3.44x, indicating sparse-runtime headroom but not validated output quality. This first release separates oracle feasibility, distilled-indexer quality, and runtime headroom, leaving a fully matched quality-latency frontier to future work.

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.