LiteTopK: Exploiting the Curse of Dimensionality for a Fused Indexer-TopK Kernel in Long-Context Sparse Attention

Top-$K$ sparse attention reduces the cost of Softmax and value aggregation by attending to only a small subset of key--value (KV) entries. However, identifying this subset still requires scoring the current query against the full KV cache and performing global Top-$K$ selection, leaving selector cost linear in context length and limiting the practical efficiency of sparse attention for long-context decoding. In this paper, we introduce ReTopK, a training-free method that accelerates dynamic Top-$K$ attention by reusing historical retrieval decisions. ReTopK builds on the observation that similar queries often attend to overlapping supports and that partially overlapping supports can still preserve most of the Exact Top-$K$ attention mass. For each attention head, it maintains a bounded cache of historical query--support pairs, retrieves the most similar cached queries for each new query, unions their stored supports with a recent window, and reranks only the resulting compact candidate set using exact current-query scores. A similarity-based fallback invokes full-history Exact Top-$K$ when reuse is unreliable, while periodic exact refreshes limit cache drift. ReTopK retains the complete KV cache and reuses only selected indices, rather than historical scores, attention weights, or outputs. Across 16K--128K contexts, ReTopK achieves the lowest PG19 perplexity and the highest NIAH and LongBench scores among the evaluated approximate methods. At 128K with $K=512$, ReTopK incurs only a 0.50% perplexity increase over Exact Top-$K$ while accelerating attention computation by $3.07\times$.

DeepSeek-V3.2 and V4 introduce Compressed Sparse Attention (CSA): a lightning indexer (a learned scoring projection over compressed keys) scores them, the top-k are selected per query, and a sparse attention kernel reads only those. Public CSA implementations materialize a [B, S, H_I, T] FP32 score tensor before the top-k reduction. With H_I=64 indexer heads and the V4-Flash compression ratio m=4, that intermediate is 256 GB at sequence length S=65,536, exceeding any single-GPU high-bandwidth-memory (HBM) budget. We present StreamIndex, a Triton implementation of the CSA pipeline whose central component is a chunked partition-merge top-k driver that never materializes the full intermediate. On synthetic-but-realistic V4-shaped inputs at the indexer-step (layer) level on a single NVIDIA H200, the materialize path runs out of memory (OOMs) at S=65,536 with V4-Flash dimensions; StreamIndex runs the same indexer to S=1,048,576 with 6.21 GB peak HBM, a 32x regime extension. Set-overlap recall against the materialize ground truth is bit-exact at small S where both fit; across three 5-point design-space sweeps (chunk size, key-tile size, top-k), mean recall rounds to 1.0000 with min recall at least 0.9980 in every cell. The chunked driver composes with TileLang's pipelined attention kernel: at S=262,144 with V4-Flash dimensions, the materialize indexer paired with TileLang attention OOMs while the chunked indexer paired with the same attention runs in 1.97 s at 18.56 GB peak. Our contribution targets the indexer step; we make no claim of a faster attention kernel or of real-checkpoint end-to-end behavior. Code: https://github.com/RightNow-AI/StreamIndex.

Sparse attention improves LLM inference efficiency by selecting a subset of key-value entries, but at the cost of potential accuracy degradation. In particular, omitting critical KV entries can induce substantial errors in model outputs. Existing methods typically operate under fixed or adaptive token budgets and provide empirical robustness or partial theoretical guarantees, yet they do not ensure zero false negatives in decoding steps, particularly since the set of relevant tokens is both query- and step-dependent. Our empirical observations confirm that missing even one critical key can lead to sharp error spikes, especially in long reasoning tasks where the set of important tokens varies throughout decoding. This observation motivates the need for indexing methods that dynamically adapt to these variations across decoding steps while guaranteeing a full recall of the relevant keys above a certain threshold. We address this challenge by reformulating sparse attention as the halfspace range searching problem. However, existing range searching indices are not suitable for modern LLM inference due to their computational and implementation overheads. To overcome this, we introduce Louver, a novel index structure tailored for efficient KV cache retrieval. Louver (i) guarantees zero false negatives with respect to a specified threshold in both theory and practice, (ii) is lightweight to integrate into existing LLM pipelines, and (iii) incorporates hardware-aware optimizations for both CPU and GPU executions. Our experiments demonstrate that Louver outperforms prior sparse attention methods in both accuracy and runtime, and is faster than highly optimized dense attentions such as FlashAttention. These results highlight that recall guarantees are a critical and overlooked dimension of sparse attention, and open a new direction for building theoretically grounded, efficient KV cache indices.