COBS: Cumulant Order Block Sparse Attention

Block sparse attention is a hardware friendly way to alleviate the key-value (KV) cache read bottleneck in large language models (LLMs). However, it is not prevalent among leading open-weight LLMs, which rely instead on dense attention or fine-grained selection, thereby motivating our analysis. We study DeepSeek's Native Sparse Attention (NSA) as a representative method, whose three-branch design lets us isolate block selection, the most challenging and consequential stage. We formalize selection and reduce it to ranking blocks by a single quantity, the attention mass: the sum of a block's attention scores. We show that if selection retrieves the blocks with the largest attention mass, block sparse attention can match the quality of dense attention. However, computing the exact attention mass requires reading every key, so the problem of block selection ultimately reduces to approximating this mass from a compact summary instead of the full keys. Via a cumulant expansion, we show why existing methods falter: their selection strategies attempt to estimate the attention mass, but are confined to a first-order approximation. Therefore, we propose COBS (Cumulant Order Block Sparse Attention), an attention method that builds on NSA, incorporating a novel selector that stores a compressed second-order statistic per block. On the 32k RULER long-context retrieval benchmark, COBS raises the NSA baseline's mean score from 0.2999 to 0.8195, approaching dense attention at 0.9040 and closing about 86% of the gap, while using only 1.21x the KV cache read traffic of the NSA baseline and 15.15x less read traffic than dense. The same model preserves short-context behavior and attains lower position-wise negative log-likelihood (NLL) than dense attention in our comparison.

SPIRe: Boosting LLM Inference Throughput with Speculative Decoding

Speculative decoding (SD) has been shown to reduce the latency of autoregressive decoding (AD) by 2-3x for small batch sizes. However, increasing throughput and therefore reducing the cost per token requires decoding with large batch sizes. Recent work shows that SD can accelerate decoding with large batch sizes too if the context is sufficiently long and the draft model's KV cache is sparse. We introduce SPIRe, a draft model that combines static sparse attention, pruned initialization, and feedback memory to increase the modeled throughput of speculative decoding by over 100% compared to speculation with a much smaller draft model and by over 35% compared to the strong baseline of sparse self-speculation. Our approach is particularly effective when context lengths vary significantly across requests.