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, which achieves lower position-wise negative log-likelihood (NLL) than dense attention in the authors' comparison.
Abstract
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.
KV-cache compression is often justified by attention maps with a few large weights. This is incomplete: large weights may not contain most of the mass, omitted values can cancel, and preserving the attention output may not preserve the task. We separate these questions. Global score gaps -- not threshold counts -- determine how many tokens are needed to retain a target mass. For a realized row, the weighted sum of omitted values is the exact missing statistic. A controlled retrieval--aggregation model explains when truncation helps and when it hurts. These results motivate CertKV, a training-free compressor that reserves one tail-summary slot per head and allocates the rest by value dispersion. Under matched budgets, CertKV 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. Compressibility depends on the mass, values, future queries, and task -- not on a sparse-looking map alone.
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
The results establish BF1 as a reproducible sparse operator and selective retrofit primitive with real long-context systems value, and evaluates numerical correctness, selected-interaction scaling, kernel performance, partial-model inference, and matched next-token language modeling.
Data-adaptive sparse attention masks substantially outperform fixed patterns (e.g., BigBird and Longformer) and can even exceed dense attention on long sequences. Existing adaptive approaches---including SBM-Transformer, Dynamic Mask Attention, and NSA---typically require additional learnable parameters, custom gradient estimators, or specialized CUDA kernels. We show that classical data compression provides an effective masking signal with \textbf{no additional parameters}. By computing per-block gzip compression ratios, we identify non-redundant content blocks and route long-range attention selectively through them. Intuitively, blocks that gzip cannot compress contain information not predictable from local repetition, making them natural long-range attention targets. Because the compression profile is input-dependent, the resulting sparse mask adapts dynamically to content without learned parameters, auxiliary losses, or custom kernels. On PG-19 byte-level language modeling at 92M parameters with 8K context, our method achieves 1.71 bits-per-byte (BPB), outperforming dense attention (2.89), BigBird (2.34), Longformer (3.21), and a reimplemented SBM-Transformer (3.38)---the only learned-mask baseline---by up to 1.67 BPB while adding no parameters. The advantage grows with sequence length, with the gap over BigBird widening from 0.05 BPB at 4K context to 0.63 BPB at 8K, while convergence is 3.3$\times$ faster.
CoSA is proposed, a two-stage training-free Sparse Attention under proxy-kernel CO-design, which couples a Kernel-Aware Proxy (KAP) with an Ordered-Skipping Kernel (OSK) and achieves a 4.93% attention speedup and reduces end-to-end Time-to-First-Token by 2.53% with negligible performance degradation.
Top-k sparse attention makes long-context LLM decoding cheap to compute: each step reads only a few thousand selected KV entries rather than the full context. Serving systems, however, typically keep the entire KV cache in GPU HBM so that every position stays selectable, so a request's memory bill still grows with its full context length--decoding hits a capacity wall long before it runs out of compute, and a context whose KV cache exceeds HBM cannot be served at all. We present HiSparse, an exact, indexer-agnostic hierarchical KV cache for sparse-attention serving. HiSparse keeps each request's full KV history in host memory and bounds its decode footprint with a small, fixed-size GPU cache; a fused CUDA kernel resolves each layer's selections--hit detection, LRU replacement, and host-to-device fetches--inside the decode CUDA graph; and, for models that share selections across layers, exact layer-wise prefetching hides roughly half of the remaining miss overhead. Because only KV placement changes, model outputs are unchanged. HiSparse is merged into upstream SGLang and evaluated across three sparse-attention families (DSA, NSA, and Quest) on H200, B200, and GH200 platforms: it improves peak generation throughput by up to 4.7x on long-context workloads while preserving comparable per-token latency and reducing time-to-first-token at high load--and a no-IO oracle shows the resolution mechanism itself adds no measurable per-token cost, leaving host-device IO as the only price of bounded residency.
Zhiqiang Xie, Zhangheng Huang, Ting-Jun Huang et al.· 0 citations
