Sigmoid Attention as a Better Substrate for Learned KV Cache Eviction

Hybrid language models interleave Gated DeltaNet (GDN) layers, whose recurrent memory has a fixed size, with full-attention layers, whose key-value (KV) cache grows with the context and dominates serving memory. In this paper, we ask whether the recurrent memory already knows what the attention memory will need. We first show that which GDN heads of Qwen3.8-27B keep long memories is fixed by the weights rather than by the document. Next, we define the future utility of a KV entry by how much removing it changes the attention output over the model's own continuations, and find that the write gate, decay and write magnitude that GDN layers emit during prefill anticipate this utility before any query is seen. Because the relation is spread across many GDN heads and layers, and a linear map recovers its trend but less of its high-utility tail than a nonlinear one, we propose GateSight, which learns it with lightweight per-head multilayer perceptrons that read these signals and no attention score. Their predicted utility decides which entries each attention layer keeps, and how much each layer keeps is set by the model's native attention output gate, whose mean differs by more than an order of magnitude across layers. Finally, at serving time, GateSight scores the cache once after prefill and physically releases discarded KV entries. Experimental results on SCBench and RULER-4096 with Qwen3.8-27B and, with the same recipe, the sparse-attention model Qwen3.8-Flash-Next, up to the 262K-token limit of the models, show that with a tenth of the attention KV cache, GateSight is the most accurate of five query-agnostic methods on three of the four model-benchmark pairs and leads KVzip on all four, by 9.5 to 47.2 points. Notably, it scores a full-length context with negligible overhead relative to prefill.

Modern LLMs with QK-normalization, gated attention, learned attention sinks, or logit softcapping exhibit weaker persistent attention sinks, on which existing KV cache eviction methods primarily rely. We observe that across these models, weaker sinks co-occur with greater value-vector dispersion relative to key-vector dispersion. Motivated by this value-side dispersion, we present ValueDiff, a value-geometric eviction that ranks tokens by the L2 deviation of their value vectors from the cache mean. The same score arises as the minimal-disturbance eviction under a max-entropy assumption about future attention. We evaluate under fixed cache budgets, with eviction at every block boundary during prefill and at every decoding step during generation. On RULER at a tight 2k token budget, ValueDiff retains 88-99% of dense across seven sink-suppressed models (best on 6 out of 7). On LongBench at the 4k budget, ValueDiff averages 92% retention across sink-suppressed models versus 83% for the strongest prior baseline. On MATH-500, ValueDiff is the strongest non-dense method on every sink-suppressed model tested at the 25% cache budget, outperforming prior methods by up to ~20 points on gated-attention models. Across all three benchmarks, value geometry emerges as the more reliable query-invariant eviction signal for sink-suppressed models.

Key-value (KV) cache eviction is essential for scaling long-context inference in Large Language Models. However, existing policies predominantly rely on empirical heuristics, lacking a rigorous characterization of token utility under the inherently nonlinear softmax attention mechanism. In this work, we rethink KV cache eviction through the lens of local information geometry, modeling the attention process as a nonlinear Gaussian communication channel. By performing a first-order Taylor expansion of the attention mapping, we derive the Jacobian Information Capacity, a novel objective that explicitly captures query relevance, softmax sensitivity, and structural diversity. Guided by this theory, we introduce Jacap, a capacity-aware eviction method that utilizes softmax-aware importance weighting and statistical leverage scores for subset selection. Extensive experiments across diverse architectures and benchmarks demonstrate that Jacap delivers superior performance in most scenarios, particularly in high-compression regimes.