# Sigmoid Attention as a Better Substrate for Learned KV Cache Eviction

arXiv: https://arxiv.org/abs/2608.23296 · HTML: https://mlsanity.com/paper/2608.23296/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in KV cache optimization, one of 12 directions in Efficient LLM inference and serving.
- Builds on 16 of its 19 references that are in the map.
- First posted on arXiv 24 Aug 2026.

## Placed in

- Efficient LLM inference and serving / [KV cache optimization](https://mlsanity.com/inference/kv-cache-optimization/)

## Builds on (most cited first, 16 of 16)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [H2O: Heavy-Hitter Oracle for Efficient Generative Inference of Large Language Models](https://mlsanity.com/paper/2306.14048/) (2023)
- [DuoAttention: Efficient Long-Context LLM Inference with Retrieval and Streaming Heads](https://mlsanity.com/paper/2410.10819/) (2024)
- [When Attention Sink Emerges in Language Models: An Empirical View](https://mlsanity.com/paper/2410.10781/) (2024)
- [Dynamic Memory Compression: Retrofitting LLMs for Accelerated Inference](https://mlsanity.com/paper/2403.09636/) (2024)
- [Theory, Analysis, and Best Practices for Sigmoid Self-Attention](https://mlsanity.com/paper/2409.04431/) (2024)
- [KeyDiff: Key Similarity-Based KV Cache Eviction for Long-Context LLM Inference in Resource-Constrained Environments](https://mlsanity.com/paper/2504.15364/) (2025)
- [D2O: Dynamic Discriminative Operations for Efficient Long-Context Inference of Large Language Models](https://mlsanity.com/paper/2406.13035/) (2024)
- [KV-Distill: Nearly Lossless Learnable Context Compression for LLMs](https://mlsanity.com/paper/2503.10337/) (2025)
- [Cache What Lasts: Token Retention for Memory-Bounded KV Cache in LLMs](https://mlsanity.com/paper/2512.03324/) (2025)
- [Fast KVzip: Efficient and Accurate LLM Inference with Gated KV Eviction](https://mlsanity.com/paper/2601.17668/) (2026)
- [In-context KV-Cache Eviction for LLMs via Attention-Gate](https://mlsanity.com/paper/2410.12876/) (2024)

## Abstract (arXiv)

Learned KV-cache eviction often faces a soft-to-hard mismatch: during training, differentiable gates typically attenuate token contributions, whereas inference saves memory only when KV entries are physically removed. We ask whether the attention substrate affects this soft-to-hard transition. Using GPT-2-scale Transformers trained on OpenWebText, we run a controlled 2×2×2 comparison over attention type, learned gating, and positional encoding. Although sigmoid attention is worse as a dense language model, learned hard eviction changes the useful operating points: sigmoid-gated models delete KV entries with negligible PPL change relative to their own no-eviction references. Under a matched live-cache protocol on the same dense backbones, learned sigmoid gates obtain lower PPL than our H2O and KeyDiff implementations, whereas softmax gates do not uniformly beat these post-hoc methods. The results suggest that attention normalization can substantially affect whether a training-time soft gate transfers cleanly to hard KV deletion.