Sigmoid Attention as a Better Substrate for Learned KV Cache Eviction

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 $2\times2\times2$ 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 H$_2$O 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.