Surfing the Activation Wave: Analyzing the Information and Geometry of LLM Hidden States for Speculative Decoding

Abstract: Decoder hidden states from different layers of LLMs often encode complementary information. However, existing speculative decoding methods typically rely on a small set of target-model layers chosen using fixed, position-based heuristics. Selecting an optimal subset of layers is inherently a combinatorial problem, making exhaustive evaluation infeasible even for moderately deep models. In this work, we present a principled framework for multi-layer hidden-state selection for speculative decoding based on two complementary criteria: informativeness, measured through matrix-entropy analysis, and diversity, quantified using centered kernel alignment (CKA). We investigate layer-wise Shannon entropy, aggregate entropy under hidden-state concatenation, and pairwise CKA dynamics across depth, revealing distinct geometric and informational compartments within decoder representations. Motivated by these findings, we propose entropy and CKA-based layer selection algorithms that favor hidden-state sets that are both highly informative and minimally redundant. As part of this framework, we introduce token-entropy filtering, which removes hidden states associated with low predictive-entropy tokens, thereby improving the quality of layer-selection statistics. In EAGLE3-style speculative decoding, our selected sets outperform fixed baseline choices, including the default $[2, N//2, N-3]$ rule, while providing a clearer explanation of why some defaults can remain competitive. Our results provide a practical recipe for multi-layer hidden-state selection for speculative decoding, insights into the geometry and information in LLM decoder states, and a foundation for extending similar analysis to related applications.