Surfing the Activation Wave: Analyzing the Information and Geometry of LLM Hidden States for Speculative Decoding
Quick Answer
This study proposes a framework for selecting hidden states in large language models (LLMs) for speculative decoding, emphasizing layer informativeness and diversity.
Quick Take
By employing matrix-entropy analysis and centered kernel alignment (CKA), the authors introduce algorithms that enhance predictive quality, outperforming traditional layer selection methods. The findings offer insights into the geometry of decoder states and pave the way for broader applications in AI.
Key Points
- Introduces a framework for multi-layer hidden-state selection in LLMs.
- Utilizes matrix-entropy analysis and centered kernel alignment for layer selection.
- Proposed algorithms outperform fixed baseline choices in speculative decoding.
- Implements token-entropy filtering to enhance layer-selection quality.
- Results provide insights into the geometry of LLM decoder representations.
DeepSignal Analysis
What happened
This study introduces a framework for selecting hidden states in large language models (LLMs) for speculative decoding, focusing on layer informativeness and diversity. The authors utilize matrix-entropy analysis and centered kernel alignment (CKA) to develop algorithms that improve predictive quality compared to traditional methods.
Key evidence
- The study reveals that decoder hidden states from different layers of LLMs encode complementary information, which is often overlooked in existing methods.
- The proposed framework employs matrix-entropy analysis and CKA to assess layer informativeness and diversity, addressing the combinatorial nature of layer selection.
- The authors demonstrate that their layer selection algorithms outperform fixed baseline choices in EAGLE3-style speculative decoding, enhancing the quality of predictions.
Why it matters
The findings contribute to a deeper understanding of the geometry and information contained within LLM decoder states. By improving layer selection for speculative decoding, the research has implications for enhancing the performance of LLMs in various applications, potentially leading to more efficient and effective AI systems.
Paper Resources
📖 Reader Mode
~2 min readAbstract:Decoder hidden states from different layers of large language models (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.
| Comments: | Accepted at multiple Neurips Workshop: Axiom, GDDL, and PriGM |
| Subjects: | Computation and Language (cs.CL); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2610.12939 [cs.CL] |
| (or arXiv:2610.12939v1 [cs.CL] for this version) | |
| https://doi.org/10.48550/arXiv.2610.12939 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Raghavv Goel Mr. [view email]
[v1]
Fri, 9 Oct 2026 03:38:26 UTC (1,550 KB)
— Originally published at arxiv.org
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