A Graph Signal Processing Perspective on Numerical Sequence Representations in LLM In-Context Learning

arXiv:2608.03015v1 Announce Type: new Abstract: Pretrained large language models (LLMs) have demonstrated in-context learning (ICL) capabilities for numerical inference over sequences serialized as text. Prior work has identified and characterized this form of numerical inference primarily through output-level evaluations such as prediction error. However, how numerical information is organized within LLM representations remains much less understood. To study this internal organization, we adopt a graph signal processing perspective in which attention induces a weighted graph over tokens, while token hidden states define signals on its nodes. Quantitative graph-spectral diagnostics and qualitative token-graph visualizations reveal that representations become more clearly differentiated by input dynamical complexity as context length increases. Simpler inputs produce attention-induced token graphs with stronger global connectivity and smoother, spectrally concentrated hidden-state signals, whereas more complex inputs produce more localized graphs and hidden-state signals with broader spectral support and greater high-frequency energy. Together, these findings point to systematic, context-dependent internal signatures associated with numerical ICL that are conserved across model families.

Abstract:Pretrained large language models (LLMs) have demonstrated in-context learning (ICL) capabilities for numerical inference over sequences serialized as text. Prior work has identified and characterized this form of numerical inference primarily through output-level evaluations such as prediction error. However, how numerical information is organized within LLM representations remains much less understood. To study this internal organization, we adopt a graph signal processing perspective in which attention induces a weighted graph over tokens, while token hidden states define signals on its nodes. Quantitative graph-spectral diagnostics and qualitative token-graph visualizations reveal that representations become more clearly differentiated by input dynamical complexity as context length increases. Simpler inputs produce attention-induced token graphs with stronger global connectivity and smoother, spectrally concentrated hidden-state signals, whereas more complex inputs produce more localized graphs and hidden-state signals with broader spectral support and greater high-frequency energy. Together, these findings point to systematic, context-dependent internal signatures associated with numerical ICL that are conserved across model families.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Signal Processing (eess.SP)

arXiv:2608.03015 [cs.LG]

(or arXiv:2608.03015v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2608.03015 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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A Graph Signal Processing Perspective on Numerical Sequence Representations in LLM In-Context Learning

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