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This research introduces a "Bayesian Cheatsheet" using Hierarchical Dirichlet Process Gaussian Mixture Models to enable efficient test-time adaptation in large language models. By structuring reasoning strategies into learnable clusters, the method allows models to dynamically retrieve and update behaviors during inference, significantly reducing generation costs on complex reasoning benchmarks like AIME and Omni-MATH. The findings underscore the potential of Bayesian nonparametric methods for creating adaptive memory modules that improve metacognitive capabilities without requiring full retraining.
Test-Time Adaptation of Reasoning Strategies with Bayesian Nonparametric Memory
arXiv:2610.06516v1 Announce Type: new Abstract: While modern large language models (LLMs) have been trained to reason through verbalized chains-of-thought, the generation cost grows substantially due to suboptimal paths to reach the final answer. Furthermore, as new insights are discovered while observing various input queries (e.g. through self-reflection), limited mechanisms exist for carrying forward these findings to be applied to subsequent problems. One can view the list of such strategies or behaviors as a growing cheatsheet, with elements retrieved from this memory module at inference-time. In this work, we consider structured cheatsheets, with learned clusters of behaviors. We introduce a Hierarchical Dirichlet Process Gaussian Mixture Model (HDP-GMM) over behavior embeddings, which shares components across domains while allowing domain-specific mixing weights, and uses the posterior predictive to retrieve relevant behaviors for a query; we call this a $\textit{Bayesian Cheatsheet}$. This mechanism allows for cheap adaptation in an online test-time training (TTT) setting, softly updating the mixture's sufficient statistics following each sample and enabling the creation of new components when the synthesized behaviors are sufficiently novel. We demonstrate that Bayesian Cheatsheet achieves clear performance gains relative to existing memory modules across reasoning benchmarks such as AIME'25, Omni-MATH, and PhysReason, even in the cold-start setting. We show that the Bayesian Cheatsheet is an adaptively reorganizing memory module, as behaviors can be re-assigned to components through a single step of collapsed Gibbs sampling. Our findings highlight the value of Bayesian-inspired memory modules for effective test-time adaptation and the role of structure in metacognitive reasoning.
Abstract:While modern large language models (LLMs) have been trained to reason through verbalized chains-of-thought, the generation cost grows substantially due to suboptimal paths to reach the final answer. Furthermore, as new insights are discovered while observing various input queries (e.g. through self-reflection), limited mechanisms exist for carrying forward these findings to be applied to subsequent problems. One can view the list of such strategies or behaviors as a growing cheatsheet, with elements retrieved from this memory module at inference-time. In this work, we consider structured cheatsheets, with learned clusters of behaviors. We introduce a Hierarchical Dirichlet Process Gaussian Mixture Model (HDP-GMM) over behavior embeddings, which shares components across domains while allowing domain-specific mixing weights, and uses the posterior predictive to retrieve relevant behaviors for a query; we call this a $\textit{Bayesian Cheatsheet}$. This mechanism allows for cheap adaptation in an online test-time training (TTT) setting, softly updating the mixture's sufficient statistics following each sample and enabling the creation of new components when the synthesized behaviors are sufficiently novel. We demonstrate that Bayesian Cheatsheet achieves clear performance gains relative to existing memory modules across reasoning benchmarks such as AIME'25, Omni-MATH, and PhysReason, even in the cold-start setting. We show that the Bayesian Cheatsheet is an adaptively reorganizing memory module, as behaviors can be re-assigned to components through a single step of collapsed Gibbs sampling. Our findings highlight the value of Bayesian-inspired memory modules for effective test-time adaptation and the role of structure in metacognitive reasoning.
Computation and Language (cs.CL)
arXiv:2610.06516 [cs.CL]
(or arXiv:2610.06516v1 [cs.CL] for this version)
https://doi.org/10.48550/arXiv.2610.06516 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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