# Test-Time Adaptation of Reasoning Strategies with Bayesian Nonparametric Memory

arXiv: https://arxiv.org/abs/2610.06516 · HTML: https://mlsanity.com/paper/2610.06516/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 41 of its 68 references that are in the map.
- First posted on arXiv 5 Oct 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 41)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
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- [CAMEL: Communicative Agents for "Mind" Exploration of Large Language Model Society](https://mlsanity.com/paper/2303.17760/) (2023)
- [MemGPT: Towards LLMs as Operating Systems](https://mlsanity.com/paper/2310.08560/) (2023)
- [A-MEM: Agentic Memory for LLM Agents](https://mlsanity.com/paper/2502.12110/) (2025)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [An Explanation of In-context Learning as Implicit Bayesian Inference](https://mlsanity.com/paper/2111.02080/) (2021)
- [Show Your Work: Scratchpads for Intermediate Computation with Language Models](https://mlsanity.com/paper/2112.00114/) (2021)
- [Generalization through Memorization: Nearest Neighbor Language Models](https://mlsanity.com/paper/1911.00172/) (2019)
- [Mem0: Building Production-Ready AI Agents with Scalable Long-Term Memory](https://mlsanity.com/paper/2504.19413/) (2025)
- [RAPTOR: Recursive Abstractive Processing for Tree-Organized Retrieval](https://mlsanity.com/paper/2401.18059/) (2024)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [Training Language Models to Self-Correct via Reinforcement Learning](https://mlsanity.com/paper/2409.12917/) (2024)
- [Agentic Context Engineering: Evolving Contexts for Self-Improving Language Models](https://mlsanity.com/paper/2510.04618/) (2025)
- [Reinforcement Learning via Self-Distillation](https://mlsanity.com/paper/2601.20802/) (2026)
- [Titans: Learning to Memorize at Test Time](https://mlsanity.com/paper/2501.00663/) (2024)
- [ReasoningBank: Scaling Agent Self-Evolving with Reasoning Memory](https://mlsanity.com/paper/2509.25140/) (2025)
- [Self-Distillation Enables Continual Learning](https://mlsanity.com/paper/2601.19897/) (2026)
- [From RAG to Memory: Non-Parametric Continual Learning for Large Language Models](https://mlsanity.com/paper/2502.14802/) (2025)
- [Dynamic Cheatsheet: Test-Time Learning with Adaptive Memory](https://mlsanity.com/paper/2504.07952/) (2025)
- [MemRL: Self-Evolving Agents via Runtime Reinforcement Learning on Episodic Memory](https://mlsanity.com/paper/2601.03192/) (2026)
- [Bayesian Low-rank Adaptation for Large Language Models](https://mlsanity.com/paper/2308.13111/) (2023)
- [Memp: Exploring Agent Procedural Memory](https://mlsanity.com/paper/2508.06433/) (2025)
- [Amortizing intractable inference in large language models](https://mlsanity.com/paper/2310.04363/) (2023)
- [The Surprising Effectiveness of Test-Time Training for Few-Shot Learning](https://mlsanity.com/paper/2411.07279/) (2024)
- [Test-Time Training on Nearest Neighbors for Large Language Models](https://mlsanity.com/paper/2305.18466/) (2023)
- [Metacognitive Capabilities of LLMs: An Exploration in Mathematical Problem Solving](https://mlsanity.com/paper/2405.12205/) (2024)
- [Self-Adapting Language Models](https://mlsanity.com/paper/2506.10943/) (2025)
- [From Isolated Conversations to Hierarchical Schemas: Dynamic Tree Memory Representation for LLMs](https://mlsanity.com/paper/2410.14052/) (2024)

## Abstract (arXiv)

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 textitBayesian 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.