# Words & Weights: Streamlining Multi-Turn Interactions via Co-Adaptation

arXiv: https://arxiv.org/abs/2603.01375 · HTML: https://mlsanity.com/paper/2603.01375/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in LLM preference optimization methods, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 25 of its 28 references that are in the map.
- First posted on arXiv 2 Mar 2026.

## Placed in

- LLM alignment / RLHF / preference optimisation / [LLM preference optimization methods](https://mlsanity.com/alignment/llm-preference-optimization-methods/)

## Builds on (most cited first, 25 of 25)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [UI-TARS: Pioneering Automated GUI Interaction with Native Agents](https://mlsanity.com/paper/2501.12326/) (2025)
- [LLMs Get Lost In Multi-Turn Conversation](https://mlsanity.com/paper/2505.06120/) (2025)
- [MINT: Evaluating LLMs in Multi-turn Interaction with Tools and Language Feedback](https://mlsanity.com/paper/2309.10691/) (2023)
- [TTRL: Test-Time Reinforcement Learning](https://mlsanity.com/paper/2504.16084/) (2025)
- [MultiChallenge: A Realistic Multi-Turn Conversation Evaluation Benchmark Challenging to Frontier LLMs](https://mlsanity.com/paper/2501.17399/) (2025)
- [A Survey on Recent Advances in LLM-Based Multi-turn Dialogue Systems](https://mlsanity.com/paper/2402.18013/) (2024)
- [Beyond Single-Turn: A Survey on Multi-Turn Interactions with Large Language Models](https://mlsanity.com/paper/2504.04717/) (2025)
- [Learning to Clarify: Multi-turn Conversations with Action-Based Contrastive Self-Training](https://mlsanity.com/paper/2406.00222/) (2024)
- [Feedback Descent: Open-Ended Text Optimization via Pairwise Comparison](https://mlsanity.com/paper/2511.07919/) (2025)
- [Test-Time Preference Optimization: On-the-Fly Alignment via Iterative Textual Feedback](https://mlsanity.com/paper/2501.12895/) (2025)
- [Linguistic Generalizability of Test-Time Scaling in Mathematical Reasoning](https://mlsanity.com/paper/2502.17407/) (2025)
- [Flexora: Flexible Low Rank Adaptation for Large Language Models](https://mlsanity.com/paper/2408.10774/) (2024)
- [Do LLMs Understand Ambiguity in Text? A Case Study in Open-world Question Answering](https://mlsanity.com/paper/2411.12395/) (2024)
- [Clarifying Ambiguities: on the Role of Ambiguity Types in Prompting Methods for Clarification Generation](https://mlsanity.com/paper/2504.12113/) (2025)
- [Design from Policies: Conservative Test-Time Adaptation for Offline Policy Optimization](https://mlsanity.com/paper/2306.14479/) (2023)
- [ReDit: Reward Dithering for Improved LLM Policy Optimization](https://mlsanity.com/paper/2506.18631/) (2025)
- [Test-Time Policy Adaptation for Enhanced Multi-Turn Interactions with LLMs](https://mlsanity.com/paper/2509.23166/) (2025)
- [Prompt and Parameter Co-Optimization for Large Language Models](https://mlsanity.com/paper/2509.24245/) (2025)

## Built on by (most cited first, 1 of 1)

- [OptiCom : A Unified Framework for State-Conditioned Composition in LLM-Driven Optimization](https://mlsanity.com/paper/2609.37221/) (2026)

## Abstract (arXiv)

Test-time policy adaptation for multi-turn interactions (T2PAM) is essential for aligning Large Language Models (LLMs) with dynamic user needs during inference time. However, existing paradigms commonly treat test-time adaptation as a single-axis problem, either purely refining instructions (Prompt Engineering) or only adjusting weights (Test-Time Training), ignoring that interaction failures stem from a coupled mix of ambiguity and incapacity. We argue that these two optimization paths are not merely additive but synergistic: semantic clarity acts as a pre-conditioner for effective parameter updates. To this end, we propose ROSA2, a framework that reformulates interaction as a joint optimization problem over the heterogeneous space of Words and Weights. By mathematically decomposing the error signal, ROSA2 utilizes textual gradients to rectify intent ambiguity and parameter updates to bridge capability gaps. Theoretically, we prove that this co-adaptation strictly reduces the required parameter shift for convergence. Empirically, ROSA2 outperforms state-of-the-art baselines by 30% on MATH while reducing interaction turns by 40%, demonstrating that refining the context unlocks the true potential of parameter updates.