# Representation-Aligned Auxiliary Supervision for Language Model Adaptation

arXiv: https://arxiv.org/abs/2610.04098 · HTML: https://mlsanity.com/paper/2610.04098/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 20 of its 24 references that are in the map.
- First posted on arXiv 2 Oct 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 20 of 20)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [Mastering Diverse Domains through World Models](https://mlsanity.com/paper/2301.04104/) (2023)
- [Recurrent World Models Facilitate Policy Evolution](https://mlsanity.com/paper/1809.01999/) (2018)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [Reinforcement Learning with Unsupervised Auxiliary Tasks](https://mlsanity.com/paper/1611.05397/) (2016)
- [Chain of Code: Reasoning with a Language Model-Augmented Code Emulator](https://mlsanity.com/paper/2312.04474/) (2023)
- [ChessGPT: Bridging Policy Learning and Language Modeling](https://mlsanity.com/paper/2306.09200/) (2023)
- [Chess as a Testbed for Language Model State Tracking](https://mlsanity.com/paper/2102.13249/) (2021)
- [Amortized Planning with Large-Scale Transformers: A Case Study on Chess](https://mlsanity.com/paper/2402.04494/) (2024)
- [Mastering Board Games by External and Internal Planning with Language Models](https://mlsanity.com/paper/2412.12119/) (2024)
- [Unlocking Reasoning Potential in Large Langauge Models by Scaling Code-form Planning](https://mlsanity.com/paper/2409.12452/) (2024)
- [Code Prompting Elicits Conditional Reasoning Abilities in Text+Code LLMs](https://mlsanity.com/paper/2401.10065/) (2024)
- [Explore the Reasoning Capability of LLMs in the Chess Testbed](https://mlsanity.com/paper/2411.06655/) (2024)
- [Learning to Reason via Program Generation, Emulation, and Search](https://mlsanity.com/paper/2405.16337/) (2024)
- [Can Large Language Models Develop Strategic Reasoning? Post-training Insights from Learning Chess](https://mlsanity.com/paper/2507.00726/) (2025)
- [Bridging the Gap between Expert and Language Models: Concept-guided Chess Commentary Generation and Evaluation](https://mlsanity.com/paper/2410.20811/) (2024)
- [DeFine: Decision-Making with Analogical Reasoning over Factor Profiles](https://mlsanity.com/paper/2410.01772/) (2024)
- [Correct Answers from Sound Reasoning: Verifiable Process Supervision for Language Models](https://mlsanity.com/paper/2605.12519/) (2026)

## Abstract (arXiv)

Language models exhibit strong reasoning capabilities, yet adapting them to structured domains remains challenging and can yield inconsistent outcomes. We identify representation compatibility, the extent to which a model effectively processes a representation for a structured task, as a key factor in adaptation. We study this in chess, which provides a controlled testbed with precise semantics, computable optimal actions, and multiple state representations, including a symbolic encoding (FEN) and a spatial format (ASCII). We find that models often process semantically equivalent inputs substantially differently, affecting both learning and generalization. Building on this observation, we propose representation-aligned auxiliary supervision, which uses environment-derived tasks expressed in compatible representations to improve adaptation to structured domains. Across models and representations, auxiliary supervision consistently improves optimal-move prediction relative to target-only training under identical target data. Tasks that expose environment dynamics provide larger and most consistent gains than surface-level or static supervision, while remaining competitive with substantially increasing the amount of target-task data. Moreover, ASCII-trained models transfer more effectively to FEN than FEN-trained models do to ASCII, even surpassing the FEN target-only baseline on FEN evaluation. The gains also extend beyond optimal-move prediction to open-ended, factually grounded commentary generation. Overall, our results show that auxiliary supervision in model-compatible representations can enable effective adaptation in structured domains.