# FAER: Auditable Utility-Aligned Trajectory Replay for Language Model Post-Training

arXiv: https://arxiv.org/abs/2610.00385 · HTML: https://mlsanity.com/paper/2610.00385/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 39 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Builds on (most cited first, 30 of 31)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Voyager: An Open-Ended Embodied Agent with Large Language Models](https://mlsanity.com/paper/2305.16291/) (2023)
- [Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems](https://mlsanity.com/paper/2005.01643/) (2020)
- [Conservative Q-Learning for Offline Reinforcement Learning](https://mlsanity.com/paper/2006.04779/) (2020)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Decision Transformer: Reinforcement Learning via Sequence Modeling](https://mlsanity.com/paper/2106.01345/) (2021)
- [D4RL: Datasets for Deep Data-Driven Reinforcement Learning](https://mlsanity.com/paper/2004.07219/) (2020)
- [Datasheets for Datasets](https://mlsanity.com/paper/1803.09010/) (2018)
- [Offline Reinforcement Learning with Implicit Q-Learning](https://mlsanity.com/paper/2110.06169/) (2021)
- [Prioritized Experience Replay](https://mlsanity.com/paper/1511.05952/) (2015)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Model Cards for Model Reporting](https://mlsanity.com/paper/1810.03993/) (2018)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [IMPALA: Scalable Distributed Deep-RL with Importance Weighted Actor-Learner Architectures](https://mlsanity.com/paper/1802.01561/) (2018)
- [Deep Reinforcement Learning at the Edge of the Statistical Precipice](https://mlsanity.com/paper/2108.13264/) (2021)
- [Deep Reinforcement Learning that Matters](https://mlsanity.com/paper/1709.06560/) (2017)
- [Improving Reproducibility in Machine Learning Research (A Report from the NeurIPS 2019 Reproducibility Program)](https://mlsanity.com/paper/2003.12206/) (2020)
- [ProcessBench: Identifying Process Errors in Mathematical Reasoning](https://mlsanity.com/paper/2412.06559/) (2024)
- [Revisiting Fundamentals of Experience Replay](https://mlsanity.com/paper/2007.06700/) (2020)

## Abstract (arXiv)

Replay selectors often rank cached trajectories by format feedback, confidence, freshness, or response length, although cache-level correctness and downstream learner utility are distinct objectives. We formalize this selection-to-learning gap and introduce FAER as an auditable full-trajectory replay framework. Its training-free fixed selector is a protocol baseline; FAER-UTILITY is the learner-aware selector fitted on disjoint calibration blocks. The normalized gradient alignment is reported as a baseline, while a disposable optimizer-aware virtual update supplies a magnitude-aware utility surface. The audit contract freezes observed fields and replay traces before evaluation labels are joined. On GSM8K with Qwen2.5-1.5B-Instruct, the matched learner study reports quality 0.6329 for the fixed selector, compared with 0.5482 for uniform and 0.6037 for format-feedback under 128 updates. Metadata-only cross-fitted calibration reaches 0.6476!±!0.0139 over eight seeds (median 0.6481; paired 95% interval [+0.079,+0.122]) at 63,276 target-run tokens; its recorded full cost is 189,642 tokens and 3.48 GPU-hours including calibration. The completed FAER-UTILITY row reaches 0.6624 at 62,844 target-run tokens and 4.26 GPU-hours. Format-feedback selects records with correctness 0.6953, compared with 0.3594 for the fixed selector, despite the different downstream ranking. The completed comparison surfaces report the learner-aware ablation, same-seed gap, policy-optimization rows, and strict zero-shot transfer.