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

Miaobo Hu, Shuhao Hu, Xiaobo Guo, Xin Wang, Bokun Wang +3

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 $0.6476\!\pm\!0.0139$ 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…