Zhimin Gao, Meibo Hu, Jiamian Wang, Zhiqiang Tao, Pichao Wang
Reasoning models are trained to produce correct answers, yet selective deployment requires ranking which answers to accept or defer, and outcome-reward training does not directly optimize the post-rationale distribution used for that decision. We identify two mismatches: expected correctness is mode-seeking rather than distribution-eliciting, and scoring an average across rationales rewards disagreement unavailable to a single-rationale decision. We introduce Post-Rationale Distribution Optimization (PRDO), which applies a proper score to the answer distribution after each sampled rationale, without target rationales or separate confidence labels. Across four 0.6--3.8-billion-parameter models on MMLU-Pro, PRDO improves Brier score, error ranking and secondary accuracy relative to budget-matched, temperature-scaled GRPO. At 20\% realized error, oracle coverage rises by \npj{Q3a_vs_grpo.qwen3-0.6b.mp.oracle_cov@0.2.ppabs}--\npj{Q3a_vs_grpo.phi-4-mini.mp.oracle_cov@0.2.ppabs} percentage points, and ranking gains transfer to unseen tasks. Matched controls identify proper, per-rationale scoring as the active design choices, while verification tasks show the boundary: better selective ranking can coexist with lower full-coverage accuracy. Code is available at https://github.com/ZimmyGao/openjev-rlcd
Despite their remarkable success, neural networks remain largely black boxes, and the mechanisms underlying their behavior are still poorly understood. Nine nanoGPT experiments established training-learning-inference relations: realized updates elicit state-dependent finite-amplitude responses; learning persistently reorganizes distributed functional support, with target-specific readout-boundary crossings determining capability transitions; inference recruits learned support without changing the learned state. Factors identified in the fifth experiment yielded a direct predictor of post-update capability transitions, achieving 91.43% accuracy and 91.49% four-way macro recall across 5,088 targets. We tested these relations and prediction across five additional neural architectures. In a seventh system, concentrated correct feedback eroded previously mastered skills; rebalanced feedback restored their accuracy from 70.31% to 99.48%. Linking inference consequences to subsequent training closes these relations into unified training-learning-inference-reinforcement dynamics.