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Hallucinations remain a major obstacle to deploying large language models (LLMs) in knowledge-intensive settings, where generated responses must be faithfully grounded in provided evidence. Reinforcement learning (RL) is a promising direction for hallucination mitigation, but response-level faithfulness rewards suffer from a granularity mismatch: localized hallucinations can cause supported content to receive spurious penalties. Although recent work introduces fine-grained feedback such as claim-level verification and token-level rewards, unbalanced credit assignment can still induce length, verbosity, or optimization-noise biases. We propose BALTO, a Balanced Token-level Policy Optimization framework for hallucination mitigation. BALTO extracts checkable factual claims, verifies them against the reference context, and projects claim-level judgments to token-level labels. A balanced token-level credit assignment mechanism is introduced into the framework. This design redistributes probability mass from unsupported content toward faithful content, rather than suppressing the entire response. We systematically analyze the limitations of response-level rewards from a theoretical standpoint, and prove BALTO's advantages in training stability and optimization efficiency for hallucination mitigation. Experiments on ConFiQA, RAGTruth, and FinLLM-Eval show that BALTO achieves the highest faithfulness across all six model--benchmark settings and consistently outperforms existing post-training baselines in Q-Score, demonstrating a stronger faithfulness--informativeness trade-off. The code is released at https://github.com/NingLi670/BALTO.

Low-precision pretraining is usually judged by validation loss. We ask whether matching loss also means learning rare facts as efficiently. We train transformers from scratch with emulated 4-bit matrix multiplications on synthetic biographies with controlled exposure counts, on their own and mixed into web text. NVFP4 needs 1.32$\times$ and 1.52$\times$ as many exposures as BF16 to match its recall while validation loss differs by only 0.5% and 2%, and 1.26$\times$ and 1.30$\times$ when both models are evaluated with BF16 matrix multiplications. Under our primary readout, the exposure cost is about 1.2$\times$ at matched loss. Zero-mean gradient noise reproduces the cost of quantizing only the backward pass, which barely moves the loss. In a controlled experiment at twice the NVFP4 error, noise fed only to Adam's second-moment estimate acts like a lower learning rate and its cost fades, whereas noise in the update lowers its signal-to-noise ratio and carries about two thirds of the cost through the end of training. Raising the learning rate to offset the smaller average step does not recover the cost, either for this noise or for NVFP4. Gradient statistics of BF16 checkpoints rank the costs of formats, partial quantizations and noise controls without fitting (Spearman 0.96). We suggest measuring rare-fact acquisition alongside loss when evaluating low-precision recipes.

Reinforcement learning is now the mainstream paradigm for training LLMs on agentic tasks, yet standard practice keeps only the best-validation checkpoint and discards the rest. We show that this is lossy: in GRPO training of LLM agents, the best-validation checkpoint fails on problems that earlier checkpoints from the same run had already solved, and the union of problems solved across checkpoints far exceeds any single one. The discarded checkpoints thus form a teacher pool obtained at no additional training cost, which on-policy distillation (OPD) can mine to recover the lost coverage. Mining this pool raises two challenges: i) which checkpoint to distill from, as no checkpoint dominates the others and complementarity to the student is problem-specific; ii) where to trust it, as even a well-chosen teacher is only locally superior, so indiscriminate distillation overwrites behavior the student has already mastered. We propose Agentic-OPD, which treats the best-validation checkpoint as the student and all saved checkpoints as frozen teacher candidates, using the student's evolving capability gaps to guide both teacher selection and supervision filtering: the HCN policy (Highest Coverage Next) dynamically selects teachers by weighted coverage of the student's unsolved problems, while the LAD module (Locality-Aware Distillation) confines transfer to failed student rollouts on problems where the teacher performs better. Across five agentic task domains and 24 benchmarks and task subsets, Agentic-OPD improves over its initialization checkpoint by up to 7.4 points, with a 4B student surpassing the latest frontier models GPT-5.6 and DeepSeek-V4.1 on deep search. Agentic-OPD recasts a finished RL run as a reusable pool of policies and establishes post-RL capability recovery as a stage orthogonal to improvements in the RL algorithm itself.