Inference-time decoding methods improve LLM reasoning by exploring multiple candidate trajectories, yet treat each trajectory as atomic: either retaining it whole or discarding it irreversibly. This wastes computation on partially promising candidates whose high-quality prefixes are abandoned alongside degraded suffixes. We introduce Selective Regenerative Decoding (SRD), which routes each candidate to discard, keep, or refine only the degraded portion of the suffix while preserving the useful prefix of borderline candidates, without requiring a larger target model. Under mild assumptions, SRD achieves a provable 1.28-to-1.36-fold gain in sample efficiency over rejection sampling with strictly higher expected trajectory quality, with the gain growing as the candidate pool grows. Across MATH500, GPQA Diamond, HotpotQA, and AlpacaEval with multiple generation-reward model pairs, SRD matches Best-of-N accuracy with substantially fewer generated tokens and outperforms speculative rejection in low-compute regimes. By enabling segment-level intervention rather than whole-trajectory selection, SRD opens a previously underexplored region of the accuracy-compute tradeoff for inference-time reasoning.
Large Vision-Language Models (LVLMs) exhibit sophisticated reasoning but remain susceptible to object hallucination. Deviating from the prevailing attention intensity assumption, we reveal a deeper dynamic structural misalignment: hallucination is triggered at decision-critical steps where specific attention heads, acting as risky mediators, decouple from visual evidence to lock onto language priors. This establishes a pathological shortcut that bypasses visual grounding. To dismantle this, we propose Fox (Faithfulness and Observational-flow via eXpression-rectification), a training-free inference-time framework. Fox diagnoses structural misalignment using a visual attention entropy probe to localize risky mediators unsupervisedly. We then execute a targeted causal intervention via numerical logit saturation to physically sever the shortcut path. Finally, a conflict-gated cooperative decoding strategy reconciles interventional faithfulness with observational fluency. Extensive experiments demonstrate that Fox achieves SOTA performance, outperforming SID by 29.1% while preserving linguistic richness. Code is available at https://github.com/Cc2021start/Fox.