Supervised fine-tuning (SFT) is central to aligning large language models (LLMs) with instruction following and task-specific reasoning. Despite its success, SFT optimizes token-level likelihoods under the implicit assumption that strictly fitting all tokens in expert demonstrations induces the desired downstream behavior. However, in reasoning tasks where correctness is defined by logical validity or final outcomes rather than exact token realizations, this assumption can lead to optimization misalignment. We empirically observe that low-probability tokens in reasoning demonstrations often correspond to realization-specific or stylistic variations, and that reducing their influence during training consistently improves generalization on reasoning benchmarks. Motivated by this insight, we propose the Bounded Log-Likelihood Loss (BLL-Loss), a simple and parameter-free alternative to standard likelihood training that bounds gradient contributions from low-probability tokens while preserving conventional optimization behavior. We provide theoretical insights and extensive empirical results demonstrating that BLL-Loss improves reasoning generalization across diverse model scales and challenging benchmarks.

Logic provides a controlled testbed for evaluating LLM-based reasoners, yet standard SAT-style benchmarks often conflate surface difficulty (length, wording, clause order) with the structural phenomena that actually determine satisfiability. We introduce a diagnostic benchmark for 2-SAT built from parameterized families of structured 2-CNF formulas, where satisfiability is characterized by the implication graph and can be tuned along interpretable axes. Our generators isolate distinct competencies and failure modes: (i) contradiction-cycle UNSAT cores with controllable size and imbalance, (ii) SAT instances with a prescribed fraction of free variables to control solution multiplicity, (iii) planted backbones that modulate propagation, (iv) late bridge clauses that couple otherwise monotone regions to probe sensitivity to ordering and revision, and (v) symmetry/duplication variants that test abstraction under renaming and redundant structure. We evaluate LLM-based reasoners on decision accuracy and assignment validity, and quantify robustness under semantics-preserving perturbations such as clause reordering, filler clauses, and variable renaming. Across models, we observe sharp performance transitions under targeted structural interventions even when surface statistics are held fixed, revealing brittleness regimes that are invisible to aggregate SAT accuracy.

Enhancing Large Reasoning Models (LRMs) for specialized domains remains a critical challenge. While recent industrial frameworks attempt to encapsulate Standard Operating Procedures into modular "skills" for dynamic retrieval, utilizing them via context engineering often proves insufficient for complex workflows, leading to "Cognitive Drift." To mitigate this, we propose $\textbf{Thought Guidance-Retrieval Augmented Generation (TG-RAG)}$, a Retrieval-Augmented framework that effectively steers the generation process without relying solely on the model's self-correction. Built upon an Expert Procedure Graph (EPG) that formalizes unstructured SOPs, the framework uniquely employs a dynamic $\textbf{``Interrupt-Retrieve-Generate" (IRG)}$ mechanism to actively inject step-specific directives into the model's reasoning process. Extensive evaluations show that TG-RAG achieves competitive performance, demonstrating advantages in specialized domains by ensuring faithful adherence to domain SOPs. Code is available at https://github.com/V1ncent-S/Thought-Guidance.

RL training of multi-turn LLM agents is unstable, and reasoning quality drives task performance. Entropy, the standard reasoning-stability monitor, only measures within-input diversity and misses whether reasoning depends on the input. We identify template collapse: stable entropy alongside input-agnostic boilerplate, invisible to entropy and existing metrics. We diagnose it via a mutual-information (MI) proxy that scores cross-input distinguishability online; across tasks, MI correlates with final performance far more strongly than entropy. We then explain collapse via a signal-to-noise ratio (SNR) mechanism: low within-input reward variance weakens task gradients, letting input-agnostic regularization dominate and erase cross-input differences. We mitigate this with SNR-Aware Filtering, prioritizing high-variance prompts each iteration. Across planning, math reasoning, web navigation, and code execution, the method consistently improves input dependence and task performance.