Process supervision has improved mathematical reasoning, where intermediate steps are naturally expressed as chains of thought. In code generation, however, process supervision remains underexplored because there is no standard notion of a step. Supervision can target lines, reasoning traces, or program states, making it unclear what to label and optimize. We propose STEP-KTODER, a framework for code preference optimization that defines steps as module-level functions in decomposed multi-function programs and assigns binary correctness labels via automatically generated unit tests. Our method provides a code-specific instantiation of stepwise KTO, combining function-level process supervision with outcome-level feedback on the full program. We evaluate on HumanEval(+), MBPP(+), BigCodeBench, and LiveCodeBench, showing that STEP-KTODER improves over outcome-only KTO and DPO. Further analysis shows that execution-based labels are essential: LLM-as-a-judge annotations systematically over-predict function failures, corrupt positive step labels, and degrade downstream preference optimization. Code is available at: https://github.com/inechnech/STEP-KTODER

Pause-token methods improve LLM reasoning by inserting special tokens into sequences. Prior work explains these gains through computational expressivity. However, there is relatively little investigation into the training dynamics of pause tokens. We explore how pause tokens reshape the training dynamics of fine-tuning. Two controlled pilots expose distinct asymmetries. On a synthetic continual-learning task, masked pauses overwrite a previously-learned distribution roughly 4× less at matched final adaptation (H1, mode retention); on a synthetic math-reasoning probe, the boundary-adjacent token comes to encode substantially more downstream-step information (H2, non-myopic compression). We formalize a training rule consistent with both — Masked Boundary Pause (MBP), pause tokens placed at reasoning-step boundaries with their loss masked. Across 1B-8B Qwen and Llama models, MBP consistently improves reasoning, achieving gains of up to 6 points on math and 2.5 points on code, while preserving general language understanding abilities. We further demonstrate that the gains from this mode-preserving strategy extend to GRPO. These results recast pause tokens as a training-dynamics intervention on the retention–adaptation trade-off, rather than merely an inference-time computation device.

Correcting flawed reasoning traces remains a significant challenge for Large Language Models (LLMs), whose autoregressive generation can propagate early mistakes into subsequent reasoning. We introduce **DCGC**, a Masked Diffusion Model (MDM) framework for global correction that uses an imperfect solution draft from an upstream solver as auxiliary context. DCGC combines task-specific Supervised Fine-Tuning (SFT) with a novel inference-time mechanism called **Dynamic Dual-CFG**. This mechanism separates problem-only and joint problem-draft branches and scales the draft-conditioned residual using a relative confidence gap. Across math, code, and knowledge reasoning benchmarks, DCGC outperforms standard sampling and simpler CFG variants, with additional results suggesting transfer to different diffusion backbones. In test-time setting where ground-truth failure labels are unavailable, DCGC improves full test set accuracy by correcting low-consensus upstream outputs, highlighting its utility as a verifier-free global correction module for difficult reasoning instances.

Recent research has devoted considerable effort to verifying the intermediate reasoning steps of chain-of-thought (CoT) trajectories using process reward models (PRMs) and other verifier models. However, training a PRM typically requires human annotators to assign reward scores to each reasoning step, which is both costly and time-consuming. Existing automated approaches, such as Monte Carlo (MC) estimation, also demand substantial computational resources due to repeated LLM rollouts. To overcome these limitations, we propose contrastive pointwise mutual information (CPMI), a novel automatic reward labeling method that leverages the model’s internal probability to infer step-level supervision while significantly reducing the computational burden of annotating dataset. CPMI quantifies how much a reasoning step increases the mutual information between the step and the correct target answer relative to hard-negative alternatives. This contrastive signal serves as a proxy for the step’s contribution to the final solution and yields a reliable reward. The experimental results show that CPMI-based labeling reduces dataset construction time by 84% and token generation by 98% compared to MC estimation, while achieving higher accuracy on process-level evaluations and mathematical reasoning benchmarks.

Transformer-based self-attention mechanism serves as the core of modern language models, yet it often suffers from localization, where attentions collapse onto a limited subset of tokens and fail to capture long-range dependencies. To address this issue, we propose Self-Attention One-step Belief Propagation (SAOBP), a refinement framework that injects multi-hop relationships through a belief propagation process. To interpret and quantify these interactions, we introduce Global Token Dependency (GTD) that captures the relative contribution of multi-hop connections within the attention graph. Empirical results indicate that SAOBP helps prevent entropy collapse in deeper layers and adaptively maintains GTD at task-appropriate levels, thereby supporting improvements in model performance. Importantly, we observe competitive gains in small-scale models, highlighting its potential for improving inference quality in resource-constrained scenarios.