Structure Enables Effective Self-Localization of Errors in LLMs

Self-correction in language models remains elusive. In this work, we explore whether language models can explicitly localize errors in incorrect reasoning, as a path toward building AI systems that can effectively correct themselves. We introduce a prompting method that structures reasoning as discrete, semantically coherent thought steps, and show that models are able to reliably localize errors within this structure, while failing to do so in conventional, unstructured chain-of-thought reasoning. Motivated by how the human brain monitors errors at discrete decision points and resamples alternatives, we introduce Iterative Correction Sampling of Thoughts (Thought-ICS), a self-correction framework. Thought-ICS iteratively prompts the model to generate reasoning one discrete and complete thought at a time--where each thought represents a deliberate decision by the model--creating natural boundaries for precise error localization. Upon verification, the model localizes the first erroneous step, and the system backtracks to generate alternative reasoning from the last correct point. When asked to correct reasoning verified as incorrect by an oracle, Thought-ICS achieves 20-40% self-correction lift. In a completely autonomous setting without external verification, it outperforms contemporary self-correction baselines.

Imbalanced Gradients in RL Post-Training of Multi-Task LLMs

Multi-task post-training of large language models (LLMs) is typically performed by mixing datasets from different tasks and optimizing them jointly. This approach implicitly assumes that all tasks contribute gradients of similar magnitudes; when this assumption fails, optimization becomes biased toward large-gradient tasks. In this paper, however, we show that this assumption fails in RL post-training: certain tasks produce significantly larger gradients, thus biasing updates toward those tasks. Such gradient imbalance would be justified only if larger gradients implied larger learning gains on the tasks (i.e., larger performance improvements) -- but we find this is not true. Large-gradient tasks can achieve similar or even much lower learning gains than small-gradient ones. Further analyses reveal that these gradient imbalances cannot be explained by typical training statistics such as training rewards or advantages, suggesting that they arise from the inherent differences between tasks. This cautions against naive dataset mixing and calls for future work on principled gradient-level corrections for LLMs.

Internalizing Self-Consistency in Language Models: Multi-Agent Consensus Alignment

Language Models (LMs) are inconsistent reasoners, often generating contradictory responses to identical prompts. While inference-time methods can mitigate these inconsistencies, they fail to address the core problem: LMs struggle to reliably select reasoning pathways leading to consistent outcomes under exploratory sampling. To address this, we formalize self-consistency as an intrinsic property of well-aligned reasoning models and introduce Multi-Agent Consensus Alignment (MACA), a reinforcement learning framework that post-trains models to favor reasoning trajectories aligned with their internal consensus using majority/minority outcomes from multi-agent debate. These trajectories emerge from deliberative exchanges where agents ground reasoning in peer arguments, not just aggregation of independent attempts, creating richer consensus signals than single-round majority voting. MACA enables agents to teach themselves to be more decisive and concise, and better leverage peer insights in multi-agent settings without external supervision, driving substantial improvements across self-consistency (+27.6% on GSM8K), single-agent reasoning (+23.7% on MATH), sampling-based inference (+22.4% Pass@20 on MATH), and multi-agent ensemble decision-making (+42.7% on MathQA). These findings, coupled with strong generalization to unseen benchmarks (+16.3% on GPQA, +11.6% on CommonsenseQA), demonstrate robust self-alignment that more reliably unlocks latent reasoning potential of language models.