Post-training large language models (LLMs) to develop reasoning capabilities has proven effective across diverse domains, such as mathematical reasoning and code generation. However, existing methods primarily focus on improving task-specific reasoning but have not adequately addressed the model's generalization capabilities across a broader range of reasoning tasks. To tackle this challenge, we introduce Critical Planning Step Learning (CPL), which leverages Monte Carlo Tree Search (MCTS) to explore diverse planning steps in multi-step reasoning tasks. Based on long-term outcomes, CPL learns step-level planning preferences to improve the model's planning capabilities and, consequently, its general reasoning capabilities. Furthermore, while effective in many scenarios for aligning LLMs, existing preference learning approaches like Direct Preference Optimization (DPO) struggle with complex multi-step reasoning tasks due to their inability to capture fine-grained supervision at each step. We propose Step-level Advantage Preference Optimization (Step-APO), which integrates an advantage estimate for step-level preference pairs obtained via MCTS into the DPO. This enables the model to more effectively learn critical intermediate planning steps, thereby further improving its generalization in reasoning tasks. Experimental results demonstrate that our method, trained exclusively on GSM8K and MATH, not only significantly improves performance on GSM8K (+10.5%) and MATH (+6.5%), but also enhances out-of-domain reasoning benchmarks, such as ARC-C (+4.0%), BBH (+1.8%), MMLU-STEM (+2.2%), and MMLU (+0.9%).

In the rapidly advancing arena of large language models (LLMs), a key challenge is to enhance their capabilities amid a looming shortage of high-quality training data. Our study starts from an empirical strategy for the light continual training of LLMs using their original pre-training data sets, with a specific focus on selective retention of samples that incur moderately high losses. These samples are deemed informative and beneficial for model refinement, contrasting with the highest-loss samples, which would be discarded due to their correlation with data noise and complexity. We then formalize this strategy into a principled framework of Instance-Reweighted Distributionally Robust Optimization (IR-DRO). IR-DRO is designed to dynamically prioritize the training focus on informative samples through an instance reweighting mechanism, streamlined by a closed-form solution for straightforward integration into established training protocols. Through rigorous experimentation with various models and datasets, our findings indicate that our sample-targeted methods significantly improve LLM performance across multiple benchmarks, in both continual pre-training and instruction tuning scenarios. Our codes are available at https://github.com/VITA-Group/HardFocusTraining.