What makes a difference in the post-training of LLMs? We investigate the training patterns of different layers in large language models (LLMs) through the lens of the gradient. We are specifically interested in how fast vs. slow thinking affects the layer-wise gradients, given the recent popularity of training LLMs on reasoning paths such as chain-of-thoughts (CoT) and process rewards. In our study, fast thinking without CoT leads to larger gradients and larger differences of gradients across layers than slow thinking (Detailed CoT), indicating the learning stability brought by the latter. Additionally, we study whether the gradient patterns can reflect the correctness of responses when training different LLMs using slow vs. fast thinking paths. The results show that the gradients of slow thinking can distinguish correct and irrelevant reasoning paths. As a comparison, we conduct similar gradient analyses on non-reasoning knowledge learning tasks, on which, however, trivially increasing the response length does not lead to similar behaviors of slow thinking. Our study strengthens fundamental understandings of LLM training and sheds novel insights on its efficiency and stability, which pave the way towards building a generalizable System-2 agent.

While Large Reasoning Models (LRMs) generate extensive chain-of-thought reasoning, we lack a principled framework for understanding how these thoughts are structured. In this paper, we introduce a novel approach by applying Schoenfeld’s Episode Theory, a classic cognitive framework for human mathematical problem-solving, to analyze the reasoning traces of LRMs. We annotated thousands of sentences and paragraphs from model-generated solutions to math problems using seven cognitive labels (e.g., Plan, Implement, Verify). The result is the first publicly available benchmark for the fine-grained analysis of machine reasoning, including a large annotated corpus and detailed annotation guidebooks. Our preliminary analysis reveals distinct patterns in LRM reasoning, such as the transition dynamics between cognitive states. This framework provides a theoretically grounded methodology for interpreting LRM cognition and enables future work on more controllable and transparent reasoning systems.

Finetuning large language models with a variety of instruction-response pairs has enhanced their capability to understand and follow instructions. Current instruction tuning primarily relies on teacher models or human intervention to generate and refine the instructions and responses for training, which are costly, non-sustainable, and may lack diversity. In this paper, we introduce Mosaic Instruction Tuning (Mosaic-IT), a human/model-free compositional data synthesis method that can efficiently create rich and diverse augmentations from existing instruction tuning data to enhance the LLMs. Mosaic-IT randomly concatenates multiple instruction data into one and trains the model to produce the corresponding responses with predefined higher-level meta-instructions to strengthen its multi-step instruction-following and format-following skills. Our extensive evaluations demonstrate a superior performance and training efficiency of Mosaic-IT, which achieves consistent performance improvements over various benchmarks and an 80% reduction in training costs compared with original instruction tuning.

Large Language Model (LLM) agents have demonstrated remarkable generalization capabilities across multi-domain tasks. Existing agent tuning approaches typically employ supervised finetuning on entire expert trajectories. However, behavior-cloning of full trajectories can introduce expert bias and weaken generalization to states not covered by the expert data. Additionally, critical steps—such as planning, complex reasoning for intermediate subtasks, and strategic decision-making—are essential to success in agent tasks, so learning these steps is the key to improving LLM agents. For more effective and efficient agent tuning, we propose ATLAS that identifies the critical steps in expert trajectories and finetunes LLMs solely on these steps with reduced costs. By steering the training’s focus to a few critical steps, our method mitigates the risk of overfitting entire trajectories and promotes generalization across different environments and tasks. In extensive experiments, an LLM finetuned on only 30% critical steps selected by ATLAS outperforms the LLM finetuned on all steps and recent open-source LLM agents. ATLAS maintains and improves base LLM skills as generalist agents interacting with diverse environments.

Large Language Models (LLMs) are increasingly aligned with human preferences through Reinforcement Learning from Human Feedback (RLHF). Among RLHF methods, Group Relative Policy Optimization (GRPO) has gained attention for its simplicity and strong performance, notably eliminating the need for a learned value function. However, GRPO implicitly assumes a balanced domain distribution and uniform semantic alignment across groups—assumptions that rarely hold in real-world datasets. When applied to multi-domain, imbalanced data, GRPO disproportionately optimizes for dominant domains, neglecting underrepresented ones and resulting in poor generalization and fairness. We propose Domain-Informed Self-Consistency Policy Optimization (DISCO), a principled extension to GRPO that addresses inter-group imbalance with two key innovations. Domain-aware reward scaling counteracts frequency bias by reweighting optimization based on domain prevalence. Difficulty-aware reward scaling leverages prompt-level self-consistency to identify and prioritize uncertain prompts that offer greater learning value. Together, these strategies promote more equitable and effective policy learning across domains. Extensive experiments across multiple LLMs and skewed training distributions show that DISCO improves generalization, outperforms existing GRPO variants by 5% on Qwen3 models, and sets new state-of-the-art results on multi-domain alignment benchmarks.

Large language models (LLMs) still lack delicate controllability over their responses, which is critical to enhancing their performance and the user experience. However, curating supervised fine-tuning (SFT) datasets to improve LLM controllability usually relies on human experts or proprietary LLMs, which requires additional costs. To bridge this gap, we propose Rule-based Data Recycling (RuleR), a data augmentation method incorporating multiple constraints into the original data samples according to predefined rules, which creates new training tasks to consolidate the controllability of LLMs. Instead of creating new data from scratch, RuleR “recycles” existing data by simply applying rule-based edits to their responses and appending the rule-instructions in their original instructions. Experimental results demonstrate RuleR’s effectiveness in improving LLM controllability while maintaining general instruction-following capabilities.

Making LLMs speak for different, especially minority groups of people, and generate statements supporting their diverse or even controversial perspectives is critical to creating an inclusive environment. However, existing LLMs lack sufficient controllability to the stance of their generated content, which often contains inconsistent, neutral, or biased statements. In this paper, we improve the controllability of LLMs in generating statements supporting an argument the user defined in the prompt. We find that multi-round debates between two LLMs with opposite stances generate higher-quality and more salient statements for each, which are important training data to improve the controllability of LLMs. Motivated by this, we develop a novel debate & tuning (“DEBATUNE”) pipeline finetuning LLMs to generate the statements obtained via debate. To examine DEBATUNE, we curate the largest dataset of debate topics so far, which covers 710 controversial topics and corresponding arguments for each topic. Evaluations by the GPT-4 judge with a novel controversy controllability metric show that LLMs’ capability of generating diverse perspectives is significantly improved by DEBATUNE. Moreover, such controllability can be generalized to unseen topics, generating high-quality statements supporting controversial arguments.

Instruction tuning is critical to large language models (LLMs) for achieving better instruction following and task adaptation capabilities but its success heavily relies on the training data quality. Many recent methods focus on improving the data quality but often overlook the compatibility of the data with the student model being finetuned. This paper introduces Selective Reflection-Tuning, a novel paradigm that synergizes a teacher LLM’s reflection and introspection for improving existing data quality with the data selection capability of the student LLM, to automatically refine existing instruction-tuning data. This teacher-student collaboration produces high-quality and student-compatible instruction-response pairs, resulting in sample-efficient instruction tuning and LLMs of superior performance. Selective Reflection-Tuning is a data augmentation and synthesis that generally improves LLM finetuning and self-improvement without collecting brand-new data. We apply our method to Alpaca and WizardLM data and achieve much stronger and top-tier 7B and 13B LLMs.