Daily Papers

We introduce TuneJury, an open, instance-level pairwise reward model for text-to-music that predicts a music preference score from a text prompt and an audio clip. The released checkpoint is trained on publicly available human-preference labels covering arena-style (A vs. B) votes, metric-alignment preference pairs, crowdsourced pairwise comparisons, and expert aesthetic ratings. The predicted score margin between two clips is well calibrated on our held-out test split, supporting data filtering via a simple score threshold. TuneJury generalizes to both held-out test pairs and out-of-distribution benchmarks, remaining competitive with prior baselines on the latter. For generators released after training, we introduce anchor calibration, a post-hoc, per-system Bradley-Terry calibration that recovers agreement at substantially better data efficiency than from-scratch retraining. The same frozen reward drives consistent reward-axis gains across three downstream applications: inference-time best-of-N selection, DITTO-style latent optimization, and expert-iteration post-training. TuneJury is available at https://github.com/yonghyunk1m/TuneJury.

Reinforcement learning (RL)-based fine-tuning has become a crucial step in post-training language models for advanced mathematical reasoning and coding. Following the success of frontier reasoning models, recent work has demonstrated that RL fine-tuning consistently improves performance, even in smaller-scale models; however, the underlying mechanisms driving these improvements are not well-understood. Understanding the effects of RL fine-tuning requires disentangling its interaction with pretraining data composition, hyperparameters, and model scale, but such problems are exacerbated by the lack of transparency regarding the training data used in many existing models. In this work, we present a systematic end-to-end study of RL fine-tuning for mathematical reasoning by training models entirely from scratch on different mixtures of fully open datasets. We investigate the effects of various RL fine-tuning algorithms (PPO, GRPO, and Expert Iteration) across models of different scales. Our study reveals that RL algorithms consistently converge towards a dominant output distribution, amplifying patterns in the pretraining data. We also find that models of different scales trained on the same data mixture will converge to distinct output distributions, suggesting that there are scale-dependent biases in model generalization. Moreover, we find that RL post-training on simpler questions can lead to performance gains on harder ones, indicating that certain reasoning capabilities generalize across tasks. Our findings show that small-scale proxies in controlled settings can elicit interesting insights regarding the role of RL in shaping language model behavior.

We present GLM-4.5, an open-source Mixture-of-Experts (MoE) large language model with 355B total parameters and 32B activated parameters, featuring a hybrid reasoning method that supports both thinking and direct response modes. Through multi-stage training on 23T tokens and comprehensive post-training with expert model iteration and reinforcement learning, GLM-4.5 achieves strong performance across agentic, reasoning, and coding (ARC) tasks, scoring 70.1% on TAU-Bench, 91.0% on AIME 24, and 64.2% on SWE-bench Verified. With much fewer parameters than several competitors, GLM-4.5 ranks 3rd overall among all evaluated models and 2nd on agentic benchmarks. We release both GLM-4.5 (355B parameters) and a compact version, GLM-4.5-Air (106B parameters), to advance research in reasoning and agentic AI systems. Code, models, and more information are available at https://github.com/zai-org/GLM-4.5.

In this report, we present a series of math-specific large language models: Qwen2.5-Math and Qwen2.5-Math-Instruct-1.5B/7B/72B. The core innovation of the Qwen2.5 series lies in integrating the philosophy of self-improvement throughout the entire pipeline, from pre-training and post-training to inference: (1) During the pre-training phase, Qwen2-Math-Instruct is utilized to generate large-scale, high-quality mathematical data. (2) In the post-training phase, we develop a reward model (RM) by conducting massive sampling from Qwen2-Math-Instruct. This RM is then applied to the iterative evolution of data in supervised fine-tuning (SFT). With a stronger SFT model, it's possible to iteratively train and update the RM, which in turn guides the next round of SFT data iteration. On the final SFT model, we employ the ultimate RM for reinforcement learning, resulting in the Qwen2.5-Math-Instruct. (3) Furthermore, during the inference stage, the RM is used to guide sampling, optimizing the model's performance. Qwen2.5-Math-Instruct supports both Chinese and English, and possess advanced mathematical reasoning capabilities, including Chain-of-Thought (CoT) and Tool-Integrated Reasoning (TIR). We evaluate our models on 10 mathematics datasets in both English and Chinese, such as GSM8K, MATH, GaoKao, AMC23, and AIME24, covering a range of difficulties from grade school level to math competition problems.

Reinforcement Learning from Human Feedback (RLHF) has emerged as a dominant approach for aligning LLM outputs with human preferences. Inspired by the success of RLHF, we study the performance of multiple algorithms that learn from feedback (Expert Iteration, Proximal Policy Optimization (PPO), Return-Conditioned RL) on improving LLM reasoning capabilities. We investigate both sparse and dense rewards provided to the LLM both heuristically and via a learned reward model. We additionally start from multiple model sizes and initializations both with and without supervised fine-tuning (SFT) data. Overall, we find all algorithms perform comparably, with Expert Iteration performing best in most cases. Surprisingly, we find the sample complexity of Expert Iteration is similar to that of PPO, requiring at most on the order of 10^6 samples to converge from a pretrained checkpoint. We investigate why this is the case, concluding that during RL training models fail to explore significantly beyond solutions already produced by SFT models. Additionally, we discuss a trade off between maj@1 and pass@96 metric performance during SFT training and how conversely RL training improves both simultaneously. We then conclude by discussing the implications of our findings for RLHF and the future role of RL in LLM fine-tuning.

We explore the use of expert iteration in the context of language modeling applied to formal mathematics. We show that at same compute budget, expert iteration, by which we mean proof search interleaved with learning, dramatically outperforms proof search only. We also observe that when applied to a collection of formal statements of sufficiently varied difficulty, expert iteration is capable of finding and solving a curriculum of increasingly difficult problems, without the need for associated ground-truth proofs. Finally, by applying this expert iteration to a manually curated set of problem statements, we achieve state-of-the-art on the miniF2F benchmark, automatically solving multiple challenging problems drawn from high school olympiads.

Pretraining produces a learned parameter vector that is typically treated as a starting point for further iterative adaptation. In this work, we instead view the outcome of pretraining as a distribution over parameter vectors, whose support already contains task-specific experts. We show that in small models such expert solutions occupy a negligible fraction of the volume of this distribution, making their discovery reliant on structured optimization methods such as gradient descent. In contrast, in large, well-pretrained models the density of task-experts increases dramatically, so that diverse, task-improving specialists populate a substantial fraction of the neighborhood around the pretrained weights. Motivated by this perspective, we explore a simple, fully parallel post-training method that samples N parameter perturbations at random, selects the top K, and ensembles predictions via majority vote. Despite its simplicity, this approach is competitive with standard post-training methods such as PPO, GRPO, and ES for contemporary large-scale models.

Many real world learning tasks involve complex or hard-to-specify objectives, and using an easier-to-specify proxy can lead to poor performance or misaligned behavior. One solution is to have humans provide a training signal by demonstrating or judging performance, but this approach fails if the task is too complicated for a human to directly evaluate. We propose Iterated Amplification, an alternative training strategy which progressively builds up a training signal for difficult problems by combining solutions to easier subproblems. Iterated Amplification is closely related to Expert Iteration (Anthony et al., 2017; Silver et al., 2017), except that it uses no external reward function. We present results in algorithmic environments, showing that Iterated Amplification can efficiently learn complex behaviors.

Two major sources of training data exist for post-training modern language models: online (model-generated rollouts) data, and offline (human or other-model demonstrations) data. These two types of data are typically used by approaches like Reinforcement Learning (RL) and Supervised Fine-Tuning (SFT), respectively. In this paper, we show that these approaches are not in contradiction, but are instances of a single optimization process. We derive a Unified Policy Gradient Estimator, and present the calculations of a wide spectrum of post-training approaches as the gradient of a common objective under different data distribution assumptions and various bias-variance tradeoffs. The gradient estimator is constructed with four interchangeable parts: stabilization mask, reference policy denominator, advantage estimate, and likelihood gradient. Motivated by our theoretical findings, we propose Hybrid Post-Training (HPT), an algorithm that dynamically selects different training signals. HPT is designed to yield both effective exploitation of demonstration and stable exploration without sacrificing learned reasoning patterns. We provide extensive experiments and ablation studies to verify the effectiveness of our unified theoretical framework and HPT. Across six mathematical reasoning benchmarks and two out-of-distribution suites, HPT consistently surpasses strong baselines across models of varying scales and families.

Post-training endows pretrained LLMs with a variety of desirable skills, including instruction-following, reasoning, and others. However, these post-trained LLMs only encode knowledge up to a cut-off date, necessitating continual adaptation. Unfortunately, existing solutions cannot simultaneously learn new knowledge from an adaptation document corpora and mitigate the forgetting of earlier learned capabilities. To address this, we introduce Distillation via Split Contexts (DiSC), a simple context-distillation based approach for continual knowledge adaptation. \methodname~derives student and teacher distributions by conditioning on distinct segments of the training example and minimizes the KL divergence between the shared tokens. This allows us to efficiently apply context-distillation without requiring explicit generation steps during training. We run experiments on four post-trained models and two adaptation domains. Compared to prior finetuning and distillation methods for continual adaptation, DiSC consistently reports the best trade-off between learning new knowledge and mitigating forgetting of previously learned skills like instruction-following, reasoning, and factual knowledge.

Class-incremental learning is becoming more popular as it helps models widen their applicability while not forgetting what they already know. A trend in this area is to use a mixture-of-expert technique, where different models work together to solve the task. However, the experts are usually trained all at once using whole task data, which makes them all prone to forgetting and increasing computational burden. To address this limitation, we introduce a novel approach named SEED. SEED selects only one, the most optimal expert for a considered task, and uses data from this task to fine-tune only this expert. For this purpose, each expert represents each class with a Gaussian distribution, and the optimal expert is selected based on the similarity of those distributions. Consequently, SEED increases diversity and heterogeneity within the experts while maintaining the high stability of this ensemble method. The extensive experiments demonstrate that SEED achieves state-of-the-art performance in exemplar-free settings across various scenarios, showing the potential of expert diversification through data in continual learning.

Language model post-training is applied to refine behaviors and unlock new skills across a wide range of recent language models, but open recipes for applying these techniques lag behind proprietary ones. The underlying training data and recipes for post-training are simultaneously the most important pieces of the puzzle and the portion with the least transparency. To bridge this gap, we introduce T\"ULU 3, a family of fully-open state-of-the-art post-trained models, alongside its data, code, and training recipes, serving as a comprehensive guide for modern post-training techniques. T\"ULU 3, which builds on Llama 3.1 base models, achieves results surpassing the instruct versions of Llama 3.1, Qwen 2.5, Mistral, and even closed models such as GPT-4o-mini and Claude 3.5-Haiku. The training algorithms for our models include supervised finetuning (SFT), Direct Preference Optimization (DPO), and a novel method we call Reinforcement Learning with Verifiable Rewards (RLVR). With T\"ULU 3, we introduce a multi-task evaluation scheme for post-training recipes with development and unseen evaluations, standard benchmark implementations, and substantial decontamination of existing open datasets on said benchmarks. We conclude with analysis and discussion of training methods that did not reliably improve performance. In addition to the T\"ULU 3 model weights and demo, we release the complete recipe -- including datasets for diverse core skills, a robust toolkit for data curation and evaluation, the training code and infrastructure, and, most importantly, a detailed report for reproducing and further adapting the T\"ULU 3 approach to more domains.

We propose Chain-of-Experts (CoE), a new Mixture-of-Experts (MoE) architecture that introduces sequential expert communication within each layer. Unlike traditional MoE models, where experts operate independently in parallel, CoE processes tokens iteratively across a chain of experts inside a layer. To support dynamic expert selection across iterations, CoE employs a dedicated router at each iteration step within a layer. This design allows tokens to re-evaluate and select different experts during each iteration, rather than being statically assigned. As a result, CoE introduces a flexible routing mechanism that increases the diversity of expert combinations and enriches the model's representational capacity. CoE demonstrates improved performance under fixed compute: on math reasoning tasks, it reduces validation loss from 1.20 to 1.12 compared to a standard MoE. Beyond performance, CoE offers a new scaling axis: depth through expert iteration, which complements conventional width/depth scaling. For example, using 2x iterations matches the performance of 3x expert selections (in width), while reducing memory usage by 17.6-42% relative to other scaling strategies. Our analysis reveals that CoE's benefits stem from its iterative residual structure and enhanced expert specialization empowered by iterative routing, which together unlock more expressive representations. Code is available at https://github.com/ZihanWang314/coe.

The expansion of machine learning into dynamic environments presents challenges in handling open-world problems where label shift, covariate shift, and unknown classes emerge. Post-training methods have been explored to address these challenges, adapting models to newly emerging data. However, these methods struggle when the initial pre-training is performed on class-imbalanced datasets, limiting generalization to minority classes. To address this, we propose a method that effectively handles open-world problems even when pre-training is conducted on imbalanced data. Our contrastive-based pre-training approach enhances classification performance, particularly for underrepresented classes. Our post-training mechanism generates reliable pseudo-labels, improving model robustness against open-world problems. We also introduce selective activation criteria to optimize the post-training process, reducing unnecessary computation. Extensive experiments demonstrate that our method significantly outperforms state-of-the-art adaptation techniques in both accuracy and efficiency across diverse open-world scenarios.

Large Language Models (LLMs) exhibit strong generalization capabilities to novel tasks when prompted with language instructions and in-context demos. Since this ability sensitively depends on the quality of prompts, various methods have been explored to automate the instruction design. While these methods demonstrated promising results, they also restricted the searched prompt to one instruction. Such simplification significantly limits their capacity, as a single demo-free instruction might not be able to cover the entire complex problem space of the targeted task. To alleviate this issue, we adopt the Mixture-of-Expert paradigm and divide the problem space into a set of sub-regions; Each sub-region is governed by a specialized expert, equipped with both an instruction and a set of demos. A two-phase process is developed to construct the specialized expert for each region: (1) demo assignment: Inspired by the theoretical connection between in-context learning and kernel regression, we group demos into experts based on their semantic similarity; (2) instruction assignment: A region-based joint search of an instruction per expert complements the demos assigned to it, yielding a synergistic effect. The resulting method, codenamed Mixture-of-Prompts (MoP), achieves an average win rate of 81% against prior arts across several major benchmarks.

Enhancing the reasoning capabilities of Large Language Models (LLMs) via post-training is often constrained by the trade-off between efficiency and catastrophic forgetting. While prior research emphasizes the role of on-policy data in mitigating forgetting, we uncover--and validate both theoretically and empirically--an overlooked yet critical mechanism: the implicit regularization inherent in Direct Preference Optimization's (DPO) reward estimate. This motivates our Surgical Post-Training (SPoT), a new paradigm designed to optimize reasoning efficiently while preserving learned prior knowledge. SPoT consists of: (1) a data rectification pipeline that employs an Oracle to surgically correct erroneous steps via minimal edits, generating data proximal to the model's distribution; and (2) a reward-based binary cross-entropy objective. Unlike the relative ranking in DPO, this objective treats reasoning correctness as a binary classification problem, enforcing decoupled supervision signals. Empirically, with only 4k rectified math data pairs, SPoT improves Qwen3-8B's accuracy by 6.2% on average across in-domain and OOD tasks, requiring merely 28 minutes of training on 8x H800 GPUs. Code: https://github.com/Visual-AI/SPoT

This work presents In-Context Policy Iteration, an algorithm for performing Reinforcement Learning (RL), in-context, using foundation models. While the application of foundation models to RL has received considerable attention, most approaches rely on either (1) the curation of expert demonstrations (either through manual design or task-specific pretraining) or (2) adaptation to the task of interest using gradient methods (either fine-tuning or training of adapter layers). Both of these techniques have drawbacks. Collecting demonstrations is labor-intensive, and algorithms that rely on them do not outperform the experts from which the demonstrations were derived. All gradient techniques are inherently slow, sacrificing the "few-shot" quality that made in-context learning attractive to begin with. In this work, we present an algorithm, ICPI, that learns to perform RL tasks without expert demonstrations or gradients. Instead we present a policy-iteration method in which the prompt content is the entire locus of learning. ICPI iteratively updates the contents of the prompt from which it derives its policy through trial-and-error interaction with an RL environment. In order to eliminate the role of in-weights learning (on which approaches like Decision Transformer rely heavily), we demonstrate our algorithm using Codex, a language model with no prior knowledge of the domains on which we evaluate it.

Post-training of language models is commonly framed as a sample-score-update loop implemented by gradient descent. A recent line of work, exemplified by RandOpt, relocates this loop to weight space, sampling Gaussian perturbations around a pretrained model and ensembling the top-K rewarded specialists at inference. While competitive with PPO and GRPO under matched training compute, this prediction-level ensemble incurs K forward passes per test example and does not extend cleanly to free-form generation. We ask whether the rewarded population can instead be folded into a single deployable model, replacing the inference-time ensemble with one consolidated update. A split-half analysis over 25 model-task pairs reveals reproducible low-rank structure in every case. We turn this geometry into CoRP (Consolidating Rewarded Perturbations), a gradient-free operator that combines reward-weighted aggregation, compatibility-aware reweighting, and a held-out validation gate, with no gradient flowing through the language model. Across five language models from 0.5B to 8B and five tasks covering math, code, and creative writing, CoRP improves the base model by 8.1 points on average. Using one tenth of RandOpt's perturbation budget, CoRP exceeds single-inference RandOpt by 6.5 points and recovers more than half of the gain of the 50-pass majority-vote ensemble, at one forward pass per test example.

Standard training pipelines for large language models (LLMs) are typically unidirectional, progressing from pre-training to post-training. However, the potential for a bidirectional process--where insights from post-training retroactively improve the pre-trained foundation--remains unexplored. We aim to establish a self-reinforcing flywheel: a cycle in which reinforcement learning (RL)-tuned model strengthens the base model, which in turn enhances subsequent post-training performance, requiring no specially trained teacher or reference model. To realize this, we analyze training dynamics and identify the mid-training (annealing) phase as a critical turning point for model capabilities. This phase typically occurs at the end of pre-training, utilizing high-quality corpora under a rapidly decaying learning rate. Building upon this insight, we introduce ReMiT (Reinforcement Learning-Guided Mid-Training). Specifically, ReMiT leverages the reasoning priors of RL-tuned models to dynamically reweight tokens during the mid-training phase, prioritizing those pivotal for reasoning. Empirically, ReMiT achieves an average improvement of 3\% on 10 pre-training benchmarks, spanning math, code, and general reasoning, and sustains these gains by over 2\% throughout the post-training pipeline. These results validate an iterative feedback loop, enabling continuous and self-reinforcing evolution of LLMs.

State-of-the-art AI systems can be significantly improved without expensive retraining via "post-training enhancements"-techniques applied after initial training like fine-tuning the system to use a web browser. We review recent post-training enhancements, categorizing them into five types: tool-use, prompting methods, scaffolding, solution selection, and data generation. Different enhancements improve performance on different tasks, making it hard to compare their significance. So we translate improvements from different enhancements into a common currency, the compute-equivalent gain: how much additional training compute would be needed to improve performance by the same amount as the enhancement. Our non-experimental work shows that post-training enhancements have significant benefits: most surveyed enhancements improve benchmark performance by more than a 5x increase in training compute, some by more than 20x. Post-training enhancements are relatively cheap to develop: fine-tuning costs are typically <1% of the original training cost. Governing the development of capable post-training enhancements may be challenging because frontier models could be enhanced by a wide range of actors.

Continual post-training (CPT) is a popular and effective technique for adapting foundation models like multimodal large language models to specific and ever-evolving downstream tasks. While existing research has primarily concentrated on methods like data replay, model expansion, or parameter regularization, the fundamental role of the learning paradigm within CPT remains largely unexplored. This paper presents a comparative analysis of two core post-training paradigms: supervised fine-tuning (SFT) and reinforcement fine-tuning (RFT), investigating their respective impacts on knowledge retention during CPT. Our experiments are conducted on a benchmark comprising seven diverse multimodal tasks, utilizing Qwen2.5-VL-7B-Instruct as the base model for continual post-training. The investigation yields two significant findings: (1) When continuously learning on downstream tasks, SFT leads to catastrophic forgetting of previously learned tasks. In contrast, RFT inherently preserves prior knowledge and achieve performance comparable to multi-task training. (2) RFT successfully protects and even enhances the model's general knowledge on standard benchmarks (e.g., MMMU and MMLU-Pro). Conversely, SFT degrades general model capabilities severely. Further analysis shows that explicit mechanisms, such as KL penalty and chain-of-thought reasoning, are not the primary factors. Instead, we find that the implicit regularization inherent to RFT is a key factor in mitigating forgetting. Finally, we propose a rollout-based instance filtering algorithm to improve the stability and efficiency of RFT. Our comprehensive study demonstrates the superiority of RFT as a robust paradigm for continual post-training.

Traditional neural network training typically follows fixed, predefined optimization recipes, lacking the flexibility to dynamically respond to instabilities or emerging training issues. In this paper, we introduce Interactive Training, an open-source framework that enables real-time, feedback-driven intervention during neural network training by human experts or automated AI agents. At its core, Interactive Training uses a control server to mediate communication between users or agents and the ongoing training process, allowing users to dynamically adjust optimizer hyperparameters, training data, and model checkpoints. Through three case studies, we demonstrate that Interactive Training achieves superior training stability, reduced sensitivity to initial hyperparameters, and improved adaptability to evolving user needs, paving the way toward a future training paradigm where AI agents autonomously monitor training logs, proactively resolve instabilities, and optimize training dynamics.

As the general capabilities of artificial intelligence (AI) agents continue to evolve, their ability to learn to master multiple complex tasks through experience remains a key challenge. Current LLM agents, particularly those based on proprietary language models, typically rely on prompts to incorporate knowledge about the target tasks. This approach does not allow the agent to internalize this information and instead relies on ever-expanding prompts to sustain its functionality in diverse scenarios. This resembles a system of notes used by a person affected by anterograde amnesia, the inability to form new memories. In this paper, we propose a novel method to train AI agents to incorporate knowledge and skills for multiple tasks without the need for either cumbersome note systems or prior high-quality demonstration data. Our approach employs an iterative process where the agent collects new experiences, receives corrective feedback from humans in the form of hints, and integrates this feedback into its weights via a context distillation training procedure. We demonstrate the efficacy of our approach by implementing it in a Llama-3-based agent that, after only a few rounds of feedback, outperforms advanced models GPT-4o and DeepSeek-V3 in tasksets requiring correct sequencing of information retrieval, tool use, and question answering.

Post-training is essential for the success of large language models (LLMs), transforming pre-trained base models into more useful and aligned post-trained models. While plenty of works have studied post-training algorithms and evaluated post-training models by their outputs, it remains understudied how post-training reshapes LLMs internally. In this paper, we compare base and post-trained LLMs mechanistically from four perspectives to better understand post-training effects. Our findings across model families and datasets reveal that: (1) Post-training does not change the factual knowledge storage locations, and it adapts knowledge representations from the base model while developing new knowledge representations; (2) Both truthfulness and refusal can be represented by linear vectors in the hidden representation space. The truthfulness direction is highly similar between the base and post-trained model, and it is effectively transferable for interventions; (3) The refusal direction is different between the base and post-trained models, and it shows limited forward transferability; (4) Differences in confidence between the base and post-trained models cannot be attributed to entropy neurons. Our study provides insights into the fundamental mechanisms preserved and altered during post-training, facilitates downstream tasks like model steering, and could potentially benefit future research in interpretability and LLM post-training.

Large Language Models (LLMs) have transformed the natural language processing landscape and brought to life diverse applications. Pretraining on vast web-scale data has laid the foundation for these models, yet the research community is now increasingly shifting focus toward post-training techniques to achieve further breakthroughs. While pretraining provides a broad linguistic foundation, post-training methods enable LLMs to refine their knowledge, improve reasoning, enhance factual accuracy, and align more effectively with user intents and ethical considerations. Fine-tuning, reinforcement learning, and test-time scaling have emerged as critical strategies for optimizing LLMs performance, ensuring robustness, and improving adaptability across various real-world tasks. This survey provides a systematic exploration of post-training methodologies, analyzing their role in refining LLMs beyond pretraining, addressing key challenges such as catastrophic forgetting, reward hacking, and inference-time trade-offs. We highlight emerging directions in model alignment, scalable adaptation, and inference-time reasoning, and outline future research directions. We also provide a public repository to continually track developments in this fast-evolving field: https://github.com/mbzuai-oryx/Awesome-LLM-Post-training.

Post-training (via supervised fine-tuning) improves instruction-following, but often induces semantic mode collapse by biasing models toward low-entropy fine-tuning data at the expense of the high-entropy pretraining distribution. Crucially, we find this trade-off worsens with scale. To close this semantic diversity gap, we propose annotation-anchored training, a principled method that enables models to adopt the preference-following behaviors of post-training without sacrificing the inherent diversity of pretraining. Our approach is simple: we pretrain on documents paired with semantic annotations, inducing a rich annotation distribution that reflects the full breadth of pretraining data, and we preserve this distribution during post-training. This lets us sample diverse annotations at inference time and use them as anchors to guide generation, effectively transferring pretraining's semantic richness into post-trained models. We find that models trained with annotation-anchored training can attain 6 times less diversity collapse than models trained with SFT, and improve with scale.

Large language model (LLM) post-training enhances latent skills, unlocks value alignment, improves performance, and enables domain adaptation. Unfortunately, post-training is known to induce forgetting, especially in the ubiquitous use-case of leveraging third-party pre-trained models, which is typically understood as a loss of parametric or factual knowledge. We argue that this accuracy-centric view is insufficient for modern foundation models and instead define forgetting as systematic model drift that degrades behavior and user experience. In this context, we introduce CapTrack, a capability-centric framework for analyzing forgetting in LLMs that combines a behavioral taxonomy with an evaluation suite built on established benchmarks and targeted adaptations. Using CapTrack, we conduct a large-scale empirical study across post-training algorithms, domains, and model families, including models up to 80B parameters. We find that forgetting extends beyond parametric knowledge, with pronounced drift in robustness and default behaviors. Instruction fine-tuning induces the strongest relative drift, while preference optimization is more conservative and can partially recover lost capabilities. Differences across model families persist, and no universal mitigation emerges.

Recent work on applying large language models (LMs) achieves impressive performance in many NLP applications. Adapting or posttraining an LM using an unlabeled domain corpus can produce even better performance for end-tasks in the domain. This paper proposes the problem of continually extending an LM by incrementally post-train the LM with a sequence of unlabeled domain corpora to expand its knowledge without forgetting its previous skills. The goal is to improve the few-shot end-task learning in these domains. The resulting system is called CPT (Continual PostTraining), which to our knowledge, is the first continual post-training system. Experimental results verify its effectiveness.

Post-training has become a primary driver of recent progress in large reasoning models, and reasoning data are often the key variable determining whether this stage succeeds. Work on post-training reasoning data has grown rapidly, yet this literature remains scattered across dataset papers, reinforcement-learning recipes, reward-model studies, benchmarks, and frontier system reports. This paper is the first primer to synthesize over 150 key public studies and system reports on post-training reasoning data. We organize the field around four questions: what data objects exist, what makes them useful, how they are constructed, and how they scale. Together, this organization provides an attribution framework for future reasoning-data releases and post-training recipes.

Large language model agents have exhibited exceptional performance across a range of complex interactive tasks. Recent approaches have utilized tuning with expert trajectories to enhance agent performance, yet they primarily concentrate on outcome rewards, which may lead to errors or suboptimal actions due to the absence of process supervision signals. In this paper, we introduce the Iterative step-level Process Refinement (IPR) framework, which provides detailed step-by-step guidance to enhance agent training. Specifically, we adopt the Monte Carlo method to estimate step-level rewards. During each iteration, the agent explores along the expert trajectory and generates new actions. These actions are then evaluated against the corresponding step of expert trajectory using step-level rewards. Such comparison helps identify discrepancies, yielding contrastive action pairs that serve as training data for the agent. Our experiments on three complex agent tasks demonstrate that our framework outperforms a variety of strong baselines. Moreover, our analytical findings highlight the effectiveness of IPR in augmenting action efficiency and its applicability to diverse models.

Our goal is to understand how post-training methods, such as fine-tuning, alignment, and unlearning, modify language model behavior and representations. We are particularly interested in the brittle nature of these modifications that makes them easy to bypass through prompt engineering or relearning. Recent results suggest that post-training induces shallow context-dependent ``circuits'' that suppress specific response patterns. This could be one explanation for the brittleness of post-training. To test this hypothesis, we design an unlearning algorithm, Layered Unlearning (LU), that creates distinct inhibitory mechanisms for a growing subset of the data. By unlearning the first i folds while retaining the remaining k - i at the ith of k stages, LU limits the ability of relearning on a subset of data to recover the full dataset. We evaluate LU through a combination of synthetic and large language model (LLM) experiments. We find that LU improves robustness to adversarial relearning for several different unlearning methods. Our results contribute to the state-of-the-art of machine unlearning and provide insight into the effect of post-training updates.

We consider the problem of ranking n experts based on their performances on d tasks. We make a monotonicity assumption stating that for each pair of experts, one outperforms the other on all tasks. We consider the sequential setting where in each round, the learner has access to noisy evaluations of actively chosen pair of expert-task, given the information available up to the actual round. Given a confidence parameter delta in (0, 1), we provide strategies allowing to recover the correct ranking of experts and develop a bound on the total number of queries made by our algorithm that hold with probability at least 1 -- delta. We show that our strategy is adaptive to the complexity of the problem (our bounds are instance dependent), and develop matching lower bounds up to a poly-logarithmic factor. Finally, we adapt our strategy to the relaxed problem of best expert identification and provide numerical simulation consistent with our theoretical results.

Multimodal Large Language Models (MLLMs) achieve strong performance through instruction tuning, but real-world deployment requires them to continually expand their capabilities, making Multimodal Continual Instruction Tuning (MCIT) essential. Recent methods leverage sparse expert routing to promote task specialization, but we find that the expert routing process suffers from drift as the data distribution evolves. For example, a grounding query that previously activated localization experts may instead be routed to irrelevant experts after learning OCR tasks. Meanwhile, the grounding-related experts can be overwritten by new tasks and lose their original functionality. Such failure reflects two problems: router drift, where expert selection becomes inconsistent over time, and expert drift, where shared experts are overwritten across tasks. Therefore, we propose StAbilized Mixture-of-Experts (SAME) for MCIT. To address router drift, SAME stabilizes expert selection by decomposing routing dynamics into orthogonal subspaces and updating only task-relevant directions. To mitigate expert drift, we regulate expert updates via curvature-aware scaling using historical input covariance in a rehearsal-free manner. SAME also introduces adaptive expert activation to freeze selected experts during training, reducing redundant computation and cross-task interference. Extensive experiments demonstrate its SOTA performance.

The cultivation of expertise for large language models (LLMs) to solve tasks of specific areas often requires special-purpose tuning with calibrated behaviors on the expected stable outputs. To avoid huge cost brought by manual preparation of instruction datasets and training resources up to hundreds of hours, the exploitation of open knowledge including a wealth of low rank adaptation (LoRA) models and instruction datasets serves as a good starting point. However, existing methods on model and data selection focus on the performance of general-purpose capabilities while neglecting the knowledge gap exposed in domain-specific deployment. In the present study, we propose to bridge such gap by introducing few human-annotated samples (i.e., K-shot) for advancing task expertise of LLMs with open knowledge. Specifically, we develop an efficient and scalable pipeline to cost-efficiently produce task experts where K-shot data intervene in selecting the most promising expert candidates and the task-relevant instructions. A mixture-of-expert (MoE) system is built to make the best use of individual-yet-complementary knowledge between multiple experts. We unveil the two keys to the success of a MoE system, 1) the abidance by K-shot, and 2) the insistence on diversity. For the former, we ensure that models that truly possess problem-solving abilities on K-shot are selected rather than those blind guessers. Besides, during data selection, instructions that share task-relevant contexts with K-shot are prioritized. For the latter, we highlight the diversity of constituting experts and that of the fine-tuning instructions throughout the model and data selection process. Extensive experimental results confirm the superiority of our approach over existing methods on utilization of open knowledge across various tasks. Codes and models will be released later.

When deployed in the real world, AI agents will inevitably face challenges that exceed their individual capabilities. Leveraging assistance from experts, whether humans or highly capable AI systems, can significantly improve both safety and performance in such situations. Since expert assistance is costly, a central challenge is determining when to consult an expert. In this paper, we explore a novel variant of this problem, termed YRC-0, in which an agent must learn to collaborate with an expert in new environments in an unsupervised manner--that is, without interacting with the expert during training. This setting motivates the development of low-cost, robust approaches for training expert-leveraging agents. To support research in this area, we introduce YRC-Bench, an open-source benchmark that instantiates YRC-0 across diverse environments. YRC-Bench provides a standardized Gym-like API, simulated experts, an evaluation pipeline, and implementations of popular baselines. Toward tackling YRC-0, we propose a validation strategy and evaluate a range of learning methods, offering insights that can inform future research. Codebase: github.com/modanesh/YRC-Bench

Large Language Models (LLMs) have emerged as powerful tools in mathematical theorem proving, particularly when utilizing formal languages such as LEAN. The major learning paradigm is expert iteration, which necessitates a pre-defined dataset comprising numerous mathematical problems. In this process, LLMs attempt to prove problems within the dataset and iteratively refine their capabilities through self-training on the proofs they discover. We propose to use large scale LEAN problem datasets Lean-workbook for expert iteration with more than 20,000 CPU days. During expert iteration, we found log-linear trends between solved problem amount with proof length and CPU usage. We train a critic model to select relatively easy problems for policy models to make trials and guide the model to search for deeper proofs. InternLM2.5-StepProver achieves open-source state-of-the-art on MiniF2F, Lean-Workbook-Plus, ProofNet, and Putnam benchmarks. Specifically, it achieves a pass of 65.9% on the MiniF2F-test and proves (or disproves) 17.0% of problems in Lean-Workbook-Plus which shows a significant improvement compared to only 9.5% of problems proved when Lean-Workbook-Plus was released. We open-source our models and searched proofs at https://github.com/InternLM/InternLM-Math and https://huggingface.co/datasets/internlm/Lean-Workbook.

Post-training has emerged as a crucial paradigm for adapting large-scale pre-trained models to various tasks, whose effects are fully reflected by delta parameters (i.e., the disparity between post-trained and pre-trained parameters). While numerous studies have explored delta parameter properties via operations like pruning, quantization, low-rank approximation, and extrapolation, a unified framework for systematically examining these characteristics has been lacking. In this paper, we propose a novel perspective based on Riemann sum approximation of the loss function to elucidate delta parameter editing operations. Our analysis categorizes existing methods into three classes based on their post-editing performance: competitive, decreased, and improved, explaining how they are expressed by the Riemann sum approximation term and how they alter the model performance. Extensive experiments on both visual and language models, including ViT, LLaMA 3, Qwen 2, and Mistral, corroborate our theoretical findings. Furthermore, we introduce extensions to existing techniques like DARE and BitDelta, highlighting their limitations in leveraging the properties of delta parameters and reorganizing them into general expressions to enhance the applicability and effectiveness of delta parameter editing in post-trained models.

Continual learning is a promising machine learning paradigm to learn new tasks while retaining previously learned knowledge over streaming training data. Till now, rehearsal-based methods, keeping a small part of data from old tasks as a memory buffer, have shown good performance in mitigating catastrophic forgetting for previously learned knowledge. However, most of these methods typically treat each new task equally, which may not adequately consider the relationship or similarity between old and new tasks. Furthermore, these methods commonly neglect sample importance in the continual training process and result in sub-optimal performance on certain tasks. To address this challenging problem, we propose Relational Experience Replay (RER), a bi-level learning framework, to adaptively tune task-wise relationships and sample importance within each task to achieve a better `stability' and `plasticity' trade-off. As such, the proposed method is capable of accumulating new knowledge while consolidating previously learned old knowledge during continual learning. Extensive experiments conducted on three publicly available datasets (i.e., CIFAR-10, CIFAR-100, and Tiny ImageNet) show that the proposed method can consistently improve the performance of all baselines and surpass current state-of-the-art methods.

Reinforcement learning (RL) post-training is a dominant approach for improving the reasoning performance of large language models (LLMs), yet growing evidence suggests that its gains arise primarily from distribution sharpening rather than the acquisition of new capabilities. Recent work has shown that sampling from the power distribution of LLMs using Markov chain Monte Carlo (MCMC) can recover performance comparable to RL post-training without relying on external rewards; however, the high computational cost of MCMC makes such approaches impractical for widespread adoption. In this work, we propose a theoretically grounded alternative that eliminates the need for iterative MCMC. We derive a novel formulation showing that the global power distribution can be approximated by a token-level scaled low-temperature one, where the scaling factor captures future trajectory quality. Leveraging this insight, we introduce a training-free and verifier-free algorithm that sharpens the base model's generative distribution autoregressively. Empirically, we evaluate our method on math, QA, and code tasks across four LLMs, and show that our method matches or surpasses one-shot GRPO without relying on any external rewards, while reducing inference latency by over 10x compared to MCMC-based sampling.

Post-training has become a crucial step for unlocking the capabilities of large language models, with reinforcement learning (RL) emerging as a critical paradigm. Recent RL-based post-training has increasingly split into two paradigms: reinforcement learning from human feedback (RLHF), which optimizes models using human preference signals in target domains, and reinforcement learning from verifiable rewards (RLVR), which operates in verifier-backed environments. The latter has dominated recent reasoning-oriented post-training because it delivers stronger gains and higher efficiency on domain-specific tasks (e.g., reasoning). However, although in-domain RL training achieves promising performance, it still requires a substantial amount of GPU compute, which remains a major barrier to broad adoption. In this work, we study the generalization ability of RLHF learned from scratch from a small set of interactions in open-ended environments, and investigate whether the conversational abilities it explicitly acquires can implicitly transfer to downstream tasks such as mathematical reasoning and code generation, namely GRLO. Specifically, on Qwen3-4B-Base backbone, GRLO improves the average performance across all domains from 24.1 to 63.1 with only 5K prompts and 22.7 GPU hours, requiring about 46times less data and 68times less compute than a strong in-domain RLVR baseline. The resulting model is even competitive with Qwen's released post-trained models which required a much larger training cost. Notably, a subsequent in-domain RLVR stage brings only selective gains, mainly on harder competition-math benchmarks. We hope GRLO offers a simple and efficient recipe for building broadly capable post-trained models. Our code and data will be available at: https://github.com/SJY8460/GRLO{https://github.com/SJY8460/GRLO}.

A natural strategy for continual learning is to weigh a Bayesian ensemble of fixed functions. This suggests that if a (single) neural network could be interpreted as an ensemble, one could design effective algorithms that learn without forgetting. To realize this possibility, we observe that a neural network classifier with N parameters can be interpreted as a weighted ensemble of N classifiers, and that in the lazy regime limit these classifiers are fixed throughout learning. We call these classifiers the neural tangent experts and show they output valid probability distributions over the labels. We then derive the likelihood and posterior probability of each expert given past data. Surprisingly, the posterior updates for these experts are equivalent to a scaled and projected form of stochastic gradient descent (SGD) over the network weights. Away from the lazy regime, networks can be seen as ensembles of adaptive experts which improve over time. These results offer a new interpretation of neural networks as Bayesian ensembles of experts, providing a principled framework for understanding and mitigating catastrophic forgetting in continual learning settings.

The advancement of general-purpose artificial intelligence relies on large language models (LLMs) that excel across a wide range of tasks, from structured reasoning to creative generation. However, post-training methods like Supervised Fine-Tuning (SFT) often struggle with generalization, favoring memorization over transferable learning. In this work, we introduce Omni-Thinker, a unified reinforcement learning (RL) framework that enhances LLM performance across diverse tasks by combining rule-based verifiable rewards with generative preference signals via LLM-as-a-Judge evaluations. Our approach enables consistent optimization across task types and scales RL-based training to subjective domains. We further investigate training strategies, demonstrating that a curriculum-based progression that orders tasks from structured to open-ended improves performance and reduces forgetting. Experimental results across four domains reveal that curriculum learning improves performance by 5.2% over joint training and 9.1% over model merging. These results highlight the importance of task-aware sampling and hybrid supervision in scaling RL-based post-training for general-purpose LLMs.

Sparsely activated neural networks with conditional computation learn to route their inputs through different "expert" subnetworks, providing a form of modularity that densely activated models lack. Despite their possible benefits, models with learned routing often underperform their parameter-matched densely activated counterparts as well as models that use non-learned heuristic routing strategies. In this paper, we hypothesize that these shortcomings stem from the gradient estimation techniques used to train sparsely activated models that use non-differentiable discrete routing decisions. To address this issue, we introduce Soft Merging of Experts with Adaptive Routing (SMEAR), which avoids discrete routing by using a single "merged" expert constructed via a weighted average of all of the experts' parameters. By routing activations through a single merged expert, SMEAR does not incur a significant increase in computational costs and enables standard gradient-based training. We empirically validate that models using SMEAR outperform models that route based on metadata or learn sparse routing through gradient estimation. Furthermore, we provide qualitative analysis demonstrating that the experts learned via SMEAR exhibit a significant amount of specialization. All of the code used in our experiments is publicly available.

Post-training, which elicits a pretrained Base model into the corresponding Instruct model, is widely considered to be superficial. In this work, we first reinforce this hypothesis by providing novel quantitative evidence from the weight level that the effective rank (eRank) remains negligibly changed. However, this superficiality also suffers a critical trade-off, improving the exploitation capabilities at the cost of limiting its exploration. To tackle this issue, we propose Timber, a simple yet effective training-free method that enhances the exploration capability of the Instruct model while preserving its exploitation. The key insight is to partially revert Instruct towards the paired Base model by subtle yet targeted refinement of the weight deltas. Extensive experiments on Llama and Qwen series demonstrate that Timber consistently improves vanilla Instruct models, particularly on Pass@k performance. Our findings offer new insights into the post-training stage at the weight level and practical strategies to refine the Instruct model without training.

While effective post-training integrates Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL), the optimal mechanism for utilizing expert trajectories remains unresolved. We propose the Plasticity-Ceiling Framework to theoretically ground this landscape, decomposing performance into foundational SFT performance and the subsequent RL plasticity. Through extensive benchmarking, we establish the Sequential SFT-then-RL pipeline as the superior standard, overcoming the stability deficits of synchronized approaches. Furthermore, we derive precise scaling guidelines: (1) Transitioning to RL at the SFT Stable or Mild Overfitting Sub-phase maximizes the final ceiling by securing foundational SFT performance without compromising RL plasticity; (2) Refuting ``Less is More'' in the context of SFT-then-RL scaling, we demonstrate that Data Scale determines the primary post-training potential, while Trajectory Difficulty acts as a performance multiplier; and (3) Identifying that the Minimum SFT Validation Loss serves as a robust indicator for selecting the expert trajectories that maximize the final performance ceiling. Our findings provide actionable guidelines for maximizing the value extracted from expert trajectories.

A fundamental challenge in formal theorem proving by LLMs is the lack of high-quality training data. Although reinforcement learning or expert iteration partially mitigates this issue by alternating between LLM generating proofs and finetuning them on correctly generated ones, performance quickly plateaus due to the scarcity of correct proofs (sparse rewards). To keep improving the models with limited data, we draw inspiration from mathematicians, who continuously develop new results, partly by proposing novel conjectures or exercises (which are often variants of known results) and attempting to solve them. We design the Self-play Theorem Prover (STP) that simultaneously takes on two roles, conjecturer and prover, each providing training signals to the other. The conjecturer is trained iteratively on previously generated conjectures that are barely provable by the current prover, which incentivizes it to generate increasingly challenging conjectures over time. The prover attempts to prove the conjectures with standard expert iteration. We evaluate STP with both Lean and Isabelle formal versifiers. With 19.8 billion tokens generated during the training in Lean, STP proves 26.3% of the statements in the LeanWorkbook dataset, doubling the previous best result of 13.2% achieved through expert iteration. The final model achieves state-of-the-art performance among whole-proof generation methods on miniF2F-test (61.7%, pass@3200), Proofnet-test (23.1%, pass@3200) and PutnamBench (8/644, pass@3200).

Post-training has demonstrated its importance in enhancing the reasoning capabilities of large language models (LLMs). The primary post-training methods can be categorized into supervised fine-tuning (SFT) and reinforcement fine-tuning (RFT). SFT is efficient and well-suited for small language models, but it may lead to overfitting and limit the reasoning abilities of larger models. In contrast, RFT generally yields better generalization but depends heavily on the strength of the base model. To address the limitations of SFT and RFT, we propose Unified Fine-Tuning (UFT), a novel post-training paradigm that unifies SFT and RFT into a single, integrated process. UFT enables the model to effectively explore solutions while incorporating informative supervision signals, bridging the gap between memorizing and thinking underlying existing methods. Notably, UFT outperforms both SFT and RFT in general, regardless of model sizes. Furthermore, we theoretically prove that UFT breaks RFT's inherent exponential sample complexity bottleneck, showing for the first time that unified training can exponentially accelerate convergence on long-horizon reasoning tasks.

Continual learning aims to equip models with the ability to retain previously learned knowledge like a human. Recent work incorporating Parameter-Efficient Fine-Tuning has revitalized the field by introducing lightweight extension modules. However, existing methods usually overlook the issue of information leakage caused by the fact that the experiment data have been used in pre-trained models. Once these duplicate data are removed in the pre-training phase, their performance can be severely affected. In this paper, we propose a new LoRA-based rehearsal-free method named DESIRE. Our method avoids imposing additional constraints during training to mitigate catastrophic forgetting, thereby maximizing the learning of new classes. To integrate knowledge from old and new tasks, we propose two efficient post-processing modules. On the one hand, we retain only two sets of LoRA parameters for merging and propose dynamic representation consolidation to calibrate the merged feature representation. On the other hand, we propose decision boundary refinement to address classifier bias when training solely on new class data. Extensive experiments demonstrate that our method achieves state-of-the-art performance on multiple datasets and strikes an effective balance between stability and plasticity. Our code will be publicly available.

Recent advances in post-training techniques have endowed Large Language Models (LLMs) with enhanced capabilities for tackling complex, logic-intensive tasks through the generation of supplementary planning tokens. This development raises a fundamental question: Are these models aware of what they "learn" and "think"? To address this, we define three core competencies: (1) awareness of learned latent policies, (2) generalization of these policies across domains, and (3) alignment between internal reasoning traces and final outputs. We empirically evaluate these abilities on several tasks, each designed to require learning a distinct policy. Furthermore, we contrast the profiles of models post-trained via Supervised Fine-Tuning (SFT), Direct Policy Optimization (DPO), and Group Relative Policy Optimization (GRPO). Our findings indicate that RL-trained models not only demonstrate greater awareness of their learned behaviors and stronger generalizability to novel, structurally similar tasks than SFT models but also often exhibit weak alignment between their reasoning traces and final outputs, an effect most pronounced in GRPO-trained models.

Adapting one's thought process based on corrective feedback is an essential ability in human learning, particularly in collaborative settings. In contrast, the current large language model training paradigm relies heavily on modeling vast, static corpora. While effective for knowledge acquisition, it overlooks the interactive feedback loops essential for models to adapt dynamically to their context. In this work, we propose a framework that treats this interactive in-context learning ability not as an emergent property, but as a distinct, trainable skill. We introduce a scalable method that transforms single-turn verifiable tasks into multi-turn didactic interactions driven by information asymmetry. We first show that current flagship models struggle to integrate corrective feedback on hard reasoning tasks. We then demonstrate that models trained with our approach dramatically improve the ability to interactively learn from language feedback. More specifically, the multi-turn performance of a smaller model nearly reaches that of a model an order of magnitude larger. We also observe robust out-of-distribution generalization: interactive training on math problems transfers to diverse domains like coding, puzzles and maze navigation. Our qualitative analysis suggests that this improvement is due to an enhanced in-context plasticity. Finally, we show that this paradigm offers a unified path to self-improvement. By training the model to predict the teacher's critiques, effectively modeling the feedback environment, we convert this external signal into an internal capability, allowing the model to self-correct even without a teacher.

Post-training of large language models involves a fundamental trade-off between supervised fine-tuning (SFT), which efficiently mimics demonstrations but tends to memorize, and reinforcement learning (RL), which achieves better generalization at higher computational cost. Dynamic Fine-Tuning (DFT) recently emerged as a promising middle ground, reweighting SFT objectives with token probabilities and achieving improvements in certain reasoning domains, though it exhibits instability in other tasks. We provide a analysis of DFT through the reward-weighted regression (RWR) framework, revealing that it corresponds to a specific auxiliary distribution choice that yields provably tighter RL bounds than standard SFT. However, our analysis also uncovers a critical limitation: this construction lacks distributional anchoring, leading to progressive drift that undermines training stability. To address this, we propose Anchored Supervised Fine-Tuning (ASFT), which augments DFT's reweighting with lightweight KL regularization to preserve tightness while ensuring stability. Empirically, ASFT consistently outperforms both SFT and DFT across mathematical reasoning, medical knowledge grounding, and code generation, achieving substantial improvements with minimal computational overhead. Our RWR framework provides a systematic lens for understanding post-training methods and demonstrates that principled theoretical analysis leads to both stronger guarantees and practical gains.

This paper proposes a novel formulation for reinforcement learning (RL) with large language models, explaining why and under what conditions the true sequence-level reward can be optimized via a surrogate token-level objective in policy gradient methods such as REINFORCE. Specifically, through a first-order approximation, we show that this surrogate becomes increasingly valid only when both the training-inference discrepancy and policy staleness are minimized. This insight provides a principled explanation for the crucial role of several widely adopted techniques in stabilizing RL training, including importance sampling correction, clipping, and particularly Routing Replay for Mixture-of-Experts (MoE) models. Through extensive experiments with a 30B MoE model totaling hundreds of thousands of GPU hours, we show that for on-policy training, the basic policy gradient algorithm with importance sampling correction achieves the highest training stability. When off-policy updates are introduced to accelerate convergence, combining clipping and Routing Replay becomes essential to mitigate the instability caused by policy staleness. Notably, once training is stabilized, prolonged optimization consistently yields comparable final performance regardless of cold-start initialization. We hope that the shared insights and the developed recipes for stable RL training will facilitate future research.

Small language models are attractive for production deployment due to their low cost, fast inference, and ease of specialization. However, adapting them to a specific task remains a challenging engineering loop, driven not by training itself but by surrounding decisions: data curation, failure diagnosis, regression avoidance, and iteration control. We present Pioneer Agent, a closed-loop system that automates this lifecycle. In cold-start mode, given only a natural-language task description, the agent acquires data, constructs evaluation sets, and iteratively trains models by jointly optimizing data, hyperparameters, and learning strategy. In production mode, given a deployed model with labeled failures, it diagnoses error patterns, constructs targeted training data, and retrains under explicit regression constraints. To evaluate this setting, we introduce AdaptFT-Bench, a benchmark of synthetic inference logs with progressively increasing noise, designed to test the full adaptation loop: diagnosis, curriculum synthesis, retraining, and verification. Across eight cold-start benchmarks spanning reasoning, math, code generation, summarization, and classification, Pioneer Agent improves over base models by 1.6-83.8 points. On AdaptFT-Bench, it improves or preserves performance in all seven scenarios, while naive retraining degrades by up to 43 points. On two production-style deployments built from public benchmark tasks, it raises intent classification from 84.9% to 99.3% and Entity F1 from 0.345 to 0.810. Beyond performance gains, the agent often discovers effective training strategies, including chain-of-thought supervision, task-specific optimization, and quality-focused data curation, purely from downstream feedback.

Continual learning is a setting where machine learning models learn novel concepts from continuously shifting training data, while simultaneously avoiding degradation of knowledge on previously seen classes which may disappear from the training data for extended periods of time (a phenomenon known as the catastrophic forgetting problem). Current approaches for continual learning of a single expanding task (aka class-incremental continual learning) require extensive rehearsal of previously seen data to avoid this degradation of knowledge. Unfortunately, rehearsal comes at a cost to memory, and it may also violate data-privacy. Instead, we explore combining knowledge distillation and parameter regularization in new ways to achieve strong continual learning performance without rehearsal. Specifically, we take a deep dive into common continual learning techniques: prediction distillation, feature distillation, L2 parameter regularization, and EWC parameter regularization. We first disprove the common assumption that parameter regularization techniques fail for rehearsal-free continual learning of a single, expanding task. Next, we explore how to leverage knowledge from a pre-trained model in rehearsal-free continual learning and find that vanilla L2 parameter regularization outperforms EWC parameter regularization and feature distillation. Finally, we explore the recently popular ImageNet-R benchmark, and show that L2 parameter regularization implemented in self-attention blocks of a ViT transformer outperforms recent popular prompting for continual learning methods.

Continual Model Merging (CMM) sequentially integrates task-specific models into a unified architecture without intensive retraining. However, existing CMM methods are hindered by a fundamental saturation-redundancy dilemma: backbone-centric approaches face parameter saturation and representation interference within fixed capacities, whereas Mixture-of-Experts (MoE) variants resort to indiscriminate expansion, incurring expert redundancy and a routing bottleneck reliant on additional data-driven optimization. To resolve these challenges, we propose MADE-IT (Manifold-Aware Dynamic Expert Evolution and Implicit rouTing), an adaptive CMM method that orchestrates expert management and activation by grounding intrinsic expert representations in manifold geometry. We introduce a projection-based subspace affinity metric coupled with a distribution-aware adaptive threshold mechanism to guide autonomous expert evolution, harmonizing diversity with architectural parsimony. Furthermore, to bypass parameterized gating networks, we design a data-free and training-free implicit routing mechanism that activates experts via feature-subspace alignment. Extensive experiments demonstrate that MADE-IT consistently outperforms strong baselines in accuracy and robustness across long-horizon and shuffled task sequences, while significantly pruning redundant experts, particularly within generic modules and early layers.

The development of state-of-the-art large language models is commonly understood as a two-stage process involving pre-training and post-training. We point out the need for an additional intermediate stage called reinforcement mid-training with potential for strong performance gains. In this paper, we formally define the problem and identify three key challenges: (1) inefficient training due to excessive reasoning steps, (2) disregard of the imbalanced token entropy distribution, and (3) underutilization of token information. To address these challenges, we propose RMT, a framework for efficient, adaptive, and unified reinforcement mid-training with various innovative components. In particular, we first introduce a dynamic token budget mechanism that constrains unnecessary reasoning steps and mitigates model overthinking. Next, we design a curriculum-based adaptive sampling method that fosters a progressive learning trajectory from easy to hard tokens. Finally, we present a dual training strategy that combines reinforcement learning with next-token prediction, ensuring targeted learning on key tokens and full exploitation of all token information. Extensive experiments demonstrate the superiority of RMT over state-of-the-art methods, achieving up to +64.91% performance improvement with only 21% of the reasoning length in language modeling. We also show that checkpoints obtained after reinforcement mid-training can benefit the subsequent post-training, yielding up to +18.76% improvement in the mathematical domain.

Unified multimodal large language models such as Show-o and Janus have achieved strong performance across both generation and understanding tasks. However, these models typically rely on large-scale datasets and require substantial computation during the pretraining stage. In addition, several post-training methods have been proposed, but they often depend on external data or are limited to task-specific customization. In this work, we introduce UniRL, a self-improving post-training approach. Our approach enables the model to generate images from prompts and use them as training data in each iteration, without relying on any external image data. Moreover, it enables the two tasks to enhance each other: the generated images are used for understanding, and the understanding results are used to supervise generation. We explore supervised fine-tuning (SFT) and Group Relative Policy Optimization (GRPO) to optimize the models. UniRL offers three key advantages: (1) it requires no external image data, as all training samples are generated by the model itself during training; (2) it not only improves individual task performance, but also reduces the imbalance between generation and understanding; and (3) it requires only several additional training steps during the post-training stage. We evaluate UniRL on top of Show-o and Janus, achieving a GenEval score of 0.77 for Show-o and 0.65 for Janus. Code and models will be released in https://github.com/showlab/UniRL.

Continual Learning (CL) aims at incrementally learning new tasks without forgetting the knowledge acquired from old ones. Experience Replay (ER) is a simple and effective rehearsal-based strategy, which optimizes the model with current training data and a subset of old samples stored in a memory buffer. To further reduce forgetting, recent approaches extend ER with various techniques, such as model regularization and memory sampling. However, the prediction consistency between the new model and the old one on current training data has been seldom explored, resulting in less knowledge preserved when few previous samples are available. To address this issue, we propose a CL method with Strong Experience Replay (SER), which additionally utilizes future experiences mimicked on the current training data, besides distilling past experience from the memory buffer. In our method, the updated model will produce approximate outputs as its original ones, which can effectively preserve the acquired knowledge. Experimental results on multiple image classification datasets show that our SER method surpasses the state-of-the-art methods by a noticeable margin.

Highly effective, task-specific prompts are often heavily engineered by experts to integrate detailed instructions and domain insights based on a deep understanding of both instincts of large language models (LLMs) and the intricacies of the target task. However, automating the generation of such expert-level prompts remains elusive. Existing prompt optimization methods tend to overlook the depth of domain knowledge and struggle to efficiently explore the vast space of expert-level prompts. Addressing this, we present PromptAgent, an optimization method that autonomously crafts prompts equivalent in quality to those handcrafted by experts. At its core, PromptAgent views prompt optimization as a strategic planning problem and employs a principled planning algorithm, rooted in Monte Carlo tree search, to strategically navigate the expert-level prompt space. Inspired by human-like trial-and-error exploration, PromptAgent induces precise expert-level insights and in-depth instructions by reflecting on model errors and generating constructive error feedback. Such a novel framework allows the agent to iteratively examine intermediate prompts (states), refine them based on error feedbacks (actions), simulate future rewards, and search for high-reward paths leading to expert prompts. We apply PromptAgent to 12 tasks spanning three practical domains: BIG-Bench Hard (BBH), as well as domain-specific and general NLP tasks, showing it significantly outperforms strong Chain-of-Thought and recent prompt optimization baselines. Extensive analyses emphasize its capability to craft expert-level, detailed, and domain-insightful prompts with great efficiency and generalizability.

Reinforcement learning (RL) post-training has enabled newer capabilities in models, such as agentic tool-use for search. However, these models struggle primarily due to limitations with sparse outcome-based rewards and a lack of training data that encapsulates questions of differing hardness, which results in models not performing deeper searches with tools to collect evidence for question-answering. To address these limitations, we introduce S^3-R1 (Synthetic data and stabilized Search R1), a framework that couples a data-centric approach with denser learning signals. We first develop a synthetic generation and curation pipeline that programmatically derives diverse, multi-hop questions from existing documents. This pipeline incorporates a retrieval-based verification step to specifically isolate questions of intermediate difficulty. We then pair this expanded training set with a reward structure that evaluates both intermediate search quality and the correctness of the final answer. This setup directly mitigates the credit assignment problems inherent to sparse rewards. Our evaluations show that S^3-R1 outperforms existing baselines by learning more effective search and synthesis strategies, yielding up to a 10% improvement in robust generalization on out-of-domain datasets.

Recent advances in reinforcement learning (RL)-based post-training have led to notable improvements in large language models (LLMs), particularly in enhancing their reasoning capabilities to handle complex tasks. However, most existing methods treat the training data as a unified whole, overlooking the fact that modern LLM training often involves a mixture of data from diverse distributions-varying in both source and difficulty. This heterogeneity introduces a key challenge: how to adaptively schedule training across distributions to optimize learning efficiency. In this paper, we present a principled curriculum learning framework grounded in the notion of distribution-level learnability. Our core insight is that the magnitude of policy advantages reflects how much a model can still benefit from further training on a given distribution. Based on this, we propose a distribution-level curriculum learning framework for RL-based LLM post-training, which leverages the Upper Confidence Bound (UCB) principle to dynamically adjust sampling probabilities for different distrubutions. This approach prioritizes distributions with either high average advantage (exploitation) or low sample count (exploration), yielding an adaptive and theoretically grounded training schedule. We instantiate our curriculum learning framework with GRPO as the underlying RL algorithm and demonstrate its effectiveness on logic reasoning datasets with multiple difficulties and sources. Our experiments show that our framework significantly improves convergence speed and final performance, highlighting the value of distribution-aware curriculum strategies in LLM post-training. Code: https://github.com/ZhentingWang/DUMP.

Reinforcement learning (RL) post-training has become a trending paradigm for enhancing the capabilities of large language models (LLMs). Most existing RL systems for LLMs operate in a fully synchronous manner, where training must wait for the rollout of an entire batch to complete. This design leads to severe inefficiencies, as extremely long trajectories can stall the entire rollout process and leave many GPUs idle. To address this issue, we propose Concurrency- Controlled Partial Rollout with Importance Sampling (CoPRIS), which mitigates long-tail inefficiencies by maintaining a fixed number of concurrent rollouts, early-terminating once sufficient samples are collected, and reusing unfinished trajectories in subsequent rollouts. To mitigate the impact of off-policy trajectories, we introduce Cross-stage Importance Sampling Correction, which concatenates buffered log probabilities from the previous policy with those recomputed under the current policy for importance sampling correction. Experiments on challenging mathematical reasoning benchmarks show that CoPRIS achieves up to 1.94x faster training while maintaining comparable or superior performance to synchronous RL systems. The code of CoPRIS is available at https://github.com/777pomingzi/CoPRIS.

Ensuring safety, factuality and overall quality in the generations of large language models is a critical challenge, especially as these models are increasingly deployed in real-world applications. The prevailing approach to addressing these issues involves collecting expensive, carefully curated datasets and applying multiple stages of fine-tuning and alignment. However, even this complex pipeline cannot guarantee the correction of patterns learned during pretraining. Therefore, addressing these issues during pretraining is crucial, as it shapes a model's core behaviors and prevents unsafe or hallucinated outputs from becoming deeply embedded. To tackle this issue, we introduce a new pretraining method that streams documents and uses reinforcement learning (RL) to improve the next K generated tokens at each step. A strong, post-trained model judges candidate generations -- including model rollouts, the original suffix, and a rewritten suffix -- for quality, safety, and factuality. Early in training, the process relies on the original and rewritten suffixes; as the model improves, RL rewards high-quality rollouts. This approach builds higher quality, safer, and more factual models from the ground up. In experiments, our method gives 36.2% and 18.5% relative improvements over standard pretraining in terms of factuality and safety, and up to 86.3% win rate improvements in overall generation quality.

Large Language Models (LLMs) offer a promising basis for creating agents that can tackle complex tasks through iterative environmental interaction. Existing methods either require these agents to mimic expert-provided trajectories or rely on definitive environmental feedback for reinforcement learning which limits their application to specific scenarios like gaming or code generation. This paper introduces a novel training method for LLM-based agents using weakly supervised signals from a critic LLM, bypassing the need for expert trajectories or definitive feedback. Our agents are trained in iterative manner, where they initially generate trajectories through environmental interaction. Subsequently, a critic LLM selects a subset of good trajectories, which are then used to update the agents, enabling them to generate improved trajectories in the next iteration. Extensive tests on the API-bank dataset show consistent improvement in our agents' capabilities and comparable performance to GPT-4, despite using open-source models with much fewer parameters.

Post-training methods, especially Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL), play an important role in improving large language models' (LLMs) complex reasoning abilities. However, the dominant two-stage pipeline (SFT then RL) suffers from a key inconsistency: SFT enforces rigid imitation that suppresses exploration and induces forgetting, limiting RL's potential for improvements. We address this inefficiency with TRAPO (Trust-Region Adaptive Policy Optimization), a hybrid framework that interleaves SFT and RL within each training instance by optimizing SFT loss on expert prefixes and RL loss on the model's own completions, unifying external supervision and self-exploration. To stabilize training, we introduce Trust-Region SFT (TrSFT), which minimizes forward KL divergence inside a trust region but attenuates optimization outside, effectively shifting toward reverse KL and yielding stable, mode-seeking updates favorable for RL. An adaptive prefix-selection mechanism further allocates expert guidance based on measured utility. Experiments on five mathematical reasoning benchmarks show that TRAPO consistently surpasses standard SFT, RL, and SFT-then-RL pipelines, as well as recent state-of-the-art approaches, establishing a strong new paradigm for reasoning-enhanced LLMs.

Post-training processes are essential phases in grounding pre-trained language models to real-world tasks, with learning from demonstrations or preference signals playing a crucial role in this adaptation. We present a unified theoretical framework bridging Supervised Fine-Tuning (SFT) and preference learning in Large Language Model (LLM) post-training. Through rigorous mathematical derivation, we demonstrate that both SFT and preference learning methods like Direct Preference Optimization (DPO) operate within the same optimal policy-reward subspace, with SFT representing a special case of implicit reward learning. Our analysis reveals a critical limitation in conventional SFT: the KL divergence term in distribution matching becomes constant with respect to the policy during optimization, failing to constrain model updates. To address this, we propose a simple yet effective learning rate reduction approach that yields significant performance improvements (up to 25\% relative gain and 6\% absolute win rate increase in instruction following tasks. Additionally, we derive alternative SFT objectives from various f-divergence functions that preserve the KL term during optimization, further enhancing post-DPO model performance. Finally, we extend the theoretical relationship between LLM logits and Q-functions from preference learning to the SFT context, providing mathematical derivations and experimental validation.

Large Multimodal Models encode extensive factual knowledge in their pre-trained weights. However, its knowledge remains static and limited, unable to keep pace with real-world developments, which hinders continuous knowledge acquisition. Effective knowledge injection thus becomes critical, involving two goals: knowledge adaptation (injecting new knowledge) and knowledge retention (preserving old knowledge). Existing methods often struggle to learn new knowledge and suffer from catastrophic forgetting. To address this, we propose KORE, a synergistic method of KnOwledge-oRientEd augmentations and constraints for injecting new knowledge into large multimodal models while preserving old knowledge. Unlike general text or image data augmentation, KORE automatically converts individual knowledge items into structured and comprehensive knowledge to ensure that the model accurately learns new knowledge, enabling accurate adaptation. Meanwhile, KORE stores previous knowledge in the covariance matrix of LMM's linear layer activations and initializes the adapter by projecting the original weights into the matrix's null space, defining a fine-tuning direction that minimizes interference with previous knowledge, enabling powerful retention. Extensive experiments on various LMMs, including LLaVA-v1.5-7B, LLaVA-v1.5-13B, and Qwen2.5-VL-7B, show that KORE achieves superior new knowledge injection performance and effectively mitigates catastrophic forgetting.

This paper studies post-training large language models (LLMs) using preference feedback from a powerful oracle to help a model iteratively improve over itself. The typical approach for post-training LLMs involves Reinforcement Learning from Human Feedback (RLHF), which traditionally separates reward learning and subsequent policy optimization. However, such a reward maximization approach is limited by the nature of "point-wise" rewards (such as Bradley-Terry model), which fails to express complex intransitive or cyclic preference relations. While advances on RLHF show reward learning and policy optimization can be merged into a single contrastive objective for stability, they yet still remain tethered to the reward maximization framework. Recently, a new wave of research sidesteps the reward maximization presumptions in favor of directly optimizing over "pair-wise" or general preferences. In this paper, we introduce Direct Nash Optimization (DNO), a provable and scalable algorithm that marries the simplicity and stability of contrastive learning with theoretical generality from optimizing general preferences. Because DNO is a batched on-policy algorithm using a regression-based objective, its implementation is straightforward and efficient. Moreover, DNO enjoys monotonic improvement across iterations that help it improve even over a strong teacher (such as GPT-4). In our experiments, a resulting 7B parameter Orca-2.5 model aligned by DNO achieves the state-of-the-art win-rate against GPT-4-Turbo of 33% on AlpacaEval 2.0 (even after controlling for response length), an absolute gain of 26% (7% to 33%) over the initializing model. It outperforms models with far more parameters, including Mistral Large, Self-Rewarding LM (70B parameters), and older versions of GPT-4.

Existing reinforcement learning (RL)-based post-training methods for large language models have advanced rapidly, yet their design has largely been guided by heuristics rather than systematic theoretical principles. This gap limits our understanding of the properties of the gradient estimators and the associated optimization algorithms, thereby constraining opportunities to improve training stability and overall performance. In this work, we provide a unified theoretical framework that characterizes the statistical properties of commonly used policy-gradient estimators under mild assumptions. Our analysis establishes unbiasedness, derives exact variance expressions, and yields an optimization-loss upper bound that enables principled reasoning about learning dynamics. Building on these results, we prove convergence guarantees and derive an adaptive learning-rate schedule governed by the signal-to-noise ratio (SNR) of gradients. We further show that the variance-optimal baseline is a gradient-weighted estimator, offering a new principle for variance reduction and naturally enhancing stability beyond existing methods. These insights motivate Optimal Baseline and Learning-Rate Policy Optimization (OBLR-PO), an algorithm that jointly adapts learning rates and baselines in a theoretically grounded manner. Experiments on Qwen3-4B-Base and Qwen3-8B-Base demonstrate consistent gains over existing policy optimization methods, validating that our theoretical contributions translate into practical improvements in large-scale post-training.

Iterative methods are ubiquitous in large-scale scientific computing applications, and a number of approaches based on meta-learning have been recently proposed to accelerate them. However, a systematic study of these approaches and how they differ from meta-learning is lacking. In this paper, we propose a framework to analyze such learning-based acceleration approaches, where one can immediately identify a departure from classical meta-learning. We show that this departure may lead to arbitrary deterioration of model performance. Based on our analysis, we introduce a novel training method for learning-based acceleration of iterative methods. Furthermore, we theoretically prove that the proposed method improves upon the existing methods, and demonstrate its significant advantage and versatility through various numerical applications.

We introduce Agent K v1.0, an end-to-end autonomous data science agent designed to automate, optimise, and generalise across diverse data science tasks. Fully automated, Agent K v1.0 manages the entire data science life cycle by learning from experience. It leverages a highly flexible structured reasoning framework to enable it to dynamically process memory in a nested structure, effectively learning from accumulated experience stored to handle complex reasoning tasks. It optimises long- and short-term memory by selectively storing and retrieving key information, guiding future decisions based on environmental rewards. This iterative approach allows it to refine decisions without fine-tuning or backpropagation, achieving continuous improvement through experiential learning. We evaluate our agent's apabilities using Kaggle competitions as a case study. Following a fully automated protocol, Agent K v1.0 systematically addresses complex and multimodal data science tasks, employing Bayesian optimisation for hyperparameter tuning and feature engineering. Our new evaluation framework rigorously assesses Agent K v1.0's end-to-end capabilities to generate and send submissions starting from a Kaggle competition URL. Results demonstrate that Agent K v1.0 achieves a 92.5\% success rate across tasks, spanning tabular, computer vision, NLP, and multimodal domains. When benchmarking against 5,856 human Kaggle competitors by calculating Elo-MMR scores for each, Agent K v1.0 ranks in the top 38\%, demonstrating an overall skill level comparable to Expert-level users. Notably, its Elo-MMR score falls between the first and third quartiles of scores achieved by human Grandmasters. Furthermore, our results indicate that Agent K v1.0 has reached a performance level equivalent to Kaggle Grandmaster, with a record of 6 gold, 3 silver, and 7 bronze medals, as defined by Kaggle's progression system.

We introduce a novel framework for incorporating human expertise into algorithmic predictions. Our approach leverages human judgment to distinguish inputs which are algorithmically indistinguishable, or "look the same" to predictive algorithms. We argue that this framing clarifies the problem of human-AI collaboration in prediction tasks, as experts often form judgments by drawing on information which is not encoded in an algorithm's training data. Algorithmic indistinguishability yields a natural test for assessing whether experts incorporate this kind of "side information", and further provides a simple but principled method for selectively incorporating human feedback into algorithmic predictions. We show that this method provably improves the performance of any feasible algorithmic predictor and precisely quantify this improvement. We find empirically that although algorithms often outperform their human counterparts on average, human judgment can improve algorithmic predictions on specific instances (which can be identified ex-ante). In an X-ray classification task, we find that this subset constitutes nearly 30% of the patient population. Our approach provides a natural way of uncovering this heterogeneity and thus enabling effective human-AI collaboration.

Recent generative reasoning breakthroughs have transformed how large language models (LLMs) tackle complex problems by dynamically retrieving and refining information while generating coherent, multi-step thought processes. Techniques such as inference-time scaling, reinforcement learning, supervised fine-tuning, and distillation have been successfully applied to models like DeepSeek-R1, OpenAI's o1 & o3, GPT-4o, Qwen-32B, and various Llama variants, resulting in enhanced reasoning capabilities. In this paper, we provide a comprehensive analysis of the top 27 LLM models released between 2023 and 2025 (including models such as Mistral AI Small 3 24B, DeepSeek-R1, Search-o1, QwQ-32B, and phi-4). Then, we present an extensive overview of training methodologies that spans general training approaches, mixture-of-experts (MoE) and architectural innovations, retrieval-augmented generation (RAG), chain-of-thought and self-improvement techniques, as well as test-time compute scaling, distillation, and reinforcement learning (RL) methods. Finally, we discuss the key challenges in advancing LLM capabilities, including improving multi-step reasoning without human supervision, overcoming limitations in chained tasks, balancing structured prompts with flexibility, and enhancing long-context retrieval and external tool integration.

Continual Learning (CL) focuses on learning from dynamic and changing data distributions while retaining previously acquired knowledge. Various methods have been developed to address the challenge of catastrophic forgetting, including regularization-based, Bayesian-based, and memory-replay-based techniques. However, these methods lack a unified framework and common terminology for describing their approaches. This research aims to bridge this gap by introducing a comprehensive and overarching framework that encompasses and reconciles these existing methodologies. Notably, this new framework is capable of encompassing established CL approaches as special instances within a unified and general optimization objective. An intriguing finding is that despite their diverse origins, these methods share common mathematical structures. This observation highlights the compatibility of these seemingly distinct techniques, revealing their interconnectedness through a shared underlying optimization objective. Moreover, the proposed general framework introduces an innovative concept called refresh learning, specifically designed to enhance the CL performance. This novel approach draws inspiration from neuroscience, where the human brain often sheds outdated information to improve the retention of crucial knowledge and facilitate the acquisition of new information. In essence, refresh learning operates by initially unlearning current data and subsequently relearning it. It serves as a versatile plug-in that seamlessly integrates with existing CL methods, offering an adaptable and effective enhancement to the learning process. Extensive experiments on CL benchmarks and theoretical analysis demonstrate the effectiveness of the proposed refresh learning. Code is available at https://github.com/joey-wang123/CL-refresh-learning.

We introduce PLaMo-100B, a large-scale language model designed for Japanese proficiency. The model was trained from scratch using 2 trillion tokens, with architecture such as QK Normalization and Z-Loss to ensure training stability during the training process. Post-training techniques, including Supervised Fine-Tuning and Direct Preference Optimization, were applied to refine the model's performance. Benchmark evaluations suggest that PLaMo-100B performs well, particularly in Japanese-specific tasks, achieving results that are competitive with frontier models like GPT-4.

Real-world digital environments are highly diverse and dynamic. These characteristics cause agents to frequently encounter unseen scenarios and distribution shifts, making continual learning in specific environments essential for computer-use agents (CUAs). However, a key challenge lies in obtaining high-quality and environment-grounded agent data without relying on costly human annotation. In this work, we introduce ACuRL, an Autonomous Curriculum Reinforcement Learning framework that continually adapts agents to specific environments with zero human data. The agent first explores target environments to acquire initial experiences. During subsequent iterative training, a curriculum task generator leverages these experiences together with feedback from the previous iteration to synthesize new tasks tailored for the agent's current capabilities. To provide reliable reward signals, we introduce CUAJudge, a robust automatic evaluator for CUAs that achieves 93% agreement with human judgments. Empirically, our method effectively enables both intra-environment and cross-environment continual learning, yielding 4-22% performance gains without catastrophic forgetting on existing environments. Further analyses show highly sparse updates (e.g., 20% parameters), which helps explain the effective and robust adaptation. Our data and code are available at https://github.com/OSU-NLP-Group/ACuRL.

Progress in many task domains emerges from repeated revisions to previous solution attempts. Training agents that can reliably self-improve over such sequences at inference-time is a natural target for reinforcement learning (RL), yet the naive approach assumes a fixed maximum iteration depth, which can be both costly and arbitrary. We present Exploratory Iteration (ExIt), a family of autocurriculum RL methods that directly exploits the recurrent structure of self-improvement tasks to train LLMs to perform multi-step self-improvement at inference-time while only training on the most informative single-step iterations. ExIt grows a task space by selectively sampling the most informative intermediate, partial histories encountered during an episode for continued iteration, treating these starting points as new self-iteration task instances to train a self-improvement policy. ExIt can further pair with explicit exploration mechanisms to sustain greater task diversity. Across several domains, encompassing competition math, multi-turn tool-use, and machine learning engineering, we demonstrate that ExIt strategies, starting from either a single or many task instances, can produce policies exhibiting strong inference-time self-improvement on held-out task instances, and the ability to iterate towards higher performance over a step budget extending beyond the average iteration depth encountered during training.

Recent advances in large language model (LLM) post-training have leveraged two distinct paradigms to enhance reasoning capabilities: reinforcement learning (RL) and knowledge distillation (KD). While RL enables the emergence of complex reasoning behaviors, it often suffers from low sample efficiency when the initial policy struggles to explore high-reward trajectories. Conversely, KD improves learning efficiency via mimicking the teacher model but tends to generalize poorly to out-of-domain scenarios. In this work, we present KDRL, a unified post-training framework that jointly optimizes a reasoning model through teacher supervision (KD) and self-exploration (RL). Specifically, KDRL leverages policy gradient optimization to simultaneously minimize the reverse Kullback-Leibler divergence (RKL) between the student and teacher distributions while maximizing the expected rule-based rewards. We first formulate a unified objective that integrates GRPO and KD, and systematically explore how different KL approximations, KL coefficients, and reward-guided KD strategies affect the overall post-training dynamics and performance. Empirical results on multiple reasoning benchmarks demonstrate that KDRL outperforms GRPO and various KD baselines while achieving a favorable balance between performance and reasoning token efficiency. These findings indicate that integrating KD and RL serves as an effective and efficient strategy to train reasoning LLMs.

Modern language model (LM) training has been divided into multiple stages, making it difficult for downstream developers to evaluate the impact of design choices made at each stage. We present EvoLM, a model suite that enables systematic and transparent analysis of LMs' training dynamics across pre-training, continued pre-training, supervised fine-tuning, and reinforcement learning. By training over 100 LMs with 1B and 4B parameters from scratch, we rigorously evaluate both upstream (language modeling) and downstream (problem-solving) reasoning capabilities, including considerations of both in-domain and out-of-domain generalization. Key insights highlight the diminishing returns from excessive pre-training and post-training, the importance and practices of mitigating forgetting during domain-specific continued pre-training, the crucial role of continued pre-training in bridging pre-training and post-training phases, and various intricate trade-offs when configuring supervised fine-tuning and reinforcement learning. To facilitate open research and reproducibility, we release all pre-trained and post-trained models, training datasets for all stages, and our entire training and evaluation pipeline.

The goal of continual learning is to find a model that solves multiple learning tasks which are presented sequentially to the learner. A key challenge in this setting is that the learner may forget how to solve a previous task when learning a new task, a phenomenon known as catastrophic forgetting. To address this challenge, many practical methods have been proposed, including memory-based, regularization-based, and expansion-based methods. However, a rigorous theoretical understanding of these methods remains elusive. This paper aims to bridge this gap between theory and practice by proposing a new continual learning framework called Ideal Continual Learner (ICL), which is guaranteed to avoid catastrophic forgetting by construction. We show that ICL unifies multiple well-established continual learning methods and gives new theoretical insights into the strengths and weaknesses of these methods. We also derive generalization bounds for ICL which allow us to theoretically quantify how rehearsal affects generalization. Finally, we connect ICL to several classic subjects and research topics of modern interest, which allows us to make historical remarks and inspire future directions.

We posit that to achieve superhuman agents, future models require superhuman feedback in order to provide an adequate training signal. Current approaches commonly train reward models from human preferences, which may then be bottlenecked by human performance level, and secondly these separate frozen reward models cannot then learn to improve during LLM training. In this work, we study Self-Rewarding Language Models, where the language model itself is used via LLM-as-a-Judge prompting to provide its own rewards during training. We show that during Iterative DPO training that not only does instruction following ability improve, but also the ability to provide high-quality rewards to itself. Fine-tuning Llama 2 70B on three iterations of our approach yields a model that outperforms many existing systems on the AlpacaEval 2.0 leaderboard, including Claude 2, Gemini Pro, and GPT-4 0613. While only a preliminary study, this work opens the door to the possibility of models that can continually improve in both axes.

In this report, we introduce Qwen2.5, a comprehensive series of large language models (LLMs) designed to meet diverse needs. Compared to previous iterations, Qwen 2.5 has been significantly improved during both the pre-training and post-training stages. In terms of pre-training, we have scaled the high-quality pre-training datasets from the previous 7 trillion tokens to 18 trillion tokens. This provides a strong foundation for common sense, expert knowledge, and reasoning capabilities. In terms of post-training, we implement intricate supervised finetuning with over 1 million samples, as well as multistage reinforcement learning. Post-training techniques enhance human preference, and notably improve long text generation, structural data analysis, and instruction following. To handle diverse and varied use cases effectively, we present Qwen2.5 LLM series in rich sizes. Open-weight offerings include base and instruction-tuned models, with quantized versions available. In addition, for hosted solutions, the proprietary models currently include two mixture-of-experts (MoE) variants: Qwen2.5-Turbo and Qwen2.5-Plus, both available from Alibaba Cloud Model Studio. Qwen2.5 has demonstrated top-tier performance on a wide range of benchmarks evaluating language understanding, reasoning, mathematics, coding, human preference alignment, etc. Specifically, the open-weight flagship Qwen2.5-72B-Instruct outperforms a number of open and proprietary models and demonstrates competitive performance to the state-of-the-art open-weight model, Llama-3-405B-Instruct, which is around 5 times larger. Qwen2.5-Turbo and Qwen2.5-Plus offer superior cost-effectiveness while performing competitively against GPT-4o-mini and GPT-4o respectively. Additionally, as the foundation, Qwen2.5 models have been instrumental in training specialized models such as Qwen2.5-Math, Qwen2.5-Coder, QwQ, and multimodal models.

With the emergence of Mixture-of-Experts (MoE), the efficient scaling of model size has accelerated the development of large language models in recent years. However, their high memory requirements prevent their use in resource-constrained environments. While knowledge distillation (KD) has been a proven method for model compression, its application to MoE teacher models remains underexplored. Through our investigation, we discover that non-activated experts in MoE models possess valuable knowledge that benefits student models. We further demonstrate that existing KD methods are not optimal for compressing MoE models, as they fail to leverage this knowledge effectively. To address this, we propose two intuitive MoE-specific KD methods for the first time: Knowledge Augmentation (KA) and Student-Aware Router (SAR), both designed to effectively extract knowledge from all experts. Specifically, KA augments knowledge by sampling experts multiple times, while SAR uses all experts and adjusts the expert weights through router training to provide optimal knowledge. Extensive experiments show that our methods outperform conventional KD methods, demonstrating their effectiveness for MoE teacher models.

As the widespread adoption of Large Language Models (LLMs) accelerates, token consumption from intermediate reasoning traces increasingly contributes to inference latency and operational cost. Recent studies suggest that many real-world tasks require little to no explicit reasoning, with additional reasoning sometimes even degrading performance. In this work, we propose Post-Reasoning, a simple yet effective approach that improves instruction-tuned models by conditioning them to justify their answers after generating the final response. By design, it enables the final answer to be obtained without additional latency or token cost, while still improving performance through simple instruction augmentation. We evaluate Post-Reasoning across \(117\) model--benchmark settings spanning \(13\) open and proprietary models, \(4\) model families, and \(9\) diverse reasoning and knowledge-intensive benchmarks, including AMC, HMMT, GSM8K, GPQA, MMLU-Pro, and BIG-Bench Hard. Post-Reasoning improves performance in over \(88.19\%\) of evaluated settings, achieving a mean relative improvements of \(17.37\%\). Furthermore, we propose supervised post-reason tuning, which further improves performance in over \(91.11\%\) of evaluated settings, and exceeds the prompt-based post-reasoning baseline by an average of \(8.01\%\), demonstrating that post-reasoning can be effectively internalized through training. Ultimately, Post-Reasoning establishes a new performance ceiling for direct-answer capabilities.

Sparsely activated Mixture-of-Experts (SMoE) has shown promise to scale up the learning capacity of neural networks, however, they have issues like (a) High Memory Usage, due to duplication of the network layers into multiple copies as experts; and (b) Redundancy in Experts, as common learning-based routing policies suffer from representational collapse. Therefore, vanilla SMoE models are memory inefficient and non-scalable, especially for resource-constrained downstream scenarios. In this paper, we ask: Can we craft a compact SMoE model by consolidating expert information? What is the best recipe to merge multiple experts into fewer but more knowledgeable experts? Our pilot investigation reveals that conventional model merging methods fail to be effective in such expert merging for SMoE. The potential reasons are: (1) redundant information overshadows critical experts; (2) appropriate neuron permutation for each expert is missing to bring all of them in alignment. To address this, we propose M-SMoE, which leverages routing statistics to guide expert merging. Specifically, it starts with neuron permutation alignment for experts; then, dominant experts and their "group members" are formed; lastly, every expert group is merged into a single expert by utilizing each expert's activation frequency as their weight for merging, thus diminishing the impact of insignificant experts. Moreover, we observed that our proposed merging promotes a low dimensionality in the merged expert's weight space, naturally paving the way for additional compression. Hence, our final method, MC-SMoE (i.e., Merge, then Compress SMoE), further decomposes the merged experts into low-rank and structural sparse alternatives. Extensive experiments across 8 benchmarks validate the effectiveness of MC-SMoE. For instance, our MC-SMoE achieves up to 80% memory and a 20% FLOPs reduction, with virtually no loss in performance.

Language model post-training has enhanced instruction-following and performance on many downstream tasks, but also comes with an often-overlooked cost on tasks with many possible valid answers. We characterize three desiderata for conditional distributional modeling: in-context steerability, valid output space coverage, and distributional alignment, and document across three model families how current post-training can reduce these properties. In particular, we disambiguate between two kinds of in-context learning: ICL for eliciting existing underlying knowledge or capabilities, and in-context steerability, where a model must use in-context information to override its priors and steer to a novel data generating distribution. To better evaluate and improve these desiderata, we introduce Spectrum Suite, a large-scale resource compiled from >40 data sources and spanning >90 tasks requiring models to steer to and match diverse distributions ranging from varied human preferences to numerical distributions and more. We find that while current post-training techniques help elicit underlying capabilities and knowledge, they hurt models' ability to flexibly steer in-context. To mitigate these issues, we propose Spectrum Tuning, a post-training method using Spectrum Suite to improve steerability and distributional coverage. We find that Spectrum Tuning often improves over pretrained models and their instruction-tuned counterparts, enhancing steerability, spanning more of the output space, and improving distributional alignment on held-out datasets.

Experience internalization converts contextual experience from past interactions into reusable parametric capability, offering a promising path toward continual learning in large language models (LLMs). While prior work has predominantly focused on single-iteration transfer, we discover that under multi-iteration experience learning, existing methods suffer from a progressive capability collapse rather than compounding improvement. We systematically examine this failure through three vital dimensions of experience internalization: (1) Experience Granularity: We find that principle-level experience is more durable than instance-level experience, as it effectively abstracts transferable strategies away from trajectory-specific details. (2) Experience Injection Pattern: Our analysis reveals that step-wise injection significantly outperforms global injection by aligning experience with intermediate decision states, a property that is critical for long-horizon tool use. (3) Internalization Regime: We demonstrate that off-policy context-distillation on high-quality teacher trajectories provides a substantially more stable training signal than on-policy context-distillation, which is inherently limited by local corrections on student-induced flawed states. Together, these insights yield a simple yet robust recipe for stable and sustainable experience internalization, providing concrete guidance for engineering self-evolving and continually learning LLMs.

Vision Language Models (VLMs), pre-trained on large-scale image-text datasets, enable zero-shot predictions for unseen data but may underperform on specific unseen tasks. Continual learning (CL) can help VLMs effectively adapt to new data distributions without joint training, but faces challenges of catastrophic forgetting and generalization forgetting. Although significant progress has been achieved by distillation-based methods, they exhibit two severe limitations. One is the popularly adopted single-teacher paradigm fails to impart comprehensive knowledge, The other is the existing methods inadequately leverage the multimodal information in the original training dataset, instead they rely on additional data for distillation, which increases computational and storage overhead. To mitigate both limitations, by drawing on Knowledge Integration Theory (KIT), we propose a Multi-Stage Knowledge Integration network (MulKI) to emulate the human learning process in distillation methods. MulKI achieves this through four stages, including Eliciting Ideas, Adding New Ideas, Distinguishing Ideas, and Making Connections. During the four stages, we first leverage prototypes to align across modalities, eliciting cross-modal knowledge, then adding new knowledge by constructing fine-grained intra- and inter-modality relationships with prototypes. After that, knowledge from two teacher models is adaptively distinguished and re-weighted. Finally, we connect between models from intra- and inter-task, integrating preceding and new knowledge. Our method demonstrates significant improvements in maintaining zero-shot capabilities while supporting continual learning across diverse downstream tasks, showcasing its potential in adapting VLMs to evolving data distributions.

Sparsely-activated Mixture-of-Experts (SMoE) models offer efficient pre-training and low latency but their large parameter counts create significant memory overhead, motivating research into expert compression. Contrary to recent findings favouring expert merging on discriminative benchmarks, we demonstrate that expert pruning is a superior strategy for generative tasks. We prove that merging introduces an irreducible error by causing a "functional subspace collapse", due to the loss of the router's independent, input-dependent control over experts. Leveraging this insight, we propose Router-weighted Expert Activation Pruning (REAP), a novel pruning criterion that considers both router gate-values and expert activation norms. Across a diverse set of SMoE models ranging from 20B to 1T parameters, REAP consistently outperforms merging and other pruning methods on generative benchmarks, especially at 50% compression. Notably, our method achieves near-lossless compression on code generation and tool-calling tasks with Qwen3-Coder-480B and Kimi-K2, even after pruning 50% of experts.

Learning from changing tasks and sequential experience without forgetting the obtained knowledge is a challenging problem for artificial neural networks. In this work, we focus on two challenging problems in the paradigm of Continual Learning (CL) without involving any old data: (i) the accumulation of catastrophic forgetting caused by the gradually fading knowledge space from which the model learns the previous knowledge; (ii) the uncontrolled tug-of-war dynamics to balance the stability and plasticity during the learning of new tasks. In order to tackle these problems, we present Progressive Learning without Forgetting (PLwF) and a credit assignment regime in the optimizer. PLwF densely introduces model functions from previous tasks to construct a knowledge space such that it contains the most reliable knowledge on each task and the distribution information of different tasks, while credit assignment controls the tug-of-war dynamics by removing gradient conflict through projection. Extensive ablative experiments demonstrate the effectiveness of PLwF and credit assignment. In comparison with other CL methods, we report notably better results even without relying on any raw data.

Sparsely-activated Mixture-of-experts (MoE) models allow the number of parameters to greatly increase while keeping the amount of computation for a given token or a given sample unchanged. However, a poor expert routing strategy (e.g. one resulting in load imbalance) can cause certain experts to be under-trained, leading to an expert being under or over-specialized. Prior work allocates a fixed number of experts to each token using a top-k function regardless of the relative importance of different tokens. To address this, we propose a heterogeneous mixture-of-experts employing an expert choice method. Instead of letting tokens select the top-k experts, we have experts selecting the top-k tokens. As a result, each token can be routed to a variable number of experts and each expert can have a fixed bucket size. We systematically study pre-training speedups using the same computational resources of the Switch Transformer top-1 and GShard top-2 gating of prior work and find that our method improves training convergence time by more than 2x. For the same computational cost, our method demonstrates higher performance in fine-tuning 11 selected tasks in the GLUE and SuperGLUE benchmarks. For a smaller activation cost, our method outperforms the T5 dense model in 7 out of the 11 tasks.

Visual instruction datasets from various distributors are released at different times and often contain a significant number of semantically redundant text-image pairs, depending on their task compositions (i.e., skills) or reference sources. This redundancy greatly limits the efficient deployment of lifelong adaptable multimodal large language models, hindering their ability to refine existing skills and acquire new competencies over time. To address this, we reframe the problem of Lifelong Instruction Tuning (LiIT) via data selection, where the model automatically selects beneficial samples to learn from earlier and new datasets based on the current state of acquired knowledge in the model. Based on empirical analyses that show that selecting the best data subset using a static importance measure is often ineffective for multi-task datasets with evolving distributions, we propose Adapt-infty, a new multi-way and adaptive data selection approach that dynamically balances sample efficiency and effectiveness during LiIT. We construct pseudo-skill clusters by grouping gradient-based sample vectors. Next, we select the best-performing data selector for each skill cluster from a pool of selector experts, including our newly proposed scoring function, Image Grounding score. This data selector samples a subset of the most important samples from each skill cluster for training. To prevent the continuous increase in the size of the dataset pool during LiIT, which would result in excessive computation, we further introduce a cluster-wise permanent data pruning strategy to remove the most semantically redundant samples from each cluster, keeping computational requirements manageable. Training with samples selected by Adapt-infty alleviates catastrophic forgetting, especially for rare tasks, and promotes forward transfer across the continuum using only a fraction of the original datasets.

Recent reinforcement learning (RL) techniques have yielded impressive reasoning improvements in language models, yet it remains unclear whether post-training truly extends a model's reasoning ability beyond what it acquires during pre-training. A central challenge is the lack of control in modern training pipelines: large-scale pre-training corpora are opaque, mid-training is often underexamined, and RL objectives interact with unknown prior knowledge in complex ways. To resolve this ambiguity, we develop a fully controlled experimental framework that isolates the causal contributions of pre-training, mid-training, and RL-based post-training. Our approach employs synthetic reasoning tasks with explicit atomic operations, parseable step-by-step reasoning traces, and systematic manipulation of training distributions. We evaluate models along two axes: extrapolative generalization to more complex compositions and contextual generalization across surface contexts. Using this framework, we reconcile competing views on RL's effectiveness. We show that: 1) RL produces true capability gains (pass@128) only when pre-training leaves sufficient headroom and when RL data target the model's edge of competence, tasks at the boundary that are difficult but not yet out of reach. 2) Contextual generalization requires minimal yet sufficient pre-training exposure, after which RL can reliably transfer. 3) Mid-training significantly enhances performance under fixed compute compared with RL only, demonstrating its central but underexplored role in training pipelines. 4) Process-level rewards reduce reward hacking and improve reasoning fidelity. Together, these results clarify the interplay between pre-training, mid-training, and RL, offering a foundation for understanding and improving reasoning LM training strategies.

Large Language Models (LLMs) have shown tremendous potential as agents, excelling at tasks that require multiple rounds of reasoning and interactions. Rejection Sampling Fine-Tuning (RFT) has emerged as an effective method for finetuning LLMs as agents: it first imitates expert-generated successful trajectories and further improves agentic skills through iterative fine-tuning on successful, self-generated trajectories. However, since the expert (e.g., GPT-4) succeeds primarily on simpler subtasks and RFT inherently favors simpler scenarios, many complex subtasks remain unsolved and persistently out-of-distribution (OOD). Upon investigating these challenging subtasks, we discovered that previously failed expert trajectories can often provide valuable guidance, e.g., plans and key actions, that can significantly improve agent exploration efficiency and acquisition of critical skills. Motivated by these observations, we propose Exploring Expert Failures (EEF), which identifies beneficial actions from failed expert trajectories and integrates them into the training dataset. Potentially harmful actions are meticulously excluded to prevent contamination of the model learning process. By leveraging the beneficial actions in expert failures, EEF successfully solves some previously unsolvable subtasks and improves agent tuning performance. Remarkably, our approach achieved a 62\% win rate in WebShop, outperforming RFT (53. 6\%) and GPT-4 (35. 6\%), and to the best of our knowledge, setting a new state-of-the-art as the first method to surpass a score of 0.81 in WebShop and exceed 81 in SciWorld.

Existing post-training techniques for large language models are broadly categorized into Supervised Fine-Tuning (SFT) and Reinforcement Fine-Tuning (RFT). Each paradigm presents a distinct trade-off: SFT excels at mimicking demonstration data but can lead to problematic generalization as a form of behavior cloning. Conversely, RFT can significantly enhance a model's performance but is prone to learn unexpected behaviors, and its performance is highly sensitive to the initial policy. In this paper, we propose a unified view of these methods and introduce Prefix-RFT, a hybrid approach that synergizes learning from both demonstration and exploration. Using mathematical reasoning problems as a testbed, we empirically demonstrate that Prefix-RFT is both simple and effective. It not only surpasses the performance of standalone SFT and RFT but also outperforms parallel mixed-policy RFT methods. A key advantage is its seamless integration into existing open-source frameworks, requiring only minimal modifications to the standard RFT pipeline. Our analysis highlights the complementary nature of SFT and RFT, and validates that Prefix-RFT effectively harmonizes these two learning paradigms. Furthermore, ablation studies confirm the method's robustness to variations in the quality and quantity of demonstration data. We hope this work offers a new perspective on LLM post-training, suggesting that a unified paradigm that judiciously integrates demonstration and exploration could be a promising direction for future research.

We present a system for training enterprise search agents via reinforcement learning that achieves state-of-the-art performance across a diverse suite of hard-to-verify agentic search tasks. Our work makes four core contributions. First, we introduce KARLBench, a multi-capability evaluation suite spanning six distinct search regimes, including constraint-driven entity search, cross-document report synthesis, tabular numerical reasoning, exhaustive entity retrieval, procedural reasoning over technical documentation, and fact aggregation over internal enterprise notes. Second, we show that models trained across heterogeneous search behaviors generalize substantially better than those optimized for any single benchmark. Third, we develop an agentic synthesis pipeline that employs long-horizon reasoning and tool use to generate diverse, grounded, and high-quality training data, with iterative bootstrapping from increasingly capable models. Fourth, we propose a new post-training paradigm based on iterative large-batch off-policy RL that is sample efficient, robust to train-inference engine discrepancies, and naturally extends to multi-task training with out-of-distribution generalization. Compared to Claude 4.6 and GPT 5.2, KARL is Pareto-optimal on KARLBench across cost-quality and latency-quality trade-offs, including tasks that were out-of-distribution during training. With sufficient test-time compute, it surpasses the strongest closed models. These results show that tailored synthetic data in combination with multi-task reinforcement learning enables cost-efficient and high-performing knowledge agents for grounded reasoning.

As post-training processes utilize increasingly large datasets and base models continue to grow in size, the computational demands and implementation challenges of existing algorithms are escalating significantly. In this paper, we propose modeling the changes at the logits level during post-training using a separate neural network (i.e., the value network). After training this network on a small base model using demonstrations, this network can be seamlessly integrated with other pre-trained models during inference, enables them to achieve similar capability enhancements. We systematically investigate the best practices for this paradigm in terms of pre-training weights and connection schemes. We demonstrate that the resulting value network has broad transferability across pre-trained models of different parameter sizes within the same family, models undergoing continuous pre-training within the same family, and models with different vocabularies across families. In certain cases, it can achieve performance comparable to full-parameter fine-tuning. Furthermore, we explore methods to enhance the transferability of the value model and prevent overfitting to the base model used during training.

The Homotopy paradigm, a general principle for solving challenging problems, appears across diverse domains such as robust optimization, global optimization, polynomial root-finding, and sampling. Practical solvers for these problems typically follow a predictor-corrector (PC) structure, but rely on hand-crafted heuristics for step sizes and iteration termination, which are often suboptimal and task-specific. To address this, we unify these problems under a single framework, which enables the design of a general neural solver. Building on this unified view, we propose Neural Predictor-Corrector (NPC), which replaces hand-crafted heuristics with automatically learned policies. NPC formulates policy selection as a sequential decision-making problem and leverages reinforcement learning to automatically discover efficient strategies. To further enhance generalization, we introduce an amortized training mechanism, enabling one-time offline training for a class of problems and efficient online inference on new instances. Experiments on four representative homotopy problems demonstrate that our method generalizes effectively to unseen instances. It consistently outperforms classical and specialized baselines in efficiency while demonstrating superior stability across tasks, highlighting the value of unifying homotopy methods into a single neural framework.

Domain-adaptive post-training of large language models (LLMs) has emerged as a promising approach for specialized domains such as medicine and finance. However, significant challenges remain in identifying optimal adaptation criteria and training strategies across varying data and model configurations. To address these challenges, we introduce FINDAP, a systematic and fine-grained investigation into domain-adaptive post-training of LLMs for the finance domain. Our approach begins by identifying the core capabilities required for the target domain and designing a comprehensive evaluation suite aligned with these needs. We then analyze the effectiveness of key post-training stages, including continual pretraining, instruction tuning, and preference alignment. Building on these insights, we propose an effective training recipe centered on a novel preference data distillation method, which leverages process signals from a generative reward model. The resulting model, Llama-Fin, achieves state-of-the-art performance across a wide range of financial tasks. Our analysis also highlights how each post-training stage contributes to distinct capabilities, uncovering specific challenges and effective solutions, providing valuable insights for domain adaptation of LLMs. Project page: https://github.com/SalesforceAIResearch/FinDap

The Mixture of Experts (MoE) architecture reduces the training and inference cost significantly compared to a dense model of equivalent capacity. Upcycling is an approach that initializes and trains an MoE model using a pre-trained dense model. While upcycling leads to initial performance gains, the training progresses slower than when trained from scratch, leading to suboptimal performance in the long term. We propose Drop-Upcycling - a method that effectively addresses this problem. Drop-Upcycling combines two seemingly contradictory approaches: utilizing the knowledge of pre-trained dense models while statistically re-initializing some parts of the weights. This approach strategically promotes expert specialization, significantly enhancing the MoE model's efficiency in knowledge acquisition. Extensive large-scale experiments demonstrate that Drop-Upcycling significantly outperforms previous MoE construction methods in the long term, specifically when training on hundreds of billions of tokens or more. As a result, our MoE model with 5.9B active parameters achieves comparable performance to a 13B dense model in the same model family, while requiring approximately 1/4 of the training FLOPs. All experimental resources, including source code, training data, model checkpoints and logs, are publicly available to promote reproducibility and future research on MoE.

AI agents have become surprisingly proficient at software engineering over the past year, largely due to improvements in reasoning capabilities. This raises a deeper question: can these systems extend their capabilities to automate AI research itself? In this paper, we explore post-training, the critical phase that turns base LLMs into useful assistants. We introduce PostTrainBench to benchmark how well LLM agents can perform post-training autonomously under bounded compute constraints (10 hours on one H100 GPU). We ask frontier agents (e.g., Claude Code with Opus 4.6) to optimize the performance of a base LLM on a particular benchmark (e.g., Qwen3-4B on AIME). Importantly, we do not provide any predefined strategies to the agents and instead give them full autonomy to find necessary information on the web, run experiments, and curate data. We find that frontier agents make substantial progress but generally lag behind instruction-tuned LLMs from leading providers: 23.2% for the best agent vs. 51.1% for official instruction-tuned models. However, agents can exceed instruction-tuned models in targeted scenarios: GPT-5.1 Codex Max achieves 89% on BFCL with Gemma-3-4B vs. 67% for the official model. We also observe several failure modes worth flagging. Agents sometimes engage in reward hacking: training on the test set, downloading existing instruction-tuned checkpoints instead of training their own, and using API keys they find to generate synthetic data without authorization. These behaviors are concerning and highlight the importance of careful sandboxing as these systems become more capable. Overall, we hope PostTrainBench will be useful for tracking progress in AI R&D automation and for studying the risks that come with it. Website and code are available at https://posttrainbench.com/.

Reinforcement learning (RL) post-training has proven effective at unlocking reasoning, self-reflection, and tool-use capabilities in large language models. As models extend to omni-modal inputs and agentic multi-turn workflows, RL training systems face three interdependent challenges: heterogeneous data flows, operational robustness at scale, and the staleness -- throughput tradeoff. We present Relax (Reinforcement Engine Leveraging Agentic X-modality), an open-source RL training engine that addresses these challenges through three co-designed architectural layers. First, an omni-native architecture builds multimodal support into the full stack -- from data preprocessing and modality-aware parallelism to inference generation -- rather than retrofitting it onto a text-centric pipeline. Second, each RL role runs as an independent, fault-isolated service that can be scaled, recovered, and upgraded without global coordination. Third, service-level decoupling enables asynchronous training via the TransferQueue data bus, where a single staleness parameter smoothly interpolates among on-policy, near-on-policy, and fully asynchronous execution. Relax achieves a 1.20times end-to-end speedup over veRL on Qwen3-4B on-policy training. Its fully async mode delivers a 1.76times speedup over colocate on Qwen3-4B and a 2.00times speedup on Qwen3-Omni-30B, while all modes converge to the same reward level. Relax supports R3 (Rollout Routing Replay)~ma2025r3 for MoE models with only 1.9\% overhead, compared to 32\% degradation in veRL under the same configuration. It further demonstrates stable omni-modal RL convergence on Qwen3-Omni across image, text, and audio, sustaining over 2{,}000 steps on video without degradation. Relax is available at https://github.com/rednote-ai/Relax.

Mixture of Experts (MoE) offers remarkable performance and computational efficiency by selectively activating subsets of model parameters. Traditionally, MoE models use homogeneous experts, each with identical capacity. However, varying complexity in input data necessitates experts with diverse capabilities, while homogeneous MoE hinders effective expert specialization and efficient parameter utilization. In this study, we propose a novel Heterogeneous Mixture of Experts (HMoE), where experts differ in size and thus possess diverse capacities. This heterogeneity allows for more specialized experts to handle varying token complexities more effectively. To address the imbalance in expert activation, we propose a novel training objective that encourages the frequent activation of smaller experts, enhancing computational efficiency and parameter utilization. Extensive experiments demonstrate that HMoE achieves lower loss with fewer activated parameters and outperforms conventional homogeneous MoE models on various pre-training evaluation benchmarks. Codes will be released upon acceptance.

Interactive tool-using agents must solve real-world tasks via multi-turn interaction with both humans and external environments, requiring dialogue state tracking, multi-step tool execution, while following complex instructions. Post-training such agents is challenging because synthesis for high-quality multi-turn tool-use data is difficult to scale, and reinforcement learning (RL) could face noisy signals caused by user simulation, leading to degraded training efficiency. We propose a unified framework that combines a self-evolving data agent with verifier-based RL. Our system, EigenData, is a hierarchical multi-agent engine that synthesizes tool-grounded dialogues together with executable per-instance checkers, and improves generation reliability via closed-loop self-evolving process that updates prompts and workflow. Building on the synthetic data, we develop an RL recipe that first fine-tunes the user model and then applies GRPO-style training with trajectory-level group-relative advantages and dynamic filtering, yielding consistent improvements beyond SFT. Evaluated on tau^2-bench, our best model reaches 73.0% pass^1 on Airline and 98.3% pass^1 on Telecom, matching or exceeding frontier models. Overall, our results suggest a scalable pathway for bootstrapping complex tool-using behaviors without expensive human annotation.

Post-training improves instruction-following and helpfulness of large language models (LLMs) but often reduces generation diversity, which leads to repetitive outputs in open-ended settings, a phenomenon known as mode collapse. Motivated by evidence that LLM layers play distinct functional roles, we hypothesize that mode collapse can be localized to specific layers and that restoring a carefully chosen range of layers to their pre-trained weights can recover diversity while maintaining high output quality. To validate this hypothesis and decide which layers to restore, we design a proxy task -- Constrained Random Character(CRC) -- with an explicit validity set and a natural diversity objective. Results on CRC reveal a clear diversity-validity trade-off across restoration ranges and identify configurations that increase diversity with minimal quality loss. Based on these findings, we propose Selective Layer Restoration (SLR), a training-free method that restores selected layers in a post-trained model to their pre-trained weights, yielding a hybrid model with the same architecture and parameter count, incurring no additional inference cost. Across three different tasks (creative writing, open-ended question answering, and multi-step reasoning) and three different model families (Llama, Qwen, and Gemma), we find SLR can consistently and substantially improve output diversity while maintaining high output quality.

Large language models store all learned knowledge in a single, fixed weight vector. Teaching a model new capabilities requires modifying those same weights, inevitably degrading previously acquired knowledge. This fundamental limitation, known as catastrophic forgetting, has resisted principled solutions for decades. Existing approaches treat weights as immutable artifacts that must be protected through techniques like regularization heuristics, replay buffers, or isolated adapter modules. The problem is none of these provide a structural guarantee against forgetting. In this work, we propose Non-Interfering Weight Fields (NIWF), a framework that replaces the fixed weight paradigm with a learned function that generates weight configurations on demand from a continuous capability coordinate space. After training on a task, we commit the occupied coordinate region by snapshotting the fields outputs on anchor points to enforce a functional lock during all future training. We validate NIWF on sequential instructionfollowing and code generation tasks using Mistral-7B, demonstrating zero forgetting on committed tasks with competitive perplexity on new tasks. The framework introduces the notion of software-like versioning for neural network intelligence, where capabilities can be committed, extended, composed, and rolled back without retraining.

Online continual learning aims to continuously train neural networks from a continuous data stream with a single pass-through data. As the most effective approach, the rehearsal-based methods replay part of previous data. Commonly used predictors in existing methods tend to generate biased dot-product logits that prefer to the classes of current data, which is known as a bias issue and a phenomenon of forgetting. Many approaches have been proposed to overcome the forgetting problem by correcting the bias; however, they still need to be improved in online fashion. In this paper, we try to address the bias issue by a more straightforward and more efficient method. By decomposing the dot-product logits into an angle factor and a norm factor, we empirically find that the bias problem mainly occurs in the angle factor, which can be used to learn novel knowledge as cosine logits. On the contrary, the norm factor abandoned by existing methods helps remember historical knowledge. Based on this observation, we intuitively propose to leverage the norm factor to balance the new and old knowledge for addressing the bias. To this end, we develop a heuristic approach called unbias experience replay (UER). UER learns current samples only by the angle factor and further replays previous samples by both the norm and angle factors. Extensive experiments on three datasets show that UER achieves superior performance over various state-of-the-art methods. The code is in https://github.com/FelixHuiweiLin/UER.

Loss of plasticity is a phenomenon where neural networks become more difficult to train during the course of learning. Continual learning algorithms seek to mitigate this effect by sustaining good predictive performance while maintaining network trainability. We develop new techniques for improving continual learning by first reconsidering how initialization can ensure trainability during early phases of learning. From this perspective, we derive new regularization strategies for continual learning that ensure beneficial initialization properties are better maintained throughout training. In particular, we investigate two new regularization techniques for continual learning: (i) Wasserstein regularization toward the initial weight distribution, which is less restrictive than regularizing toward initial weights; and (ii) regularizing weight matrix singular values, which directly ensures gradient diversity is maintained throughout training. We present an experimental analysis that shows these alternative regularizers can improve continual learning performance across a range of supervised learning tasks and model architectures. The alternative regularizers prove to be less sensitive to hyperparameters while demonstrating better training in individual tasks, sustaining trainability as new tasks arrive, and achieving better generalization performance.

Mathematical programming -- the task of expressing operations and decision-making problems in precise mathematical language -- is fundamental across domains, yet remains a skill-intensive process requiring operations research expertise. Recent advances in large language models for complex reasoning have spurred interest in automating this task, translating natural language into executable optimization models. Current approaches, however, achieve limited accuracy, hindered by scarce and noisy training data without leveraging domain knowledge. In this work, we systematically integrate optimization expertise to improve formulation accuracy for mixed-integer linear programming, a key family of mathematical programs. Our approach first cleans training data through class-based error analysis to explicitly prevent common mistakes within each optimization class. We then develop multi-turn inference strategies that guide LLMs with class-specific error summaries and solver feedback, enabling iterative refinement. Experiments across multiple base LLMs demonstrate that combining cleaned data with domain-informed prompting and feedback improves formulation accuracy by 14 percentage points on average, enabling further progress toward robust LLM-assisted optimization formulation.

Experts advising decision-makers are likely to display expertise which varies as a function of the problem instance. In practice, this may lead to sub-optimal or discriminatory decisions against minority cases. In this work we model such changes in depth and breadth of knowledge as a partitioning of the problem space into regions of differing expertise. We provide here new algorithms that explicitly consider and adapt to the relationship between problem instances and experts' knowledge. We first propose and highlight the drawbacks of a naive approach based on nearest neighbor queries. To address these drawbacks we then introduce a novel algorithm - expertise trees - that constructs decision trees enabling the learner to select appropriate models. We provide theoretical insights and empirically validate the improved performance of our novel approach on a range of problems for which existing methods proved to be inadequate.

Mixture-of-Experts (MoE) Large Language Models (LLMs) suffer from severely sub-optimal expert pathways-our study reveals that naive expert selection learned from pretraining leaves a surprising 10-20% accuracy gap for improvement. Motivated by this observation, we develop a novel class of test-time optimization methods to re-weight or "re-mixing" the experts in different layers jointly for each test sample. Since the test sample's ground truth is unknown, we propose to optimize a surrogate objective defined by the sample's "successful neighbors" from a reference set of samples. We introduce three surrogates and algorithms based on mode-finding, kernel regression, and the average loss of similar reference samples/tasks. To reduce the cost of optimizing whole pathways, we apply our algorithms merely to the core experts' mixing weights in critical layers, which enjoy similar performance but save significant computation. This leads to "Critical-Layer, Core-Expert, Collaborative Pathway Optimization (C3PO)". We apply C3PO to two recent MoE LLMs and examine it on six widely-used benchmarks. It consistently improves the base model by 7-15% in accuracy and outperforms widely used test-time learning baselines, e.g., in-context learning and prompt/prefix tuning, by a large margin. Moreover, C3PO enables MoE LLMs with 1-3B active parameters to outperform LLMs of 7-9B parameters, hence improving MoE's advantages on efficiency. Our thorough ablation study further sheds novel insights on achieving test-time improvement on MoE.

A major problem with Active Learning (AL) is high training costs since models are typically retrained from scratch after every query round. We start by demonstrating that standard AL on neural networks with warm starting fails, both to accelerate training and to avoid catastrophic forgetting when using fine-tuning over AL query rounds. We then develop a new class of techniques, circumventing this problem, by biasing further training towards previously labeled sets. We accomplish this by employing existing, and developing novel, replay-based Continual Learning (CL) algorithms that are effective at quickly learning the new without forgetting the old, especially when data comes from an evolving distribution. We call this paradigm Continual Active Learning (CAL). We show CAL achieves significant speedups using a plethora of replay schemes that use model distillation and that select diverse, uncertain points from the history. We conduct experiments across many data domains, including natural language, vision, medical imaging, and computational biology, each with different neural architectures and dataset sizes. CAL consistently provides a 3x reduction in training time, while retaining performance.

Mixture-of-Experts (MoE) models have shown remarkable capability in instruction tuning, especially when the number of tasks scales. However, previous methods simply merge all training tasks (e.g. creative writing, coding, and mathematics) and apply fixed sampling weights, without considering the importance of different tasks as the model training state changes. In this way, the most helpful data cannot be effectively distinguished, leading to suboptimal model performance. To reduce the potential redundancies of datasets, we make the first attempt and propose a novel dynamic data mixture for MoE instruction tuning. Specifically, inspired by MoE's token routing preference, we build dataset-level representations and then capture the subtle differences among datasets. Finally, we propose to dynamically adjust the sampling weight of datasets by their inter-redundancies, thus maximizing global performance under a limited training budget. The experimental results on two MoE models demonstrate the effectiveness of our approach on both downstream knowledge \& reasoning tasks and open-ended queries. Code and models are available at https://github.com/Spico197/MoE-SFT .

We introduce Goedel-Prover-V2, a series of open-source language models that set a new state-of-the-art in automated theorem proving. Built on the standard expert iteration and reinforcement learning pipeline, our approach incorporates three key innovations: (1) Scaffolded data synthesis: We generate synthetic tasks of increasing difficulty to train the model to master increasingly complex theorems; (2) Verifier-guided self-correction: We enable the model to iteratively revise its proofs by leveraging feedback from the Lean compiler; (3) Model averaging: We merge model checkpoints to mitigate the decrease in model output diversity in later stages of training. Our small model, Goedel-Prover-V2-8B, reaches 84.6% pass@32 on MiniF2F and outperforms DeepSeek-Prover-V2-671B under the same metric, despite being 80X smaller. Our flagship model, Goedel-Prover-V2-32B, achieves 88.1% on MiniF2F at pass@32 in standard mode and 90.4% in self-correction mode, outperforming prior SOTA by a large margin. Additionally, our flagship model solves 86 problems on PutnamBench at pass@184, securing the first place among open-source models on the leaderboard, surpassing DeepSeek-Prover-V2-671B's record of solving 47 problems by pass@1024 with a significantly smaller model size and compute budget. At the time of its release (July-August 2025), Goedel-Prover-V2 achieves the strongest overall performance among all open-source theorem provers. It also ranks among the top-performing models--including closed-source systems with publicly reported performance--under a constrained test-time compute budget. Our models, code, and data are released at https://github.com/Goedel-LM/Goedel-Prover-V2.

Training large language models (LLMs) to spend more time thinking and reflection before responding is crucial for effectively solving complex reasoning tasks in fields such as science, coding, and mathematics. However, the effectiveness of mechanisms like self-reflection and self-correction depends on the model's capacity to accurately assess its own performance, which can be limited by factors such as initial accuracy, question difficulty, and the lack of external feedback. In this paper, we delve into a two-player paradigm that separates the roles of reasoning and critique models, where the critique model provides step-level feedback to supervise the reasoning (actor) model during both test-time and train-time. We first propose AutoMathCritique, an automated and scalable framework for collecting critique data, resulting in a dataset of 76,321 responses paired with step-level feedback. Fine-tuning language models with this dataset enables them to generate natural language feedback for mathematical reasoning. We demonstrate that the critique models consistently improve the actor's performance on difficult queries at test-time, especially when scaling up inference-time computation. Motivated by these findings, we introduce the critique-based supervision to the actor's self-training process, and propose a critique-in-the-loop self-improvement method. Experiments show that the method improves the actor's exploration efficiency and solution diversity, especially on challenging queries, leading to a stronger reasoning model. Lastly, we take the preliminary step to explore training self-talk reasoning models via critique supervision and showcase its potential. Our code and datasets are at https://mathcritique.github.io/{https://mathcritique.github.io/}.

Large language models have demonstrated impressive reasoning capabilities but are inherently limited by their knowledge reservoir. Retrieval-augmented reasoning mitigates this limitation by allowing LLMs to query external resources, but existing methods often retrieve irrelevant or noisy information, hindering accurate reasoning. In this paper, we propose AutoRefine, a reinforcement learning post-training framework that adopts a new ``search-and-refine-during-think'' paradigm. AutoRefine introduces explicit knowledge refinement steps between successive search calls, enabling the model to iteratively filter, distill, and organize evidence before generating an answer. Furthermore, we incorporate tailored retrieval-specific rewards alongside answer correctness rewards using group relative policy optimization. Experiments on single-hop and multi-hop QA benchmarks demonstrate that AutoRefine significantly outperforms existing approaches, particularly in complex, multi-hop reasoning scenarios. Detailed analysis shows that AutoRefine issues frequent, higher-quality searches and synthesizes evidence effectively.

Answering complex natural language questions often necessitates multi-step reasoning and integrating external information. Several systems have combined knowledge retrieval with a large language model (LLM) to answer such questions. These systems, however, suffer from various failure cases, and we cannot directly train them end-to-end to fix such failures, as interaction with external knowledge is non-differentiable. To address these deficiencies, we define a ReAct-style LLM agent with the ability to reason and act upon external knowledge. We further refine the agent through a ReST-like method that iteratively trains on previous trajectories, employing growing-batch reinforcement learning with AI feedback for continuous self-improvement and self-distillation. Starting from a prompted large model and after just two iterations of the algorithm, we can produce a fine-tuned small model that achieves comparable performance on challenging compositional question-answering benchmarks with two orders of magnitude fewer parameters.

In the experts problem, on each of T days, an agent needs to follow the advice of one of n ``experts''. After each day, the loss associated with each expert's advice is revealed. A fundamental result in learning theory says that the agent can achieve vanishing regret, i.e. their cumulative loss is within o(T) of the cumulative loss of the best-in-hindsight expert. Can the agent perform well without sufficient space to remember all the experts? We extend a nascent line of research on this question in two directions: bullet We give a new algorithm against the oblivious adversary, improving over the memory-regret tradeoff obtained by [PZ23], and nearly matching the lower bound of [SWXZ22]. bullet We also consider an adaptive adversary who can observe past experts chosen by the agent. In this setting we give both a new algorithm and a novel lower bound, proving that roughly n memory is both necessary and sufficient for obtaining o(T) regret.

Knowledge distillation has emerged as an effective strategy for compressing large language models' (LLMs) knowledge into smaller, more efficient student models. However, standard one-shot distillation methods often produce suboptimal results due to a mismatch between teacher-generated rationales and the student's specific learning requirements. In this paper, we introduce the UNDO: UNderstanding Distillation as Optimization framework, designed to bridge this gap by iteratively identifying the student's errors and prompting the teacher to refine its explanations accordingly. Each iteration directly targets the student's learning deficiencies, motivating the teacher to provide tailored and enhanced rationales that specifically address these weaknesses. Empirical evaluations on various challenging mathematical and commonsense reasoning tasks demonstrate that our iterative distillation method, UNDO, significantly outperforms standard one-step distillation methods, achieving performance gains of up to 20%. Additionally, we show that teacher-generated data refined through our iterative process remains effective even when applied to different student models, underscoring the broad applicability of our approach. Our work fundamentally reframes knowledge distillation as an iterative teacher-student interaction, effectively leveraging dynamic refinement by the teacher for better knowledge distillation.

LLM post-training involves many diverse datasets, each targeting a specific behavior. But these datasets encode incidental patterns alongside intended ones: correlations between formatting and content, narrow phrasings across diverse problems, and implicit associations arising from the discrete data curation process. These patterns are often invisible to developers yet salient to models, producing behaviors that surprise their creators, such as rejecting true facts presented in a particular question format. We call this chunky post-training: the model learns spurious correlations as a result of distinct chunks of post-training data. We introduce SURF, a black-box pipeline which surfaces these unintended behaviors at run time, and TURF, a tool that traces these failures back to specific post-training data. Applying these tools to frontier models (Claude 4.5, GPT-5.1, Grok 4.1, Gemini 3) and open models (Tülu 3), we show that chunky post-training produces miscalibrated behaviors, which often result from imbalanced or underspecified chunks of post-training data.