Reinforcement learning (RL) has become popular in enhancing the reasoning capabilities of large language models (LLMs), with Group Relative Policy Optimization (GRPO) emerging as a widely used algorithm in recent systems. Despite GRPO's widespread adoption, we identify a previously unrecognized phenomenon we term Lazy Likelihood Displacement (LLD), wherein the likelihood of correct responses marginally increases or even decreases during training. This behavior mirrors a recently discovered misalignment issue in Direct Preference Optimization (DPO), attributed to the influence of negative gradients. We provide a theoretical analysis of GRPO's learning dynamic, identifying the source of LLD as the naive penalization of all tokens in incorrect responses with the same strength. To address this, we develop a method called NTHR, which downweights penalties on tokens contributing to the LLD. Unlike prior DPO-based approaches, NTHR takes advantage of GRPO's group-based structure, using correct responses as anchors to identify influential tokens. Experiments on math reasoning benchmarks demonstrate that NTHR effectively mitigates LLD, yielding consistent performance gains across models ranging from 0.5B to 3B parameters.

With the recent surge in personalized learning, Intelligent Tutoring Systems (ITS) that can accurately track students' individual knowledge states and provide tailored learning paths based on this information are in demand as an essential task. This paper focuses on the core technology of Knowledge Tracing (KT) models that analyze students' sequences of interactions to predict their knowledge acquisition levels. However, existing KT models suffer from limitations such as restricted input data formats, cold start problems arising with new student enrollment or new question addition, and insufficient stability in real-world service environments. To overcome these limitations, a Practical Interlinked Concept Knowledge Tracing (PICKT) model that can effectively process multiple types of input data is proposed. Specifically, a knowledge map structures the relationships among concepts considering the question and concept text information, thereby enabling effective knowledge tracing even in cold start situations. Experiments reflecting real operational environments demonstrated the model's excellent performance and practicality. The main contributions of this research are as follows. First, a model architecture that effectively utilizes diverse data formats is presented. Second, significant performance improvements are achieved over existing models for two core cold start challenges: new student enrollment and new question addition. Third, the model's stability and practicality are validated through delicate experimental design, enhancing its applicability in real-world product environments. This provides a crucial theoretical and technical foundation for the practical implementation of next-generation ITS.

Reinforcement Learning with Verifiable Rewards (RLVR) has become a central approach for improving the reasoning ability of large language models. Recent work studies RLVR through token entropy, arguing that high-entropy tokens drive exploration and should receive stronger updates. However, they overlook the fact that most of a reasoning trajectory consists of low-entropy segments that encode stable and reusable structural patterns. Through qualitative and quantitative analyses, we find that the overlap of low-entropy segments across correct responses strongly correlates with model accuracy, while overlaps involving incorrect responses exhibit stable but unproductive patterns. Motivated by these findings, we propose LESS, a correctness-aware reinforcement framework that performs fine-grained advantage modulation over low-entropy segments. LESS amplifies segments unique to correct responses, suppresses those unique to incorrect ones, and neutralizes segments shared by both, while preserving high-entropy exploration in the underlying RL algorithm. Instantiated on top of the popular GRPO, LESS consistently improves accuracy over strong RL baselines across three backbones and six math benchmarks, achieves stronger robustness of the performance floor.

Reinforcement learning-based post-training of large language models (LLMs) has recently gained attention, particularly following the release of DeepSeek R1, which applied GRPO for fine-tuning. Amid the growing hype around improved reasoning abilities attributed to RL post-training, we critically examine the formulation and assumptions underlying these methods. We start by highlighting the popular structural assumptions made in modeling LLM training as a Markov Decision Process (MDP), and show how they lead to a degenerate MDP that doesn't quite need the RL/GRPO apparatus. The two critical structural assumptions include (1) making the MDP states be just a concatenation of the actions-with states becoming the context window and the actions becoming the tokens in LLMs and (2) splitting the reward of a state-action trajectory uniformly across the trajectory. Through a comprehensive analysis, we demonstrate that these simplifying assumptions make the approach effectively equivalent to an outcome-driven supervised learning. Our experiments on benchmarks including GSM8K and Countdown using Qwen-2.5 base models show that iterative supervised fine-tuning, incorporating both positive and negative samples, achieves performance comparable to GRPO-based training. We will also argue that the structural assumptions indirectly incentivize the RL to generate longer sequences of intermediate tokens-which in turn feeds into the narrative of "RL generating longer thinking traces." While RL may well be a very useful technique for improving the reasoning abilities of LLMs, our analysis shows that the simplistic structural assumptions made in modeling the underlying MDP render the popular LLM RL frameworks and their interpretations questionable.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as an effective approach for improving the reasoning abilities of large language models (LLMs). The Group Relative Policy Optimization (GRPO) family has demonstrated strong performance in training LLMs with RLVR. However, as models train longer and scale larger, more training prompts become residual prompts, those with zero variance rewards that provide no training signal. Consequently, fewer prompts contribute to training, reducing diversity and hindering effectiveness. To fully exploit these residual prompts, we propose the Explore Residual Prompts in Policy Optimization (ERPO) framework, which encourages exploration on residual prompts and reactivates their training signals. ERPO maintains a history tracker for each prompt and adaptively increases the sampling temperature for residual prompts that previously produced all correct responses. This encourages the model to generate more diverse reasoning traces, introducing incorrect responses that revive training signals. Empirical results on the Qwen2.5 series demonstrate that ERPO consistently surpasses strong baselines across multiple mathematical reasoning benchmarks.

While generative models, especially large language models (LLMs), are ubiquitous in today's world, principled mechanisms to assess their (in)correctness are limited. Using the conformal prediction framework, previous works construct sets of LLM responses where the probability of including an incorrect response, or error, is capped at a desired user-defined tolerance level. However, since these methods are based on p-values, they are susceptible to p-hacking, i.e., choosing the tolerance level post-hoc can invalidate the guarantees. We therefore leverage e-values to complement generative model outputs with e-scores as a measure of incorrectness. In addition to achieving the same statistical guarantees as before, e-scores provide users flexibility in adaptively choosing tolerance levels after observing the e-scores themselves, by upper bounding a post-hoc notion of error called size distortion. We experimentally demonstrate their efficacy in assessing LLM outputs for different correctness types: mathematical factuality and property constraints satisfaction.

As Generative Artificial Intelligence is adopted across the financial services industry, a significant barrier to adoption and usage is measuring model performance. Historical machine learning metrics can oftentimes fail to generalize to GenAI workloads and are often supplemented using Subject Matter Expert (SME) Evaluation. Even in this combination, many projects fail to account for various unique risks present in choosing specific metrics. Additionally, many widespread benchmarks created by foundational research labs and educational institutions fail to generalize to industrial use. This paper explains these challenges and provides a Risk Assessment Framework to allow for better application of SME and machine learning Metrics

The main focus of research on Knowledge Tracing (KT) models is on model developments with the aim of improving predictive accuracy. Most of these models make the most incorrect predictions when students choose a distractor, leading to student errors going undetected. We present an approach to add new capabilities to KT models by capturing predictive uncertainty and demonstrate that a larger predictive uncertainty aligns with model incorrect predictions. We show that uncertainty in KT models is informative and that this signal would be pedagogically useful for application in an educational learning platform that can be used in a limited resource setting where understanding student ability is necessary.

Reinforcement learning with verifiable rewards (RL VR) has emerged to be a predominant paradigm for mathematical reasoning tasks, offering stable improvements in reasoning ability. However, Outcome Reward Models (ORMs) in RL VR are too coarse-grained to distinguish flawed reasoning within correct answers or valid reasoning within incorrect answers. This lack of granularity introduces noisy and misleading gradients significantly and hinders further progress in reasoning process quality. While Process Reward Models (PRMs) offer fine-grained guidance for intermediate steps, they frequently suffer from inaccuracies and are susceptible to reward hacking. To resolve this dilemma, we introduce PRocess cOnsistency Filter (PROF), an effective data process curation method that harmonizes noisy, fine-grained process rewards with accurate, coarse-grained outcome rewards. Our approach retains correct responses with higher averaged process values and incorrect responses with lower averaged process values, while maintaining positive/negative training sample balance. Extensive experiments demonstrate that our method not only consistently improves the final accuracy over 4% compared to the blending approaches, but also strengthens the quality of intermediate reasoning steps. Codes and training recipes are available at https://github.com/Chenluye99/PROF . V erifiable rewards have spurred the widest attention recently because they can reliably improve the performance on reasoning tasks with easily verifiable outcomes, such as mathematical and coding problems (Cobbe et al., 2021; Jaech et al., 2024; Shao et al., 2024; Xiong et al., 2025b). However, since the verifiers can only verify the outcome results, the rewards are too sparse and coarse to measure and supervise the reasoning quality in intermediate steps.

Large Language Models (LLMs) have made remarkable progress in enhancing step-by-step reasoning through reinforcement learning. However, the Group Relative Policy Optimization (GRPO) algorithm, which relies on sparse reward rules, often encounters the issue of identical rewards within groups, leading to the advantage collapse problem. Existing works typically address this challenge from two perspectives: enforcing model reflection to enhance response diversity, and introducing internal feedback to augment the training signal (advantage). In this work, we begin by analyzing the limitations of model reflection and investigating the policy entropy of responses at the fine-grained sample level. Based on our experimental findings, we propose the EDGE-GRPO algorithm, which adopts \textbf{E}ntropy-\textbf{D}riven Advantage and \textbf{G}uided \textbf{E}rror Correction to effectively mitigate the problem of advantage collapse. Extensive experiments on several main reasoning benchmarks demonstrate the effectiveness and superiority of our approach. It is available at https://github.com/ZhangXJ199/EDGE-GRPO.