Reinforcement Learning with Verifiable Rewards (RLVR) has achieved substantial gains in single-attempt accuracy (Pass@1) on reasoning tasks, yet often suffers from reduced multi-sample coverage (Pass@K), indicating diversity collapse. We identify a structural cause for this degradation: common RLVR objectives, such as GRPO, are indifferent to how probability mass is distributed among correct solutions. Combined with stochastic training dynamics, this indifference induces a self-reinforcing collapse, in which probability mass concentrates on a narrow subset of correct outputs while alternative valid solutions are suppressed. We formalize this collapse mechanism and further characterize the optimal policy structure under two complementary criteria: robustness and entropy-regularized optimality, which identify the Uniform-Correct Policy as uniquely optimal. Motivated by this analysis, we propose Uniform-Correct Policy Optimization (UCPO), a modification to GRPO that adds a conditional uniformity penalty on the policy's distribution over correct solutions. The penalty redistributes gradient signal toward underrepresented correct responses, encouraging uniform allocation of probability mass within the correct set. Across three models (1.5B-7B parameters) and five mathematical reasoning benchmarks, UCPO improves Pass@K and diversity while maintaining competitive Pass@1, achieving up to +10\% absolute improvement on AIME24 at Pass@64 and up to 45\% higher equation-level diversity within the correct set. The code is available at https://github.com/AnamikaLochab/UCPO.

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.

While scaling the length of responses at test-time has been shown to markedly improve the reasoning abilities and performance of large language models (LLMs), it often results in verbose outputs and increases inference cost. Prior approaches for efficient test-time scaling, typically using universal budget constraints or query-level length optimization, do not leverage historical information from previous encounters with the same problem during training. We hypothesize that this limits their ability to progressively make solutions more concise over time. To address this, we present History-Aware Policy Optimization (HAPO), which keeps track of a history state (e.g., the minimum length over previously generated correct responses) for each problem. HAPO employs a novel length reward function based on this history state to incentivize the discovery of correct solutions that are more concise than those previously found. Crucially, this reward structure avoids overly penalizing shorter incorrect responses with the goal of facilitating exploration towards more efficient solutions. By combining this length reward with a correctness reward, HAPO jointly optimizes for correctness and efficiency. We use HAPO to train DeepSeek-R1-Distill-Qwen-1.5B, DeepScaleR-1.5B-Preview, and Qwen-2.5-1.5B-Instruct, and evaluate HAPO on several math benchmarks that span various difficulty levels. Experiment results demonstrate that HAPO effectively induces LLMs' concise reasoning abilities, producing length reductions of 33-59% with accuracy drops of only 2-5%.

Reinforcement learning with verifiable rewards (RLVR) is a promising approach for training language models (LMs) on reasoning tasks that elicit emergent long chains of thought (CoTs). Unlike supervised learning, it updates the model using both correct and incorrect samples via policy gradients. To better understand its mechanism, we decompose the learning signal into reinforcing correct responses and penalizing incorrect ones, referred to as Positive and Negative Sample Reinforcement (PSR and NSR), respectively. We train Qwen2.5-Math-7B, Qwen3-4B and Llama-3.1-8B-Instruct on a mathematical reasoning dataset and uncover a surprising result: training with only negative samples -- without reinforcing correct responses -- can be highly effective: it consistently improves performance over the base model across the entire Pass@$k$ spectrum $k$ up to 256), often matching or surpassing PPO and GRPO. In contrast, reinforcing only correct responses improves Pass@1 but degrades performance at higher $k$, due to reduced diversity. These inference-scaling trends highlight that solely penalizing incorrect responses may contribute more to performance than previously recognized. Through gradient analysis, we show that NSR works by suppressing incorrect generations and redistributing probability mass toward other plausible candidates, guided by the model's prior beliefs. It refines the model's existing knowledge rather than introducing entirely new behaviors. Building on this insight, we propose a simple variant of the RL objective that upweights NSR, and show that it consistently improves overall Pass@$k$ performance on MATH, AIME 2025, and AMC23. Our code is available at https://github.com/TianHongZXY/RLVR-Decomposed.

Astronomical image interpretation presents a significant challenge for applying multimodal large language models (MLLMs) to specialized scientific tasks. Existing benchmarks focus on general multimodal capabilities but fail to capture the complexity of astronomical data. To bridge this gap, we introduce AstroMMBench, the first comprehensive benchmark designed to evaluate MLLMs in astronomical image understanding. AstroMMBench comprises 621 multiple-choice questions across six astrophysical subfields, curated and reviewed by 15 domain experts for quality and relevance. We conducted an extensive evaluation of 25 diverse MLLMs, including 22 open-source and 3 closed-source models, using AstroMMBench. The results show that Ovis2-34B achieved the highest overall accuracy (70.5%), demonstrating leading capabilities even compared to strong closed-source models. Performance showed variations across the six astrophysical subfields, proving particularly challenging in domains like cosmology and high-energy astrophysics, while models performed relatively better in others, such as instrumentation and solar astrophysics. These findings underscore the vital role of domain-specific benchmarks like AstroMMBench in critically evaluating MLLM performance and guiding their targeted development for scientific applications. AstroMMBench provides a foundational resource and a dynamic tool to catalyze advancements at the intersection of AI and astronomy.

In this work, we focus on mathematical problem-solving to explore enhancement of the mathematical reasoning abilities of pretrained LLMs. We investigate instruction tuning (Longpre et al., 2023; Wang

ICL guides are known to improve task-specific performance, but their impact on cross-domain cognitive abilities remains unexplored. This study examines how ICL guides affect reasoning across different knowledge domains using six variants of the GPT-OSS:20b model: one baseline model and five ICL configurations (simple, chain-of-thought, random, appended text, and symbolic language). The models were subjected to 840 tests spanning general knowledge questions, logic riddles, and a mathematical olympiad problem. Statistical analysis (ANOVA) revealed significant behavioral modifications (p less than 0.001) across ICL variants, demonstrating a phenomenon termed "optimized fragility." ICL models achieved 91%-99% accuracy on general knowledge tasks while showing degraded performance on complex reasoning problems, with accuracy dropping to 10-43% on riddles compared to 43% for the baseline model. Notably, no significant differences emerged on the olympiad problem (p=0.2173), suggesting that complex mathematical reasoning remains unaffected by ICL optimization. These findings indicate that ICL guides create systematic trade-offs between efficiency and reasoning flexibility, with important implications for LLM deployment and AI safety.