Related papers: Beyond Accuracy: Dissecting Mathematical Reasoning…

While reinforcement learning with verifiable rewards (RLVR) significantly enhances LLM reasoning by optimizing the conditional distribution P(y|x), its potential is fundamentally bounded by the base model's existing output distribution.…

Pre-trained Large Language Model (LLM) exhibits broad capabilities, yet, for specific tasks or domains their attainment of higher accuracy and more reliable reasoning generally depends on post-training through Supervised Fine-Tuning (SFT)…

Reasoning abilities, especially those for solving complex math problems, are crucial components of general intelligence. Recent advances by proprietary companies, such as o-series models of OpenAI, have made remarkable progress on reasoning…

Mathematical reasoning tasks have become prominent benchmarks for assessing the reasoning capabilities of LLMs, especially with reinforcement learning (RL) methods such as GRPO showing significant performance gains. However, accuracy…

Generating grounded and trustworthy responses remains a key challenge for large language models (LLMs). While retrieval-augmented generation (RAG) with citation-based grounding holds promise, instruction-tuned models frequently fail even in…

Reinforcement learning with verifiable rewards (RLVR) has achieved remarkable success in enhancing the reasoning capabilities of large language models (LLMs). However, existing RLVR methods often suffer from exploration inefficiency due to…

Mathematical reasoning is a challenging task for large language models (LLMs), while the scaling relationship of it with respect to LLM capacity is under-explored. In this paper, we investigate how the pre-training loss, supervised data…

Scaling model size and training data has led to great advances in the performance of Large Language Models (LLMs). However, the diminishing returns of this approach necessitate alternative methods to improve model capabilities, particularly…

The reasoning ability of large language models (LLMs) can be unleashed with reinforcement learning (RL) (OpenAI, 2024; DeepSeek-AI et al., 2025a; Zeng et al., 2025). The success of existing RL attempts in LLMs usually rely on high-quality…

Large language models (LLMs) achieve strong performance by generating long chains of thought, but longer traces always introduce redundant or ineffective reasoning steps. One typical behavior is that they often perform unnecessary…

Recent AI advancements, such as OpenAI's new models, are transforming LLMs into LRMs (Large Reasoning Models) that perform reasoning during inference, taking extra time and compute for higher-quality outputs. We aim to uncover the…

Large language models (LLMs) have demonstrated remarkable capabilities in complex reasoning tasks. However, existing approaches mainly rely on imitation learning and struggle to achieve effective test-time scaling. While reinforcement…

Post-training of large language models routinely interleaves supervised fine-tuning (SFT) with reinforcement learning (RL). These two methods have different objectives: SFT minimizes the cross-entropy loss between model outputs and expert…

Optimization modeling is fundamental to decision-making across diverse domains. Despite progress in automating optimization formulation from natural language descriptions, Large Language Models (LLMs) often struggle to generate formally…

As a subfield of machine learning, reinforcement learning (RL) aims at empowering one's capabilities in behavioural decision making by using interaction experience with the world and an evaluative feedback. Unlike traditional supervised…

Frontier reasoning models have exhibited incredible capabilities across a wide array of disciplines, driven by posttraining large language models (LLMs) with reinforcement learning (RL). However, despite the widespread success of this…

When language models (LMs) are trained via reinforcement learning (RL) to generate natural language "reasoning chains", their performance improves on a variety of difficult question answering tasks. Today, almost all successful applications…

Reinforcement learning (RL) has emerged as a powerful paradigm for enhancing the reasoning capabilities of large language models (LLMs). While RL has demonstrated substantial performance gains, it still faces key challenges, including low…

This study investigates the effectiveness of reinforcement learning (RL) fine-tuning techniques on a compact language model (Qwen2.5-0.5B Base) for two challenging tasks: instruction following and mathematical reasoning. We compare…

Recent studies have demonstrated the effectiveness of LLM test-time scaling. However, existing approaches to incentivize LLMs' deep thinking abilities generally require large-scale data or significant training efforts. Meanwhile, it remains…