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Reinforcement learning with offline data suffers from Q-value extrapolation errors. To address this issue, we first demonstrate that linear extrapolation of the Q-function beyond the data range is particularly problematic. To mitigate this,…

The extrapolation capability of Large Language Models (LLMs) based on Rotary Position Embedding is currently a topic of considerable interest. The mainstream approach to addressing extrapolation with LLMs involves modifying RoPE by…

Long chain-of-thought (CoT) significantly enhances the reasoning capabilities of large language models (LLMs). However, extensive reasoning traces lead to inefficiencies and increased time-to-first-token (TTFT). We propose a training…

Large language models (LLMs) acquire extensive prior knowledge through large-scale pretraining and can be further enhanced via supervised fine-tuning (SFT) or reinforcement learning (RL)-based post-training. A growing body of evidence has…

Reasoning large language models (LLMs) excel in complex tasks, which has drawn significant attention to reinforcement learning (RL) for LLMs. However, existing approaches allocate an equal number of rollouts to all questions during the RL…

Advances in training, post-training, and inference-time methods have enabled frontier reasoning models to win gold medals in math competitions and settle challenging open problems. Gaining trust in the responses of these models requires…

Aligning large language models (LLMs) with human preferences through reinforcement learning (RLHF) can lead to reward hacking, where LLMs exploit failures in the reward model (RM) to achieve seemingly high rewards without meeting the…

Reinforcement Learning with Verifiable Rewards (RLVR) has proven effective for enhancing Large Language Models (LLMs) on complex reasoning tasks. However, existing methods suffer from an exploration dilemma: the sharply peaked initial…

In modern deep learning, algorithmic choices (such as width, depth, and learning rate) are known to modulate nuanced resource tradeoffs. This work investigates how these complexities necessarily arise for feature learning in the presence of…

Training Large Language Models (LLMs) incurs significant cost; hence, any strategy that accelerates model convergence is helpful. In this paper, we investigate the ability of a simple idea checkpoint averaging along the trajectory of a…

Checkpoint averaging is a simple and effective method to boost the performance of converged neural machine translation models. The calculation is cheap to perform and the fact that the translation improvement almost comes for free, makes it…

The "alignment tax" of post-training is typically framed as a drop in task accuracy. We show it also involves a severe loss of calibration, making models overconfident, less reliable, and model outputs less diverse. We show that this…

Recent advancements in reasoning-focused language models such as OpenAI's O1 and DeepSeek-R1 have shown that scaling test-time computation-through chain-of-thought reasoning and iterative exploration-can yield substantial improvements on…

Advanced reasoning in LLMs on challenging domains like mathematical reasoning can be tackled using verifiable rewards based reinforced fine-tuning (ReFT). In standard ReFT frameworks, a behavior model generates multiple completions with…

Large Language Models (LLMs) increasingly rely on reinforcement learning with verifiable rewards (RLVR) to elicit reliable chain-of-thought reasoning. However, the training process remains bottlenecked by the computationally expensive…

Reinforcement learning (RL) has improved the reasoning abilities of large language models (LLMs), yet state-of-the-art methods still fail to learn on many training problems. On hard problems, on-policy RL rarely explores even a single…

Test-time scaling improves language model reasoning by spending additional compute to explore multiple solution trajectories. The key challenge is to maximize accuracy while minimizing the total number of generated tokens during reasoning.…

Reinforcement learning (RL) has emerged as a powerful framework for improving the reasoning capabilities of large language models (LLMs). However, most existing RL approaches rely on sparse outcome rewards, which fail to credit correct…

Large Language Models (LLMs) require instruction fine-tuning to perform different downstream tasks. However, the instruction fine-tuning phase still demands significant computational resources and labeled data, lacking a paradigm that can…

Reinforcement learning with verifiable rewards (RLVR) has become a dominant paradigm for improving reasoning in large language models (LLMs), yet the underlying geometry of the resulting parameter trajectories remains underexplored. In this…