Large language models (LLMs) have demonstrated impressive performance on reasoning-intensive tasks, but enhancing their reasoning abilities typically relies on either reinforcement learning (RL) with verifiable signals or supervised fine-tuning (SFT) with high-quality long chain-of-thought (CoT) demonstrations, both of which are expensive. In this paper, we study a novel problem of incentivizing the reasoning capacity of LLMs without expensive high-quality demonstrations and reinforcement learning. We investigate whether the reasoning capabilities of LLMs can be effectively incentivized via supervision from significantly weaker models. We further analyze when and why such weak supervision succeeds in eliciting reasoning abilities in stronger models. Our findings show that supervision from significantly weaker reasoners can substantially improve student reasoning performance, recovering close to 94% of the gains of expensive RL at a fraction of the cost. Experiments across diverse benchmarks and model architectures demonstrate that weak reasoners can effectively incentivize reasoning in stronger student models, consistently improving performance across a wide range of reasoning tasks. Our results suggest that this simple weak-to-strong paradigm is a promising and generalizable alternative to costly methods for incentivizing strong reasoning capabilities at inference-time in LLMs. Code is at https://github.com/W2SR-ARR/Code.

We study the post-training of large language models (LLMs) with human preference data. Recently, direct preference optimization and its variants have shown considerable promise in aligning language models, eliminating the need for reward models and online sampling. Despite these benefits, these methods rely on explicit assumptions about the Bradley-Terry (BT) model, which makes them prone to overfitting and results in suboptimal performance, particularly on reasoning-heavy tasks. To address these challenges, we propose a principled preference fine-tuning algorithm called InfoPO, which effectively and efficiently aligns large language models using preference data. InfoPO eliminates the reliance on the BT model and prevents the likelihood of the chosen response from decreasing. Extensive experiments confirm that InfoPO consistently outperforms established baselines on widely used open benchmarks, particularly in reasoning tasks.

Large Language Models (LLMs) require alignment via reinforcement learning (RL) to effectively perform task-specific objectives, such as human preference alignment and enhanced reasoning. While Proximal Policy Optimization (PPO) is widely adopted, its computational overhead, stemming from additional value model requirements, limits applicability. Existing alternatives, like Group Relative Policy Optimization (GRPO), mitigate computational costs but remain sensitive to reward model quality. To address this, we introduce Group Preference Reward Shaping (GPRS), a novel method that leverages preference-based comparisons rather than precise numerical rewards. GPRS requires no extra model components and remains robust across varying reward model sizes and qualities. Extensive experiments demonstrate that GPRS consistently outperforms existing critic-model-free RL algorithms in Reinforcement Learning from Human Feedback (RLHF) and reasoning tasks, providing stable and good alignment performance.

Traditional scaling laws in natural language processing suggest that increasing model size and training data enhances performance. However, recent studies reveal deviations, particularly in large language models, where performance improvements decelerate—a phenomenon known as sub-scaling. This paper revisits these scaling laws by examining the impact of data quality and training strategies on model performance. Through extensive empirical analysis of over 400 models, we identify high data density and non-optimal resource allocation as key factors contributing to sub-scaling. High data density leads to diminishing returns due to redundant information, while optimal resource allocation is crucial for sustained performance improvements. We propose a sub-optimal scaling law that better predicts performance in sub-scaling regimes, highlighting the importance of data quality and diversity.