Recent advancements in large language models (LLMs) have shifted the post-training paradigm from traditional instruction tuning and human preference alignment toward reinforcement learning (RL) focused on reasoning capabilities. However, most current methods rely on rule-based evaluations of answer correctness, overlooking the importance of confidence-aware reasoning, especially for small to medium-sized models. These models often receive rewards for speculative answers without generating coherent reasoning chains. To address this limitation, we propose a novel confidence-based reward model tailored for enhancing STEM reasoning capabilities. Unlike conventional approaches, our model penalizes not only incorrect answers but also low-confidence correct responses, thereby promoting more robust and logically consistent reasoning. We validate the effectiveness of our approach through static evaluations, Best-of-N inference tests, and PPO-based RL training. Our method outperforms several state-of-the-art open-source reward models across diverse STEM benchmarks. We release our codes and model in https://github.com/qianxiHe147/C2RM.

Real-world instructions with multiple constraints pose a significant challenge to existing large language models (LLMs). An observation is that the LLMs exhibit dramatic performance fluctuation when disturbing the order of the incorporated constraints. Yet, none of the existing works has systematically investigated this position bias problem in the field of multi-constraint instruction following. To bridge this gap, we design a probing task where we quantitatively measure the difficulty distribution of the constraints by a novel Difficulty Distribution Index (CDDI). Through the experimental results, we find that LLMs are more performant when presented with the constraints in a “hard-to-easy” order. This preference can be generalized to LLMs with different architecture or different sizes of parameters. Additionally, we conduct an explanation study, providing an intuitive insight into the correlation between the LLM’s attention and constraint orders. Our code and dataset are publicly available at https://github.com/meowpass/PBIF.

It is crucial for large language models (LLMs) to follow instructions that involve multiple constraints. In real-world scenarios, user instructions often contain soft constraints, which are semantically related and cannot be rule-based verified, posing challenges for LLMs. To enhance the soft constraint following ability of LLMs, we initially design a pipeline to construct datasets with high-quality outputs for instructions containing soft constraints automatically. Additionally, to fully utilize the positive and negative samples generated during the data construction process, we choose Direct Preference Optimization (DPO) as the training method. Furthermore, taking into account the difficulty of soft constraints indicated by the number of constraints, we design a curriculum learning training paradigm based on the constraint quantity. We experimentally evaluate the effectiveness of our methods in improving LLMs’ soft constraint following ability and analyze the factors driving the improvements.