Xiao Liang

Yiyao Yu, Yuxiang Zhang, Dongdong Zhang et al.

Large Language Models (LLMs) have made notable progress in mathematical reasoning, yet often rely on single-paradigm reasoning, limiting their effectiveness across diverse tasks. We introduce Chain-of-Reasoning (CoR), a novel unified framework integrating multiple reasoning paradigms--Natural Language Reasoning (NLR), Algorithmic Reasoning (AR), and Symbolic Reasoning (SR)--to enable synergistic collaboration. CoR generates multiple potential answers via different reasoning paradigms and synthesizes them into a coherent final solution. We propose a Progressive Paradigm Training (PPT) strategy for models to progressively master these paradigms, leading to CoR-Math-7B. Experimental results demonstrate that CoR-Math-7B significantly outperforms current SOTA models, achieving up to a 41.0% absolute improvement over GPT-4o in theorem proving and a 15.0% improvement over RL-based methods on the MATH benchmark in arithmetic tasks. These results show the enhanced mathematical comprehension ability of our model, enabling zero-shot generalization across tasks.

Xiao Liang, Dan Nguyen, Steve Jiang

Generalizability is a concern when applying a deep learning (DL) model trained on one dataset to other datasets. Training a universal model that works anywhere, anytime, for anybody is unrealistic. In this work, we demonstrate the generalizability problem, then explore potential solutions based on transfer learning (TL) by using the cone-beam computed tomography (CBCT) to computed tomography (CT) image conversion task as the testbed. Previous works have converted CBCT to CT-like images. However, all of those works studied only one or two anatomical sites and used images from the same vendor's scanners. Here, we investigated how a model trained for one machine and one anatomical site works on other machines and other sites. We trained a model on CBCT images acquired from one vendor's scanners for head and neck cancer patients and applied it to images from another vendor's scanners and for other disease sites. We found that generalizability could be a significant problem for this particular application when applying a trained DL model to datasets from another vendor's scanners. We then explored three practical solutions based on TL to solve this generalization problem: the target model, which is trained on a target domain from scratch; the combined model, which is trained on both source and target domain datasets from scratch; and the adapted model, which fine-tunes the trained source model to a target domain. We found that when there are sufficient data in the target domain, all three models can achieve good performance. When the target dataset is limited, the adapted model works the best, which indicates that using the fine-tuning strategy to adapt the trained model to an unseen target domain dataset is a viable and easy way to implement DL models in the clinic.