Large Language Models (LLMs) have made notable progress in mathematical reasoning, yet they often rely on single-paradigm reasoning that limits their effectiveness across diverse tasks. In this paper, we introduce Chain-of-Reasoning (CoR), a novel unified framework that integrates multiple reasoning paradigms — Natural Language Reasoning (NLR), Algorithmic Reasoning (AR), and Symbolic Reasoning (SR) — to enable synergistic collaboration. CoR generates multiple potential answers using different reasoning paradigms and synthesizes them into a coherent final solution. We propose a Progressive Paradigm Training (PPT) strategy that allows models to progressively master these paradigms, culminating in the development of at 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 tasks and a 15% improvement over RL-based methods on the MATH benchmark in arithmetic tasks. These results show the enhanced mathematical comprehensive ability of our model, enabling zero-shot generalization across tasks.The code is available at https://github.com/microsoft/CoR.

We propose a new paradigm for universal information extraction (IE) that is compatible with any schema format and applicable to a list of IE tasks, such as named entity recognition, relation extraction, event extraction and sentiment analysis. Our approach converts the text-based IE tasks as the token-pair problem, which uniformly disassembles all extraction targets into joint span detection, classification and association problems with a unified extractive framework, namely UniEX. UniEX can synchronously encode schema-based prompt and textual information, and collaboratively learn the generalized knowledge from pre-defined information using the auto-encoder language models. We develop a traffine attention mechanism to integrate heterogeneous factors including tasks, labels and inside tokens, and obtain the extraction target via a scoring matrix. Experiment results show that UniEX can outperform generative universal IE models in terms of performance and inference-speed on 14 benchmarks IE datasets with the supervised setting. The state-of-the-art performance in low-resource scenarios also verifies the transferability and effectiveness of UniEX.

Large-scale pre-trained language models (PLMs) bring new opportunities to challenging problems, especially those that need high-level intelligence, such as the math word problem (MWPs). However, directly applying existing PLMs to MWPs can fail as the generation process lacks sufficient supervision and thus lacks fast adaptivity as humans. We notice that human reasoning has a dual reasoning framework that consists of an immediate reaction system (system 1) and a delicate reasoning system (system 2), where the entire reasoning is determined by their interaction. This inspires us to develop a cooperative reasoning-induced PLM for solving MWPs, called Cooperative Reasoning (CoRe), resulting in a human-like reasoning architecture with system 1 as the generator and system 2 as the verifier. In our approach, the generator is responsible for generating reasoning paths, and the verifiers are used to supervise the evaluation in order to obtain reliable feedback for the generator. We evaluate our CoRe framework on several mathematical reasoning datasets and achieve decent improvement over state-of-the-art methods, up to 9.6% increase over best baselines.