A Cognitive Solver with Autonomously Knowledge Learning for Reasoning Mathematical Answers

Reasoning answers to mathematical problems requires machines to think and operate like a human to learn knowledge from mathematical data, which is one of the fundamental tasks for exploring general artificial intelligence. Most solutions focus on mimicking how humans understand problems, which generate the necessary expressions for answers. However, they are still far from enough since they ignore the core ability of humans to acquire knowledge from experience. In this paper, we propose a Cognitive Solver (CogSolver) that is capable of autonomously learning knowledge from scratch to solve mathematical problems, inspired by two cognitive science theories. Specifically, we draw one insight from the dual process theory to establish an intelligent BRAIN-ARM framework, and refer to another information processing theory to summarize the knowledge learning process into Store-Apply-Update steps. In CogSolver, the BRAIN system stores three types of mathematical knowledge, including semantics knowledge, relation knowledge, and mathematic rule knowledge. Then, the ARM system applies the knowledge in BRAIN to answer the problems. Specifically, we design a knowledge-aware module and a commutative module in ARM to improve its reasoning ability, where the knowledge is organically integrated into answer reasoning process. After solving the problems, BRAIN updates the stored knowledge according to the feedback of ARM, where we develop knowledge filters to eliminate the redundant ones and further form a more reasonable knowledge base. Our CogSolver carries out the above three steps iteratively, which behaves more like a human. We conduct extensive experiments on real-world math word problem datasets. The experimental results demonstrate the improvement in answer reasoning and clearly show how CogSolver gains knowledge from the problems, leading to superior interpretability. Our codes are available at https://github.com/bigdata-ustc/CogSolver.