Using Large Language Model to Solve and Explain Physics Word Problems Approaching Human Level

Our work demonstrates that large language model (LLM) pre-trained on texts can not only solve pure math word problems, but also physics word problems, whose solution requires calculation and inference based on prior physical knowledge. We collect and annotate the first physics word problem dataset-PhysQA, which contains over 1000 junior high school physics word problems (covering Kinematics, Mass&Density, Mechanics, Heat, Electricity). Then we use OpenAI' s GPT3.5 to generate the answer of these problems and found that GPT3.5 could automatically solve 49.3% of the problems through zero-shot learning and 73.2% through few-shot learning. This result demonstrates that by using similar problems and their answers as prompt, LLM could solve elementary physics word problems approaching human level performance. In addition to solving problems, GPT3.5 can also summarize the knowledge or topics covered by the problems, provide relevant explanations, and generate new physics word problems based on the input. Our work is the first research to focus on the automatic solving, explanation, and generation of physics word problems across various types and scenarios, and we achieve an acceptable and state-of-the-art accuracy. This underscores the potential of LLMs for further applications in secondary education.Comment: 9 pages, 6 figure

Fast Policy Extragradient Methods for Competitive Games with Entropy Regularization

This paper investigates the problem of computing the equilibrium of competitive games, which is often modeled as a constrained saddle-point optimization problem with probability simplex constraints. Despite recent efforts in understanding the last-iterate convergence of extragradient methods in the unconstrained setting, the theoretical underpinnings of these methods in the constrained settings, especially those using multiplicative updates, remain highly inadequate, even when the objective function is bilinear. Motivated by the algorithmic role of entropy regularization in single-agent reinforcement learning and game theory, we develop provably efficient extragradient methods to find the quantal response equilibrium (QRE) -- which are solutions to zero-sum two-player matrix games with entropy regularization -- at a linear rate. The proposed algorithms can be implemented in a decentralized manner, where each player executes symmetric and multiplicative updates iteratively using its own payoff without observing the opponent's actions directly. In addition, by controlling the knob of entropy regularization, the proposed algorithms can locate an approximate Nash equilibrium of the unregularized matrix game at a sublinear rate without assuming the Nash equilibrium to be unique. Our methods also lead to efficient policy extragradient algorithms for solving (entropy-regularized) zero-sum Markov games at similar rates. All of our convergence rates are nearly dimension-free, which are independent of the size of the state and action spaces up to logarithm factors, highlighting the positive role of entropy regularization for accelerating convergence

Semi-Supervised Self-Taught Deep Learning for Finger Bones Segmentation

Segmentation stands at the forefront of many high-level vision tasks. In this study, we focus on segmenting finger bones within a newly introduced semi-supervised self-taught deep learning framework which consists of a student network and a stand-alone teacher module. The whole system is boosted in a life-long learning manner wherein each step the teacher module provides a refinement for the student network to learn with newly unlabeled data. Experimental results demonstrate the superiority of the proposed method over conventional supervised deep learning methods.Comment: IEEE BHI 2019 accepte