Harmonia: A Unified Architecture for Efficient Deep Symbolic Regression

Tianyun Ma, Yuanbo Wen, Xinkai Song, Pengwei Jin, Di Huang, Husheng Han, Ziyuan Nan, Zhongkai Yu, Shaohui Peng, Yongwei Zhao, Huaping Chen, Zidong Du, Xing Hu, Qi Guo

Abstract: Symbolic regression (SR), the process of formulating a mathematical expression based on observed data points, is a fundamental task in artificial intelligence but is often hindered by its intense computational demands. Deep-learning-based SR methods (DSR) aim to alleviate these demands by breaking down the SR process into two stages: 1) neural network (NN) inference and 2) Broyden-Fletcher–Goldfarb-Shanno (BFGS) optimization. Although NN accelerators can expedite the NN stage, the performance of the BFGS optimization is compromised due to its poor performance for the variety of transcendental functions. Moreover, the distinct computational characteristics of NN inference and BFGS cause not only low hardware utilization but also significant area waste. To address these issues, we propose Harmonia, a unified architecture with the neural transcendental function unit (NTFU) and the Unified Array for efficient DSR. The NTFU utilizes the radial basis function network (RBFN) as a universal approximator for various transcendental functions, which significantly reduces the heavy transcendental function computation cost. We further propose an efficient training algorithm called random nonlinear optimization (RNO) to obtain a lightweight RBFN without accuracy loss. Moreover, Harmonia supports configurable dataflow which integrates the two computing stages into the Unified Array. Experimental results show that Harmonia achieves hardware utilization of 83.83%, on average. Compared to the GPU baseline, Harmonia achieves $4.8\times $ speedup and $47.6\times $ energy saving, alongside considerable low area cost.