Computing-in-memory architecture for Kolmogorov-Arnold networks based on tunable Gaussian-like memory cells

Abstract

Abstract Inspired by the Kolmogorov-Arnold representation theorem, the Kolmogorov-Arnold networks serve as promising alternatives to multilayer perceptrons. Kolmogorov-Arnold networks utilize a superposition of finite basis functions to implement variable continuous univariate activation functions, offering greater flexibility and adaptability. However, the hardware implementation of its basis functions remains costly, making it challenging to achieve complex computations with minimal equipment. Here, we designed the device defined as Gaussian-like memory cell, composed of a Gaussian transistor and a memristor, to ensure the tunable Gaussian-like current-voltage responses. Furthermore, we constructed the circuits based on Gaussian-like memory cells to accommodate the parallel inference computation of Kolmogorov-Arnold networks. This study demonstrates that the proposed architecture based on Gaussian-like memory cells can effectively maintain the algorithmic advantages across various tasks including one-dimensional function regression, image recognition, partial differential equation solving, and time-series forecasting. Notably, the proposed architecture achieves significant improvements in energy efficiency. The results provide a promising avenue for computing-in-memory architecture for Kolmogorov-Arnold networks, and expand the flexibility and efficiency of the neuromorphic computing paradigm.