A Brain-Inspired Machine Learning Paradigm for Nature-Powered Equation Solving
Keywords: Nature-Powered Computing, Dynamical Systems
TL;DR: A nature-powered AI paradigm that employs an expressive, self-trainable dynamical system to solve a wide spectrum of problems.
Abstract: Solving equations is fundamental to human understanding of the world. While modern machine learning methods are powerful equation solvers, their escalating complexity and extreme operational costs hinder sustainable development. In contrast, nature effortlessly solves complex equations through dynamical systems that instinctively evolve to low-energy states without explicit instructions. However, existing attempts to leverage dynamical systems are limited by low expressivity and a lack of training support. To this end, we propose DS-Solver, a nature-powered AI paradigm employing an expressive, self-trainable dynamical system capable of accurately solving a wide spectrum of equations with extraordinary efficiency. (1) We enhance system expressivity by enriching node dynamics with coupled real-valued and polarized shadow nodes, capturing complex interactions inherent in the real world. (2) We propose an on-device learning method that leverages intrinsic electrical signals as loss, enabling the dynamical system to instantly train itself at negligible cost. Experimental results across key equations from diverse domains demonstrate that DS-Solver achieves 42\% higher accuracy than current SOTA -- while offering orders-of-magnitude improvements in speed and energy efficiency over traditional neural network solutions on GPUs for both inference and training, showcasing its broader impact in overcoming persistent computational bottlenecks across various critical fields.
Primary Area: foundation or frontier models, including LLMs
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Submission Number: 5144
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