Function learning forms the foundation of numerous scientific and engineering tasks. While modern machine learning (ML) methods model complex functions effectively, their escalating complexity and computational demands pose challenges to efficient deployment. In contrast, natural dynamical systems exhibit remarkable computational efficiency in representing and solving complex functions. However, existing dynamical system approaches are limited by low expressivity and inefficient training. To this end, we propose EADS, an Expressive and self-Adaptive Dynamical System capable of accurately learning a wide spectrum of functions with extraordinary efficiency. Specifically, (1) drawing inspiration from biological dynamical systems, we integrate hierarchical architectures and heterogeneous dynamics into EADS, significantly enhancing its capacity to represent complex functions. (2) We propose an efficient on-device training method that leverages intrinsic electrical signals to update parameters, making EADS self-adaptive at negligible cost. Experimental results across diverse domains demonstrate that EADS achieves higher accuracy than existing works, while offering orders-of-magnitude speedups and energy efficiency over traditional neural network solutions on GPUs for both inference and training, showcasing its broader impact in overcoming computational bottlenecks across various fields.

Many scientific and engineering tasks require learning functions that map inputs (like measurements or signals) to outputs (such as predictions or control actions). Modern machine-learning models can approximate these functions effectively, but they’re becoming ever more complex, slow, and energy-hungry.We introduce EADS, a novel machine-learning paradigm that builds upon an extremely computationally efficient electronic dynamical system. EADA has layered processing stages and varied dynamics, enabling it to represent a wide variety of functions. It employs an on-device training mechanism that leverages the system’s own electrical signals to update its parameters efficiently.We evaluate EADS across diverse function-learning tasks. EADS not only delivers superior accuracy but also achieves orders-of-magnitude faster runtime and dramatically lower energy consumption compared to conventional methods running on GPUs.