An Expressive and Self-Adaptive Dynamical System for Efficient Function Learning

Chuan Liu, Chunshu Wu, Ruibing Song, Ang Li, Ying Nian Wu, Tong Geng
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:39841-39852, 2025.

Abstract

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 on-device training method that leverages intrinsic electrical signals to update parameters, making EADS self-adaptive with exceptional efficiency. Experimental results across diverse domains demonstrate that EADS achieves higher accuracy than existing works, while offering orders-of-magnitude speedups over traditional neural network solutions on GPUs for both inference and training, showcasing its broader impact in overcoming computational bottlenecks across various fields.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-liu25cc, title = {An Expressive and Self-Adaptive Dynamical System for Efficient Function Learning}, author = {Liu, Chuan and Wu, Chunshu and Song, Ruibing and Li, Ang and Wu, Ying Nian and Geng, Tong}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {39841--39852}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/liu25cc/liu25cc.pdf}, url = {https://proceedings.mlr.press/v267/liu25cc.html}, abstract = {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 on-device training method that leverages intrinsic electrical signals to update parameters, making EADS self-adaptive with exceptional efficiency. Experimental results across diverse domains demonstrate that EADS achieves higher accuracy than existing works, while offering orders-of-magnitude speedups over traditional neural network solutions on GPUs for both inference and training, showcasing its broader impact in overcoming computational bottlenecks across various fields.} }
Endnote
%0 Conference Paper %T An Expressive and Self-Adaptive Dynamical System for Efficient Function Learning %A Chuan Liu %A Chunshu Wu %A Ruibing Song %A Ang Li %A Ying Nian Wu %A Tong Geng %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-liu25cc %I PMLR %P 39841--39852 %U https://proceedings.mlr.press/v267/liu25cc.html %V 267 %X 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 on-device training method that leverages intrinsic electrical signals to update parameters, making EADS self-adaptive with exceptional efficiency. Experimental results across diverse domains demonstrate that EADS achieves higher accuracy than existing works, while offering orders-of-magnitude speedups over traditional neural network solutions on GPUs for both inference and training, showcasing its broader impact in overcoming computational bottlenecks across various fields.
APA
Liu, C., Wu, C., Song, R., Li, A., Wu, Y.N. & Geng, T.. (2025). An Expressive and Self-Adaptive Dynamical System for Efficient Function Learning. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:39841-39852 Available from https://proceedings.mlr.press/v267/liu25cc.html.

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