Topological mechanical neural networks as classifiers towards machine learning

Recently, a new frontier has emerged where physical systems are engineered to leverage intrinsic physical processes to learn and perform machine learning tasks. Here, we explore the potential of topological neural networks, focusing on mechanical systems, as classifiers. Firstly, we demonstrate that untrained topological mechanical neural networks (TMNNs) can function effectively as classifiers. Next, for supervised classification, we use the adjoint method to derive in situ backpropagation for TMNNs, an efficient two-step training method consistent with local rules, requiring only local information from the TMNNs to calculate gradients and update the networks. We then demonstrate our approach with classification tasks of Iris Flowers, Penguins, and Seeds, achieving high accuracy. Besides, the robustness of TMNNs is tested through bond pruning, which minimally affects classification accuracy. Furthermore, we demonstrate parallel classification via frequency-division multiplexing, assigning different tasks to distinct frequencies, enhancing efficiency. Our work not only introduces a training method for wave-based mechanical neural networks, but also discovers TMNNs as promising hardware for classifiers towards machine learning.

Funding: Office of Naval Research (MURI N00014-20-1-2479) and National Science Foundation Center for Complex Particle Systems (Award #2243104).