Topological mechanical neural networks as classifiers through in situ backpropagation learning

Recently, a new frontier in computing has emerged with physical neural networks(PNNs) harnessing intrinsic physical processes for learning. Here, we explore topological mechanical neural networks(TMNNs) inspired by the quantum spin Hall effect(QSHE) in topological metamaterials, for machine learning classification tasks. TMNNs utilize pseudospin states and the robustness of the QSHE, making them damage-tolerant for binary classification. We first demonstrate data clustering using untrained TMNNs. Then, for specific tasks, we derive an in situ backpropagation algorithm - a two-step, local-rule method that updates TMNNs using only local information, enabling in situ physical learning. TMNNs achieve high accuracy in classifications of Iris flowers, Penguins, and Seeds while maintaining robustness against bond pruning. Furthermore, we demonstrate parallel classification via frequency-division multiplexing, assigning different tasks to distinct frequencies for enhanced efficiency. Our work introduces in situ backpropagation for wave-based mechanical neural networks and positions TMNNs as promising neuromorphic computing hardware for classification tasks.