Recent advances unveiled physical neural networks as promising machine learning platforms, offering faster and more energy-efficient information processing. Compared with extensively-studied optical neural networks, the development of mechanical neural networks (MNNs) remains nascent and faces significant challenges, including heavy computational demands and learning with approximate gradients. Here, we introduce the mechanical analogue of in situ backpropagation to enable highly efficient training of MNNs. We demonstrate that the exact gradient can be obtained locally in MNNs, enabling learning through their immediate vicinity. With the gradient information, we showcase the successful training of MNNs for behavior learning and machine learning tasks, achieving high accuracy in regression and classification. Furthermore, we present the retrainability of MNNs involving task-switching and damage, demonstrating the resilience. Our findings, which integrate the theory for training MNNs and experimental and numerical validations, pave the way for mechanical machine learning hardware and autonomous self-learning material systems.

翻译：近期研究进展揭示了物理神经网络作为有前景的机器学习平台，具有更快速和更节能的信息处理能力。相较于广泛研究的光学神经网络，机械神经网络（MNNs）的发展仍处于初期阶段，面临计算需求大以及依赖近似梯度进行学习等重大挑战。本文引入原位反向传播的机械类比方法，实现了MNN的高效训练。我们证明，MNN中可在局部获得精确梯度，从而通过其邻近区域实现学习。利用梯度信息，我们成功展示了MNN在行为学习与机器学习任务中的训练成果，在回归和分类任务中实现了高精度。此外，我们展示了MNN在任务切换和损伤情况下的可重训练性，验证了其鲁棒性。本研究整合了MNN训练的理论基础与实验及数值验证，为机械机器学习硬件和自主自学习材料系统铺平了道路。