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.

我们介绍了一种高效的机械神经网络 (MNN) 训练方法，该方法通过机械模拟的现场反向传播实现了在 MNN 中获取准确梯度信息的能力，从而成功地训练了 MNN 并实现了高精度的回归和分类任务，同时展示了 MNN 的重训练性和鲁棒性。我们的研究结果为机械机器学习硬件和自主自学材料系统铺平了道路。