We numerically demonstrate a network of coupled oscillators that can learn to solve a classification task from a set of examples -- performing both training and inference through the nonlinear evolution of the system. We accomplish this by combining three key elements to achieve learning: A long- term memory that stores learned responses, analogous to the synapses in biological brains; a short- term memory that stores the neural activations, similar to the firing patterns of neurons; and an evolution law that updates the synapses in response to novel examples, inspired by synaptic plasticity. Achieving all three elements in wave-based information processors such as metamaterials is a significant challenge. Here, we solve it by leveraging the material multistability to implement long-term memory, and harnessing symmetries and thermal noise to realize the learning rule. Our analysis reveals that the learning mechanism, although inspired by synaptic plasticity, also shares parallelisms with bacterial evolution strategies, where mutation rates increase in the presence of noxious stimuli.

翻译：我们通过数值模拟展示了一个耦合振荡器网络，该系统能够从一组示例中学习解决分类任务——通过系统的非线性演化同时完成训练和推理。为实现这一学习能力，我们融合了三个关键要素：存储学习响应的长期记忆（类似于生物大脑中的突触）、存储神经激活的短期记忆（类似于神经元的放电模式），以及受突触可塑性启发、能根据新样本更新突触的演化规律。在超材料等基于波的信息处理器中同时实现这三个要素是一项重大挑战。本文通过利用材料多稳态性实现长期记忆，并借助对称性和热噪声实现学习规则，成功解决了这一难题。我们的分析表明，该学习机制虽受突触可塑性启发，但也与细菌进化策略存在相似性——后者在有害刺激下会提高突变率。