Most materials are changed by their history and show memory of things past. However, it is not clear when a system can continually learn new memories in sequence, without interfering with or entirely overwriting earlier memories. Here, we study the learning of multiple stable states in sequence by an elastic material that undergoes plastic changes as it is held in different configurations. We show that an elastic network with linear or nearly linear springs cannot learn continually without overwriting earlier states for a broad class of plasticity rules. On the other hand, networks of sufficiently nonlinear springs can learn continually, without erasing older states, using even simple plasticity rules. We trace this ability to cusped energy contours caused by strong nonlinearities and thus show that elastic nonlinearities play the role of Bayesian priors used in sparse statistical regression. Our model shows how specific material properties allow continual learning of new functions through deployment of the material itself.

中文翻译：

---

机械网络中多记忆的持续学习

大多数材料会因其历史而发生变化，并显示出对过去事物的记忆。但是，尚不清楚系统何时可以连续学习新的内存而不干扰或完全覆盖以前的内存。在这里，我们研究了一种弹性材料按顺序学习多个稳定状态的过程，这种弹性材料会因保持在不同的构型而发生塑性变化。我们表明，具有线性或接近线性弹簧的弹性网络如果不覆盖大量可塑性规则的早期状态，就无法连续学习。另一方面，具有足够非线性的弹簧网络甚至可以使用简单的可塑性规则连续学习，而不会删除较旧的状态。我们将这种能力追踪到由强非线性引起的等高线能量轮廓，因此表明弹性非线性在稀疏统计回归中起着贝叶斯先验的作用。我们的模型显示了特定的材料特性如何通过材料本身的部署来不断学习新功能。