标题： 通过训练学习：从循环调节无序球体包装中出现的返回点记忆 显示英文标题

标题： Learning by training: emergent return-point memory from cyclically tuning disordered sphere packings

摘要： 许多活体和人工系统通过适应变化的环境或多样的训练数据来提高其适应性或性能。 然而，尚不清楚这种环境变化如何影响适应过程，过程中学到了什么，以及是否保留了过去条件的记忆。 在本工作中，我们使用受循环逆向设计作用的无序系统来研究这些问题，使它们能够获得跨越选定范围的目标弹性性质。 我们证明，这些系统会演变为一个临界吸收流形（MAM），该流形编码了与循环驱动系统中观察到的返回点记忆非常相似的训练范围记忆。 我们进一步提出了一种普遍的机制，用于形成MAMs及其对应记忆，该机制基于训练量中的梯度不连续性。 我们的模型提供了一个简单且广泛适用的物理框架，用于理解自适应系统在环境变化下如何学习以及如何保留过去的经历记忆。 显示英文摘要

摘要： Many living and artificial systems improve their fitness or performance by adapting to changing environments or diverse training data. However, it remains unclear how such environmental variation influences adaptation, what is learned in the process, and whether memory of past conditions is retained. In this work, we investigate these questions using athermal disordered systems that are subject to cyclic inverse design, enabling them to attain target elastic properties spanning a chosen range. We demonstrate that such systems evolve toward a marginally absorbing manifold (MAM), which encodes memory of the training range that closely resembles return-point memory observed in cyclically driven systems. We further propose a general mechanism for the formation of MAMs and the corresponding memory that is based on gradient discontinuities in the trained quantities. Our model provides a simple and broadly applicable physical framework for understanding how adaptive systems learn under environmental change and how they retain memory of past experiences.