用弹簧和棍子模拟学习过程，能逼近任意连续函数。
Learning with springs and sticks
- 用棍子实现分段线性逼近，弹簧势能编码误差损失
- 系统通过耗散收敛至低能态，回归性能媲美多层感知机
- 发现热力学学习屏障，环境波动会阻碍学习
学习是一种物理过程。本文研究一种由弹簧和棍子构成的简单动力系统，可任意逼近任意连续函数。核心思路是：用棍子模拟目标函数的分段线性近似，利用弹簧的势能编码期望的均方误差损失函数，并通过耗散机制收敛到最小能量状态。我们将该仿真系统应用于回归任务，结果表明其性能与多层感知机相当。此外，我们研究了系统的热力学性质，发现系统自由能的变化与其学习数据分布的能力存在关联。实验中我们观察到一种由环境波动引起的‘热力学学习屏障’——当系统自由能变化触及该屏障时，学习将无法进行。我们认为这一简单模型有助于从物理视角更深入理解学习系统。
原文摘要 · Abstract (English)
Learning is a physical process. Here, we aim to study a simple dynamical system composed of springs and sticks capable of arbitrarily approximating any continuous function. The main idea of our work is to use the sticks to mimic a piecewise-linear approximation of the given function, use the potential energy of springs to encode a desired mean squared error loss function, and converge to a minimum-energy configuration via dissipation. We apply the proposed simulation system to regression tasks and show that its performance is comparable to that of multi-layer perceptrons. In addition, we study the thermodynamic properties of the system and find a relation between the free energy change of the system and its ability to learn an underlying data distribution. We empirically find a \emph{thermodynamic learning barrier} for the system caused by the fluctuations of the environment, whereby the system cannot learn if its change in free energy hits such a barrier. We believe this simple model can help us better understand learning systems from a physical point of view.
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