发表机构
Department of Physics, College of Science, Northeastern University（东北大学理学院物理系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过构建微观统计力学系统，精确实现了任意深度ReLU网络的计算，揭示其分段线性行为源于一级相变，为深度神经计算提供了物理基础。
AI 中文摘要
理解深度修正线性单元（ReLU）网络中分段线性计算的物理起源仍是一个基本挑战。在此，我们建立了任意ReLU网络的精确统计力学实现。从微观构型空间及其状态多重性出发，我们构建了一个配分函数，而无需预先指定神经网络激活函数。所得系统可等价描述为具有后选择的级联量子操作或费米子输运模型。我们严格证明，在$\beta\to+\infty$极限下，该系统的热力学可观测量精确再现了任意深度ReLU网络的隐藏状态、输出和损失函数。至关重要的是，我们证明了ReLU网络的分段线性行为源于微观系统中的一级相变，其中不连续点与ReLU网络线性区域的边界精确重合。这项工作为深度神经计算建立了精确的物理基础，并为神经架构设计提供了新颖的统计力学视角。
英文摘要
Understanding the physical origin of the piecewise-linear computation in deep rectified linear unit (ReLU) networks remains a fundamental challenge. Here we establish an exact statistical-mechanical realization of arbitrary ReLU networks. Starting from a microscopic configuration space and its state multiplicities, we construct a partition function without prescribing a neural-network activation function. The resulting system admits equivalent descriptions in terms of cascaded quantum operations with post selection, or fermionic transport model. We rigorously prove that in $β\to+\infty$ limit, the thermodynamic observables of this system exactly reproduce the hidden states, outputs, and loss function of an arbitrary deep ReLU network. Crucially, we demonstrate that the piecewise-linear behavior of the ReLU network emerges from a first-order phase transition in the microscopic system, where the discontinuities precisely coincide with the boundaries of linear regions of ReLU network. This work establishes an exact physical foundation for deep neural computation and provides a novel statistical-mechanical perspective on neural architecture design.
Comments7 pages, 3 figures
