← 研踪 PaperTrailarXiv:2610.24775 · v2
Global Convergence in Deep Networks via the Second Law of Thermodynamics
首次提交 2026-10-18 00:35
版本更新 2026-11-08 00:00
雷达观测 2026-11-10 11:14
摘要
Existing convergence analyses of finite-width overparameterized deep neural networks under standard parameterization often rely on parameters remaining close to their initialization and typically neglect the role of noise, despite empirical evidence that stochasticity can improve optimization and generalization. To bridge this gap, we study $L_2$-regularized continuous-time Langevin dynamics (CLD) with isotropic noise, for training feedforward networks with smooth activations. We introduce a change-of-measure inequality, inspired by the second law of thermodynamics, that enables control of key properties of the training dynamics under the time-evolving parameter distribution. Leveraging a sharpened lower bound on the minimum eigenvalue of the Neural Tangent Kernel (NTK) at initialization, we show that injected noise helps preserve NTK stability with high probability without confining the weights to a small neighborhood of their initialization. As a result, we derive a non-asymptotic upper bound on the expected training loss. Our analysis yields explicit conditions on width and noise temperature that guarantee convergence to a finite loss floor. Finally, we experimentally show the network Jacobian can change from initialization, departing the commonly analyzed lazy regime.
作者备注：Accepted to NeurIPS 2026
观测到的版本
相邻记录可能跳过中间版本；首次发现 v2 及以上也会标为版本更新。
v2 · 2026-11-08 00:00 · 最新观测版本
Global Convergence in Deep Networks via the Second Law of Thermodynamics
Existing convergence analyses of finite-width overparameterized deep neural networks under standard parameterization often rely on parameters remaining close to their initialization and typically neglect the role of noise, despite empirical evidence that stochasticity can improve optimization and generalization. To bridge this gap, we study $L_2$-regularized continuous-time Langevin dynamics (CLD) with isotropic noise, for training feedforward networks with smooth activations. We introduce a change-of-measure inequality, inspired by the second law of thermodynamics, that enables control of key properties of the training dynamics under the time-evolving parameter distribution. Leveraging a sharpened lower bound on the minimum eigenvalue of the Neural Tangent Kernel (NTK) at initialization, we show that injected noise helps preserve NTK stability with high probability without confining the weights to a small neighborhood of their initialization. As a result, we derive a non-asymptotic upper bound on the expected training loss. Our analysis yields explicit conditions on width and noise temperature that guarantee convergence to a finite loss floor. Finally, we experimentally show the network Jacobian can change from initialization, departing the commonly analyzed lazy regime.
查看此版本解读 →查看此版本原文 ↗