发现神经网络训练存在先变激活模式、后调权重的双时间尺度现象。
Regime Change Hypothesis: Foundations for Decoupled Dynamics in Neural Network Training
- 基于ReLU结构,分析激活模式变化与权重更新的关系。
- 激活模式变化比权重更新早3倍衰减,表明后期训练稳定在固定激活区域。
- 为监控训练过程和设计新优化策略提供通用工具,适合研究者参考。
尽管深度神经网络(DNN)表现优异,其内部训练动态仍难以刻画。在基于ReLU的模型中,特定输入引发的激活模式决定了网络分段线性行为的区域。本文据此提出:训练是否具有双时间尺度特性——早期显著改变激活模式,后期主要在相对稳定的激活区域内微调权重?我们首先证明局部稳定性:除测度为零的参数与输入外,微小参数扰动可保持固定输入的激活模式不变,表明激活区域内存在局部仿射行为。随后,我们在全连接、卷积及Transformer模型中,使用固定验证集追踪每轮迭代的权重变化与激活模式变化。结果表明,在所有测试架构中,激活模式变化的衰减速率是权重更新幅度的3倍,说明训练后期常处于较稳定的激活区域。该发现为监测训练动态提供了可跨架构通用的工具,并启发对分段线性网络的解耦优化策略研究。代码与实验配置将在论文接受后公开。
原文摘要 · Abstract (English)
Despite the empirical success of DNN, their internal training dynamics remain difficult to characterize. In ReLU-based models, the activation pattern induced by a given input determines the piecewise-linear region in which the network behaves affinely. Motivated by this geometry, we investigate whether training exhibits a two-timescale behavior: an early stage with substantial changes in activation patterns and a later stage where weight updates predominantly refine the model within largely stable activation regimes. We first prove a local stability property: outside measure-zero sets of parameters and inputs, sufficiently small parameter perturbations preserve the activation pattern of a fixed input, implying locally affine behavior within activation regions. We then empirically track per-iteration changes in weights and activation patterns across fully-connected and convolutional architectures, as well as Transformer-based models, where activation patterns are recorded in the ReLU feed-forward (MLP/FFN) submodules, using fixed validation subsets. Across the evaluated settings, activation-pattern changes decay 3 times earlier than weight-update magnitudes, showing that late-stage training often proceeds within relatively stable activation regimes. These findings provide a concrete, architecture-agnostic instrument for monitoring training dynamics and motivate further study of decoupled optimization strategies for piecewise-linear networks. For reproducibility, code and experiment configurations will be released upon acceptance.
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