arXiv:2605.29152cs.LGmath.OC2026-05

训练会遗忘初始化,影响模型泛化能力。

Do Deep Networks Forget Initialization? A Forgetting-Time View of Practical Inductive Bias

论文配图:Do Deep Networks Forget Initialization? A Forgetting-Time View of Practical Inductive Bias
图 1 · 摘自论文原文
  • 通过控制初始化尺度,测量训练后对初始偏置的依赖程度。
  • 低学习率SGD下测试准确率随初始化尺度波动26.5个百分点,仍保持99.5%训练精度。
  • 自适应优化器和大学习率会使初始化记忆消失,提升泛化能力。

随机初始化的神经网络施加函数先验,但实际使用的是训练后的预测器。我们探究训练过程中初始偏置有多少保留下来。为此引入‘初始化记忆’:验证选择的预测器对随机初始化尺度的依赖程度。在ResNet上进行受控的CIFAR-10实验,发现初始化记忆已能清晰区分不同训练模式。在低学习率SGD下,即使训练准确率达≥99.5%,测试准确率仍随初始化尺度变化达26.5个百分点(如ResNet-9,批量大小b=128)。延长至5000轮,该差异基本不变,说明非欠拟合。相比之下,Adam类方法几乎消除依赖。当高学习率搭配显式L₂范数控制时,SGD也可被设计为遗忘。从遗忘时间尺度解释:梯度流类动态可保留初始化记忆,而随机有限步效应、显式范数衰减及自适应预条件会按正则化强度所决定的尺度抹去记忆。因此,训练网络的实际归纳偏置并非仅来自架构先验,而是经由训练动态过滤后的先验;提升泛化的正则化手段恰恰是擦除初始化记忆的关键。

原文摘要 · Abstract (English)

Randomly initialized neural networks induce a prior over functions, but the predictor used in practice is produced only after training. We ask how much of this initial bias survives the training pipeline. To make the question measurable, we introduce initialization memory: the dependence of the validation-selected predictor on the scale of the random initialization. We perform controlled CIFAR-10 experiments on ResNets where initialization memory already sharply separates training regimes. Low-learning-rate SGD can interpolate while still remembering its initialization: on ResNet-9 with batch size $b=128$, test accuracy varies by $26.5$ percentage points across initialization scales despite $\ge99.5\%$ training accuracy. This is not undertraining: extending the same low-learning-rate regime to $5{,}000$ epochs leaves the spread essentially unchanged. In contrast, Adam-family methods largely erase the dependence. SGD can also be made to forget when larger learning rates are paired with explicit $L_2$ norm control. We interpret these findings in terms of the time scale of forgetting: gradient-flow-like dynamics can preserve initialization memory, whereas stochastic finite-step effects, explicit norm decay, and adaptive preconditioning erase it on scales governed by the size of explicit or implicit regularization. The practical inductive bias of a trained network is therefore not the architectural prior alone, but the architectural prior after being filtered by the forgetting dynamics of the training pipeline; and the same regularizers that improve generalization are precisely those that erase memory of initialization.

深度学习归纳偏置优化器泛化

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