发表机构
University of Southern California（南加州大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究标签噪声下深度网络记忆损坏标签过程中Fisher秩膨胀现象，推导相关公式并确定条件，通过实验验证其与记忆的关系及随损坏严重程度的变化，建立其作为连接多种因素的谱特征。
AI 中文摘要
用标签噪声训练的深度网络在记忆损坏标签之前通常会先学习干净结构。我们表明这种转变在每个样本最后一层梯度的中心散度中留下了谱特征。其有效秩在记忆期间短暂扩展，在拟合损坏标签后收缩，我们称之为Fisher秩膨胀。损坏标签通过将谱质量注入低能量或以前未使用的特征方向来增加有效秩，增加梯度谱的熵。我们推导了一阶留一法归因公式，确定了损坏样本比干净样本贡献更强的条件，并解释了为什么一旦归一化的Fisher梯度谱稳定，归因信号就会减弱。我们在CIFAR-10、CIFAR-100和CIFAR-10N上使用SmallCNN、ResNet18和视觉Transformer测试了这些预测。在各种设置下，Fisher有效秩呈现出与记忆一致的膨胀-收缩轨迹。在峰值秩检查点，损坏样本在最高秩贡献样本中富集，在五种子合成损坏实验中，前100个噪声分数从69.2%到96.2%，在CIFAR-10N上为94.4%±1.9%。一阶谱归因在卷积模型中与精确的留一法贡献紧密匹配，在视觉Transformer中仍然富集。峰值有效秩随着损坏严重程度单调增加，从干净训练时的28.88±1.95增加到60%损坏时的97.09±1.78。在几种设置下，追溯确定的秩膨胀开始时间早于可观察到的测试性能下降。这些结果将Fisher秩膨胀确立为一种谱特征，将损坏样本富集、损坏严重程度以及从结构学习到记忆的转变联系起来。
英文摘要
Deep networks trained with label noise often learn clean structure before memorizing corrupted labels. We show that this transition leaves a spectral signature in the centered scatter of per-example last-layer gradients. Its effective rank transiently expands during memorization and contracts after corrupted labels are fit. We call this phenomenon Fisher Rank Inflation. Corrupted labels increase effective rank by injecting spectral mass into low-energy or previously unused eigendirections, increasing the entropy of the gradient spectrum. We derive a first-order leave-one-out attribution formula, identify conditions under which corrupted examples contribute more strongly than clean examples, and explain why attribution signals weaken once the normalized Fisher-gradient spectrum stabilizes. We test these predictions on CIFAR-10, CIFAR-100, and CIFAR-10N using SmallCNN, ResNet18, and Vision Transformers. Across settings, Fisher effective rank exhibits a consistent inflation--collapse trajectory aligned with memorization. At peak-rank checkpoints, corrupted examples are enriched among the highest rank-contributing samples, with top-100 noisy fractions from \(69.2\%\) to \(96.2\%\) across five-seed synthetic-corruption experiments and \(94.4\%\pm1.9\%\) on CIFAR-10N. First-order spectral attribution closely matches exact leave-one-out contributions in convolutional models and remains enriched in the Vision Transformer. Peak effective rank increases monotonically with corruption severity, from \(28.88\pm1.95\) under clean training to \(97.09\pm1.78\) at \(60\%\) corruption. In several settings, the retrospectively identified onset of rank inflation precedes observable test degradation. These results establish Fisher Rank Inflation as a spectral signature connecting corrupted-example enrichment, corruption severity, and the transition from structure learning to memorization.
