Understanding how large neural networks avoid memorizing training data is key to explaining their high generalization performance. To examine the structure of when and where memorization occurs in a deep network, we use a recently developed replica-based mean field theoretic geometric analysis method. We find that all layers preferentially learn from examples which share features, and link this behavior to generalization performance. Memorization predominately occurs in the deeper layers, due to decreasing object manifolds' radius and dimension, whereas early layers are minimally affected. This predicts that generalization can be restored by reverting the final few layer weights to earlier epochs before significant memorization occurred, which is confirmed by the experiments. Additionally, by studying generalization under different model sizes, we reveal the connection between the double descent phenomenon and the underlying model geometry. Finally, analytical analysis shows that networks avoid memorization early in training because close to initialization, the gradient contribution from permuted examples are small. These findings provide quantitative evidence for the structure of memorization across layers of a deep neural network, the drivers for such structure, and its connection to manifold geometric properties.
翻译:理解大型神经网络如何避免记忆化培训数据是解释其高一般化性能的关键所在。 为了检查深网络中何时和何地发生的记忆化结构, 我们使用最近开发的基于复制的场均平均理论几何分析方法。 我们发现, 所有层都偏好地从特征共有的示例中学习, 并将这种行为与一般化性能联系起来。 记忆化主要发生在更深层, 因为天体元的半径和维度越来越小, 而早期层受到最小的影响 。 这预示着通过将最后几层重量恢复到发生重大记忆化之前的早期小区, 而实验证实了这一点。 此外, 通过研究不同模型大小的概括化, 我们揭示了双向下流现象与基本模型几何性能之间的联系。 最后, 分析表明, 网络避免早期的记忆化是因为接近初始化, 由各种模型产生的梯度贡献很小。 这些发现为深层神经网络的间层的间化结构提供了定量证据, 以及这种结构的驱动因素及其与几何形特性的连接提供了数量证据。