In this paper, the authors test the memorization abilities of deep neural networks and quantify differences in gradient-based optimization of deep neural networks trained on real vs noisy data. They also challenge traditional notions of the effective capacity of DNNs, arguing that dataset-independent definitions cannot explain the generalization performance of DNNs. The traditionalist view of generalization often claims that a model with sufficient capacity can fit the training set but might yield poor generalization due to overparameterization.
However, deep neural networks can still fit the data despite being overparameterized, thus challenging our notions of generalization. The authors also show that regularization techniques can differentially hinder memorization while training on random data in DNNs while still learning about real data. To test the memorization capabilities of DNNs, they perform experiments on MNIST and CIFAR10 datasets using Multi-layer perceptrons and CNNs. They observe that ‘easy examples’ or inputs which the models fit very easily (over a few passes) exist more commonly in real data, thus showing that the model is not memorizing naively but fitting specific patterns before others. To quantify this difference better, they introduce a loss sensitivity metric where they measure the norm of the loss gradient concerning the last sample seen by the model. By computing the metric for each sample, they can find out which samples contribute more towards the model’s loss. For real data, they see that only a subset of the training set has high loss sensitivity, while loss sensitivity is high for almost every input in the random data. The authors argue that the model doesn’t memorize the same way when it sees random inputs vs when it sees real data.
The authors introduce the notion of critical samples - a subset of a dataset, where for each sample x, there exists at least one sample x’, which is in the proximity of x. They measure the complexity of a decision boundary in terms of a critical sample ratio, i.e. the number of critical samples divided by the total number of samples. They use this metric to show that the CSR is higher for random data than real data, thus showing that the decision surfaces for noisy data are much more complex. To find critical samples, the authors use a Langevin adversarial sample search (LASS) which builds on the Fast Gradient Sign Method (FGSM).
The authors also argue that regularization can affect memorization and limit the speed of memorization of noise data without significantly impacting learning on real data. When comparing the same model trained on random data vs real data, they see that the validation performance stabilizes or plateaus after a point for real data but keeps increasing for randomly labelled data. The authors claim that this is an artefact of using regularizers, and the regularizers play a role in limiting ‘memorization’ in the real data case. However, they are still looking at the aspect of ‘memorization’ or ‘generalization’ through the lens of test error performance, thus bringing us to the central question of how we ideally measure generalizability in neural networks.
To summarize, the authors feel that it is still unclear why DNNs find generalizable solutions on real data and believe that apart from deep learning priors and hierarchical representations, the data itself plays a role in generalizability.