In this paper, the authors question the notion of generalizability in neural networks and how conventional proofs fail to hold in the case of large-scale neural networks.
They do so by performing extensive experiments which test out model performance on rather unconventional datasets:- Datasets where the labels have been shuffled or transformed differently; They observe that the deep neural networks converge on training on random labels, effectively challenging our intuitions on what the models are learning. They also see that if they replace the true images with completely unstructured random noise (sampled from a gaussian distribution), model generalization is unaffected, i.e. the models are still able to fit(on the training data) well. The experiments, which we shall present in more detail below, also question theories of generalizability based on uniform convergence bounds, margin theory, and algorithmic stability.
More specifically, they present experiments that help us understand what practices allow generalization and if we can ideally measure generalization. In the label-randomization test, they replace each label with a label chosen from a set of valid labels (randomly). They observe that model performance while training is equivalent to that when training on original labels; They observe test error which isn’t much better than random chance. This leads to several important implications:
1. The model complexity of neural networks allows it to learn or rather memorize a given dataset
2. Training time is mostly unaffected even on random labels, showing that the model can fit using the same computational resources if it were fitting on the meaningful/original dataset.
Zhang et al. also test neural networks on seemingly random inputs or rather inputs with added noise and can observe that the neural networks can capture the raw signal even in the presence of 90% noise.
They also perform some other variations of the label-shuffling experiment, such as:
- Shuffling pixels: They shuffle each image in the training set with a particular seed.
- Random Pixels: They apply random permutation to each image in the training set
- Sampling pixels from a Gaussian distribution: They generate the training set using gaussian noise
The authors test the above experiment using both CNNs and Multi-layer perceptrons and observe zero loss on the training set. They also see that the model doesn’t need any extra help (in the form of regularization or hyperparameter tuning) to converge to such losses. Even if we try to understand model behaviour by inspecting the properties of the algorithm i.e stochastic gradient descent, we see that defining a notion of uniform stability is a hard task. Uniform stability measures how sensitive an algorithm can be, to the replacement of a single example; It does not take into account the specifics of the data distribution. Even the weakest stability measure that bounds the generalization error(and takes data into account) can’t be interpreted fully.
Zhang et al also inspect the role of regularization in the context of generalization in NNs. Regularization is often deemed as a tool in ML to mitigate overfitting and help confine learning to a subset of hypothesis space with manageable complexity. Zhang et al introduce the notion of implicit and explicit regularization. Explicit regularization is regularization techniques such as data augmentation, weight decay and dropout, while methods like batch normalization and early stopping are considered to be implicit. The fine difference lies in the unintended consequence of regularization brought by the latter. To compare the role of regularization, they repeat the random-label experiments with and without regularization. The experiment results show that the explicit regularization techniques allow for better convergence but are not essential, i.e the model can converge even in the absence of regularization.