Although machine learning models typically experience a drop in performance on out-of-distribution data, accuracies on in- versus out-of-distribution data are widely observed to follow a single linear trend when evaluated across a testbed of models.
Models that are more accurate on the out-of-distribution data relative to this baseline exhibit effective robustness and are exceedingly rare. Identifying such models, and understanding their properties, is key to improving out-of-distribution performance. We conduct a thorough empirical investigation of effective robustness during fine-tuning and surprisingly find that models pre-trained on larger datasets exhibit effective robustness during training that vanishes at convergence. We study how properties of the data influence effective robustness, and we show that it increases with the larger size, more diversity, and higher example difficulty of the dataset. We also find that models that display effective robustness are able to correctly classify 10% of the examples that no other current testbed model gets correct. Finally, we discuss several strategies for scaling effective robustness to the high-accuracy regime to improve the out-of-distribution accuracy of state-of-the-art models.
Existing work on understanding deep learning often employs measures that compress all data-dependent information into a few numbers. In this work, we adopt a perspective based on the role of individual examples. We introduce a measure of the computat
ional difficulty of making a prediction for a given input: the (effective) prediction depth. Our extensive investigation reveals surprising yet simple relationships between the prediction depth of a given input and the models uncertainty, confidence, accuracy and speed of learning for that data point. We further categorize difficult examples into three interpretable groups, demonstrate how these groups are processed differently inside deep models and showcase how this understanding allows us to improve prediction accuracy. Insights from our study lead to a coherent view of a number of separately reported phenomena in the literature: early layers generalize while later layers memorize; early layers converge faster and networks learn easy data and simple functions first.
We propose a new framework for reasoning about generalization in deep learning. The core idea is to couple the Real World, where optimizers take stochastic gradient steps on the empirical loss, to an Ideal World, where optimizers take steps on the po
pulation loss. This leads to an alternate decomposition of test error into: (1) the Ideal World test error plus (2) the gap between the two worlds. If the gap (2) is universally small, this reduces the problem of generalization in offline learning to the problem of optimization in online learning. We then give empirical evidence that this gap between worlds can be small in realistic deep learning settings, in particular supervised image classification. For example, CNNs generalize better than MLPs on image distributions in the Real World, but this is because they optimize faster on the population loss in the Ideal World. This suggests our framework is a useful tool for understanding generalization in deep learning, and lays a foundation for future research in the area.
Convolution is one of the most essential components of architectures used in computer vision. As machine learning moves towards reducing the expert bias and learning it from data, a natural next step seems to be learning convolution-like structures f
rom scratch. This, however, has proven elusive. For example, current state-of-the-art architecture search algorithms use convolution as one of the existing modules rather than learning it from data. In an attempt to understand the inductive bias that gives rise to convolutions, we investigate minimum description length as a guiding principle and show that in some settings, it can indeed be indicative of the performance of architectures. To find architectures with small description length, we propose $beta$-LASSO, a simple variant of LASSO algorithm that, when applied on fully-connected networks for image classification tasks, learns architectures with local connections and achieves state-of-the-art accuracies for training fully-connected nets on CIFAR-10 (85.19%), CIFAR-100 (59.56%) and SVHN (94.07%) bridging the gap between fully-connected and convolutional nets.
Generalization of deep networks has been of great interest in recent years, resulting in a number of theoretically and empirically motivated complexity measures. However, most papers proposing such measures study only a small set of models, leaving o
pen the question of whether the conclusion drawn from those experiments would remain valid in other settings. We present the first large scale study of generalization in deep networks. We investigate more then 40 complexity measures taken from both theoretical bounds and empirical studies. We train over 10,000 convolutional networks by systematically varying commonly used hyperparameters. Hoping to uncover potentially causal relationships between each measure and generalization, we analyze carefully controlled experiments and show surprising failures of some measures as well as promising measures for further research.
Despite existing work on ensuring generalization of neural networks in terms of scale sensitive complexity measures, such as norms, margin and sharpness, these complexity measures do not offer an explanation of why neural networks generalize better w
ith over-parametrization. In this work we suggest a novel complexity measure based on unit-wise capacities resulting in a tighter generalization bound for two layer ReLU networks. Our capacity bound correlates with the behavior of test error with increasing network sizes, and could potentially explain the improvement in generalization with over-parametrization. We further present a matching lower bound for the Rademacher complexity that improves over previous capacity lower bounds for neural networks.
In an attempt to better understand generalization in deep learning, we study several possible explanations. We show that implicit regularization induced by the optimization method is playing a key role in generalization and success of deep learning m
odels. Motivated by this view, we study how different complexity measures can ensure generalization and explain how optimization algorithms can implicitly regularize complexity measures. We empirically investigate the ability of these measures to explain different observed phenomena in deep learning. We further study the invariances in neural networks, suggest complexity measures and optimization algorithms that have similar invariances to those in neural networks and evaluate them on a number of learning tasks.
We present a generalization bound for feedforward neural networks in terms of the product of the spectral norm of the layers and the Frobenius norm of the weights. The generalization bound is derived using a PAC-Bayes analysis.
With a goal of understanding what drives generalization in deep networks, we consider several recently suggested explanations, including norm-based control, sharpness and robustness. We study how these measures can ensure generalization, highlighting
the importance of scale normalization, and making a connection between sharpness and PAC-Bayes theory. We then investigate how well the measures explain different observed phenomena.
We argue that the optimization plays a crucial role in generalization of deep learning models through implicit regularization. We do this by demonstrating that generalization ability is not controlled by network size but rather by some other implicit
control. We then demonstrate how changing the empirical optimization procedure can improve generalization, even if actual optimization quality is not affected. We do so by studying the geometry of the parameter space of deep networks, and devising an optimization algorithm attuned to this geometry.
