Related papers: Do highly over-parameterized neural networks gener…
The literature on "benign overfitting" in overparameterized models has been mostly restricted to regression or binary classification; however, modern machine learning operates in the multiclass setting. Motivated by this discrepancy, we…
In this work, we propose a new training method for finding minimum weight norm solutions in over-parameterized neural networks (NNs). This method seeks to improve training speed and generalization performance by framing NN training as a…
A recent line of work has shown that an overparametrized neural network can perfectly fit the training data, an otherwise often intractable nonconvex optimization problem. For (fully-connected) shallow networks, in the best case scenario,…
One of the major open problems in machine learning is to characterize generalization in the overparameterized regime, where most traditional generalization bounds become inconsistent even for overparameterized linear regression. In many…
We perform an average case analysis of the generalization dynamics of large neural networks trained using gradient descent. We study the practically-relevant "high-dimensional" regime where the number of free parameters in the network is on…
Previous theoretical work on deep learning and neural network optimization tend to focus on avoiding saddle points and local minima. However, the practical observation is that, at least in the case of the most successful Deep Convolutional…
We study the minimal error of the Empirical Risk Minimization (ERM) procedure in the task of regression, both in the random and the fixed design settings. Our sharp lower bounds shed light on the possibility (or impossibility) of adapting…
Machine learning algorithms use error function minimization to fit a large set of parameters in a preexisting model. However, error minimization eventually leads to a memorization of the training dataset, losing the ability to generalize to…
Overparameterized neural networks can be highly accurate on average on an i.i.d. test set yet consistently fail on atypical groups of the data (e.g., by learning spurious correlations that hold on average but not in such groups).…
We study the high-dimensional asymptotics of empirical risk minimization (ERM) in over-parametrized two-layer neural networks with quadratic activations trained on synthetic data. We derive sharp asymptotics for both training and test…
It has been observed \citep{zhang2016understanding} that deep neural networks can memorize: they achieve 100\% accuracy on training data. Recent theoretical results explained such behavior in highly overparametrized regimes, where the…
Neural networks trained via gradient descent with random initialization and without any regularization enjoy good generalization performance in practice despite being highly overparametrized. A promising direction to explain this phenomenon…
This paper is motivated by an open problem around deep networks, namely, the apparent absence of over-fitting despite large over-parametrization which allows perfect fitting of the training data. In this paper, we analyze this phenomenon in…
Classic supervised learning involves algorithms trained on $n$ labeled examples to produce a hypothesis $h \in \mathcal{H}$ aimed at performing well on unseen examples. Meta-learning extends this by training across $n$ tasks, with $m$…
It is well-known that modern neural networks are vulnerable to adversarial examples. To mitigate this problem, a series of robust learning algorithms have been proposed. However, although the robust training error can be near zero via some…
Deep neural networks (DNNs) generalize remarkably well without explicit regularization even in the strongly over-parametrized regime where classical learning theory would instead predict that they would severely overfit. While many…
Generalization performance of classifiers in deep learning has recently become a subject of intense study. Deep models, typically over-parametrized, tend to fit the training data exactly. Despite this "overfitting", they perform well on…
Deep learning models have lately shown great performance in various fields such as computer vision, speech recognition, speech translation, and natural language processing. However, alongside their state-of-the-art performance, it is still…
We derive a tight generalization bound for quantum machine learning that is applicable to a wide range of supervised tasks, data, and models. Our bound is both efficiently computable and free of big-O notation. Furthermore, we point out…
Classic ensembles generalize better than any single component model. In contrast, recent empirical studies find that modern ensembles of (overparameterized) neural networks may not provide any inherent generalization advantage over single…