We study the fundamental problem of learning a single neuron, ie, a function of the form
$\x\mapsto\sigma (\vec w\cdot\x) $ for monotone activations $\sigma:\R\mapsto\R $, with …

We consider a binary classification problem when the data comes from a mixture of two
rotationally symmetric distributions satisfying concentration and anti-concentration …

We study robust adversarial training of two-layer neural networks as a bi-level optimization
problem. In particular, for the inner loop that implements the adversarial attack during …

We consider a one-hidden-layer leaky ReLU network of arbitrary width trained by stochastic
gradient descent (SGD) following an arbitrary initialization. We prove that SGD produces …

Numerous recent works show that overparameterization implicitly reduces variance for min-
norm interpolators and max-margin classifiers. These findings suggest that ridge …

Adversarial training (AT) refers to integrating adversarial examples--inputs altered with
imperceptible perturbations that can significantly impact model predictions--into the training …

Learning adversarially robust models require invariant predictions to a small neighborhood
of its natural inputs, often encountering insufficient model capacity. There is research …

Benign overfitting, where classifiers memorize noisy training data yet still achieve a good
generalization performance, has drawn great attention in the machine learning community …

Recent empirical and theoretical studies have established the generalization capabilities of
large machine learning models that are trained to (approximately or exactly) fit noisy data. In …

Interval Bound Propagation (IBP) is so far the base of state-of-the-art methods for training
neural networks with certifiable robustness guarantees when potential adversarial …