On the Implicit Bias in Deep-Learning Algorithms Page 1 DEEP LEARNING HAS been highly
successful in recent years and has led to dramatic improvements in multiple domains …

Optimization is a critical component in deep learning. We think optimization for neural
networks is an interesting topic for theoretical research due to various reasons. First, its …

Physics-informed neural networks (PINNs) are demonstrating remarkable promise in
integrating physical models with gappy and noisy observational data, but they still struggle …

We study how neural networks trained by gradient descent extrapolate, ie, what they learn
outside the support of the training distribution. Previous works report mixed empirical results …

Abstract The classical Universal Approximation Theorem holds for neural networks of
arbitrary width and bounded depth. Here we consider the natural 'dual'scenario for networks …

A recent line of work studies overparametrized neural networks in the “kernel regime,” ie
when during training the network behaves as a kernelized linear predictor, and thus, training …

The generalization mystery of overparametrized deep nets has motivated efforts to
understand how gradient descent (GD) converges to low-loss solutions that generalize well …

Abstract We present Neural Kernel Fields: a novel method for reconstructing implicit 3D
shapes based on a learned kernel ridge regression. Our technique achieves state-of-the-art …

We study the conjectured relationship between the implicit regularization in neural networks,
trained with gradient-based methods, and rank minimization of their weight matrices …

We develop a variational framework to understand the properties of the functions learned by
neural networks fit to data. We propose and study a family of continuous-domain linear …