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Neural networks are universal function approximators which are known to generalize well despite being dramatically overparameterized. We study this phenomenon from the point of view of the spectral bias of neural networks. Our contributions…

We consider neural networks with rational activation functions. The choice of the nonlinear activation function in deep learning architectures is crucial and heavily impacts the performance of a neural network. We establish optimal bounds…

We provide a detailed asymptotic study of gradient flow trajectories and their implicit optimization bias when minimizing the exponential loss over "diagonal linear networks". This is the simplest model displaying a transition between…

Linear Regression and neural networks are widely used to model data. Neural networks distinguish themselves from linear regression with their use of activation functions that enable modeling nonlinear functions. The standard argument for…

The scope of research in the domain of activation functions remains limited and centered around improving the ease of optimization or generalization quality of neural networks (NNs). However, to develop a deeper understanding of deep…

We study the training dynamics of a shallow neural network with quadratic activation functions and quadratic cost in a teacher-student setup. In line with previous works on the same neural architecture, the optimization is performed…

Common nonlinear activation functions used in neural networks can cause training difficulties due to the saturation behavior of the activation function, which may hide dependencies that are not visible to vanilla-SGD (using first order…

Graph neural networks (GNNs) are a class of neural networks that allow to efficiently perform inference on data that is associated to a graph structure, such as, e.g., citation networks or knowledge graphs. While several variants of GNNs…

ReLU neural networks define piecewise linear functions of their inputs. However, initializing and training a neural network is very different from fitting a linear spline. In this paper, we expand empirically upon previous theoretical work…

Today's most powerful machine learning approaches are typically designed to train stateless architectures with predefined layers and differentiable activation functions. While these approaches have led to unprecedented successes in areas…

Previous research has shown that fully-connected networks with small initialization and gradient-based training methods exhibit a phenomenon known as condensation during training. This phenomenon refers to the input weights of hidden…

Long training times of deep neural networks are a bottleneck in machine learning research. The major impediment to fast training is the quadratic growth of both memory and compute requirements of dense and convolutional layers with respect…

Neural network-based function approximation plays a pivotal role in the advancement of scientific computing and machine learning. Yet, training such models faces several challenges: (i) each target function often requires training a new…

Many neural network architectures rely on the choice of the activation function for each hidden layer. Given the activation function, the neural network is trained over the bias and the weight parameters. The bias catches the center of the…

Neural networks has recently attracted much interest as useful representations of quantum many body ground states, which might help address the infamous sign problem. Most attention was directed at their representability properties, while…

Diagonal linear networks are neural networks with linear activation and diagonal weight matrices. Their theoretical interest is that their implicit regularization can be rigorously analyzed: from a small initialization, the training of…

Initialization of neural network parameters, such as weights and biases, has a crucial impact on learning performance; if chosen well, we can even avoid the need for additional training with backpropagation. For example, algorithms based on…

Based on the tree architecture, the objective of this paper is to design deep neural networks with two or more hidden layers (called deep nets) for realization of radial functions so as to enable rotational invariance for near-optimal…

In this paper, we describe a conceptual design methodology to design distributed neural network architectures that can perform efficient inference within sensor networks with communication bandwidth constraints. The different sensor…

Quantum neural networks (QNNs), represented by parameterized quantum circuits, can be trained in the paradigm of supervised learning to map input data to predictions. Much work has focused on theoretically analyzing the expressive power of…