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We propose a general framework for deriving generalization bounds for parallel positively homogeneous neural networks--a class of neural networks whose input-output map decomposes as the sum of positively homogeneous maps. Examples of such…
Deep learning empirically achieves high performance in many applications, but its training dynamics has not been fully understood theoretically. In this paper, we explore theoretical analysis on training two-layer ReLU neural networks in a…
Quality-Diversity (QD) algorithms excel at discovering diverse repertoires of skills, but are hindered by poor sample efficiency and often require tens of millions of environment steps to solve complex locomotion tasks. Recent advances in…
Latent space models are effective tools for statistical modeling and exploration of network data. These models can effectively model real world network characteristics such as degree heterogeneity, transitivity, homophily, etc. Due to their…
Despite achieving excellent performance on benchmarks, deep neural networks often underperform in real-world deployment due to sensitivity to minor, often imperceptible shifts in input data, known as distributional shifts. These shifts are…
Uncertainty quantification for full-waveform inversion provides a probabilistic characterization of the ill-conditioning of the problem, comprising the sensitivity of the solution with respect to the starting model and data noise. This…
There has been a significant recent surge in deep neural network (DNN) techniques. Most of the existing DNN techniques have restricted model formats/assumptions. To overcome their limitations, we propose the nonparametric transformation…
The distribution of a neural network's latent representations has been successfully used to detect out-of-distribution (OOD) data. This work investigates whether this distribution moreover correlates with a model's epistemic uncertainty,…
Quantized or low-bit neural networks are attractive due to their inference efficiency. However, training deep neural networks with quantized activations involves minimizing a discontinuous and piecewise constant loss function. Such a loss…
Artificial neural networks (NNs) have become the de facto standard in machine learning. They allow learning highly nonlinear transformations in a plethora of applications. However, NNs usually only provide point estimates without…
Pruning neural networks has proven to be a successful approach to increase the efficiency and reduce the memory storage of deep learning models without compromising performance. Previous literature has shown that it is possible to achieve a…
We introduce frequency propagation, a learning algorithm for nonlinear physical networks. In a resistive electrical circuit with variable resistors, an activation current is applied at a set of input nodes at one frequency, and an error…
We focus at the interface between multiscale computations, bifurcation theory and social networks. In particular we address how the Equation-Free approach, a recently developed computational framework, can be exploited to systematically…
The increasingly wide use of deep machine learning techniques in computational mechanics has significantly accelerated simulations of problems that were considered unapproachable just a few years ago. However, in critical applications such…
Sparse deep learning aims to address the challenge of huge storage consumption by deep neural networks, and to recover the sparse structure of target functions. Although tremendous empirical successes have been achieved, most sparse deep…
This book develops an effective theory approach to understanding deep neural networks of practical relevance. Beginning from a first-principles component-level picture of networks, we explain how to determine an accurate description of the…
A key task in actuarial modelling involves modelling the distributional properties of losses. Classic (distributional) regression approaches like Generalized Linear Models (GLMs; Nelder and Wedderburn, 1972) are commonly used, but…
Recurrent neural networks are a successful neural architecture for many time-dependent problems, including time series analysis, forecasting, and modeling of dynamical systems. Training such networks with backpropagation through time is a…
The impressive performance of deep neural networks (DNNs) has immensely strengthened the line of research that aims at theoretically analyzing their effectiveness. This has incited research on the reaction of DNNs to noisy input, namely…
Real-world time series data often exhibits substantial missing values, posing challenges for advanced analysis. A common approach to addressing this issue is imputation, where the primary challenge lies in determining the appropriate values…