Capacity of two-layer feedforward neural networks with binary weights
Publications associées (38)
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Many feedforward neural networks (NNs) generate continuous and piecewise-linear (CPWL) mappings. Specifically, they partition the input domain into regions on which the mapping is affine. The number of these so-called linear regions offers a natural metric ...
2024
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This paper rethinks Sharpness-Aware Minimization (SAM), which is originally formulated as a zero-sum game where the weights of a network and a bounded perturbation try to minimize/maximize, respectively, the same differentiable loss. We argue that SAM shou ...
2024
This thesis focuses on two selected learning problems: 1) statistical inference on graphs models, and, 2) gradient descent on neural networks, with the common objective of defining and analysing the measures that characterize the fundamental limits.In the ...
EPFL2023
Deep neural networks have completely revolutionized the field of machinelearning by achieving state-of-the-art results on various tasks ranging fromcomputer vision to protein folding. However, their application is hindered bytheir large computational and m ...
Despite the widespread empirical success of ResNet, the generalization properties of deep ResNet are rarely explored beyond the lazy training regime. In this work, we investigate scaled ResNet in the limit of infinitely deep and wide neural networks, of wh ...
In the rapidly evolving landscape of machine learning research, neural networks stand out with their ever-expanding number of parameters and reliance on increasingly large datasets. The financial cost and computational resources required for the training p ...
This thesis consists of three applications of machine learning techniques to risk management. The first chapter proposes a deep learning approach to estimate physical forward default intensities of companies. Default probabilities are computed using artifi ...
EPFL2022
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Controlling the parameters' norm often yields good generalisation when training neural networks. Beyond simple intuitions, the relation between parameters' norm and obtained estimators theoretically remains misunderstood. For one hidden ReLU layer networks ...
2023
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We present a statistical framework to benchmark the performance of reconstruction algorithms for linear inverse problems, in particular, neural-network-based methods that require large quantities of training data. We generate synthetic signals as realizati ...
Deep neural networks have become ubiquitous in today's technological landscape, finding their way in a vast array of applications. Deep supervised learning, which relies on large labeled datasets, has been particularly successful in areas such as image cla ...
