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Sharp asymptotics on the compression of two-layer neural networks

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				The capabilities of deep learning systems have advanced much faster than our ability to understand them. Whilst the gains from deep neural networks (DNNs) are significant, they are accompanied by a growing risk and gravity of a bad outcome. This is tr ...

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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 ...

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This paper focuses on over-parameterized deep neural networks (DNNs) with ReLU activation functions and proves that when the data distribution is well-separated, DNNs can achieve Bayesoptimal test error for classification while obtaining (nearly) zero-trai ...

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Deep spiking neural networks (SNNs) offer the promise of low-power artificial intelligence. However, training deep SNNs from scratch or converting deep artificial neural networks to SNNs without loss of performance has been a challenge. Here we propose an ...

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Deep learning has achieved remarkable success in various challenging tasks such as generating images from natural language or engaging in lengthy conversations with humans.The success in practice stems from the ability to successfully train massive neural ...

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We introduce Neural Network (NN for short) approximation architectures for the numerical solution of Boundary Integral Equations (BIEs for short). We exemplify the proposed NN approach for the boundary reduction of the potential problem in two spatial dime ...

SPRINGER/PLENUM PUBLISHERS2023

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A central question of machine learning is how deep nets manage to learn tasks in high dimensions. An appealing hypothesis is that they achieve this feat by building a representation of the data where information irrelevant to the task is lost. For image da ...

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Despite their incredible performance, it is well reported that deep neural networks tend to be overoptimistic about their prediction confidence. Finding effective and efficient calibration methods for neural networks is therefore an important endeavour tow ...

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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 ...

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