598 citations · 2.9k across the 89 of their papers we have counts for
7 papers · 1 filter
Optimization Landscape and Expressivity of Deep CNNs
Quynh Nguyen, Matthias Hein
We analyze the loss landscape and expressiveness of practical deep convolutional neural networks (CNNs) with shared weights and max pooling layers. We show that such CNNs produce l…
Community detection in networks via nonlinear modularity eigenvectors
Francesco Tudisco, Pedro Mercado, Matthias Hein
Revealing a community structure in a network or dataset is a central problem arising in many scientific areas. The modularity function is an established measure quantifying the…
Variants of RMSProp and Adagrad with Logarithmic Regret Bounds
Mahesh Chandra Mukkamala, Matthias Hein
Adaptive gradient methods have become recently very popular, in particular as they have been shown to be useful in the training of deep neural networks. In this paper we have analy…
Formal Guarantees on the Robustness of a Classifier against Adversarial Manipulation
Matthias Hein, Maksym Andriushchenko
Recent work has shown that state-of-the-art classifiers are quite brittle, in the sense that a small adversarial change of an originally with high confidence correctly classified i…
The loss surface of deep and wide neural networks
Quynh Nguyen, Matthias Hein
While the optimization problem behind deep neural networks is highly non-convex, it is frequently observed in practice that training deep networks seems possible without getting st…
The Perron-Frobenius Theorem for Multi-homogeneous Maps
Antoine Gautier, Francesco Tudisco, Matthias Hein
We introduce the notion of order-preserving multi-homogeneous mapping which allows to study Perron-Frobenius type theorems and nonnegative tensors in unified fashion. We prove a we…