832 citations · 1.3k across the 79 of their papers we have counts for
11 papers · 1 filter
Learning curves for Gaussian process regression with power-law priors and targets
Hui Jin, Pradeep Kr. Banerjee, Guido Montúfar
We characterize the power-law asymptotics of learning curves for Gaussian process regression (GPR) under the assumption that the eigenspectrum of the prior and the eigenexpansion c…
Training Wasserstein GANs without gradient penalties
Dohyun Kwon, Yeoneung Kim, Guido Montúfar +1
We propose a stable method to train Wasserstein generative adversarial networks. In order to enhance stability, we consider two objective functions using the -transform based on…
The Geometry of Memoryless Stochastic Policy Optimization in Infinite-Horizon POMDPs
Johannes Müller, Guido Montúfar
We consider the problem of finding the best memoryless stochastic policy for an infinite-horizon partially observable Markov decision process (POMDP) with finite state and action s…
Geometry of Linear Convolutional Networks
Kathlén Kohn, Thomas Merkh, Guido Montúfar +1
We study the family of functions that are represented by a linear convolutional neural network (LCN). These functions form a semi-algebraic subset of the set of linear maps from in…
On the Expected Complexity of Maxout Networks
Hanna Tseran, Guido Montúfar
Learning with neural networks relies on the complexity of the representable functions, but more importantly, the particular assignment of typical parameters to functions of differe…
Weisfeiler and Lehman Go Cellular: CW Networks
Cristian Bodnar, Fabrizio Frasca, Nina Otter +4
Graph Neural Networks (GNNs) are limited in their expressive power, struggle with long-range interactions and lack a principled way to model higher-order structures. These problems…
Information Complexity and Generalization Bounds
Pradeep Kr. Banerjee, Guido Montúfar
We present a unifying picture of PAC-Bayesian and mutual information-based upper bounds on the generalization error of randomized learning algorithms. As we show, Tong Zhang's info…
Sharp bounds for the number of regions of maxout networks and vertices of Minkowski sums
Guido Montúfar, Yue Ren, Leon Zhang
We present results on the number of linear regions of the functions that can be represented by artificial feedforward neural networks with maxout units. A rank-k maxout unit is a f…
Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks
Cristian Bodnar, Fabrizio Frasca, Yu Guang Wang +4
The pairwise interaction paradigm of graph machine learning has predominantly governed the modelling of relational systems. However, graphs alone cannot capture the multi-level int…
Wasserstein Proximal of GANs
Alex Tong Lin, Wuchen Li, Stanley Osher +1
We introduce a new method for training generative adversarial networks by applying the Wasserstein-2 metric proximal on the generators. The approach is based on Wasserstein informa…
How Framelets Enhance Graph Neural Networks
Xuebin Zheng, Bingxin Zhou, Junbin Gao +4
This paper presents a new approach for assembling graph neural networks based on framelet transforms. The latter provides a multi-scale representation for graph-structured data. We…