292 citations · 770 across the 46 of their papers we have counts for
6 papers · 1 filter
Hyper Input Convex Neural Networks for Shape Constrained Learning and Optimal Transport
Shayan Hundrieser, Insung Kong, Johannes Schmidt-Hieber
We introduce Hyper Input Convex Neural Networks (HyCNNs), a novel neural network architecture designed for learning convex functions. HyCNNs combine the principles of Maxout networ…
Spike-timing-dependent Hebbian learning as noisy gradient descent
Niklas Dexheimer, Sascha Gaudlitz, Johannes Schmidt-Hieber
Hebbian learning is a key principle underlying learning in biological neural networks. We relate a Hebbian spike-timing-dependent plasticity rule to noisy gradient descent with res…
On the VC dimension of deep group convolutional neural networks
Anna Sepliarskaia, Sophie Langer, Johannes Schmidt-Hieber
We study the generalization capabilities of Group Convolutional Neural Networks (GCNNs) with ReLU activation function by deriving upper and lower bounds for their Vapnik-Chervonenk…
Understanding the Effect of GCN Convolutions in Regression Tasks
Juntong Chen, Johannes Schmidt-Hieber, Claire Donnat +1
Graph Convolutional Networks (GCNs) have become a pivotal method in machine learning for modeling functions over graphs. Despite their widespread success across various application…
Interpreting learning in biological neural networks as zero-order optimization method
Johannes Schmidt-Hieber
Recently, significant progress has been made regarding the statistical understanding of artificial neural networks (ANNs). ANNs are motivated by the functioning of the brain, but d…
The Kolmogorov-Arnold representation theorem revisited
Johannes Schmidt-Hieber
There is a longstanding debate whether the Kolmogorov-Arnold representation theorem can explain the use of more than one hidden layer in neural networks. The Kolmogorov-Arnold repr…