8 papers
Separation Capacity of Scattering Networks
Konstantin Häberle, Helmut Bölcskei
In this paper, we attempt to enhance the theoretical understanding of convolutional neural networks (CNNs) as feature extractors in classification tasks by analyzing them through t…
Recovering Governing Equations from Solution Data: Identifiability Bounds for Linear and Nonlinear ODEs
Yang Pan, Helmut Bölcskei
Learning governing equations from observed solution data is a fundamental challenge in scientific machine learning, yet the theoretical conditions under which a ground-truth ODE ca…
Generating Rectifiable Measures through Neural Networks
Erwin Riegler, Alex Bühler, Yang Pan +1
We derive universal approximation results for the class of (countably) -rectifiable measures. Specifically, we prove that -rectifiable measures can be approximated as push-fo…
Recurrent neural networks approximate continuous functions
Valentin Abadie, Clemens Hutter, Helmut Bölcskei
Classical approximation theorems ask for a new neural network whenever the target accuracy is improved. This paper studies the opposite possibility: can the network be chosen once…
Covering Numbers for Deep ReLU Networks with Applications to Function Approximation and Nonparametric Regression
Weigutian Ou, Helmut Bölcskei
Covering numbers of (deep) ReLU networks have been used to characterize approximation-theoretic performance, to upper-bound prediction error in nonparametric regression, and to qua…
Complete Identification of Deep ReLU Neural Networks by Many-Valued Logic
Yani Zhang, Helmut Bölcskei
Deep ReLU neural networks admit nontrivial functional symmetries: vastly different architectures and parameters (weights and biases) can realize the same function. We address the c…