4 papers
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…
A Quantifier-Reversal Approximation Paradigm for Recurrent Neural Networks
Clemens Hutter, Valentin Abadie, Helmut Bölcskei
Classical neural network approximation results take the form: for every function and every error tolerance , one constructs a neural network whose architecture and weight…
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…
Three Quantization Regimes for ReLU Networks
Weigutian Ou, Philipp Schenkel, Helmut Bölcskei
We establish the fundamental limits in the approximation of Lipschitz functions by deep ReLU neural networks with finite-precision weights. Specifically, three regimes, namely unde…