4 papers indexed
Konstantin Häberle, Helmut Bölcskei
We aim to identify scattering network architectures that maximize the separation capacity on data with low intrinsic dimension. The networks we consider employ a fixed monomial nonlinearity and no pooling, so that the only design variable is the frame generated by the network fil…
Konstantin Häberle, Helmut Bölcskei
The success of deep learning models in classification and regression is widely attributed to the low-dimensional structure that real-world data tend to exhibit, despite their high-dimensional representation. This work attempts to provide a mathematical framework for binary classi…
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 the lens of Cover's function-counting theory. Specifically, our focus lies on the notion of separatio…
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 can be uniquely and stably identified from multiple solution observations remain largely undeveloped,…