5 papers
Upper bounds on the number of causal pieces in spiking neural networks
Dominik Dold, Dennis Elbrächter, Philipp Petersen
The input space of single-spike neural networks decomposes into causal pieces, and the number of causal pieces has been shown to provide a lower bound on the approximation error fo…
Compositional Approximation Can Strictly Outperform Superpositional Approximation
Dennis Elbrächter, Philipp Petersen
Many classically studied function classes are known to be approximated optimally by superpositional methods, i.e. with approximants constructed as the linear combination of element…
Certified and accurate computation of function space norms of deep neural networks
Johannes Gründler, Moritz Maibaum, Philipp Petersen
Neural network methods for PDEs require reliable error control in function space norms. However, trained neural networks can typically only be probed at a finite number of point va…
Equivalence of approximation by networks of single- and multi-spike neurons
Dominik Dold, Philipp Christian Petersen
In a spiking neural network, is it enough for each neuron to spike at most once? In recent work, approximation bounds for spiking neural networks have been derived, quantifying how…
Sustainable AI: Mathematical Foundations of Spiking Neural Networks
Adalbert Fono, Manjot Singh, Ernesto Araya +3
Deep learning's success comes with growing energy demands, raising concerns about the long-term sustainability of the field. Spiking neural networks, inspired by biological neurons…