2 papers
math.NA2025
Trustworthy AI in numerics: On verification algorithms for neural network-based PDE solvers
Emil Haugen, Alexei Stepanenko, Anders C. Hansen
We present new algorithms for a posteriori verification of neural networks (NNs) approximating solutions to PDEs. These verification algorithms compute accurate estimates of …
cs.LG2024
The Boundaries of Verifiable Accuracy, Robustness, and Generalisation in Deep Learning
Alexander Bastounis, Alexander N. Gorban, Anders C. Hansen +5
In this work, we assess the theoretical limitations of determining guaranteed stability and accuracy of neural networks in classification tasks. We consider classical distribution-…