An introduction to Simplicial-map Neural Networks

Abstract: In a recently accepted project RexasiPro, we deal with a critical environment where trustworthy is decisive. One of our approaches are simplicial-map neural networks (SMNNs) which are explicitly defined using simplicial maps between triangulations of the input and output spaces. Its combinatorial definition lets us prove and guarantee several nice properties following trustworthy AI principles. In "Two-hidden-layer feed-forward networks are universal approximators: A constructive approach", the first definition of SMNNs was given and its universal approximator property was proved. Later, in "Simplicial-Map Neural Networks Robust to Adversarial Examples", its robustness against adversarial examples was described.

machine learningmathematical physicscommutative algebraalgebraic geometryalgebraic topologycombinatoricsdifferential geometrynumber theoryrepresentation theory

Audience: researchers in the topic

Machine Learning Seminar

Series comments: Online machine learning in pure mathematics seminar, typically held on Wednesday. This seminar takes place online via Zoom.

For recordings of past talks and copies of the speaker's slides, please visit the seminar homepage at: kasprzyk.work/seminars/ml.html