I will introduce some theoretical results related to the convergence and generalization capabilities of neural networks, in light of articles published at the NeurIPS 2023 conference in December. The first part of the presentation will summarize some important, earlier results, and then it will cover numerous articles based on these, which were presented at NeurIPS. The aim of the presentation is to provide a comprehensive overview of the current state of the field and the currently popular research directions.

I will overview some applications of supervised and reinforcement learning methods to knot theory that might be useful in other areas of mathematics.

A reprezentációtanulás, vagyis adatokból magasabb szintű ismeret, „tudás” kinyerése a mesterséges intelligencia kutatásának egy kiemelt kérdése. Új, tudományos és társadalmi hasznosulás szempontjából is jelentős terület az önfelügyelt reprezentáció tanulás, amely a felügyelt tanuláshoz képest jóval nagyobb léptékű adatbázisokon, széles körben alkalmazható nagy modellek tanítását teszi lehetővé. Nagy nyelvi modellek tanításának mára alapeleme az önfelügyelt tanítás, és gépi látásban is több sikeres megközelítést publikáltak. Kevesebb kutatás irányul azonban arra, hogy a vizuális önfelügyelt előtanítással kialakított hálók összetett gépi látási feladatokon (pl.

Mode Combinability: Exploring Convex Combinations of Permutation Aligned Models Adrián Csiszárik, Melinda F. Kiss, Péter Kőrösi-Szabó, Márton Muntag, Gergely Papp, Dániel Varga As recently discovered (Ainsworth-Hayase-Srinivasa 2022 and others), two wide neural networks with identical network topology and trained on similar data can be permutation-aligned. That is, we can shuffle their neurons (channels) so that linearly interpolating between the two networks in parameter space becomes a meaningful operation (linear mode connectivity).

Contemporary robotics relies heavily on addressing key challenges like odometry, localization, depth perception, semantic segmentation, the creation of new viewpoints, and navigation with precision and efficiency. Implicit neural representation techniques, notably Neural Radiance Fields (NeRFs) and Generalizable NeRFs (GeNeRFs), are increasingly employed to tackle these issues. This talk focuses on exposing certain critical, but subtle flaws inherent in GeNeRFs. Adversarial attacks, while not new to various machine learning frameworks, present a significant threat.

Sets of points with the property that no two elements of the set are one unit distance apart are called unit-distance avoiding sets. If a point is in the unit-distance avoiding set, then the unit circle drawn around it does not intersect the set, but there is no restriction regarding the interior and the exterior of this circle. When searching for unit-distance avoiding sets with high densities, the following construction naturally comes to mind: an open disc with a unit diameter is unit-distance avoiding, as all distances between its two points are less than 1.