Pigeons do not jump high / Using o-minimality to compute lower bounds on sample complexity of neural networks (part 2)

Pigeons do not jump high 15h00

Por Ludovic Patey (Institut Camille Jordain, Lyon).

Por Carlos Florentino (Faculdade de Ciências da Universidade de Lisboa).

Por Inês Martins Rodrigues (aluna de doutoramento da FCUL).

Abstract: The Robinson-Schensted correspondence, introduced by Schensted (1961) in its most well-known form, presents a bijective correspondence between permutations and pairs of standard Young tableaux of the same shape. Knuth (1970) presented a generalization, the RSK correspondence, for semistandard Young tableaux.

Por Alexandre Baraviera (Instituto de Matemática e Estatística - Universidade Federal do Rio Grande do Sul).

Por Alex Usvyatsov (Universidade de Lisboa, CMAF-CIO).

Abstract: I will discuss the concept of sample complexity in statistical learning theory. Then I will show how definability of many hypothesis classes (for example, essentially all artificial neural networks used in practice) in o-minimal structures, helps to compute tighter lower bounds on sample complexity for these hypothesis classes.

Por Herwig Hauser (Fakultät für Mathematik, Universität Wien).

Por Lucio Boccardo (Dipartimento di Matematica, "Sapienza" Università di Roma).

Abstract: We present a review on the Stampacchia-Calderon-Zygmund theory for linear elliptic operators of second order with discontinuous coefficients and the corresponding theory for nonlinear operators of Leray-Lions type with nonregular data.

We shall also discuss classical and recent results, including work in progress, on the continuous dependence of the solutions with respect to right hand sides.

Por Ivan Kuznetsov (Lavrentyev Institute of Hydrodynamics – Siberian Division of the Russian Academy of Sciences, Novosibirsk State University).

Por Yannick Privat (Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie).

Numerous exciting results circle around the quality of specific power series: formal, convergent, algebraic, Gevrey, Mahler, D-finite, P-recursive, differentially algebraic, holonomic, hypergeometric, lacunary, G-functions, ..., with often sharp contrasts between characteristic zero and positive characteristic.