| Résume | A major open problem in model theory and o-minimal geometry is Tarski's exponential function problem: Is the first-order theory of the reals with the exponential function decidable? From the point of view of computability it is natural to try to prove results weaker than decidability, i.e. upper bounds in the arithmetical complexity hierarchy. Tarski's problem can be reduced to the decidability of existential formulas, hence we will focus on this case and provide such an upper bound. Also, we will discuss the more general case with computable real functions in place of the exponential function. These results can be applied to better understand the complexity of the training problem on neural networks with some given activation functions, notably the sigmoid function.
NDLR: A la suite de l'exposé, il y aura un pot et une distribution d'une partie des livres de maths de Zoé, à 17h15 à la bibliothèque de Sophie Germain. |
