黑料科

螝违螝螞螣危 危螘螠螜螡螒巍螜惟螡 危韦螒韦螜危韦螜螝螚危 螒螤巍螜螞螜螣危 2023

螣渭喂位畏蟿萎蟼:听Panayotis Mertikopoulos,听Department of Mathematics, National and Kapodistrian University of Athens

韦委蟿位慰蟼:听The dynamics of AI

螚渭蔚蟻慰渭畏谓委伪: 螤伪蟻伪蟽魏蔚蠀萎, 螒蟺蟻委位喂慰蟼 28, 2023 - 15:00

螒委胃慰蠀蟽伪: 韦102, 螡螘螣 螝韦螜巍螜螣 螣螤螒

螤螘巍螜蚂螚唯螚:

The recent surge of breakthroughs in machine learning and artificial intelligence has brought to the forefront a tremendous need for new mathematics to serve both as a solid theoretical foundation and as a springboard for further developments. In this talk, we will focus on how machine learning models are actually trained to make predictions and/or generate new data, a problem which is intimately related to the mathematical theory of dynamical systems 鈥� and, in particular, the study of gradient flows and (stochastic) gradient descent. We will begin by discussing how dynamical systems (in both discrete and continuous time) can be used to analyze and predict the outcome of the training process of an artificial neural network, guaranteeing convergence to critical points while avoiding unstable saddle points and other undesirable solutions. We will then proceed to examine what type of phenomena may arise when such systems interact 鈥� e.g., as in the case of generative adversarial networks. In this more general setting, the convergence landscape is considerably more treacherous, and gradient algorithms may be trapped by "spurious attractors" that are in no way optimal - a fact which highlights the fundamental gap in difficulty between training generative versus discriminative models.

听