(in Polish) M'AI: Continuous networks 1000-1M26CN

The course is devoted to modern machine learning methods based on continuous models, which constitute one of the most dynamically developing approaches in contemporary artificial intelligence. Particular emphasis will be placed on continuous-depth neural networks, neural ordinary differential equations (Neural ODEs), physics-informed neural networks (PINNs), neural operators, and dynamical models used in scientific machine learning.
In contrast to classical deep learning architectures based on a finite number of layers, continuous neural networks interpret the information propagation process as a continuous evolution described by differential equations. Such an approach makes it possible to use tools from mathematical analysis, dynamical systems theory, and numerical methods to study the properties of neural models, including their stability, generalization ability, and interpretability.
The aim of the course is to present the mathematical foundations of continuous neural models and to show their connections with ordinary and partial differential equations, control theory, optimization, and numerical analysis. Students will become familiar with both theoretical and practical aspects related to the implementation of modern continuous-time deep learning models.
An important element of the course will be the interpretation of popular deep learning architectures — such as ResNet — as discretizations of differential equations, naturally leading to Neural ODE-type models. Methods of continuous backpropagation, adjoint methods, as well as issues related to the stability and computational efficiency of continuous models will also be discussed.
The course combines a rigorous mathematical approach with practical aspects of implementation, showing how contemporary mathematics becomes the language of artificial intelligence.

Form of classes:
Lectures: general theoretical introduction;
Classes: analytical approach to neural networks.
Several-day workshop sessions (outside Warsaw, depending on available funding) are also planned.