GAMM2025

Session

PP02: Theoretical Foundations of Deep Learning

PP02

8 Apr 2025, 14:00

Lecture and Conference Centre

Conveners

PP02: Theoretical Foundations of Deep Learning: PP02.01

• Gitta Kutyniok
• Christopher Bülte

725. Representation of control Lyapunov functions with neural networks

Mario Sperl

08/04/2025, 14:00

In this talk, we explore the representation of control Lyapunov functions using neural networks. First, we demonstrate that, under suitable assumptions regarding the decomposition of a given control system into subsystems, a smooth control Lyapunov function with a separable structure exists. This separable structure enables its representation via neural networks requiring a number of neurons...

726. Adaptive Step Sizes for Stochastic Gradient Descent

Frederik Köhne

08/04/2025, 14:20

The choice of the step size (or learning rate) in stochastic optimization algorithms, such as stochastic gradient descent, plays a central role in the training of machine learning models.

Both theoretical investigations and empirical analyses emphasize that an optimal step size not only requires taking into account the nonlinearity of the underlying problem, but also relies on accounting...

727. Generalisation Error for Semi-Supervised Learning Using Graph Neural Networks

Nil Ayday

08/04/2025, 14:40

Graph Neural Networks (GNNs) have become powerful tools for modeling complex relationships in graph-structured data across various domains. The success of GNNs comes from their graph convolution process, which allows information to propagate through the graph structure, so that each node can aggregate information from its neighbours. This process uses graph information (the connections between...

728. Data-Driven Spatial Adaptivity for Regularising Inverse Problems

Sebastian Neumayer

08/04/2025, 15:00

In this talk, I will discuss various way to introduce spatial adaptivity into filter-based regularisation functionals. With this adaptivity, we are able to cancel out the filter responses to structure. Hence, we can interpret it as boosting the initial regulariser based on the data. A direct question if is we can repeat this process to get even better solutions. If we try this naively, the...

729. Neural Sampling from Boltzmann Densities

Jannis Chemseddine

08/04/2025, 15:20

We deal with the task of sampling from an unnormalized Boltzmann density ρD by learning a Boltzmann curve given by energies ft starting in a simple density ρZ. First, we examine conditions under which Fisher-Rao flows are absolutely continuous in the Wasserstein geometry. Second, we address specific interpolations ft and the learning of the related density/velocity pairs (ρt,vt). It was...

730. Algebraic structures and invariants of Gradient Flow for Linear Neural Networks

Angelica Torres

08/04/2025, 15:40

Gradient descent methods are a popular choice for minimizing the approximation error of different neural network models. Understanding their trajectories can be used to study implicit bias or the existence of spurious minima in the optimization process. In this work we study the polynomials defining algebraic varieties that contain the trajectories of the Gradient flow for deep linear neural...