Time: 15:30-18:00

Location: Uni Wien, Oskar-Morgenstern-Platz 1, SR13

There will be coffee and cake between the talks and Pizza afterwards.

Speaker 1 (OeAW): Daniel Haider

Title: The injectivity of ReLU layers and other non-linear measurements

Abstract: Non-linearities frequently arise in applications, either due to technical constraints or as intentional elements of model design. A

prominent instance of the latter is to use the composition of affine linear mappings and non-linear activation functions as layers of

artificial neural networks. Among many layer designs, ReLU layers - i.e., layers using $\operatorname{ReLU}(t) = \max(0,t)$ as activation -

are the most widely used layer types due to their simplicity and effectiveness. By performing hard thresholding, the ReLU function

naturally acts as a sparsifier, where a black-box machinery determines which and how much information of the input is suppressed. Assessing whether the original input can be reconstructed from the output is therefore crucial for improving the interpretability and functionality of the associated models.

In this talk, we present a frame theoretic perspective to approach the injectivity of ReLU layers and show how it is linked to other situations

where non-linearities occur. To check injectivity in practice, we derive an injectivity characterization via the bias vector of the ReLU layer,

and to do the reconstruction, we modify the classic frame algorithm.

This is joint work with M. Ehler, D. Freeman, H. Eckert, and P. Balazs.

Speaker 2 (ISTA):  Lorenzo Pigozzi (Seiringer group)

Title: Mathematical Insights into Density Functional Theory

Abstract: Density Functional Theory (DFT) is one of the most widely used methods in computational chemistry and physics, providing an efficient framework for studying the electronic structure of atoms, molecules, and solids. This talk focuses on the mathematical foundations of DFT, in particular Lieb's framework, which rigorously defines the universal functional using convex analysis and variational principles. Key properties of , such as convexity and lower semicontinuity, will be discussed along with their practical implications.

The talk will also explore the Local Density Approximation (LDA) as a practical realization of, highlighting its strengths, limitations, and connection to Lieb's approach. By linking theory and application, the talk provides some key ideas for the foundations of DFT and outlines challenges