Seminario IMC: Geometry, Robustness, and Dimensionality: From Spiking Networks to General Loss Landscapes
24 de Abril, 2026
El Instituto de Ingeniería Matemática y Computacional (IMC) invita al seminario que se dictará el miércoles 29 de abril.
Miércoles 29 de abril de 2026, 13:40 hrs. (Presencial en sala segundo piso (DILAB), Edificio Carreras Interdisciplinarias). Link Zoom disponible escribiendo a imc@uc.cl)
ABSTRACT
The rapid scaling of artificial neural networks (ANNs) has highlighted the dual need for energy-efficient architectures and a deeper theoretical understanding of how models learn. This talk addresses both challenges, moving from the specific functional properties of Spiking Neural Networks (SNNs) to broader questions regarding the geometry of neural network loss landscapes.
In the first part, I characterize the complexity and robustness of discrete-time Leaky Integrate-and-Fire (LIF) SNNs. We demonstrate that these networks realize piecewise constant functions on polyhedral regions and quantify how latency—a temporal dimension unique to SNNs—drives expressive power. Using Boolean function analysis, I further show that wide LIF-SNNs exhibit an inherent simplicity bias, where their Fourier spectra concentrate on low-frequency components, ensuring average-case stability under input perturbations.
The final part of the talk transitions to a broader investigation of neural network optimization. I will present current work-in-progress regarding the intrinsic dimension of loss landscapes in general neural networks. By analyzing the minimum subspace dimension required to reach high-quality solutions, we can better understand the structural redundancy of overparameterized models. I will conclude by discussing the implications of these geometric properties for model compression and the efficiency of the optimization process across diverse architectures.
BIO
Ernesto Araya is a postdoctoral researcher at the Bavarian AI Chair for Mathematical Foundations of AI at LMU Munich. He earned his PhD in Applied Mathematics in 2020 from Université Paris-Saclay under the supervision of Yohann de Castro, focusing on statistical inference on graphs, followed by a postdoctoral fellowship in the MODAL group at Inria Lille. His research interests sit at the intersection of mathematical statistics, high-dimensional probability, and deep learning theory. He maintains an active research program in statistical inference and matching problems while simultaneously investigating the geometric foundations of neural networks, with a focus on the intrinsic dimension of loss landscapes and the formal analysis of spiking architectures.
