Zeit und Ort

Dienstag, 21.7.26, 14:15–15:15, Seminarraum 226, HH10

Zusammenfassung

In this talk we summarize the results of the author’s master thesis, enti- tled ’Space-Time ResNet Approximation of ODEs’. First, we analyze multiple operations regarding feedforward neural networks and residual neural networks (ResNets). Then, using those operations, we show that ResNets are able to ap- proximate solutions to ordinary differential equations (ODEs) with a parameter growth rate of O(| ln(ε)|8).

Zeit und Ort

Dienstag, 30.6.26, 14:15–15:15, Seminarraum 226, HH10

Zusammenfassung

Deep neural networks have achieved remarkable performance across numerous domains, including computer vision, natural language processing, and speech recognition. How- ever, the computational and memory demands of these models present significant chal- lenges for deployment on resource-constrained devices such as mobile phones, embed- ded systems, and edge computing platforms. Model quantization has emerged as a critical technique to address these limitations by reducing the numerical precision of network parameters and activations from high-precision floating-point representations to lower-bit fixed-point or integer formats. This thesis investigates the effects of quantization on neural network performance, with particular emphasis on memory effciency and numerical robustness. We provide a comprehensive analysis of quantization techniques, including uniform and non-uniform quantization, symmetric and asymmetric schemes, and various calibration methods. The theoretical foundations of quantization are examined through the lens of informa- tion theory and numerical analysis, establishing a rigorous framework for understanding precision-accuracy trade-offs [11]. Our work explores post-training quantization (PTQ) methodologies, analyzing their respective advantages and limitations. We examine the impact of reduced precision on model accuracy, inference latency, and memory footprint across different neural net- work architectures. Furthermore, we investigate the numerical stability of quantized networks and analyze error propagation through network layers under various quanti- zation configurations. The findings of this research contribute to a deeper understanding of how quantiza- tion affects neural network behavior and provide practical guidelines for implementing effcient quantized models without significant performance degradation. This work has implications for enabling widespread deployment of deep learning on edge devices and reducing the environmental footprint of large-scale machine learning systems.

Zeit und Ort

Dienstag, 23.6.26, 14:15–15:15, Seminarraum 226, HH10

Zeit und Ort

Dienstag, 16.6.26, 14:15–15:15, Seminarraum 226, HH10

Zusammenfassung

Elastic rods arise in numerous applications ranging from engineering structures to biological filaments. In this talk, I present a variational framework for the numerical approximation of inextensible elastic rods governed by bending energy. The dynamics are modeled by an \(H^2\)-gradient flow, which is discretized in space using cubic finite elements and in time by an implicit scheme with linearized constraints. I establish the convergence of the discrete energy functionals via \(\Gamma\)-convergence and analyze the resulting minimizing movements using the theory of curves of maximal slope and the Sandier-Serfaty framework. These results provide a rigorous justification of the numerical scheme and clarify the interplay between spatial and temporal discretization. Finally, I discuss the physical interpretation of the model as an approximation of the motion of elastic rods in viscous fluids.