Seminar Details
2022-11-29 (14h) : Welcome Seminar
At Euler building (room a.002)
Organized by Mathematical Engineering
Section 1: Double descent in deep learning: Exploring the impact of common regularization, compression and optimization strategies
Speaker :
Massion, Bastien
Abstract :
For a decade, deep neural networks have revolutionized the domain of machine learning and artificial intelligence. The driving force behind this success is their unprecedented generalization abilities. The mechanisms behind this generalization have long been a mystery. Indeed, it defies the classical bias-variance trade-off as deep learning models are highly overparameterized but still avoid overfitting. The double descent phenomenon has been proposed to characterize this behaviour: the generalization error follows the classical U-shape curve in function of the model complexity but decreases again when the number of parameters exceeds the number of training data, reaching the modern learning regime. Many explanations of the phenomenon have since then been proposed, relying on implicit regularization of the model. Yet, a lot of work has still to be done to measure the impact on double descent of several techniques commonly used in deep learning. This work aims to explore 3 aspects of training. First, explicit orthogonal regularization of neural network weights. Then, low-rank matrix factorization of these weights for compression purposes. Finally, the impact of dropout and momentum in model training.
Section 2: Data-driven control of Markovian Jump Linear Systems: a step towards complexity
Speaker :
Adrien Banse (PhD UCLouvain/INMA)
Abstract :
Hybrid systems are dynamical systems whose dynamics is characterised by both continuous and discrete behaviours. Their hybrid characteristic makes these systems notoriously extremely hard to control and analyse. However, they often generate rich data (harvested from cameras, lidars, etc.), to which the engineer has access in large quantities. In my thesis, I plan to tackle the following question: how to control such complex systems in a data-driven fashion? It means, from datasets containing observations of a hybrid system, what can we say about its stability, or how can we design a controller to stabilise it? In particular, Markovian Jump Linear Systems (MJLS), while popular tools for modelling complex hybrid systems, have remained untouched in the framework of data-driven control. My goal, in four years from now, is to prove theorems providing firm probabilistic guarantees on the stability and stabilisation of MJLS. I will proceed in an incremental way, starting by considering a simpler system that I have already studied, namely constrained switching linear systems. I also plan to provide a proof of concept by applying my methods to networked controlled systems, a known application of MJLS
Section 3: Investigation of the neural circuitry involved in the control of movements
Speaker :
Astrid Doyen (PhD UCLouvain/INMA)
Abstract :
Reaching movements are movements that we perform thousands of times in everyday life. Computationally, the control of these movements can be represented by the Optimal Feedback Control model, which explains most human behaviours. Among those behaviours, one can mention motor adaptation, i.e., the ability of humans to adapt to new tools or environments, and online change in control policy, i.e., the ability of humans to rapidly change the command sent to the arm following a change in task or movement parameters during the movement. In the Optimal Feedback Control model, these behaviours are attributed to different structures, but it is not known yet if it is also the case biologically. Therefore, this research aims to highlight experimentally potential interferences between both mechanisms to give insight into the biological structures involved in these behaviours and to particularly investigate the role in both tasks of the basal ganglia, a group of subcortical nuclei known to be involved in learning and selection of the most appropriate motor behavioural programs. The Optimal Feedback Control model can then be extended by considering the experimental results.