Representation learning with structured invariance

Invariance is crucial for neural networks, enabling them to generalize effectively across variations of the input data by focusing on key attributes while filtering out irrelevant details. In this thesis, we study representation learning in neural networks through the lens of structured invariance. We start by studying the properties and limitations of the invariance that neural networks can learn from the data. Next, we develop a method to extract the structure of invariance learned by a neural network, providing a more nuanced analysis of the quality of learned invariance. In the next chapter, we focus on contrastive learning, demonstrating how more structured supervision results in a better quality of learned representations. The last two chapters that follow, focus on practical aspects of representation learning with structured invariance in computer vision

Observer-based robust fault estimation for fault-tolerant control

A control system is fault-tolerant if it possesses the capability of optimizing the system stability and admissible performance subject to bounded faults, complexity and modeling uncertainty. Based on this definition this thesis is concerned with the theoretical developments of the combination of robust fault estimation (FE) and robust active fault tolerant control (AFTC) for systems with both faults and uncertainties.This thesis develops robust strategies for AFTC involving a joint problem of on-line robust FE and robust adaptive control. The disturbances and modeling uncertainty affect the FE and FTC performance. Hence, the proposed robust observer-based fault estimator schemes are combined with several control methods to achieve the desired system performance and robust active fault tolerance. The controller approaches involve concepts of output feedback control, adaptive control, robust observer-based state feedback control. A new robust FE method has been developed initially to take into account the joint effect of both fault and disturbance signals, thereby rejecting the disturbances and enhancing the accuracy of the fault estimation. This is then extended to encompass the robustness with respect to modeling uncertainty.As an extension to the robust FE and FTC scheme a further development is made for direct application to smooth non-linear systems via the use of linear parameter-varying systems (LPV) modeling.The main contributions of the research are thus:- The development of a robust observer-based FE method and integration design for the FE and AFTC systems with the bounded time derivative fault magnitudes, providing the solution based on linear matrix inequality (LMI) methodology. A stability proof for the integrated design of the robust FE within the FTC system.- An improvement is given to the proposed robust observer-based FE method and integrated design for FE and AFTC systems under the existence of different disturbance structures.- New guidance for the choice of learning rate of the robust FE algorithm.- Some improvement compared with the recent literature by considering the FTC problem in a more general way, for example by using LPV modeling

Quantum Phase Transitions and Dynamics in Perturbed Flatbands

In recent years, there has been a growing interest in flatband systems which exhibit macroscopic degeneracies. These systems offer a valuable mathematical framework for the extreme sensitivity to perturbations and interactions. This sensitivity unveils a wide variety of exotic and unconventional physical phenomena. Moreover, the progress in their experimental realization contributes to the expanding landscape of exploration in this field. This thesis aims to summarize all the works throughout the Ph.D. program. Firstly, an in-depth exploration was conducted on the impact of weak quasiperiodic perturbations on one-dimensional two-band all-bands-flat lattices. These tight-binding Hamiltonian are diagonalized through a sequence of local unitary transformations. By adjusting the quasiperiodic potential parameters, the key achievement involves finding a critical-to-insulator transition and identifying fractality edges in the flatband systems with quasiperiodic perturbations. Next, the investigation delved into the effects of on-site interactions among hard-core bosons in one- and two-dimensional cross-stitch lattices. One key finding is that groundstate energy primarily depends on compact localized states. Moreover, the presence of barriers of compact localized states trap bosons, leading to the emergence of non-ergodic excitation and Hilbert space fragmentation. Lastly, a compact localized eigenstate of the one-dimensional diamond chain using an electric circuit was successfully generated via local (linear and non-linear) driving. This achievement opens up a versatile circuit platform for the generation of flatbands and holds promise for potential applications in the field of quantum information. I hope these collective efforts have expanded the frontiers of the field and made a meaningful contribution to the scientific community.Comment: PhD thesis (2024 Feb.

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum