Dictionary Identifiability from Few Training Samples

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Block Krylov subspace methods (KSMs) comprise building blocks in many state-of-the-art solvers for large-scale matrix equations as they arise, for example, from the discretization of partial differential equations. While extended and rational block Krylov ...

An integer program (IP) is a problem of the form

\min \{f(x) : \, Ax = b, \ l \leq x \leq u, \ x \in \Z^n\}

, where

A \in \Z^{m \times n}

b \in \Z^m

l,u \in \Z^n

, and

f: \Z^n \rightarrow \Z

is a separable convex objective function. The problem o ...

This work is concerned with the computation of the action of a matrix function f(A), such as the matrix exponential or the matrix square root, on a vector b. For a general matrix A, this can be done by computing the compression of A onto a suitable Krylov ...

In this PhD manuscript, we explore optimisation phenomena which occur in complex neural networks through the lens of

2

-layer diagonal linear networks. This rudimentary architecture, which consists of a two layer feedforward linear network with a diagonal ...

Reinforcement learning (RL) is inherently rife with non-stationarity since the states and rewards the agent observes during training depend on its changing policy. Therefore, networks in deep RL must be capable of adapting to new observations and fitting n ...

We consider the problem of efficiently solving Sylvester and Lyapunov equations of medium and large scale, in case of rank-structured data, i.e., when the coefficient matrices and the right-hand side have low-rank off-diagonal blocks. This comprises proble ...

Animal behaviour alternates between stochastic exploration and goal-directed actions, which are generated by the underlying neural dynamics. Previously, we demonstrated that the compositional Restricted Boltzmann Machine (cRBM) can decompose whole-brain ac ...

In this thesis we address the computation of a spectral decomposition for symmetric banded matrices. In light of dealing with large-scale matrices, where classical dense linear algebra routines are not applicable, it is essential to design alternative tech ...

The work presented in this thesis lies at the intersection of Machine Learning (ML) and control theory. The first part is dedicated to the design of Deep Neural Network (DNN) architectures with specific numerical properties, inspired by dynamical systems m ...

Matrix equations of the kind A(1)X(2)+A(0)X+A(-1)=X, where both the matrix coefficients and the unknown are semi-infinite matrices belonging to a Banach algebra, are considered. These equations, where coefficients are quasi-Toeplitz matrices, are encounter ...

Proteins are foundational biomolecules of life playing a crucial role in a myriad of biological processes. Their function often requires interplay with other biomolecules, including proteins themselves. Protein-protein interactions (PPIs) are essential for ...

Today, machine learning algorithms are often distributed across multiple machines to leverage more computing power and more data. However, the use of a distributed framework entails a variety of security threats. In particular, some of the machines may mis ...

Mismatches between samples and their respective channel or target commonly arise in several real-world applications. For instance, whole-brain calcium imaging of freely moving organisms, multiple-target tracking or multi-person contactless vital sign monit ...

Established techniques that enable robots to learn from demonstrations are based on learning a stable dynamical system (DS). To increase the robots' resilience to perturbations during tasks that involve static obstacle avoidance, we propose incorporating b ...

Conventional ultrasound (US) image reconstruction methods rely on delay-and-sum (DAS) beamforming, which is a relatively poor solution of the image reconstruction problem. An alternative to DAS consists in using iterative techniques which require both an a ...

Human babies have a natural desire to interact with new toys and objects, through which they learn how the world around them works, e.g., that glass shatters when dropped, but a rubber ball does not. When their predictions are proven incorrect, such as whe ...

The focus of this thesis is on developing efficient algorithms for two important problems arising in model reduction, estimation of the smallest eigenvalue for a parameter-dependent Hermitian matrix and solving large-scale linear matrix equations, by extra ...

Learning in interdisciplinary spaces is key for generating new models of thinking (Aboelela et al., 2007, p. 341 in Tobi & Kampen, 2018); interdisciplinary thinking nurtures creativity and a critical enquiry of social challenges thanks to the entanglement ...

Sparse matrices are favorable objects in machine learning and optimization. When such matrices are used, in place of dense ones, the overall complexity requirements in optimization can be significantly reduced in practice, both in terms of space and run-ti ...

Deploying compute-intensive deep neural networks (DNNs) on resource-constrained end devices has become a prominent trend, enabling localized intelligence. However, efficiently deploying these DNNs at scale poses challenges. To address this, extensive resea ...

Dictionary Identifiability from Few Training Samples

Chattez avec Graph Search

Compress-and-restart block Krylov subspace methods for Sylvester matrix equations

New Results in Integer and Lattice Programming

SPEEDING UP KRYLOV SUBSPACE METHODS FOR COMPUTING f(A)b VIA RANDOMIZATION

Deep Learning Theory Through the Lens of Diagonal Linear Networks

No Representation, No Trust: Connecting Representation, Collapse, and Trust Issues in PPO

Solving Rank-Structured Sylvester And Lyapunov Equations

The Recurrent Temporal Restricted Boltzmann Machine Captures Neural Assembly Dynamics in Whole-brain Activity

Fast hierarchical solvers for symmetric eigenvalue problems

Navigating the Loop: From Control Systems to Neural Networks and Back

On quadratic matrix equations with infinite size coefficients encountered in QBD stochastic processes

Engineering novel protein interactions with therapeutic potential using deep learning-guided surface design

Robust Machine Learning - Distributed Methods for Safe AI

Shuffled multi-channel sparse signal recovery

Learning Barrier-Certified Polynomial Dynamical Systems for Obstacle Avoidance with Robots

Ultrafast ultrasound imaging as an inverse problem: Matrix-free sparse image reconstruction

Seeking the new, learning from the unexpected: Computational models of surprise and novelty in the brain

Low-rank methods for parameter-dependent eigenvalue problems and matrix equations

Designing the Future Workforce through STEAM Education

Convex block-sparse linear regression with expanders - provably

RAPNet: Resolution-Adaptive and Predictive Early Exit Network for Efficient Image Recognition