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Recent studies have shown that proximal gradient (PG) method and accelerated gradient method (APG) with restarting can enjoy a linear convergence under a weaker condition than strong convexity, namely a quadratic growth condition (QGC).…
Recent deep learning-based methods have shown promising results and runtime advantages in deformable image registration. However, analyzing the effects of hyperparameters and searching for optimal regularization parameters prove to be too…
In this paper we study the nonperturbative corrections to the generalized Konishi anomaly that come from the strong coupling dynamics of the gauge theory. We consider U(N) gauge theory with adjoint and Sp(N) or SO(N) gauge theory with…
We study nonstationary newsvendor problems under nonparametric demand models and general distributional measures of nonstationarity, addressing the practical challenges of unknown degree of nonstationarity and demand censoring. We propose a…
We derive steerability criteria applicable for both finite and infinite dimensional quantum systems using covariance matrices of local observables. We show that these criteria are useful to detect a wide range of entangled states…
We introduce Quantum Graph Attention Networks (QGATs) as trainable quantum encoders for inductive learning on graphs, extending the Quantum Graph Neural Networks (QGNN) framework. QGATs leverage parameterized quantum circuits to encode node…
Graphical models are commonly used to represent conditional dependence relationships between variables. There are multiple methods available for exploring them from high-dimensional data, but almost all of them rely on the assumption that…
We present practical Levenberg-Marquardt variants of Gauss-Newton and natural gradient methods for solving non-convex optimization problems that arise in training deep neural networks involving enormous numbers of variables and huge data…
We develop arbitrarily high-order, stationarity-preserving stabilized finite element methods for multidimensional nonlinear hyperbolic balance laws on Cartesian grids. We aim at approximating all the steady states of the problem at hand,…
In this article we continue our investigation of the thin obstacle problem with variable coefficients which was initiated in \cite{KRS14}, \cite{KRSI}. Using a partial Hodograph-Legendre transform and the implicit function theorem, we prove…
An open question in the Deep Learning community is why neural networks trained with Gradient Descent generalize well on real datasets even though they are capable of fitting random data. We propose an approach to answering this question…
Graph neural networks have emerged as a powerful tool for learning spatiotemporal interactions. However, conventional approaches often rely on predefined graphs, which may obscure the precise relationships being modeled. Additionally,…
This paper establishes a nonlinear separation principle based on contraction theory and derives sharp stability conditions for recurrent neural networks (RNNs). First, we introduce a nonlinear separation principle that guarantees global…
In models of oceanic and atmospheric flows, thermodynamic functions and conservative variables may be defined up to a certain degree of arbitrariness, in the sense that, for a given set of observable quantities such as pressure and…
The continuum limit of loop quantum gravity is still an open problem. Indeed, no proper dynamics in known to start with and we still lack the mathematical tools to study its would-be continuum limit. In the present PhD dissertation, we will…
We propose graph-dependent implicit regularisation strategies for distributed stochastic subgradient descent (Distributed SGD) for convex problems in multi-agent learning. Under the standard assumptions of convexity, Lipschitz continuity,…
We develop a criterion to certify whether causal effects are identifiable in linear structural equation models with latent variables. Linear structural equation models correspond to directed graphs whose nodes represent the random variables…
The use of attention-based deep learning models in stochastic filtering, e.g. transformers and deep Kalman filters, has recently come into focus; however, the potential for these models to solve stochastic filtering problems remains largely…
Uncertainty quantification is essential in safety-critical settings--from autonomous driving to aviation, finance, and health--where decisions must rely on conservative bounds rather than point estimates. Predictor-level intervals (e.g.,…
In the problem of structured prediction with graph representation learning (GRL for short), the hypothesis returned by the algorithm maps the set of features in the \emph{receptive field} of the targeted vertex to its label. To understand…