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Stochastic branching algorithms provide a useful alternative to grid-based schemes for the numerical solution of partial differential equations, particularly in high-dimensional settings. However, they require a strict control of the…
We propose a general solution approach for min-max-robust counterparts of combinatorial optimization problems with uncertain linear objectives. We focus on the discrete scenario case, but our approach can be extended to other types of…
We study a design framework for robust, independently verifiable, and workload-balanced distributed algorithms working on a common input. An algorithm based on the framework is essentially a distributed encoding procedure for a…
We introduce the concepts of Grover operators and Grover kernels to systematically analyse Grover's searching algorithms. Then, we investigate a one-parameter family of quantum searching algorithms of Grover's type and we show that the…
Neural Ordinary Differential Equations (ODEs) represent a significant advancement at the intersection of machine learning and dynamical systems, offering a continuous-time analog to discrete neural networks. Despite their promise, deploying…
This monograph develops a unified, application-driven framework for kernel methods grounded in reproducing kernel Hilbert spaces (RKHS) and optimal transport (OT). Part I lays the theoretical and numerical foundations on positive-definite…
Using vanilla NeuralODEs to model large and/or complex systems often fails due two reasons: Stability and convergence. NeuralODEs are capable of describing stable as well as instable dynamic systems. Selecting an appropriate numerical…
In this paper, we study certifying the robustness of ReLU neural networks against adversarial input perturbations. To diminish the relaxation error suffered by the popular linear programming (LP) and semidefinite programming (SDP)…
Classical neural ODEs trained with explicit methods are intrinsically limited by stability, crippling their efficiency and robustness for stiff learning problems that are common in graph learning and scientific machine learning. We present…
Controlled ordinary differential equations driven by continuous bounded variation curves can be considered a continuous time analogue of recurrent neural networks for the construction of expressive features of the input curves. We ask up to…
This paper develops a nonlinear operator dynamic that progressively removes the influence of a prescribed feature subspace while retaining maximal structure elsewhere. The induced sequence of positive operators is monotone, admits an exact…
We introduce a new family of deep neural network models. Instead of specifying a discrete sequence of hidden layers, we parameterize the derivative of the hidden state using a neural network. The output of the network is computed using a…
Nonlinear spectroscopy is widely used for studying physical systems. Conventional nonlinear optical spectroscopy and magnetic resonance spectroscopy, which use classical probes such as electromagnetic waves, can only access certain types of…
In this paper, we consider smooth convex optimization problems with simple constraints and inexactness in the oracle information such as value, partial or directional derivatives of the objective function. We introduce a unifying framework,…
We study approaches for the exact solution of the \NP--hard minimum spanning tree problem under conflict constraints. Given a graph $G(V,E)$ and a set $C \subset E \times E$ of conflicting edge pairs, the problem consists of finding a…
Classical numerical methods solve partial differential equations (PDEs) efficiently on regular meshes, but many of them become unstable on irregular domains. In practice, multiphysics interactions such as diffusion, damage, and healing…
Many inverse problems and signal processing problems involve low-rank regularizers based on the nuclear norm. Commonly, proximal gradient methods (PGM) are adopted to solve this type of non-smooth problems as they can offer fast and…
Given an undirected weighted graph $G(V,E)$, a constrained sketch over a terminal set $T\subset V$ is a subgraph $G'$ that connects the terminal vertices while satisfying a given set of constraints. Examples include Steiner trees…
Modern cryptographic protocols rely on sophisticated hash functions to generate quasi-unique numbers that serve as signatures for user authentication and other security verifications. The security could be compromised by finding texts…
The Volterra signature extends the classical path signature by incorporating general matrix-valued kernel into its iterated integral structure, yielding a flexible notion of memory for time series. Its components can be viewed as successive…