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The univariate integer-valued time series has been extensively studied, but literature on multivariate integer-valued time series models is quite limited and the complex correlation structure among the multivariate integer-valued time…

Discovering new physical products and processes often demands enormous experimentation and expensive simulation. To design a new product with certain target characteristics, an extensive search is performed in the design space by trying out…

We propose the Inverse Neural Operator (INO), a two-stage framework for recovering hidden ODE parameters from sparse, partial observations. In Stage 1, a Conditional Fourier Neural Operator (C-FNO) with cross-attention learns a…

We define and analyse a least-squares finite element method for a first-order reformulation of the obstacle problem. Moreover, we derive variational inequalities that are based on similar but non-symmetric bilinear forms. A priori error…

Efficient unsupervised training and inference in deep generative models remains a challenging problem. One basic approach, called Helmholtz machine, involves training a top-down directed generative model together with a bottom-up auxiliary…

First-order methods for solving convex optimization problems have been at the forefront of mathematical optimization in the last 20 years. The rapid development of this important class of algorithms is motivated by the success stories…

Model-based optimization methods and discriminative learning methods have been the two dominant strategies for solving various inverse problems in low-level vision. Typically, those two kinds of methods have their respective merits and…

These notes focus on the minimization of convex functionals using first-order optimization methods, which are fundamental in many areas of applied mathematics and engineering. The primary goal of this document is to introduce and analyze…

We provide first the functional analysis background required for reduced order modeling and present the underlying concepts of reduced basis model reduction. The projection-based model reduction framework under affinity assumptions,…

We present a framework for synthesising formulas in first-order logic (FOL) from examples, which unifies and advances state-of-the-art approaches for inference of transition system invariants. To do so, we study and categorise the existing…

We propose a new deep recurrent neural network (RNN) architecture for sequential signal reconstruction. Our network is designed by unfolding the iterations of the proximal gradient method that solves the l1-l1 minimization problem. As such,…

This paper introduces a new periodic fractional autoregressive process (PFAR) driven by fractional Gaussian noise (fGn) to model time series of precipitation evapotranspiration. Compared with the similar model in [\emph{Water Resources…

For the efficient execution of deep convolutional neural networks (CNN) on edge devices, various approaches have been presented which reduce the bit width of the network parameters down to 1 bit. Binarization of the first layer was always…

We describe a recently developed algebraic framework for proving first-order statements about linear operators by computations with noncommutative polynomials. Furthermore, we present our new SageMath package operator_gb, which offers…

Proximal operations are among the most common primitives appearing in both practical and theoretical (or high-level) optimization methods. This basic operation typically consists in solving an intermediary (hopefully simpler) optimization…

By removing parameters from deep neural networks, unstructured pruning methods aim at cutting down memory footprint and computational cost, while maintaining prediction accuracy. In order to tackle this otherwise intractable problem, many…

A new method for the unsupervised learning of sparse representations using autoencoders is proposed and implemented by ordering the output of the hidden units by their activation value and progressively reconstructing the input in this…

We introduce \textit{basic inequalities} for first-order iterative optimization algorithms, forming a simple and versatile framework that connects implicit and explicit regularization. While related inequalities appear in the literature, we…

The forward-forward algorithm presents a new method of training neural networks by updating weights during an inference, performing parameter updates for each layer individually. This immediately reduces memory requirements during training…

Learning maps between function spaces with a strong inductive bias is a central challenge in soft computing, especially when training data are scarce and standard deep architectures overfit. We introduce a \emph{neural integral operator}…