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Recently, inverse problems have attracted more and more attention in computational mathematics and become increasingly important in engineering applications. After the discretization, many of inverse problems are reduced to linear systems.…
Machine learning for robot manipulation promises to unlock generalization to novel tasks and environments. But how should we measure the progress of these policies towards generalization? Evaluating and quantifying generalization is the…
Matrices resulting from the discretization of a kernel function, e.g., in the context of integral equations or sampling probability distributions, can frequently be approximated by interpolation. In order to improve the efficiency, a…
Dynamical models identified from data are frequently employed in control system design. However, decoupling system identification from controller synthesis can result in situations where no suitable controller exists after a model has been…
Generalizations of linear numeration systems in which the set of natural numbers is recognizable by finite automata are obtained by describing an arbitrary infinite regular language following the lexicographic ordering. For these systems of…
In mathematics, LaTeX is the de facto standard to prepare documents, e.g., scientific publications. While some formulae are still developed using pen and paper, more complicated mathematical expressions used more and more often with…
Practical checkers based on refinement types use the combination of implicit semantic sub-typing and parametric polymorphism to simplify the specification and automate the verification of sophisticated properties of programs. However, a…
Extrapolation -- the ability to make inferences that go beyond the scope of one's experiences -- is a hallmark of human intelligence. By contrast, the generalization exhibited by contemporary neural network algorithms is largely limited to…
In this work, we propose an Implicit Regularization Enhancement (IRE) framework to accelerate the discovery of flat solutions in deep learning, thereby improving generalization and convergence. Specifically, IRE decouples the dynamics of…
Linearization is a standard approach in the computation of eigenvalues, eigenvectors and invariant subspaces of matrix polynomials and rational matrix value functions. An important source of linearizations are the so called Fiedler…
Generalization is a central challenge for the deployment of reinforcement learning (RL) systems in the real world. In this paper, we show that the sequential structure of the RL problem necessitates new approaches to generalization beyond…
This paper proposes an algorithm for computing regularized solutions to linear rational expectations models. The algorithm allows for regularization cross-sectionally as well as across frequencies. A variety of numerical examples illustrate…
Data augmentation is used in machine learning to make the classifier invariant to label-preserving transformations. Usually this invariance is only encouraged implicitly by including a single augmented input during training. However,…
Meta-learning approaches enable machine learning systems to adapt to new tasks given few examples by leveraging knowledge from related tasks. However, a large number of meta-training tasks are still required for generalization to unseen…
In the study of periodic media, conditionally convergent series are frequently encountered and their regularization is crucial for applications. We derive an identity that regularizes two-dimensional generalized Eisenstein series for all…
Parameter identification problems typically consist of a model equation, e.g. a (system of) ordinary or partial differential equation(s), and the observation equation. In the conventional reduced setting, the model equation is eliminated…
The paper discusses regularization properties of artificial data for deep learning. Artificial datasets allow to train neural networks in the case of a real data shortage. It is demonstrated that the artificial data generation process,…
This paper introduces a general approach for synthesizing procedural models of the state-transitions of a given discrete system. The approach is general in that it accepts different target languages for modeling the state-transitions of a…
Regularization is a popular technique to solve the overfitting problem of machine learning algorithms. Most regularization technique relies on parameter selection of the regularization coefficient. Plug-in method and cross-validation…
In recent years there has been increasing interest in the field of Open-Set Recognition, which allows a classification model to identify inputs as "unknown" when it encounters an object or class not in the training set. This ability to flag…