Related papers: Proofs and additional experiments on Second order …

Learning-based and data-driven techniques have recently become a subject of primary interest in the field of reconstruction and regularization of inverse problems. Besides the development of novel methods, yielding excellent results in…

In this chapter we provide a theoretically founded investigation of state-of-the-art learning approaches for inverse problems from the point of view of spectral reconstruction operators. We give an extended definition of regularization…

In this contribution we revisit regular model checking, a powerful framework that has been successfully applied for the verification of infinite-state systems, especially parameterized systems (concurrent systems with an arbitrary number of…

We present an adaptation of two recent low-rank approximation technique proposed for first-order model reduction systems to the second-order systems. The resulting reduced order models are guaranteed to keep the second order structure which…

The Eulerian and Lagrangian second-order perturbation theories are solved explicitly in closed forms in $\Omega \neq 1$ and $\Lambda \neq 0$ {}Friedmann-Lema\^{\i}tre models. I explicitly write the second-order theories in terms of closed…

Reinforcement learning (RL) commonly relies on scalar rewards with limited ability to express temporal, conditional, or safety-critical goals, and can lead to reward hacking. Temporal logic expressible via the more general class of…

Let $G$ be the product of finitely many trees $T_1\times T_2 \times \cdots \times T_N$, each of which is regular with degree at least three. We consider Bernoulli bond percolation and the Ising model on this graph, giving a short proof that…

This paper investigates the use of extended Kalman filtering to train recurrent neural networks with rather general convex loss functions and regularization terms on the network parameters, including $\ell_1$-regularization. We show that…

We introduce exact macroscopic on-line learning dynamics of two-layer neural networks with ReLU units in the form of a system of differential equations, using techniques borrowed from statistical physics. For the first experiments,…

In this paper, we propose an ordered time series classification framework that is robust against missing classes in the training data, i.e., during testing we can prescribe classes that are missing during training. This framework relies on…

This paper investigates the learning, or system identification, of a class of piecewise-affine dynamical systems known as linear complementarity systems (LCSs). We propose a violation-based loss which enables efficient learning of the LCS…

Evolutionary computation can be used to optimize several different aspects of neural network architectures. For instance, the TaylorGLO method discovers novel, customized loss functions, resulting in improved performance, faster training,…

In the present paper we consider controllability and observability of second order linear time invariant systems in matrix form. Without reducing into first order systems we show how the classical conditions for first order linear systems…

In this article, we give a precise mathematical meaning to `linear? time' that matches experimental behaviour of the algorithm. The sorting algorithm is not our own, it is a variant of radix sort with counting sort as a subroutine. The true…

Machine learning techniques for the solution of inverse problems have become an attractive approach in the last decade, while their theoretical foundations are still in their infancy. In this chapter we want to pursue the study of…

This paper is a contribution to graded model theory, in the context of mathematical fuzzy logic. We study characterizations of classes of graded structures in terms of the syntactic form of their first-order axiomatization. We focus on…

Multiple model reduction techniques have been proposed to tackle linear and non linear problems. Intrusive model order reduction techniques exhibit high accuracy levels, however, they are rarely used as a standalone industrial tool, because…

We provide a new proof of a important theorem in the Lagrangian formalism about necessary and sufficient conditions for a second-order variational system of equations to follow from a first-order Lagrangian.

In this paper we present a constructive proof of cut elimination for a system of full second order logic with the structural rules absorbed and using sets instead of sequences. The standard problem of the cutrank growth is avoided by using…

We provide a statistical analysis of regularization-based continual learning on a sequence of linear regression tasks, with emphasis on how different regularization terms affect the model performance. We first derive the convergence rate…