Related papers: On a new notion of regularizer
In representation learning (RL), how to make the learned representations easy to interpret and less overfitted to training data are two important but challenging issues. To address these problems, we study a new type of regulariza- tion…
How can complexity theory and algorithms benefit from practical advances in computing? We give a short overview of some prior work using practical computing to attack problems in computational complexity and algorithms, informally describe…
We find that second order quantification is problematic when a quantified concept variable is supposed to function predicatively. This issue is analyzed and it is shown that a constructive interpretation of the falling under relation…
A novel definition of the Laplacian of 1/r is presented, suitable for advanced undergraduates.
Transformers have achieved state-of-the-art performance in numerous tasks. In this paper, we propose a continuous-time formulation of transformers. Specifically, we consider a dynamical system whose governing equation is parametrized by…
We introduce a new notion of "regularity structure" that provides an algebraic framework allowing to describe functions and / or distributions via a kind of "jet" or local Taylor expansion around each point. The main novel idea is to…
We establish a general principle which states that regularizing an inverse problem with a convex function yields solutions which are convex combinations of a small number of atoms. These atoms are identified with the extreme points and…
A generalization of Hurwitz stable polynomials to real rational functions is considered. We establishe an analogue of the Hurwitz stability criterion for rational functions and introduce a new type of determinants that can be treated as a…
We present methods for obtaining new solutions to the bispectral problem. We achieve this by giving its abstract algebraic version suitable for generalizations. All methods are illustrated by new classes of bispectral operators.
Work in progress concerning alternative formalizations of arithmetic.
We describe an approximate rational arithmetic with round-off errors (both absolute and relative) controlled by the user. The rounding procedure is based on the continued fraction expansion of real numbers. Results of computer experiments…
In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.
A new simple geometrical interpretation of complex numbers is presented. It differs from their usual interpretation as points in the complex plane. From the new point of view the complex numbers are rather operations on vectors than points.…
In these notes we collect some results from several of the authors' works in order to make available a single source and show how the approximate geometric methods for regulation have been developed, and how the control design strategy has…
A family of regularization functionals is said to admit a linear representer theorem if every member of the family admits minimizers that lie in a fixed finite dimensional subspace. A recent characterization states that a general class of…
Reuse of data in new contexts beyond the purposes for which it was originally collected has contributed to technological innovation and reducing the consent burden on data subjects. One of the legal mechanisms that makes such reuse possible…
We present a comprehensive survey of constructions of the real numbers (from either the rationals or the integers) in a unified fashion, thus providing an overview of most (if not all) known constructions ranging from the earliest attempts…
Optimizations in a traditional compiler are applied sequentially, with each optimization destructively modifying the program to produce a transformed program that is then passed to the next optimization. We present a new approach for…
Formal explainability guarantees the rigor of computed explanations, and so it is paramount in domains where rigor is critical, including those deemed high-risk. Unfortunately, since its inception formal explainability has been hampered by…
Principles of analogical reasoning have recently been applied in the context of machine learning, for example to develop new methods for classification and preference learning. In this paper, we argue that, while analogical reasoning is…