Related papers: On Function Description
Similarity metric which is not positive definite, and present a general theorem which provides a large family of similarity metrics which are positive definite.
Approximations of functions with finite data often do not respect certain "structural" properties of the functions. For example, if a given function is non-negative, a polynomial approximation of the function is not necessarily also…
The sensitivity of image classifiers to small perturbations in the input is often viewed as a defect of their construction. We demonstrate that this sensitivity is a fundamental property of classifiers. For any arbitrary classifier over the…
The Quantum Oracle Classification (QOC) problem is to classify a function, given only quantum black box access, into one of several classes without necessarily determining the entire function. Generally, QOC captures a very wide range of…
A standard informal method for analyzing the asymptotic complexity of a program is to extract a recurrence that describes its cost in terms of the size of its input, and then to compute a closed-form upper bound on that recurrence. We give…
Extending the lambda-calculus with a construct for sharing, such as let expressions, enables a special representation of terms: iterated applications are decomposed by introducing sharing points in between any two of them, reducing to the…
The diverse world of machine learning applications has given rise to a plethora of algorithms and optimization methods, finely tuned to the specific regression or classification task at hand. We reduce the complexity of algorithm design for…
The provably asymptotically fastest algorithm within a factor of 5 for formally described problems will be constructed. The main idea is to enumerate all programs provably equivalent to the original problem by enumerating all proofs. The…
Fairness for Machine Learning has received considerable attention, recently. Various mathematical formulations of fairness have been proposed, and it has been shown that it is impossible to satisfy all of them simultaneously. The literature…
We introduce a new notion of complexity of functions and we show that it has the following properties: (i) it governs a PAC Bayes-like generalization bound, (ii) for neural networks it relates to natural notions of complexity of functions…
We investigate uniqueness problems for an entire function that shares two small functions of finite order with their difference operators. In particular, we give a generalization of a result in $[2]$.
In this paper we present results on asymptotic characteristics of multivariate function classes in the uniform norm. Our main interest is the approximation of functions with mixed smoothness parameter not larger than $1/2$. Our focus will…
The recently presented COCO detection challenge will most probably be the reference benchmark in object detection in the next years. COCO is two orders of magnitude larger than Pascal and has four times the number of categories; so in all…
Recent advancements in large language models have demonstrated remarkable capabilities across various NLP tasks. But many questions remain, including whether open-source models match closed ones, why these models excel or struggle with…
In this paper, we describe an algorithm that efficiently collect relations in class groups of number fields defined by a small defining polynomial. This conditional improvement consists in testing directly the smoothness of principal ideals…
Various software efforts embrace the idea that object oriented programming enables a convenient implementation of the chain rule, facilitating so-called automatic differentiation via backpropagation. Such frameworks have no mechanism for…
This article shows a correspondence between abstract interpretation of imperative programs and the refinement calculus: in the refinement calculus, an abstract interpretation of a program is a specification which is a function. This…
We analyze combinatorial optimization problems with ordinal, i.e., non-additive, objective functions that assign categories (like good, medium and bad) rather than cost coefficients to the elements of feasible solutions. We review different…
Numerous definitions for complexity have been proposed over the last half century, with little consensus achieved on how to use the term. A definition of complexity is supplied here that is closely related to the Kolmogorov Complexity and…
We start by an introduction to the basic concepts of computability theory and the introduction of the concept of Turing machine and computation universality. Then se turn to the exploration of trade-offs between different measures of…