Related papers: Constructions of Efficiently Implementable Boolean…
Let a Boolean function be available as a black-box (oracle) and one likes to devise an algorithm to test whether it has certain property or it is $\epsilon$-far from having that property. The efficiency of the algorithm is judged by the…
One of the elegant achievements in the history of proof theory is the characterization of the provably total recursive functions of an arithmetical theory by its proof-theoretic ordinal as a way to measure the time complexity of the…
We establish a lower bound for deciding the satisfiability of the conjunction of any two Boolean formulas from a set called a full representation of Boolean functions of $n$ variables - a set containing a Boolean formula to represent each…
We consider a class of optimization problems that involve determining the maximum value that a function in a particular class can attain subject to a collection of difference constraints. We show that a particular linear programming…
This paper advances the theoretical understanding of active learning label complexity for decision trees as binary classifiers. We make two main contributions. First, we provide the first analysis of the disagreement coefficient for…
We study the power of negation in the Boolean and algebraic settings and show the following results. * We construct a family of polynomials $P_n$ in $n$ variables, all of whose monomials have positive coefficients, such that $P_n$ can be…
Multi-task learning aims to acquire a set of functions, either regressors or classifiers, that perform well for diverse tasks. At its core, the idea behind multi-task learning is to exploit the intrinsic similarity across data sources to…
Linear algebra computations are foundational for neural networks and machine learning, often handled through arrays. While many functional programming languages feature lists and recursion, arrays in linear algebra demand constant-time…
In this paper we propose a new methodology to represent the results of the robust ordinal regression approach by means of a family of representative value functions for which, taken two alternatives $a$ and $b$, the following two conditions…
Many recent theoretical works on \emph{meta-learning} aim to achieve guarantees in leveraging similar representational structures from related tasks towards simplifying a target task. The main aim of theoretical guarantees on the subject is…
We show that for any positive integer $d$, there are families of switched linear systems---in fixed dimension and defined by two matrices only---that are stable under arbitrary switching but do not admit (i) a polynomial Lyapunov function…
We give a (strongly) history-independent two-choice balls-and-bins algorithm on $n$ bins that supports both insertions and deletions on a set of up to $m$ balls, while guaranteeing a maximum load of $m / n + O(1)$ with high probability, and…
Using semi-tensor product of matrices, the structures of several kinds of symmetric games are investigated via the linear representation of symmetric group in the structure vector of games as its representation space. First of all, the…
Building resilience into today's complex infrastructures is critical to the daily functioning of society and its ability to withstand and recover from natural disasters, epidemics, and cyber-threats. This study proposes quantitative…
We consider sequences of integers defined by a system of linear inequalities with integer coefficients. We show that when the constraints are strong enough to guarantee that all the entries are nonnegative, the generating function for the…
We propose a holistic framework for constructing sensitivity measures for any elicitable functional $T$ of a response variable. The sensitivity measures, termed score-based sensitivities, are constructed via scoring functions that are…
We consider the problem of directly optimizing a non-linear function of an outcome, where this outcome itself is the sum of many small contributions. The non-linearity of the function means that the problem is not equivalent to the…
We study actions of groups by homeomorphisms on $\mathbf{R}$ (or an interval) that are minimal, have solvable germs at $\pm \infty$ and contain a pair of elements of a certain type. We call such actions coherent. We establish that such an…
We study the numerical and Boolean expressiveness of MPLang, a declarative language that captures the computation of graph neural networks (GNNs) through linear message passing and activation functions. We begin with A-MPLang, the fragment…
We examine multi-task benchmarks in machine learning through the lens of social choice theory. We draw an analogy between benchmarks and electoral systems, where models are candidates and tasks are voters. This suggests a distinction…