Related papers: Black-Box Complexity of the Binary Value Function
We present a constructive SAT-based algorithm to determine the multiplicative complexity of a Boolean function, i.e., the smallest number of AND gates in any logic network that consists of 2-input AND gates, 2-input XOR gates, and…
We provide the first convergence guarantee for full black-box variational inference (BBVI), also known as Monte Carlo variational inference. While preliminary investigations worked on simplified versions of BBVI (e.g., bounded domain,…
Recently, Deshpande et al. introduced a new measure of the complexity of a Boolean function. We call this measure the "goal value" of the function. The goal value of $f$ is defined in terms of a monotone, submodular utility function…
Complexity theory offers a variety of concise computational models for computing boolean functions - branching programs, circuits, decision trees and ordered binary decision diagrams to name a few. A natural question that arises in this…
Abduction is a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining how the world behaves it aims at finding an explanation for some observed manifestation. In this paper we focus on propositional…
Variational Bayesian neural networks (BNNs) perform variational inference over weights, but it is difficult to specify meaningful priors and approximate posteriors in a high-dimensional weight space. We introduce functional variational…
We investigate shift-invariant transformations, also known as rotation-symmetric vectorial Boolean functions, on $n$ bits that are induced from Boolean functions on $k$ bits, for $k\leq n$. We consider such transformations that are not…
We present an information-theoretic approach to lower bound the oracle complexity of nonsmooth black box convex optimization, unifying previous lower bounding techniques by identifying a combinatorial problem, namely string guessing, as a…
We present several families of total boolean functions which have exact quantum query complexity which is a constant multiple (between 1/2 and 2/3) of their classical query complexity, and show that optimal quantum algorithms for these…
Determining the maximal separation between sensitivity and block sensitivity of Boolean functions is of interest for computational complexity theory. We construct a sequence of Boolean functions with bs(f) = 1/2 s(f)^2 + 1/2 s(f). The best…
Many real-world optimisation problems are defined over both categorical and continuous variables, yet efficient optimisation methods such asBayesian Optimisation (BO) are not designed tohandle such mixed-variable search spaces. Recent…
We develop a new algorithm for factoring a bivariate polynomial $F\in \mathbb{K}[x,y]$ which takes fully advantage of the geometry of the Newton polygon of $F$. Under a non degeneracy hypothesis, the complexity is…
We consider the problem of converting an arbitrary approximation algorithm for a single-parameter optimization problem into a computationally efficient truthful mechanism. We ask for reductions that are black-box, meaning that they require…
The structure of data organization is widely recognized as having a substantial influence on the efficacy of machine learning algorithms, particularly in binary classification tasks. Our research provides a theoretical framework suggesting…
We initiate the study of a new model of query complexity of Boolean functions where, in addition to 0 and 1, the oracle can answer queries with ``unknown''. The query algorithm is expected to output the function value if it can be…
In this paper we establish some bounds on the complexity of disjunctive normal forms of boolean function from narrow subclasses (e.g. functions takes value 0 in a limited number of points). The bounds are obtained by reduction the initial…
We consider an unconstrained continuous optimization problem where, in each iteration, gradient estimates may be arbitrarily corrupted with a probability greater than 1/2. Additionally, function value estimates may exhibit heavy-tailed…
Leveraging prior knowledge on intraclass variance due to transformations is a powerful method to improve the sample complexity of deep neural networks. This makes them applicable to practically important use-cases where training data is…
It has been recently proposed that the naive semiclassical prediction of non-unitary black hole evaporation can be understood in the fundamental description of the black hole as a consequence of ignorance of high-complexity information.…
Bayesian Optimization (BO) is a widely used approach for blackbox optimization that leverages a Gaussian process (GP) model and an acquisition function to guide future sampling. While effective in low-dimensional settings, BO faces…