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A probability distribution over the Boolean cube is monotone if flipping the value of a coordinate from zero to one can only increase the probability of an element. Given samples of an unknown monotone distribution over the Boolean cube, we…
The problem of checking whether a recursive query can be rewritten as query without recursion is a fundamental reasoning task, known as the boundedness problem. Here we study the boundedness problem for Unions of Conjunctive Regular Path…
We propose a new encoding of the first-order connection method as a Boolean satisfiability problem. The encoding eschews tree-like presentations of the connection method in favour of matrices, as we show that tree-like calculi have a number…
It has long been known that any Boolean function that depends on n input variables has both degree and exact quantum query complexity of Omega(log n), and that this bound is achieved for some functions. In this paper we study the case of…
Reversible logic represents the basis for many emerging technologies and has recently been intensively studied. However, most of the Boolean functions of practical interest are irreversible and must be embedded into a reversible function…
Fourier analysis on the discrete hypercubes $\{-1,1\}^n$ has found numerous applications in learning theory. A recent breakthrough involves the use of a classical result from Fourier analysis, the Bohnenblust--Hille inequality, in the…
We make progress on two important problems regarding attribute efficient learnability. First, we give an algorithm for learning decision lists of length $k$ over $n$ variables using $2^{\tilde{O}(k^{1/3})} \log n$ examples and time…
We investigate the complexity of training a two-layer ReLU neural network with weight decay regularization. Previous research has shown that the optimal solution of this problem can be found by solving a standard cone-constrained convex…
We consider the problem of actively learning an unknown binary decision tree using only membership queries, a setting in which the learner must reason about a large hypothesis space while maintaining formal guarantees. Rather than…
In algebraic terms, the insertion of $n$-powers in words may be modelled at the language level by considering the pseudovariety of ordered monoids defined by the inequality $1\le x^n$. We compare this pseudovariety with several other…
In query learning, the goal is to identify an unknown object while minimizing the number of "yes" or "no" questions (queries) posed about that object. A well-studied algorithm for query learning is known as generalized binary search (GBS).…
This paper is concerned with certifying that a given point is near an exact root of an overdetermined or singular polynomial system with rational coefficients. The difficulty lies in the fact that consistency of overdetermined systems is…
We consider the problem of learning unions of rectangles over the domain $[b]^n$, in the uniform distribution membership query learning setting, where both b and n are "large". We obtain poly$(n, \log b)$-time algorithms for the following…
The approximate degree of a Boolean function is the least degree of a real multilinear polynomial approximating it in the $\ell_\infty$-norm over the Boolean hypercube. We show that the approximate degree of the Bipartite Perfect Matching…
The cross-media retrieval problem has received much attention in recent years due to the rapid increasing of multimedia data on the Internet. A new approach to the problem has been raised which intends to match features of different…
The exact complexity of geometric cuts and bisections is the longstanding open problem including even the dimension one. In this paper, we resolve this problem for dimension one (the real line) by designing an exact polynomial time…
Set-membership estimation is usually formulated in the context of set-valued calculus and no probabilistic calculations are necessary. In this paper, we show that set-membership estimation can be equivalently formulated in the probabilistic…
We contribute to a better understanding of the class of functions that can be represented by a neural network with ReLU activations and a given architecture. Using techniques from mixed-integer optimization, polyhedral theory, and tropical…
Not all people are equally easy to identify: color statistics might be enough for some cases while others might require careful reasoning about high- and low-level details. However, prevailing person re-identification(re-ID) methods use…
We address the problem of general supervised learning when data can only be accessed through an (indefinite) similarity function between data points. Existing work on learning with indefinite kernels has concentrated solely on…