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In this paper we investigate a neural network model in which weights between computational nodes are modified according to a local learning rule. To determine whether local learning rules are sufficient for learning, we encode the network…
Monotone co-design enables compositional engineering design by modeling components through feasibility relations between required resources and provided functionalities. However, its standard boolean formulation cannot natively represent…
Musical chords, harmonies or melodies in Just Intonation have note frequencies which are described by a base frequency multiplied by rational numbers. For any local section, these notes can be converted to some base frequency multiplied by…
We study settings where gradient penalties are used alongside risk minimization with the goal of obtaining predictors satisfying different notions of monotonicity. Specifically, we present two sets of contributions. In the first part of the…
We analyze a stylized model of co-evolution between any two purely competing species (e.g., host and parasite), both sexually reproducing. Similarly to a recent model of Livnat \etal~\cite{evolfocs14} the fitness of an individual depends on…
In this paper, we scale evolutionary algorithms to high-dimensional optimization problems that deceptively possess a low effective dimensionality (certain dimensions do not significantly affect the objective function). To this end, an…
In recent years, manifold methods have moved into focus as tools for dimension reduction. Assuming that the high-dimensional data actually lie on or close to a low-dimensional nonlinear manifold, these methods have shown convincing results…
Recent releases such as o3 highlight human-like "thinking with images" reasoning that combines tool use with stepwise verification, yet most open-source approaches still rely on text-only chains, rigid visual schemas, or single-step…
We give an adaptive algorithm which tests whether an unknown Boolean function $f\colon \{0, 1\}^n \to\{0, 1\}$ is unate, i.e. every variable of $f$ is either non-decreasing or non-increasing, or $\epsilon$-far from unate with one-sided…
Cardinality estimation is a key component of database query optimization. Recent studies have demonstrated that learned cardinality estimation techniques can surpass traditional methods in accuracy. However, a significant barrier to their…
The nonlinearity of a Boolean function is a key property in deciding its suitability for cryptographic purposes, e.g. as a combining function in stream ciphers, and so the nonlinearity computation is an important problem for applications.…
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 deal with the shape reconstruction of inclusions in elastic bodies. For solving this inverse problem in practice, data fitting functionals are used. Those work better than the rigorous monotonicity methods from [5], but have no…
In this note, we develop a bounded-error quantum algorithm that makes $\tilde O(n^{1/4}\varepsilon^{-1/2})$ queries to a Boolean function $f$, accepts a monotone function, and rejects a function that is $\varepsilon$-far from being…
This work presents a study of perturbations of symmetric Boolean functions. In particular, it establishes a connection between exponential sums of these perturbations and Diophantine equations of the form $$ \sum_{l=0}^n \binom{n}{l}…
A new algorithm for the symbolic computation of polynomial conserved densities for systems of nonlinear evolution equations is presented. The algorithm is implemented in Mathematica. The program condens.m automatically carries out the…
Information theoretic analysis of large evolved programs produced by running genetic programming for up to a million generations has shown even functions as smooth and well behaved as floating point addition and multiplication loose entropy…
With the number of fully-sequenced genomes now well over a hundred it has become possible to start investigating if there are any quantitative regularities in the genetic make-up of genomes. In (physics/0307001), I originally showed that…
An algorithm for computing the nonlinearity of a Boolean function from its algebraic normal form (ANF) is proposed. By generalizing the expression of the weight of a Boolean function in terms of its ANF coefficients, a formulation of the…
Understanding the characteristics of neural networks is important but difficult due to their complex structures and behaviors. Some previous work proposes to transform neural networks into equivalent Boolean expressions and apply…