Related papers: Discrepancy Algorithms for the Binary Perceptron
We introduce two notions of discrepancy between binary vectors, which are not metric functions in general but nonetheless capture the mathematical structure of the binary asymmetric channel. In turn, these lead to two new fundamental…
Online classification is a central problem in optimization, statistical learning and data science. Classical algorithms such as the perceptron offer efficient updates and finite mistake guarantees on linearly separable data, but they do not…
This report will be a literature review on a result in algorithmic discrepancy theory. We will begin by providing a quick overview on discrepancy theory and some major results in the field, and then focus on an important result by Shachar…
Linear Complementarity Problems (LCPs) with sufficient matrices form an important subclass of LCPs, and it remains a significant open question whether problems in this class can be solved in polynomial time. Kojima, Megiddo, Noma, and…
We study the potential of deep learning to resolve the combinatorial problem in SUSY-like events with two invisible particles at the LHC. As a concrete example, we focus on dileptonic $t \bar t$ events, where the combinatorial problem…
We study the replica-symmetric saddle point equations for the Ising perceptron with Gaussian disorder and margin $\kappa\ge 0$. We prove that for each $\kappa\ge 0$ there is a critical capacity $\alpha_c(\kappa)=\frac{2}{\pi\,\mathbb…
We introduce a class of specially structured linear programming (LP) problems, which has favorable modeling capability for important application problems in different areas such as optimal transport, discrete tomography and economics. To…
On-line and batch learning of a perceptron in a discrete weight space, where each weight can take $2 L+1$ different values, are examined analytically and numerically. The learning algorithm is based on the training of the continuous…
Within a Kuhn-Tucker cavity method introduced in a former paper, we study optimal stability learning for situations, where in the replica formalism the replica symmetry may be broken, namely (i) the case of a simple perceptron above the…
We study the binary perceptron, a random constraint satisfaction problem that asks to find a Boolean vector in the intersection of independently chosen random halfspaces. A striking feature of this model is that at every positive constraint…
The use of high-dimensional features has become a normal practice in many computer vision applications. The large dimension of these features is a limiting factor upon the number of data points which may be effectively stored and processed,…
Several proposed techniques for distinguishing between optical coherent states are analyzed under a physically realistic model of photodetection. Quantum error probabilities are derived for the Kennedy receiver, the Dolinar receiver and the…
We propose an efficient method to explore models which which produce like-sign tops at the LHC, using the total charge asymmetry of single lepton events instead of like-sign dileptons. As an example, the method is implemented on a Z' Model,…
The analysis of the decoding failure rate of the bit-flipping algorithm has received increasing attention. For a binary linear code we consider the minimum number of rows in a parity-check matrix such that the bit-flipping algorithm is able…
The theory behind compressive sampling pre-supposes that a given sequence of observations may be exactly represented by a linear combination of a small number of basis vectors. In practice, however, even small deviations from an exact…
Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with…
Phase retrieval in real or complex Hilbert spaces is the task of recovering a vector, up to an overall unimodular multiplicative constant, from magnitudes of linear measurements. In this paper, we assume that the vector is normalized, but…
The min-knapsack problem with compactness constraints extends the classical knapsack problem, in the case of ordered items, by introducing a restriction ensuring that they cannot be too far apart. This problem has applications in…
Binary optimization, a representative subclass of discrete optimization, plays an important role in mathematical optimization and has various applications in computer vision and machine learning. Usually, binary optimization problems are…
We consider the Ising perceptron with gaussian disorder, which is equivalent to the discrete cube $\{-1,+1\}^N$ intersected by $M$ random half-spaces. The perceptron's capacity is $\alpha_N \equiv M_N/N$ for the largest integer $M_N$ such…