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We introduce a new variant of the $k$-deck problem, which in its traditional formulation asks for determining the smallest $k$ that allows one to reconstruct any binary sequence of length $n$ from the multiset of its $k$-length…
We introduce stronger notions for approximate single-source shortest-path distances, show how to efficiently compute them from weaker standard notions, and demonstrate the algorithmic power of these new notions and transformations. One…
In this paper, a new localized radial basis function (RBF) method based on partition of unity (PU) is proposed for solving boundary and initial-boundary value problems. The new method is benefited from a direct discretization approach and…
Given a directed graph, we show how to efficiently find a shortest (directed, simple) cycle on an even number of vertices. As far as we know, no polynomial-time algorithm was previously known for this problem. In fact, finding any even…
Learning compact binary codes for image retrieval task using deep neural networks has attracted increasing attention recently. However, training deep hashing networks for the task is challenging due to the binary constraints on the hash…
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…
We continue to consider the discrete decreasing minimization problem on an integral base-polyhedron treated in Part I. The problem is to find a lexicographically minimal integral vector in an integral base-polyhedron, where the components…
This paper addresses the design of practical shortlength coding schemes for Distributed Hypothesis Testing (DHT). While most prior work on DHT has focused on informationtheoretic analyses, deriving bounds on Type-II error exponents via…
The irregular strip-packing problem consists of the computation of a non-overlapping placement of a set of polygons onto a rectangular strip of fixed width and the minimal length possible. Recent performance gains of the Mixed-Integer…
Binary Neural Networks (BNNs), neural networks with weights and activations constrained to -1(0) and +1, are an alternative to deep neural networks which offer faster training, lower memory consumption and lightweight models, ideal for use…
A efficient incremental learning algorithm for classification tasks, called NetLines, well adapted for both binary and real-valued input patterns is presented. It generates small compact feedforward neural networks with one hidden layer of…
The current paper studies the problem of minimizing a loss $f(\boldsymbol{x})$ subject to constraints of the form $\boldsymbol{D}\boldsymbol{x} \in S$, where $S$ is a closed set, convex or not, and $\boldsymbol{D}$ is a matrix that fuses…
Binary neural networks (BNNs) have been widely adopted to reduce the computational cost and memory storage on edge-computing devices by using one-bit representation for activations and weights. However, as neural networks become…
It has been recently established that a deterministic infinite horizon discounted optimal control problem in discrete time is closely related to a certain infinite dimensional linear programming problem and its dual. In the present paper,…
Deep neural network models, though very powerful and highly successful, are computationally expensive in terms of space and time. Recently, there have been a number of attempts on binarizing the network weights and activations. This greatly…
Work introduces a hierarchical binary tree-based reduction that replaces standard self-attention. The core idea is to use a recursive Gated Linear Unit merge operation, achieving O(n) total merge operations O(log n) parallel depth O(n d^2)…
Regularized risk minimization with the binary hinge loss and its variants lies at the heart of many machine learning problems. Bundle methods for regularized risk minimization (BMRM) and the closely related SVMStruct are considered the best…
Uniform confidence bands for functions are widely used in empirical analysis. A variety of simple implementation methods (most notably multiplier bootstrap) have been proposed and theoretically justified. However, an implementation over a…
In this contribution we are concerned with tight a posteriori error estimation for projection based model order reduction of $\inf$-$\sup$ stable parameterized variational problems. In particular, we consider the Reduced Basis Method in a…
Direct search is one of the most popular derivative-free optimization paradigms, that relies on exploring the variable space using polling directions. To analyze and implement direct search, one typically relies on positive spanning sets.…