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We develop a systematic approach, based on convex programming and real analysis, for obtaining upper bounds on the capacity of the binary deletion channel and, more generally, channels with i.i.d. insertions and deletions. Other than the…
Several fundamental problems that arise in optimization and computer science can be cast as follows: Given vectors $v_1,\ldots,v_m \in \mathbb{R}^d$ and a constraint family ${\cal B}\subseteq 2^{[m]}$, find a set $S \in \cal{B}$ that…
One way to define the Matching Cut problem is: Given a graph $G$, is there an edge-cut $M$ of $G$ such that $M$ is an independent set in the line graph of $G$? We propose the more general Conflict-Free Cut problem: Together with the graph…
A fundamental aspect of limitations in learning any computation in neural architectures is characterizing their optimal capacities. An important, widely-used neural architecture is known as autoencoders where the network reconstructs the…
We consider the quantum decoding problem. It consists in recovering a codeword given a superposition of noisy versions of this codeword. By measuring the superposition, we get back to the classical decoding problem. It appears for the first…
Motivated by the increasing need to understand the distributed algorithmic foundations of large-scale graph computations, we study some fundamental graph problems in a message-passing model for distributed computing where $k \geq 2$…
Combinatorial optimization lies at the core of many real-world problems. Especially since the rise of graph neural networks (GNNs), the deep learning community has been developing solvers that derive solutions to NP-hard problems by…
Models with dominant advection always posed a difficult challenge for projection-based reduced order modelling. Many methodologies that have recently been proposed are based on the pre-processing of the full-order solutions to accelerate…
Structured reconstruction is a non-trivial dense prediction problem, which extracts structural information (\eg, building corners and edges) from a raster image, then reconstructs it to a 2D planar graph accordingly. Compared with common…
Training neural networks is a challenging non-convex optimization problem, and backpropagation or gradient descent can get stuck in spurious local optima. We propose a novel algorithm based on tensor decomposition for guaranteed training of…
Excellent performance has been achieved on instance segmentation but the quality on the boundary area remains unsatisfactory, which leads to a rising attention on boundary refinement. For practical use, an ideal post-processing refinement…
Error feedback (EF), also known as error compensation, is an immensely popular convergence stabilization mechanism in the context of distributed training of supervised machine learning models enhanced by the use of contractive communication…
Neural networks are widely used for image-related tasks but typically demand considerable computing power. Once a network has been trained, however, its memory- and compute-footprint can be reduced by compression. In this work, we focus on…
We consider the problem of learning causal networks with interventions, when each intervention is limited in size under Pearl's Structural Equation Model with independent errors (SEM-IE). The objective is to minimize the number of…
Graph prediction problems prevail in data analysis and machine learning. The inverse prediction problem, namely to infer input data from given output labels, is of emerging interest in various applications. In this work, we develop…
This work focuses on developing methods for approximating the solution operators of a class of parametric partial differential equations via neural operators. Neural operators have several challenges, including the issue of generating…
We study progression-free sets in the abelian groups $G=(\mathbb{Z}_m^n,+)$. Let $r_k(\mathbb{Z}_m^n)$ denote the maximal size of a set $S \subset \mathbb{Z}_m^n$ that does not contain a proper arithmetic progression of length $k$. We give…
Many modern large-scale machine learning problems benefit from decentralized and stochastic optimization. Recent works have shown that utilizing both decentralized computing and local stochastic gradient estimates can outperform…
A problem with Convolutional Neural Networks (CNNs) is that they require large datasets to obtain adequate robustness; on small datasets, they are prone to overfitting. Many methods have been proposed to overcome this shortcoming with CNNs.…
In the Flexible Graph Connectivity (FGC) problem, we are given an undirected multigraph on $n$ vertices with nonnegative edge costs, where each edge is classified as either safe or unsafe. Given integer parameters $p$ and $q$, the goal in…