Related papers: Hellinger volume and number-on-the-forehead commun…
A computable expression for the rate-distortion (RD) function proposed by Heegard and Berger has eluded information theory for nearly three decades. Heegard and Berger's single-letter achievability bound is well known to be optimal for…
It has long been known that the existence of certain superquantum nonlocal correlations would cause communication complexity to collapse. The absurdity of a world in which any nonlocal binary function could be evaluated with a constant…
A strong converse shows that no procedure can beat the asymptotic (as blocklength $n\to\infty$) fundamental limit of a given information-theoretic problem for any fixed error probability. A second-order converse strengthens this conclusion…
Federated learning (FL) is a popular machine learning technique that enables multiple users to collaboratively train a model while maintaining the user data privacy. A significant challenge in FL is the communication bottleneck in the…
In communication complexity the Arthur-Merlin (AM) model is the most natural one that allows both randomness and non-determinism. Presently we do not have any super-logarithmic lower bound for the AM-complexity of an explicit function.…
We present efficient algorithms to decide whether two given counting functions on non-abelian free groups or monoids are at bounded distance from each other and to decide whether two given counting quasimorphisms on non-abelian free groups…
The main contribution of this work is to relate information complexity to "tension" [Prabhakaran and Prabhakaran, 2014] - an information-theoretic quantity defined with no reference to protocols - and to illustrate that it allows deriving…
The class $FORMULA[s] \circ \mathcal{G}$ consists of Boolean functions computable by size-$s$ de Morgan formulas whose leaves are any Boolean functions from a class $\mathcal{G}$. We give lower bounds and (SAT, Learning, and PRG) algorithms…
Communication on heterogeneous edge networks is a fundamental bottleneck in Federated Learning (FL), restricting both model capacity and user participation. To address this issue, we introduce two novel strategies to reduce communication…
We present a novel computational methodology for solving the scalar nonlinear Helmholtz equation (NLH) that governs the propagation of laser light in Kerr dielectrics. The methodology addresses two well-known challenges in nonlinear optics:…
The efficient communication of noisy data has applications in several areas of machine learning, such as neural compression or differential privacy, and is also known as reverse channel coding or the channel simulation problem. Here we…
Federated Learning (FL) is an emerging learning framework that enables edge devices to collaboratively train ML models without sharing their local data. FL faces, however, a significant challenge due to the high amount of information that…
In this note, we study the relation between the parity decision tree complexity of a boolean function $f$, denoted by $\mathrm{D}_{\oplus}(f)$, and the $k$-party number-in-hand multiparty communication complexity of the XOR functions…
The hierarchical interpolative factorization (HIF) offers an efficient way for solving or preconditioning elliptic partial differential equations. By exploiting locality and low-rank properties of the operators, the HIF achieves…
We introduce a new theoretical framework for deriving lower bounds on data movement in bilinear algorithms. Bilinear algorithms are a general representation of fast algorithms for bilinear functions, which include computation of matrix…
Motivated by a problem arising from Density Functional Theory, we provide the sharp next-order asymptotics for a class of multimarginal optimal transport problems with cost given by singular, long-range pairwise interaction potentials. More…
The privacy-utility tradeoff problem is formulated as determining the privacy mechanism (random mapping) that minimizes the mutual information (a metric for privacy leakage) between the private features of the original dataset and a…
One of the best lower bound methods for the quantum communication complexity of a function H (with or without shared entanglement) is the logarithm of the approximate rank of the communication matrix of H. This measure is essentially…
We derive lower limits on the inefficiency and classical communication costs of dilution between two-term bipartite pure states that are partially entangled. We first calculate explicit relations between the allowable error and classical…
In this article we establish new bounds on the quantum communication complexity of distributed problems. Specifically, we consider the amount of communication that is required to transform a bipartite state into another, typically more…