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We describe new lower bounds for randomized communication complexity and query complexity which we call the partition bounds. They are expressed as the optimum value of linear programs. For communication complexity we show that the…
Motivated by applications in model-free finance and quantitative risk management, we consider Fr\'echet classes of multivariate distribution functions where additional information on the joint distribution is assumed, while uncertainty in…
Neural networks (NNs) are now routinely implemented on systems that must operate in uncertain environments, but the tools for formally analyzing how this uncertainty propagates to NN outputs are not yet commonplace. Computing tight bounds…
In systems neuroscience, most models posit that brain regions communicate information under constraints of efficiency. Yet, evidence for efficient communication in structural brain networks characterized by hierarchical organization and…
We consider a model of bilateral trade with private values. The value of the buyer and the cost of the seller are jointly distributed. The true joint distribution is unknown to the designer, however, the marginal distributions of the value…
In this paper a new div-curl result is established in an open set $\Omega$ of $\mathbb{R}^N$, $N\geq 2$, for the product of two sequences of vector-valued functions which are bounded respectively in $L^p(\Omega)^N$ and $L^q(\Omega)^N$, with…
For a discrete or a continuous source model, we study the problem of secret-key generation with one round of rate-limited public communication between two legitimate users. Although we do not provide new bounds on the wiretap secret-key…
Given a graph and a subset of its nodes, referred to as source nodes, the minimum broadcast problem asks for the minimum number of steps in which a signal can be transmitted from the sources to all other nodes in the graph. In each step,…
We consider the problem of distilling efficient network topologies for collective communications. We provide an algorithmic framework for constructing direct-connect topologies optimized for the latency vs. bandwidth trade-off associated…
We show that the exact worst-case performance of fixed-step first-order methods for unconstrained optimization of smooth (possibly strongly) convex functions can be obtained by solving convex programs. Finding the worst-case performance of…
The cryptogenography problem, introduced by Brody, Jakobsen, Scheder, and Winkler (ITCS 2014), is to collaboratively leak a piece of information known to only one member of a group (i)~without revealing who was the origin of this…
The focus of this paper is on the public communication required for generating a maximal-rate secret key (SK) within the multiterminal source model of Csisz{\'a}r and Narayan. Building on the prior work of Tyagi for the two-terminal…
We present an optimal gradient method for smooth strongly convex optimization. The method is optimal in the sense that its worst-case bound on the distance to an optimal point exactly matches the lower bound on the oracle complexity for the…
According to Kumar's recent surprising result (ToCT'20), a small border Waring rank implies that the polynomial can be approximated as a sum of a constant and a small product of linear polynomials. We prove the converse of Kumar's result…
The Gap-Hamming-Distance problem arose in the context of proving space lower bounds for a number of key problems in the data stream model. In this problem, Alice and Bob have to decide whether the Hamming distance between their $n$-bit…
The question of how much communication is required between collaborating parties to compute a function of their data is of fundamental importance in the fields of theoretical computer science and information theory. In this work, the focus…
We focus on modeling the relationship between an input feature vector and the predicted outcome of a trained decision tree using mixed-integer optimization. This can be used in many practical applications where a decision tree or tree…
We derive an algorithm to compute satisfiability bounds for arbitrary {\omega}-regular properties in an Interval-valued Markov Chain (IMC) interpreted in the adversarial sense. IMCs generalize regular Markov Chains by assigning a range of…
We study the problem of joint optimization involving coding and control policies for a controlled Markovian sytem over a finite-rate noiseless communication channel. While structural results on the optimal encoding and control have been…
The use of continuous instead of discrete tokens during the Chain-of-Thought (CoT) phase of reasoning LLMs has garnered attention recently, based on the intuition that a continuous mixture of discrete tokens could simulate a superposition…