Related papers: Matrix Multiplication and Number On the Forehead C…
Data dissemination is a fundamental task in distributed computing. This paper studies broadcast problems in various innovative models where the communication network connecting $n$ processes is dynamic (e.g., due to mobility or failures)…
This paper is motivated by the problem of error control in network coding when errors are introduced in a random fashion (rather than chosen by an adversary). An additive-multiplicative matrix channel is considered as a model for random…
Matrix congruence extends naturally to the setting of tensors. We apply methods from tensor decomposition, algebraic geometry and numerical optimization to this group action. Given a tensor in the orbit of another tensor, we compute a…
We study the algorithmic problem of multiplying large matrices that are rectangular. We prove that the method that has been used to construct the fastest algorithms for rectangular matrix multiplication cannot give algorithms with…
This work explores three-player game training dynamics, under what conditions three-player games converge and the equilibria the converge on. In contrast to prior work, we examine a three-player game architecture in which all players…
We study the problem of computing an $\epsilon$-approximate Nash equilibrium of a two-player, bilinear game with a bounded payoff matrix $A \in \mathbb{R}^{m \times n}$, when the players' strategies are constrained to lie in simple sets. We…
In current molecular communication (MC) systems, performing computational operations at the nanoscale remains challenging, restricting their applicability in complex scenarios such as adaptive biochemical control and advanced nanoscale…
In a large-scale and distributed matrix multiplication problem $C=A^{\intercal}B$, where $C\in\mathbb{R}^{r\times t}$, the coded computation plays an important role to effectively deal with "stragglers" (distributed computations that may…
The Metaverse play-to-earn games have been gaining popularity as they enable players to earn in-game tokens which can be translated to real-world profits. With the advancements in augmented reality (AR) technologies, users can play AR games…
Multi-round competitions often double or triple the points awarded in the final round, calling it a bonus, to maximize spectators' excitement. In a two-player competition with $n$ rounds, we aim to derive the optimal bonus size to maximize…
We develop a method that integrates the tree of thoughts and multi-agent framework to enhance the capability of pre-trained language models in solving complex, unfamiliar games. The method decomposes game-solving into four incremental tasks…
In this work, we focus on separable convex optimization problems with box constraints and a set of triangular linear constraints. The solution is given in closed-form as a function of some Lagrange multipliers that can be computed through…
We show that the border support rank of the tensor corresponding to two-by-two matrix multiplication is seven over the complex numbers. We do this by constructing two polynomials that vanish on all complex tensors with format…
Most contemporary multi-task learning methods assume linear models. This setting is considered shallow in the era of deep learning. In this paper, we present a new deep multi-task representation learning framework that learns cross-task…
We consider communication problems in the setting of mobile agents deployed in an edge-weighted network. The assumption of the paper is that each agent has some energy that it can transfer to any other agent when they meet (together with…
In split machine learning (ML), different partitions of a neural network (NN) are executed by different computing nodes, requiring a large amount of communication cost. To ease communication burden, over-the-air computation (OAC) can…
Sparse matrix multiplication is an important component of linear algebra computations. Implementing sparse matrix multiplication on an associative processor (AP) enables high level of parallelism, where a row of one matrix is multiplied in…
The last decade has witnessed an explosion in the development of models, theory and computational algorithms for "big data" analysis. In particular, distributed computing has served as a natural and dominating paradigm for statistical…
A general theory for constructing linear secret sharing schemes over a finite field $\Fq$ from toric varieties is introduced. The number of players can be as large as $(q-1)^r-1$ for $r\geq 1$. We present general methods for obtaining the…
Recently, there has been an increasing interest in designing distributed convex optimization algorithms under the setting where the data matrix is partitioned on features. Algorithms under this setting sometimes have many advantages over…