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Knowledge is a network of interconnected concepts. Yet, precisely how the topological structure of knowledge constrains its acquisition remains unknown, hampering the development of learning enhancement strategies. Here we study the…
We show strong (and surprisingly simple) lower bounds for weakly learning intersections of halfspaces in the improper setting. Strikingly little is known about this problem. For instance, it is not even known if there is a polynomial-time…
An upper dominating set in a graph is a minimal (with respect to set inclusion) dominating set of maximum cardinality. The problem of finding an upper dominating set is generally NP-hard. We study the complexity of this problem in classes…
We define a quantum model for multiparty communication complexity and prove a simulation theorem between the classical and quantum models. As a result of our simulation, we show that if the quantum k-party communication complexity of a…
A central question in computer science and statistics is whether efficient algorithms can achieve the information-theoretic limits of statistical problems. Many computational-statistical tradeoffs have been shown under average-case…
Prior work on Sign Language Translation has shown that having a mid-level sign gloss representation (effectively recognizing the individual signs) improves the translation performance drastically. In fact, the current state-of-the-art in…
In a variant of communication complexity tasks, two or more separated parties cooperate to compute a function of their local data, using a limited amount of communication. It is known that communication of quantum systems and shared…
Complex systems can be effectively modeled via graphs that encode networked interactions, where relations between entities or nodes are often quantified by signed edge weights, e.g., promotion/inhibition in gene regulatory networks, or…
Identification capacity has been established as a relevant performance metric for various goal-/task-oriented applications, where the receiver may be interested in only a particular message that represents an event or a task. For example,…
In this paper we study the tradeoff between parallelism and communication cost in a map-reduce computation. For any problem that is not "embarrassingly parallel," the finer we partition the work of the reducers so that more parallelism can…
Round complexity is an extensively studied metric of distributed algorithms. In contrast, our knowledge of the \emph{message complexity} of distributed computing problems and its relationship (if any) with round complexity is still quite…
The knowledge that data lies close to a particular submanifold of the ambient Euclidean space may be useful in a number of ways. For instance, one may want to automatically mark any point far away from the submanifold as an outlier or to…
Multi-task learning is a framework that enforces different learning tasks to share their knowledge to improve their generalization performance. It is a hot and active domain that strives to handle several core issues; particularly, which…
Learning to communicate in order to share state information is an active problem in the area of multi-agent reinforcement learning (MARL). The credit assignment problem, the non-stationarity of the communication environment and the creation…
Let G = (A U P, E) be a bipartite graph where A denotes a set of agents, P denotes a set of posts and ranks on the edges denote preferences of the agents over posts. A matching M in G is rank-maximal if it matches the maximum number of…
Semantic correspondence methods have advanced to obtaining high-quality correspondences employing complicated networks, aiming to maximize the model capacity. However, despite the performance improvements, they may remain constrained by the…
We develop information geometric techniques to understand the representations learned by deep networks when they are trained on different tasks using supervised, meta-, semi-supervised and contrastive learning. We shed light on the…
The Natarajan dimension is a fundamental tool for characterizing multi-class PAC learnability, generalizing the Vapnik-Chervonenkis (VC) dimension from binary to multi-class classification problems. This work establishes upper bounds on…
We introduce a class of communication tests where the task is to communicate partial ignorance by means of a physical system. We present a full characterization of the implementations of these tests in the qubit case and partial results for…
Reducing communication - either between levels of a memory hierarchy or between processors over a network - is a key component of performance optimization (in both time and energy) for many problems, including dense linear algebra, particle…