Related papers: The communication complexity of functions with lar…
Consensus is one of the most thoroughly studied problems in distributed computing, yet there are still complexity gaps that have not been bridged for decades. In particular, in the classical message-passing setting with processes' crashes,…
Optimizing parameters of Two-Prover-One-Round Game (2P1R) is an important task in PCPs literature as it would imply a smaller PCP with the same or stronger soundness. While this is a basic question in PCPs community, the connection between…
The peculiarity of adversarial team games resides in the asymmetric information available to the team members during the play, which makes the equilibrium computation problem hard even with zero-sum payoffs. The algorithms available in the…
In secure multiparty computation (MPC), mutually distrusting users collaborate to compute a function of their private data without revealing any additional information about their data to other users. While it is known that information…
Large parts of professional human communication proceed in a request-reply fashion, whereby requests contain specifics of the information desired while replies can deliver the required information. However, time limitations often force…
We consider the classical problem of maximizing a monotone submodular function subject to a cardinality constraint, which, due to its numerous applications, has recently been studied in various computational models. We consider a clean…
Two parties observing correlated random variables seek to run an interactive communication protocol. How many bits must they exchange to simulate the protocol, namely to produce a view with a joint distribution within a fixed statistical…
In the first part of this two-part letter, we introduced methods to study the impact of dependency on the expected value of functions of two random variables. In this second part, we present tools to derive worst- and best-case bounds on…
Recently, various distributed strategies for large language model training have been proposed. However, these methods provided limited solutions for the trade-off between memory consumption and communication cost. In this paper, we rethink…
Orca 1 learns from rich signals, such as explanation traces, allowing it to outperform conventional instruction-tuned models on benchmarks like BigBench Hard and AGIEval. In Orca 2, we continue exploring how improved training signals can…
The most trivial way to simulate classically the communication of a quantum state is to transmit the classical description of the quantum state itself. However, this requires an infinite amount of classical communication if the simulation…
We introduce a simple model illustrating the role of context in communication and the challenge posed by uncertainty of knowledge of context. We consider a variant of distributional communication complexity where Alice gets some information…
We settle the complexities of the maximum-cardinality bipartite matching problem (BMM) up to poly-logarithmic factors in five models of computation: the two-party communication, AND query, OR query, XOR query, and quantum edge query models.…
We consider quantum XOR games, defined in [11], from the perspective of unitary correlations defined in [7]. We show that Connes' embedding problem has a positive answer if and only if every quantum XOR game has entanglement bias equal to…
In repeated interactions between individuals, we do not expect that exactly the same situation will occur from one time to another. Contrary to what is common in models of repeated games in the literature, most real situations may differ a…
We show that disjointness requires randomized communication Omega(n^{1/(k+1)}/2^{2^k}) in the general k-party number-on-the-forehead model of complexity. The previous best lower bound for k >= 3 was log(n)/(k-1). Our results give a…
We consider a number of fundamental statistical and graph problems in the message-passing model, where we have $k$ machines (sites), each holding a piece of data, and the machines want to jointly solve a problem defined on the union of the…
Designing protocols enhancing cooperation for multi-agent systems remains a grand challenge. Cheap talk, defined as costless, non-binding communication before formal action, serves as a pivotal solution. However, existing theoretical…
We consider the communication complexity of some fundamental convex optimization problems in the point-to-point (coordinator) and blackboard communication models. We strengthen known bounds for approximately solving linear regression,…
Recent thinking models trained with reinforcement learning and backward-checking CoT often suffer from overthinking: they produce excessively long outputs even on simple problems, wasting computation. Existing evaluations, based on token…