We study the computations that Bayesian agents undertake when exchanging opinions over a network. The agents act repeatedly on their private information and take myopic actions that maximize their expected utility according to a fully rational posterior be ...
We study the phenomenon of intransitivity in models of dice and voting. First, we follow a recent thread of research for n-sided dice with pairwise ordering induced by the probability, relative to 1/2, that a throw from one die is higher than the other. We ...
This paper introduces the notion of "Initial Alignment" (INAL) between a neural network at initialization and a target function. It is proved that if a network and a Boolean target function do not have a noticeable INAL, then noisy gradient descent on a fu ...
This paper considers "delta-almost Reed-Muller codes", i.e., linear codes spanned by evaluations of all but a delta fraction of monomials of degree at most d. It is shown that for any delta > 0 and any epsilon > 0, there exists a family of delta-almost Ree ...
How does the geometric representation of a dataset change after the application of each randomly initialized layer of a neural network? The celebrated Johnson-Lindenstrauss lemma answers this question for linear fully-connected neural networks (FNNs), stat ...
We strengthen the results from a recent work by the second author, achieving bounds on the weight distribution of binary linear codes that are successful under block-MAP (as well as bit-MAP) decoding on the BEC. We conclude that a linear code that is succe ...
