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Dynamical Properties of Dense Associative Memory
Kazushi Mimura, Jun'ichi Takeuchi, Yuto Sumikawa, Yoshiyuki Kabashima, Anthony C. C. Coolen
https://arxiv.org/abs/2506.00851

Dynamical Properties of Dense Associative Memory
The dense associative memory is one of the basic modern Hopfield networks and can store large numbers of memory patterns. While the stationary state storage capacity has been investigated so far, its dynamical properties have not been discussed. In this paper, we analyze the dynamics by means of an exact approach based on generating functional analysis. It allows us to investigate convergence properties as well as the size of the attraction basins. We also analyze the stationary state of the up…

Rotating Carroll Black Holes: A No Go Theorem
Ivan Kol\'a\v{r}, David Kubiznak, Poula Tadros
https://arxiv.org/abs/2506.10451 https://

Rotating Carroll Black Holes: A No Go Theorem
Recently, there has been a lot of interest in Carroll black holes and in particular whether or not one could find a Carrollian analogue of a rotating black hole spacetime. Here we show that every stationary and axisymmetric solution (and thence also a black hole) of Carrollian general relativity in any number of $d\geq 3$ dimensions is necessarily also static. Using this result, we construct a unique stationary and axisymmetric black hole in three dimensions - a static Carroll BTZ black hole. A…