Abstract: The Log-Approximate-Rank Conjecture was a long-standing conjecture which posited that the randomised communication complexity of a function and log of the approximate rank of its communication matrix are polynomially related.
In this work, we introduce a function F that refutes this conjecture. We will discuss a drawback of rank-like measures and see a proof that F has small approximate rank, yet is hard for randomised communication (joint work with Arkadev Chattopadhyay and Nikhil Mande).
