Phylogenetic models of molecular evolution are central to diverse problems in biology, but maximum likelihood estimation of model parameters is a computationally expensive task, in some cases prohibitively so. To address this challenge, we here introduce CherryML, a broadly applicable method that achieves several orders of magnitude speedup. We demonstrate its utility by applying it to estimate a general 400 × 400 rate matrix for amino acid co-evolution at protein contact sites.
While sorting is an important procedure in computer science, the argsort operator -which takes as input a vector and returns its sorting permutation -has a discrete image and thus zero gradients almost everywhere. This prohibits end-toend, gradient-based learning of models that rely on the argsort operator. A natural way to overcome this problem is to replace the argsort operator with a continuous relaxation. Recent work has shown a number of ways to do this, but the relaxations proposed so far are computationally complex. In this work we propose a simple continuous relaxation for the argsort operator which has the following qualities: it can be implemented in three lines of code, achieves stateof-the-art performance, is easy to reason about mathematically -substantially simplifying proofs -and is faster than competing approaches. We open source the code to reproduce all of the experiments and results.
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