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Physarum Powered Differentiable Linear Programming Layers and Applications.

ABSTRACT: Consider a learning algorithm, which involves an internal call to an optimization routine such as a generalized eigenvalue problem, a cone programming problem or even sorting. Integrating such a method as a layer(s) within a trainable deep neural network (DNN) in an efficient and numerically stable way is not straightforward - for instance, only recently, strategies have emerged for eigendecomposition and differentiable sorting. We propose an efficient and differentiable solver for general linear programming problems which can be used in a plug and play manner within DNNs as a layer. Our development is inspired by a fascinating but not widely used link between dynamics of slime mold (physarum) and optimization schemes such as steepest descent. We describe our development and show the use of our solver in a video segmentation task and meta-learning for few-shot learning. We review the existing results and provide a technical analysis describing its applicability for our use cases. Our solver performs comparably with a customized projected gradient descent method on the first task and outperforms the differentiable CVXPY-SCS solver on the second task. Experiments show that our solver converges quickly without the need for a feasible initial point. Our proposal is easy to implement and can easily serve as layers whenever a learning procedure needs a fast approximate solution to a LP, within a larger network.

SUBMITTER: Meng Z

PROVIDER: S-EPMC8415120 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:Subspecies nomenclature systems of pathogens are increasingly based on sequence data. The use of phylogenetics to identify and differentiate between clusters of genetically similar pathogens is particularly prevalent in virology from the nomenclature of human papillomaviruses to highly pathogenic avian influenza (HPAI) H5Nx viruses. These nomenclature systems rely on absolute genetic distance thresholds to define the maximum genetic divergence tolerated between viruses designated as closely related. However, the phylogenetic clustering methods used in these nomenclature systems are limited by the arbitrariness of setting intra and intercluster diversity thresholds. The lack of a consensus ground truth to define well-delineated, meaningful phylogenetic subpopulations amplifies the difficulties in identifying an informative distance threshold. Consequently, phylogenetic clustering often becomes an exploratory, ad hoc exercise. Phylogenetic Clustering by Linear Integer Programming (PhyCLIP) was developed to provide a statistically principled phylogenetic clustering framework that negates the need for an arbitrarily defined distance threshold. Using the pairwise patristic distance distributions of an input phylogeny, PhyCLIP parameterizes the intra and intercluster divergence limits as statistical bounds in an integer linear programming model which is subsequently optimized to cluster as many sequences as possible. When applied to the hemagglutinin phylogeny of HPAI H5Nx viruses, PhyCLIP was not only able to recapitulate the current WHO/OIE/FAO H5 nomenclature system but also further delineated informative higher resolution clusters that capture geographically distinct subpopulations of viruses. PhyCLIP is pathogen-agnostic and can be generalized to a wide variety of research questions concerning the identification of biologically informative clusters in pathogen phylogenies. PhyCLIP is freely available at http://github.com/alvinxhan/PhyCLIP, last accessed March 15, 2019.

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Physarum Powered Differentiable Linear Programming Layers and Applications.

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