Papers

Many physical phenomena are described by Hamiltonian mechanics using an energy function (Hamiltonian). Recently, the Hamiltonian neural network, which approximates the Hamiltonian by a neural network, and its extensions have attracted much attention. This is a very powerful method, but theoretical studies are limited. In this study, by combining the statistical learning theory and KAM theory, we provide a theoretical analysis of the behavior of Hamiltonian neural networks when the learning error is not completely zero. A Hamiltonian neural network with non-zero errors can be considered as a perturbation from the true dynamics, and the perturbation theory of the Hamilton equation is widely known as KAM theory. To apply KAM theory, we provide a generalization error bound for Hamiltonian neural networks by deriving an estimate of the covering number of the gradient of the multi-layer perceptron, which is the key ingredient of the model. This error bound gives an $L^\infty$ bound on the Hamiltonian that is required in the application of KAM theory.

poster session 5 @ blue 4, poster session 7 @ blue 4, oral session 7 @ blue 4, poster session 5, poster session 7, oral session 7

Mixed communities of organisms are found in many environments -- from the human gut to marine ecosystems -- and can have profound impact on human health and the environment. Metagenomics studies the genomic material of such communities through high-throughput sequencing that yields DNA subsequences for subsequent analysis. A fundamental problem in the standard workflow, called binning, is to discover clusters, of genomic subsequences, associated with the constituent organisms. Inherent noise in the subsequences, various biological constraints that need to be imposed on them and the skewed cluster size distribution exacerbate the difficulty of this unsupervised learning problem. In this paper, we present a new formulation using a graph where the nodes are subsequences and edges represent homophily information. In addition, we model biological constraints providing heterophilous signal about nodes that cannot be clustered together. We solve the binning problem by developing new algorithms for (i) graph representation learning that preserves both homophily relations and heterophily constraints (ii) constraint-based graph clustering method that addresses the problems of skewed cluster size distribution. Extensive experiments, on real and synthetic datasets, demonstrate that our approach, called RepBin, outperforms a wide variety of competing methods. Our constraint-based graph representation learning and clustering methods, that may be useful in other domains as well, advance the state-of-the-art in both metagenomics binning and graph representation learning.

poster session 5 @ blue 4, poster session 7 @ blue 4, oral session 7 @ blue 4, poster session 5, poster session 7, oral session 7

Single-cell RNA sequencing (scRNA-seq) provides high-throughput information about the genome-wide gene expression levels at the single-cell resolution, bringing a precise understanding on the transcriptome of individual cells. Unfortunately, the rapidly growing scRNA-seq data and the prevalence of dropout events pose substantial challenges for cell type annotation. Here, we propose a single-cell model-based deep graph embedding clustering (scTAG) method, which simultaneously learns cell–cell topology representations and identifies cell clusters based on deep graph convolutional network. scTAG integrates the zero-inflated negative binomial (ZINB) model into a topology adaptive graph convolutional autoencoder to learn the low-dimensional latent representation and adopts Kullback–Leibler (KL) divergence for the clustering tasks. By simultaneously optimizing the clustering loss, ZINB loss, and the cell graph reconstruction loss, scTAG jointly optimizes cluster label assignment and feature learning with the topological structures preserved in an end-to-end manner. Extensive experiments on 16 single-cell RNA-seq datasets from diverse yet representative single-cell sequencing platforms demonstrate the superiority of scTAG over various state-of-the-art clustering methods. The code is available at https://github.com/Philyzh8/scTAG.

poster session 5 @ blue 4, poster session 7 @ blue 4, oral session 7 @ blue 4, poster session 5, poster session 7, oral session 7