Matt Thomson

Xiaoqiao Chen, Sisi Chen, Matt Thomson

Sequencing costs currently prohibit the application of single-cell mRNA-seq to many biological and clinical analyses. Targeted single-cell mRNA-sequencing reduces sequencing costs by profiling reduced gene sets that capture biological information with a minimal number of genes. Here, we introduce an active learning method (ActiveSVM) that identifies minimal but highly-informative gene sets that enable the identification of cell-types, physiological states, and genetic perturbations in single-cell data using a small number of genes. Our active feature selection procedure generates minimal gene sets from single-cell data through an iterative cell-type classification task where misclassified cells are examined at each round of analysis to identify maximally informative genes through an `active' support vector machine (ActiveSVM) classifier. By focusing computational resources on misclassified cells, ActiveSVM scales to analyze data sets with over a million single cells. We demonstrate that ActiveSVM feature selection identifies gene sets that enable ~90% cell-type classification accuracy across a variety of data sets including cell atlas and disease characterization data sets. The method generalizes to reveal genes that respond to genetic perturbations and to identify region specific gene expression patterns in spatial transcriptomics data. The discovery of small but highly informative gene sets should enable substantial reductions in the number of measurements necessary for application of single-cell mRNA-seq to clinical tests, therapeutic discovery, and genetic screens.

Guruprasad Raghavan, Matt Thomson

The geometry of weight spaces and functional manifolds of neural networks play an important role towards 'understanding' the intricacies of ML. In this paper, we attempt to solve certain open questions in ML, by viewing them through the lens of geometry, ultimately relating it to the discovery of points or paths of equivalent function in these spaces. We propose a mathematical framework to evaluate geodesics in the functional space, to find high-performance paths from a dense network to its sparser counterpart. Our results are obtained on VGG-11 trained on CIFAR-10 and MLP's trained on MNIST. Broadly, we demonstrate that the framework is general, and can be applied to a wide variety of problems, ranging from sparsification to alleviating catastrophic forgetting.

Guruprasad Raghavan, Jiayi Li, Matt Thomson

Biological neural networks have evolved to maintain performance despite significant circuit damage. To survive damage, biological network architectures have both intrinsic resilience to component loss and also activate recovery programs that adjust network weights through plasticity to stabilize performance. Despite the importance of resilience in technology applications, the resilience of artificial neural networks is poorly understood, and autonomous recovery algorithms have yet to be developed. In this paper, we establish a mathematical framework to analyze the resilience of artificial neural networks through the lens of differential geometry. Our geometric language provides natural algorithms that identify local vulnerabilities in trained networks as well as recovery algorithms that dynamically adjust networks to compensate for damage. We reveal striking vulnerabilities in commonly used image analysis networks, like MLP's and CNN's trained on MNIST and CIFAR10 respectively. We also uncover high-performance recovery paths that enable the same networks to dynamically re-adjust their parameters to compensate for damage. Broadly, our work provides procedures that endow artificial systems with resilience and rapid-recovery routines to enhance their integration with IoT devices as well as enable their deployment for critical applications.