Revealing hidden patterns in deep neural network feature space continuum via manifold learning.

Deep neural networks (DNNs) extract thousands to millions of task-specific features during model training for inference and decision-making. While visualizing these features is critical for comprehending the learning process and improving the performance of the DNNs, existing visualization techniques work only for classification tasks. For regressions, the feature points lie on a high dimensional continuum having an inherently complex shape, making a meaningful visualization of the features intractable. Given that the majority of deep learning applications are regression-oriented, developing a conceptual framework and computational method to reliably visualize the regression features is of great significance. Here, we introduce a manifold discovery and analysis (MDA) method for DNN feature visualization, which involves learning the manifold topology associated with the output and target labels of a DNN. MDA leverages the acquired topological information to preserve the local geometry of the feature space manifold and provides insightful visualizations of the DNN features, highlighting the appropriateness, generalizability, and adversarial robustness of a DNN. The performance and advantages of the MDA approach compared to the existing methods are demonstrated in different deep learning applications.

Leveraging data-driven self-consistency for high-fidelity gene expression recovery.

Single cell RNA sequencing is a promising technique to determine the states of individual cells and classify novel cell subtypes. In current sequence data analysis, however, genes with low expressions are omitted, which leads to inaccurate gene counts and hinders downstream analysis. Recovering these omitted expression values presents a challenge because of the large size of the data. Here, we introduce a data-driven gene expression recovery framework, referred to as self-consistent expression recovery machine (SERM), to impute the missing expressions. Using a neural network, the technique first learns the underlying data distribution from a subset of the noisy data. It then recovers the overall expression data by imposing a self-consistency on the expression matrix, thus ensuring that the expression levels are similarly distributed in different parts of the matrix. We show that SERM improves the accuracy of gene imputation with orders of magnitude enhancement in computational efficiency in comparison to the state-of-the-art imputation techniques.