Sheaf Neural Networks NeurIPS 2020 Workshop on Topological Data Analysis and Beyond
We present a generalization of graph convolutional networks by generalizing the diffusion operation using the sheaf Laplacian.
The Emergence of Higher-Order Structure in Scientific and Technological Knowledge Networks arXiv preprint arXiv:2009.13620
We use tools from algebraic topology to characterize the higher-order structure of knowledge networks in science and technology across scale and time.
Applying SVM algorithms toward predicting host–guest interactions with cucurbituril Physical Chemistry Chemical Physics
DFT, NMR, ITC, and cell confluence data are used to generate predictive algorithms of supramolecular binding to cucurbituril and experimentally validate these predictions.
Path Homologies of Deep Feedforward Networks Proceedings of the 18th IEEE International Conference on Machine Learning and Applications (ICMLA)
We characterize two types directed homology–path homology and directed rips homology–with respect to feedforward neural networks’ parameter connectivity.
Characterizing the Shape of Activation Space in Deep Neural Networks Proceedings of the 18th IEEE International Conference on Machine Learning and Applications (ICMLA)
A method for computing persistent homology of activation space within neural networks. We also provide some empirical results about how this topological perspective can inform us about how neural networks process inputs.
Adversary Detection in Neural Networks via Persistent Homology arXiv preprint arXiv:1711.10056
We show that a multi-scale analysis of neural network activations is able to capture the existence of adversarial inputs within neural networks.
PCA, Dimensionality, and NSD
Presented (virtually) at the NSD Mini Conference August 2020.
Path Homologies of Deep Networks
Presented at ICMLA 2019.
Analyzing Deep Neural Networks with Persistent Homology
Presented at GTDAML 2019.