Motivated by deep learning regimes with multiple interacting yet distinct model components, we introduce learning diagrams, graphical depictions of training setups that capture parameterized learning as data rather than code. A learning diagram compiles to a unique loss function on which component models are trained. The result of training on this loss is a collection of models whose predictions ``agree" with one another. We show that a number of popular learning setups such as few-shot multi-task learning, knowledge distillation, and multi-modal learning can be depicted as learning diagrams. We further implement learning diagrams in a library that allows users to build diagrams of PyTorch and Flux.jl models. By implementing some classic machine learning use cases, we demonstrate how learning diagrams allow practitioners to build complicated models as compositions of smaller components, identify relationships between workflows, and manipulate models during or after training. Leveraging a category theoretic framework, we introduce a rigorous semantics for learning diagrams that puts such operations on a firm mathematical foundation.

Spectral partitioning (clustering) algorithms use eigenvectors to solve network analysis problems. The relationship between numerical accuracy and network mining quality is insufficiently understood. We show that analyzing numerical accuracy and network mining quality together leads to an algorithmic improvement. Specifically, we study spectral partitioning using sweep cuts of approximate eigenvectors of the normalized graph Laplacian. We introduce a novel, theoretically sound, parameter free stopping criterion for iterative eigensolvers designed for graph partitioning. On a corpus of social networks, we validate this stopping criterion by showing the number of iterations is reduced by a factor of 4.15 on average, and the conductance is increased by only a factor of 1.24 on average. Regression analysis of these results shows that the decrease in the number of iterations needed is greater for problems with a small spectral gap, thus our stopping criterion helps more on harder problems. Experiments show that alternative stopping criteria are insufficient to ensure low conductance partitioning on real world networks. While our method guarantees partitions that satisfy the Cheeger Inequality, we find that it typically beats this guarantee on real world graphs.

In this work we present a new local, vertex-level measure of community change. Our measure detects vertices that change community membership due to the actions (edges) of a vertex itself and not only due to global community shifts. The local nature of our measure is important for analyzing real graphs because communities may change to a large degree from one snapshot in time to the next. Using both real and synthetic graphs, we compare our measure to an alternative, global approach. Both approaches detect community switching vertices in a synthetic example with little overall community change. However, when communities do not evolve smoothly over time, the global approach flags a very large number of vertices, while our local method does not.

In this paper we propose a new methodology for gaining insight into the temporal aspects of social networks. In order to develop higher-level, large-scale data analysis methods for classification, prediction, and anomaly detection, a solid foundation of analytical techniques is required. We present a novel approach to the analysis of these networks that leverages time series and statistical techniques to quantitatively describe the temporal nature of a social network. We report on the application of our approach toward a real data set and successfully visualize high-level changes to the network as well as discover outlying vertices.