The Infinity Mirror Test for Graph Models

Abstract

Graph models, like other machine learning models, have implicit and explicit biases built-in, which often impact performance in nontrivial ways. The model's faithfulness is often measured by comparing the newly generated graph against the source graph using any number or combination of graph properties. Differences in the size or topology of the generated graph therefore indicate a loss in the model. Yet, in many systems, errors encoded in loss functions are subtle and not well understood. In the present work, we introduce the Infinity Mirror test for analyzing the robustness of graph models. This straightforward stress test works by repeatedly fitting a model to its own outputs. A hypothetically perfect graph model would have no deviation from the source graph; however, the model's implicit biases and assumptions are exaggerated by the Infinity Mirror test, exposing potential issues that were previously obscured. Through an analysis of thousands of experiments on synthetic and real-world graphs, we show that several conventional graph models degenerate in exciting and informative ways. We believe that the observed degenerative patterns are clues to the future development of better graph models.Index termsgraph models, methodology, biases

Attributed Graph Modeling with Vertex Replacement Grammars

“…GNNs offer excellent modeling capacity in downstream machine learning tasks but can be difficult to train, have enormous parameter spaces, and do not readily permit human inspection. Despite performing well on link prediction and node classification tasks, some GNN architectures fail to preserve the topological fidelity of the input graphs [10]. AVRGs, on the other hand, can capture and model the subtle intricacies in both topological and attribute spaces without requiring supervision, deep neural architectures, and training.…”