Temporal Geometry of Deep Networks: Hyperbolic Representations of Training Dynamics for Intrinsic Explainability

Ambarish Moharil

Intrinsic explainability remains a challenging problem, particularly in contexts where multilayer perceptrons (MLPs) require dynamic re-training within an optimization environment. This paper investigates how MLPs and their training dynamics can be represented and studied in non-Euclidean spaces; our representation features the Poincaré model of hyperbolic geometry. We aim to capture the geometric evolution of their weighted topology and self-organization over time. Instead of restricting the analysis to single checkpoints---as per established measure-based explainability methods---we construct temporal \textit{parameter graphs}, i.e., snapshots over time $T$ steps of the optimization/training process for MLPs. This reflects the view that neural networks encode information not only in their weights but also in the trajectory traced during training. Drawing on the idea that many complex networks admit embeddings in hidden metric spaces where distances correspond to connection likelihood, we present a geometric and temporal graph-based metalearning framework for obtaining dynamic hyperbolic representations of the underlying neural parameter graphs. Our model embeds temporal…