Topological Parallax: A Geometric Specification for Deep Perception Models
This work addresses the problem of ensuring safety and robustness in AI systems by providing a theoretical framework for evaluating model-dataset geometric alignment, though it appears incremental as it builds on existing topological data analysis methods.
The authors introduced topological parallax as a tool to compare the geometric structure of trained deep learning models to reference datasets, proving that this similarity is essential for trustworthy interpolation and perturbation, and conjecturing it adds value to debates on overfitting and generalization.
For safety and robustness of AI systems, we introduce topological parallax as a theoretical and computational tool that compares a trained model to a reference dataset to determine whether they have similar multiscale geometric structure. Our proofs and examples show that this geometric similarity between dataset and model is essential to trustworthy interpolation and perturbation, and we conjecture that this new concept will add value to the current debate regarding the unclear relationship between overfitting and generalization in applications of deep-learning. In typical DNN applications, an explicit geometric description of the model is impossible, but parallax can estimate topological features (components, cycles, voids, etc.) in the model by examining the effect on the Rips complex of geodesic distortions using the reference dataset. Thus, parallax indicates whether the model shares similar multiscale geometric features with the dataset. Parallax presents theoretically via topological data analysis [TDA] as a bi-filtered persistence module, and the key properties of this module are stable under perturbation of the reference dataset.