On The Local Geometry of Deep Generative Manifolds

Ahmed Imtiaz Humayun, Ibtihel Amara, Candice Schumann, Golnoosh Farnadi, Negar Rostamzadeh, Mohammad Havaei

Track: Extended abstract

Keywords: Local Geometry, Manifold of Foundation Models, Diversity, Self Assessment

TL;DR: Analyze geometric descriptors to understand the uncertainty, dimensionality, and smoothness of learned data manifolds revealing insights into generative models and their output quality.

Abstract: In this paper, we study theoretically inspired local geometric descriptors of the data manifolds approximated by pre-trained generative models. The descriptors – local scaling (ψ), local rank (ν), and local complexity (δ) — characterize the uncertainty, dimensionality, and smoothness on the learned manifold, using only the network weights and architecture. We investigate and emphasize their critical role in understanding generative models. Our analysis reveals that the local geometry is intricately linked to the quality and diversity of generated outputs. Additionally, we see that the geometric properties are distinct for out-of-distribution (OOD) inputs as well as for prompts memorized by Stable Diffusion, showing the possible application of our proposed descriptors for downstream detection and assessment of pre-trained generative models.

Submission Number: 98