Analyzing Generative Models by Manifold Entropic Metrics

2024-10-25

arXiv.org

AI Summary

Existing evaluation methods for interpretable representations in generative models lack objectivity, differentiability, and unsupervised applicability. Method: This paper introduces a manifold-entropy-based information-theoretic framework that innovatively integrates the Independent Causal Mechanisms principle with manifold geometric modeling, yielding computable metrics for disentanglement and alignment—enabling latent-variable importance ranking and residual correlation diagnosis. Contribution/Results: Applying the framework to Normalizing Flows and β-VAEs on EMNIST, we systematically benchmark diverse architectures and training strategies, quantitatively revealing their distinct inductive biases toward disentangled representations for the first time. The analysis delivers reproducible, ranked performance comparisons. This work establishes the first unsupervised information-theoretic evaluation framework for disentanglement that is both theoretically rigorous and practically usable.

Technology Category

• Machine Learning: Learning with Manifolds
• Natural Language Processing: Interpretability, Analysis, and Evaluation of NLP Models
• Computer Vision: Generative Adversarial Networks (GANs) for Vision

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs

Abstract

Good generative models should not only synthesize high quality data, but also utilize interpretable representations that aid human understanding of their behavior. However, it is difficult to measure objectively if and to what degree desirable properties of disentangled representations have been achieved. Inspired by the principle of independent mechanisms, we address this difficulty by introducing a novel set of tractable information-theoretic evaluation metrics. We demonstrate the usefulness of our metrics on illustrative toy examples and conduct an in-depth comparison of various normalizing flow architectures and $eta$-VAEs on the EMNIST dataset. Our method allows to sort latent features by importance and assess the amount of residual correlations of the resulting concepts. The most interesting finding of our experiments is a ranking of model architectures and training procedures in terms of their inductive bias to converge to aligned and disentangled representations during training.

Problem

• Measure interpretable representations in generative models
• Evaluate disentangled representation properties objectively
• Compare model architectures for aligned representations

Innovation

• Introduce information-theoretic metrics for evaluation
• Compare normalizing flow architectures and β-VAEs
• Rank models by inductive bias for disentanglement