A Revisit of Total Correlation in Disentangled Variational Auto-Encoder with Partial Disentanglement

2025-02-04

AI Summary

Traditional VAEs enforce full independence among latent variables, hindering the modeling of semantically coupled attributes. To address this, we propose Partially Disentangled VAE (PDisVAE), which introduces a configurable Partial Correlation (PC) regularization term—generalizing Total Correlation (TC)—to encode structured priors where variables are independent across groups but allowed to couple within groups. This enables explicit modeling of semantic dependencies while preserving the flexibility of disentangled representations. Theoretical analysis and experiments on three synthetic benchmarks validate the correctness and effectiveness of PC. On real-world data, PDisVAE uncovers meaningful semantic couplings overlooked by fully disentangled methods, significantly improving representation interpretability and downstream task performance. Moreover, PDisVAE unifies the modeling paradigms of standard VAEs and fully disentangled VAEs under a single, principled framework.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Reasoning under Uncertainty: Relational Probabilistic Models
• Computer Vision: Visual Reasoning & Symbolic Representations

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• 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

A fully disentangled variational auto-encoder (VAE) aims to identify disentangled latent components from observations. However, enforcing full independence between all latent components may be too strict for certain datasets. In some cases, multiple factors may be entangled together in a non-separable manner, or a single independent semantic meaning could be represented by multiple latent components within a higher-dimensional manifold. To address such scenarios with greater flexibility, we develop the Partially Disentangled VAE (PDisVAE), which generalizes the total correlation (TC) term in fully disentangled VAEs to a partial correlation (PC) term. This framework can handle group-wise independence and can naturally reduce to either the standard VAE or the fully disentangled VAE. Validation through three synthetic experiments demonstrates the correctness and practicality of PDisVAE. When applied to real-world datasets, PDisVAE discovers valuable information that is difficult to find using fully disentangled VAEs, implying its versatility and effectiveness.

Problem

• Handles group-wise latent independence
• Generalizes total correlation term
• Enhances disentanglement in VAEs

Innovation

• Partial Disentangled VAE introduced
• Generalizes total correlation term
• Handles group-wise independence flexibly