Heavy-Tailed Class-Conditional Priors for Long-Tailed Generative Modeling

2025/09/02 by Aymene Mohammed Bouayed, Samuel Deslauriers‐Gauthier, Bouayed, Aymene Mohammed +5
Computer Science · Social Sciences · #Adversarial Robustness in Machine Learning #Artificial Intelligence (cs.AI) #Computer Vision and Pattern Recognition (cs.CV) #Ethics and Social Impacts of AI #FOS: Computer and information sciences #Generative Adversarial Networks and Image Synthesis #Machine Learning (cs.LG) #Machine Learning (stat.ML)

paper · pdf · doi:10.48550/arxiv.2509.02154

openalex publication_date 2025/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Variational Autoencoders (VAEs) with global priors trained under an imbalanced empirical class distribution can lead to underrepresentation of tail classes in the latent space. While t³VAE improves robustness via heavy-tailed Student's t-distribution priors, its single global prior still allocates mass proportionally to class frequency. We address this latent geometric bias by introducing C-t³VAE, which assigns a per-class Student's t joint prior over latent and output variables. This design promotes uniform prior mass across class-conditioned components. To optimize our model we derive a closed-form objective from the γ-power divergence, and we introduce an equal-weight latent mixture for class-balanced generation. On SVHN-LT, CIFAR100-LT, and CelebA datasets, C-t³VAE consistently attains lower FID scores than t³VAE and Gaussian-based VAE baselines under severe class imbalance while remaining competitive in balanced or mildly imbalanced settings. In per-class F1 evaluations, our model outperforms the conditional Gaussian VAE across highly imbalanced settings. Moreover, we identify the mild imbalance threshold ρ< 5, for which Gaussian-based models remain competitive. However, for ρ≥ 5 our approach yields improved class-balanced generation and mode coverage.

Citations

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Related

• t³-Variational Autoencoder: Learning Heavy-tailed Data with Student's t and Power Divergence
• Symmetric Equilibrium Learning of VAEs
• Improving VAE generations of multimodal data through data-dependent conditional priors
• Soft-Constrained Optimization of Latent Space in Variational Autoencoders
• How to train your VAE