{"ID":2875370,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.02154","arxiv_id":"2509.02154","title":"Heavy-Tailed Class-Conditional Priors for Long-Tailed Generative Modeling","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 $t^3$VAE 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-$t^3$VAE, 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-$t^3$VAE consistently attains lower FID scores than $t^3$VAE 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 $ρ\u003c 5$, for which Gaussian-based models remain competitive. However, for $ρ\\geq 5$ our approach yields improved class-balanced generation and mode coverage.","short_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 $t^3$VAE improves robustness via heavy-tailed Student's $t$-distribution priors, its single global prior still allocates mass proportiona...","url_abs":"https://arxiv.org/abs/2509.02154","url_pdf":"https://arxiv.org/pdf/2509.02154v2","authors":"[\"Aymene Mohammed Bouayed\",\"Samuel Deslauriers-Gauthier\",\"Adrian Iaccovelli\",\"David Naccache\"]","published":"2025-09-02T10:03:10Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\",\"cs.CV\",\"stat.ML\"]","methods":"[\"Variational Autoencoder\"]","has_code":false}