Optimizing Latent Dimension Allocation in Hierarchical VAEs: Balancing Attenuation and Information Retention for OOD Detection

Out-of-distribution (OOD) detection is a critical task in machine learning, particularly for safety-critical applications where unexpected inputs must be reliably flagged. While hierarchical variational autoencoders (HVAEs) offer improved representational capacity over traditional VAEs, their performance is highly sensitive to how latent dimensions are distributed across layers. Existing approaches often allocate latent capacity arbitrarily, leading to ineffective representations or posterior collapse. In this work, we introduce a theoretically grounded framework for optimizing latent dimension allocation in HVAEs, drawing on principles from information theory to formalize the trade-off between information loss and representational attenuation. We prove the existence of an optimal allocation ratio $r^{\ast}$ under a fixed latent budget, and empirically show that tuning this ratio consistently improves OOD detection performance across datasets and architectures. Our approach outperforms baseline HVAE configurations and provides practical guidance for principled latent structure design, leading to more robust OOD detection with deep generative models.