Kaniadakis-driven beta-VAE Latent Spaces: Unveiling a "Relativistic" Topology for Breast Cancer Diagnosis

This work proposes a paradigm shift in the analysis of genomic data through the use of Variational Autoencoders (beta-VAE) based on Kaniadakis deformed statistics. Starting from the limitations of classical Shannon-Boltzmann statistics—which often fail to capture the out-of-equilibrium nature of tumor gene expression—we explored regularization regimes with beta parameters both higher and lower than unity to differentiate our approach from the classical VAE. While Tsallis statistics initially suggested increased latent resolution, its inherent numerical instability and sensitivity to gradients limited its practical efficacy. In contrast, the introduction of Kaniadakis kappa-statistics, characterized by a mathematical structure based on relativistic-derived hyperbolic symmetry, ensured exceptional stability and a sharp separation of diagnostic classes. Results obtained from real-world cancer data demonstrate that the Kaniadakis-driven model prevents latent space collapse even under high disentanglement pressure (beta=4), revealing a bimodal separation distributed across all latent neurons. This approach allows for the isolation of the pathological signal with surgical precision, treating cancer as a complex information system governed by non-extensive dynamics.