Hyperbolic Prototype-Residual Autoencoder for Interpretable Generative Latent Organization.

Interpretable organization of latent spaces remains a central challenge in generative modeling. Most generative models rely on continuous latent variables, but the learned space often lacks an explicit structure that explains how samples are organized or how semantic variation can be controlled. This paper proposes a hyperbolic prototype-residual autoencoder that organizes generative latent representations using a fixed prototype tree embedded in the Poincaré ball. Each encoded sample is assigned to a prototype by hyperbolic distance, and the decoder reconstructs or generates images from a prototype-residual representation. The prototype serves as a semantic anchor, while the residual captures local instance-level variation around the selected prototype. The framework combines prototype semantic learning, MMD-based latent spreading, and structural regularizers to align encoder-decoder behavior with the predefined hyperbolic hierarchy. Prototype semantic learning encourages fixed prototypes to decode into representative visual anchors, while MMD encourages encoded samples to occupy broad regions of the hyperbolic latent space. Experiments on MNIST and CelebA show interpretable coarse-to-fine behavior through radial decoding and prototype decoding, suggesting that fixed hyperbolic prototype trees provide an effective scaffold for prototype-guided image reconstruction and generation.