CvB: Conditioned Vector-Bundle Autoencoders with an Active Connection

Standard autoencoders learn decodable latent spaces, but do not explicitly distin- guish manifold location from local variation or specify how local features should be compared across locations. We introduce Conditioned Vector Bundle Networks (CvB), an autoencoder that organizes latent representations into base coordinates and base-conditioned fibers linked by learned linear transport. The model jointly optimizes reconstruction, fiber alignment, and transport composition consistency, with regularization that discourages base–fiber redundancy and fiber collapse. This construction provides an explicit mechanism for coordinating local features across the learned base. Across ten random seeds, CvB achieves mean adjusted Rand indices of 0.511 on MNIST and 0.405 on Fashion-MNIST, compared with 0.422 and 0.352 for autoencoders with matched latent dimensions. Controlled ablations identify fiber alignment as the principal contributor to these clustering gains. In a separate experiment using 4,000 MNIST training samples, CvB re- duces measured relative topological distortion from 140.58 to 26.28 compared with the matched autoencoder. Digit-label probes further show that identity is concentrated in the base: balanced prediction accuracy reaches 0.741 from base coordinates and 0.196 from fiber coordinates, whereas removing transport shifts identity information into the fiber. These results support learned fiber transport as an inductive bias for organizing decodable representations of manifold-structured data