Train to Stitch: Topology-Preserving Regularization for Interoperable Representations

As large, powerful pre-trained models become more prevalent, there is growing interest in developing methods that allow different neural networks to be seamlessly combined with little or no direct communication between them. Take autoencoder-based data compression as an example: the ability to independently choose architectures and train encoder and decoder models, while still ensuring they work together, could fundamentally transform how such models are built, deployed, and updated. In this work, we introduce a novel approach that leverages topological regularization to align the latent spaces of two independently trained autoencoder models, entirely eliminating the need for coordination during training. We provide a conditional theoretical analysis showing how the structural agreement encouraged by our regularizer can translate into approximate geometric compatibility between independently learned representations. Reconstruction experiments validate this approach empirically, substantially narrowing the interoperability gap across multiple datasets.