  The emergence of similar representations between independently trained neural
models has sparked significant interest in the representation learning
community, leading to the development of various methods to obtain
communication between latent spaces. "Latent space communication" can be
achieved in two ways: i) by independently mapping the original spaces to a
shared or relative one; ii) by directly estimating a transformation from a
source latent space to a target one. In this work, we combine the two into a
novel method to obtain latent space translation through the relative space. By
formalizing the invertibility of angle-preserving relative representations and
assuming the scale invariance of decoder modules in neural models, we can
effectively use the relative space as an intermediary, independently projecting
onto and from other semantically similar spaces. Extensive experiments over
various architectures and datasets validate our scale invariance assumption and
demonstrate the high accuracy of our method in latent space translation. We
also apply our method to zero-shot stitching between arbitrary pre-trained text
and image encoders and their classifiers, even across modalities. Our method
has significant potential for facilitating the reuse of models in a practical
manner via compositionality.
