  Neural networks embed the geometric structure of a data manifold lying in a
high-dimensional space into latent representations. Ideally, the distribution
of the data points in the latent space should depend only on the task, the
data, the loss, and other architecture-specific constraints. However, factors
such as the random weights initialization, training hyperparameters, or other
sources of randomness in the training phase may induce incoherent latent spaces
that hinder any form of reuse. Nevertheless, we empirically observe that, under
the same data and modeling choices, the angles between the encodings within
distinct latent spaces do not change. In this work, we propose the latent
similarity between each sample and a fixed set of anchors as an alternative
data representation, demonstrating that it can enforce the desired invariances
without any additional training. We show how neural architectures can leverage
these relative representations to guarantee, in practice, invariance to latent
isometries and rescalings, effectively enabling latent space communication:
from zero-shot model stitching to latent space comparison between diverse
settings. We extensively validate the generalization capability of our approach
on different datasets, spanning various modalities (images, text, graphs),
tasks (e.g., classification, reconstruction) and architectures (e.g., CNNs,
GCNs, transformers).
