Relative representations for cognitive graphs

Although the latent spaces learned by distinct neural networks are not generally directly comparable, recent work in machine learning has shown that it is possible to use the similarities and differences among latent space vectors to derive "relative representations" with comparable representational power to their "absolute" counterparts, and which are nearly identical across models trained on similar data distributions. Apart from their intrinsic interest in revealing the underlying structure of learned latent spaces, relative representations are useful to compare representations across networks as a generic proxy for convergence, and for zero-shot model stitching. In this work we examine an extension of relative representations to discrete state-space models, using Clone-Structured Cognitive Graphs (CSCGs) for 2D spatial localization and navigation as a test case. Our work shows that the probability vectors computed during message passing can be used to define relative representations on CSCGs, enabling effective communication across agents trained using different random initializations and training sequences, and on only partially similar spaces. We introduce a technique for zero-shot model stitching that can be applied post hoc, without the need for using relative representations during training. This exploratory work is intended as a proof-of-concept for the application of relative representations to the study of cognitive maps in neuroscience and AI.