Shrink the longest: improving latent space isotropy with symplicial geometry

Abstract: Although transformer-based models have been dominating the field of deep learning, various studies of their embedding space have shown that they suffer from "representation degeneration problem": embeddings tend to be distributed in a narrow cone, making the latent space highly anisotropic. Increasing the isotropy has shown to improve performance in downstream tasks both in static and contextual LLMs. However, most of approaches either add inference overhead or require substantial amount of data for model reparametrization. We propose a novel regularization technique based on simplicial geometry to improve the isotropy of latent representations. The core idea of our method is based on maximizing the persistent entropy of barcodes obtained using Vietoris-Rips filtration from contextual embeddings in the underlying latent space. We demonstrate that the method leads to an increase in downstream performance while significantly lowering the anisotropy during fine-tuning by exploiting existing geometric structures instead of reparametrization.