Shrink the longest: improving latent space isotropy with symplicial geometry

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 language models. 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.

The more polypersonal the better -- a short look on space geometry of fine-tuned layers

The interpretation of deep learning models is a rapidly growing field, with particular interest in language models. There are various approaches to this task, including training simpler models to replicate neural network predictions and analyzing the latent space of the model. The latter method allows us to not only identify patterns in the model's decision-making process, but also understand the features of its internal structure. In this paper, we analyze the changes in the internal representation of the BERT model when it is trained with additional grammatical modules and data containing new grammatical structures (polypersonality). We find that adding a single grammatical layer causes the model to separate the new and old grammatical systems within itself, improving the overall performance on perplexity metrics.