Algebraic Positional Encodings

Konstantinos Kogkalidis, Jean-Philippe Bernardy, Vikas Garg

Keywords: positional encodings, transformers, structured attention, group theory

TL;DR: Positional encodings as group homomorphisms: it's beautiful and it works.

Abstract: We introduce a novel positional encoding strategy for Transformer-style models, addressing the shortcomings of existing, often ad hoc, approaches. Our framework provides a flexible mapping from the algebraic specification of a domain to an interpretation as orthogonal operators. This design preserves the algebraic characteristics of the source domain, ensuring that the model upholds the desired structural properties. Our scheme can accommodate various structures, including sequences, grids and trees, as well as their compositions. We conduct a series of experiments to demonstrate the practical applicability of our approach. Results suggest performance on par with or surpassing the current state-of-the-art, without hyperparameter optimizations or ``task search'' of any kind. Code is available through https://aalto-quml.github.io/ape/.

Primary Area: Deep learning architectures

Submission Number: 3373