Papers › Algebraic Positional Encodings

Algebraic Positional Encodings

26 Dec 2023arXiv:2312.16045archive 2025-07-28

Konstantinos Kogkalidis, Jean-Philippe Bernardy, Vikas Garg

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 its desired structural properties. Our scheme can accommodate various structures, ncluding 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 hyper-parameter optimizations or "task search" of any kind. Code is available at https://github.com/konstantinosKokos/ape.

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