Algebraic Positional Encodings
This addresses the need for more principled positional encodings in AI models, offering a flexible solution for various domains, though it appears incremental in improving existing approaches.
The paper tackles the problem of positional encoding in Transformer models by introducing a novel algebraic framework that maps domain specifications to orthogonal operators, preserving structural properties across sequences, grids, and trees. Results show performance on par with or surpassing state-of-the-art methods without hyperparameter optimization.
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.