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 will be made available at
\url{github.com/konstantinosKokos/UnitaryPE}.

我们介绍了一种新颖的位置编码策略，用于 Transformer 风格模型，解决了现有方法的不足之处。我们的框架提供了一种灵活的映射，从一个领域的代数规范到正交操作符的解释。该设计保留了源域的代数特性，确保模型满足所需的结构属性。我们的方案可以适应各种结构，包括序列、网格和树形结构，以及它们的组合。我们进行了一系列实验证明我们方法的实际适用性。结果表明，在没有超参数优化或任何 “任务搜索” 的情况下，性能可以达到或超过当前的最新水平。代码将在 github.com/konstantinosKokos/UnitaryPE 上提供。