The rotation-based approach proposed in RoNet can be extended to handle more complex manifold structures beyond the circular manifold assumed in this work by incorporating advanced mathematical techniques and models. One way to extend the approach is to utilize non-linear transformations in higher-dimensional spaces. By employing techniques such as manifold learning, kernel methods, or deep neural networks, the rotation mechanism can be adapted to handle more intricate and non-linear manifold structures. These methods can help capture the underlying structure of the data distribution in a more comprehensive manner, allowing for more complex transformations and interpolations between domains.
Additionally, the rotation module can be enhanced to learn more sophisticated rotation planes that align with the specific characteristics of the data distribution. By incorporating adaptive mechanisms that dynamically adjust the rotation plane based on the data distribution, the approach can effectively handle diverse and complex manifold structures. Techniques such as attention mechanisms, reinforcement learning, or hierarchical modeling can be integrated to improve the flexibility and adaptability of the rotation-based approach in capturing complex manifold structures.