The assumptions about the relationship between local and global image semantics could be relaxed or improved by incorporating more advanced splitting functions that can better capture the complex structures present in images. One approach could involve leveraging object detection or semantic segmentation techniques to identify and split images based on meaningful objects or regions rather than simple patch-based splitting. This would allow for a more accurate representation of the visual content and ensure that important semantic elements are not divided across multiple patches. Additionally, exploring non-linear relationships between local and global semantics could provide a more nuanced understanding of how different parts of an image contribute to the overall meaning.