LieRE: Generalizing Rotary Position Encodings

While Rotary Position Embeddings (RoPE) for natural language performs well and has become widely adopted, its adoption for other modalities has been slower. Here, we introduce Lie group Relative position Encodings (LieRE) that goes beyond RoPE in supporting higher dimensional inputs. We evaluate the performance of LieRE on 2D and 3D image classification tasks and observe that LieRE leads to marked improvements in performance (up to 6 efficiency (3.5x reduction), data efficiency (30 RoFormer, DeiT III, RoPE-Mixed and Vision-Llama