Rotary Positional Encodings (RoPE) are currently the most popular positional encodings used in modern language models. RoPE rotates two-dimensional chunks of query and key vectors, operating as a function of their relative positional offset. The position-wise rates of rotation in RoPE typically follow a geometric sequence specified by a fixed base-frequency hyperparameter. Prior work has improved performance by either increasing this parameter to slow rotation or by applying RoPE to only a subset of QK dimensions. In this work we modify RoPE by learning a scalar per frequency, treating frequencies as learnable parameters rather than hyperparameters. We validate Learned RoPE by training a ladder of language models from scratch, ranging from 52M to 2.5B parameters. We observe and analyze the emergence of a high-norm, positional LeRoPE band. LeRoPE consistently outperforms RoPE and partial RoPE across all scales, with RoPE requiring 3.4% more compute (FLOPs) to match LeRoPE at the largest scale.

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