Optimizing the Learnable RoPE Theta Parameter in Transformers

Rotary Position Embedding (RoPE) enhances Transformer models by encoding relative positions through a frequency parameter <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\theta $ </tex-math></inline-formula>, but conventional implementations fix <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\theta $ </tex-math></inline-formula>, constraining adaptability. We conduct the first systematic study of learnable RoPE <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\theta $ </tex-math></inline-formula>, introducing four optimization strategies—separate learning rates, layer-wise initialization, cosine annealing scheduling, and sigmoid-based constraints—to stabilize and refine positional learning. Our approach demonstrates modest but consistent benefits across multiple datasets including Tiny Shakespeare, WikiText-103, and IWSLT’14, achieving measurable gains in validation loss, perplexity, and BLEU scores relative to a fixed-<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\theta $ </tex-math></inline-formula> baseline while maintaining high inference throughput and requiring minimal architectural modifications. Ablation experiments quantify each strategy’s contribution and offer practical integration guidelines. This adaptive position encoding framework provides a foundation for large-scale pretraining and diverse sequence modeling applications.