Exploring the impact of fixed theta values in RoPE on character-level language model performance and efficiency

Rotary Positional Embedding (RoPE) is a widely used technique in Transformers, influenced by the hyperparameter theta (θ). However, the impact of varying *fixed* theta values, especially the trade-off between performance and efficiency on tasks like character-level modeling, remains under-explored. This paper presents a systematic evaluation of RoPE with fixed theta values (ranging from 500 to 50,000) on a character-level GPT model across three datasets: Tiny Shakespeare, Enwik8, and Text8, compared against the standard θ = 10, 000 baseline. However, all non-default theta configurations incur significant computational overhead: inference speed is approximately halved across all datasets, suggesting implementation—specific bottlenecks rather than theta—dependent costs. This study quantifies a critical performance—efficiency trade-off when tuning fixed RoPE theta. Our findings emphasize the practical need to balance generalization gains with computational budgets during model development and deployment, contributing empirical insights into RoPE hyperparameter sensitivity and demonstrating that optimal theta selection is highly dataset-dependent. These insights suggest that future positional encoding designs could benefit from adaptive θ scheduling or dataset-specific θ optimization strategies to maximize both performance and computational efficiency.