Rotary Outliers and Rotary Offset Features in Large Language Models

Transformer-based Large Language Models (LLMs) rely on positional encodings to provide sequence position information to their attention mechanism. Rotary Positional Encodings (RoPE), which encode relative position by rotating queries and keys, have become widely used in modern LLMs. We study the features and patterns that emerge in queries and keys when using rotary embeddings. Our analysis reveals consistent patterns within the same model across layers and attention heads and across different models and architectures. We present and apply analysis techniques and show how the queries and keys use RoPE to construct various attention patterns, including attention sinks. We find and analyze outliers across models in queries and keys and find that they are likely to be found in rotary features with partial cycles. We derive bounds that tell us what rotary frequencies are likely to be selected as outlier features and at what minimum angle the query-key rotary pairs in these features tend to be above and verify the bounds empirically with models of significant architectural differences.