Accumulated Transformations Improve LLM Length Extrapolation, Then Degrade.

This paper delves into the mechanisms behind the length extrapolation capabilities of Large Language Models (LLMs), particularly focusing on attention mechanisms that use accumulated transformations, such as PaTH Attention. The study explores why replacing position-indexed rotations with token-dependent accumulated rotations, even simpler SO(2) rotations, initially leads to strong extrapolation performance but eventually degrades at very long context lengths. The researchers provide a theoretical explanation, proving that accumulated orthogonal transformations, under certain regularity conditions, cause their products to become incoherent after a finite number of steps. This incoherence effectively suppresses attention to distant tokens, creating a "finite mixing window" that is independent of the overall context length. This allows per-token suppression learned during training to transfer to longer evaluation lengths, preserving the target signal for nearby tokens. However, a lower bound demonstrates that this approach must eventually degrade as the set of far tokens grows, indicating that without explicit control over "far-mass," the near signal cannot be perfectly preserved. Experiments support these findings, showing that random and learned accumulated rotations improve extrapolation over RoPE, but still degrade at extreme lengths, unlike ALiBi which maintains stability through explicit far-mass control.