Copying Under Repetition: From Prefix Matching to Position Hashing

Anxin Guo, Tianlong Huang, Chenxiao Yang, Zhiyuan Li

Frontier LLMs can copy random text almost flawlessly, yet they often overrun or truncate long blocks of repeated characters. In repeated strings, matching local content no longer reliably identifies where copying should continue or when it should stop. Nevertheless, we show that a two-layer transformer with $O(\log\log N)$-bit precision and $O(\log N/\log\log N)$ width can copy every string up to a chosen design horizon $N$ and terminate correctly under arbitrary repetition. We use RoPE-style rotations of attention values and outputs (VO-rotations) with small prime periods to encode distances from delimiter anchors modulo those primes. By the Chinese Remainder Theorem, these periodic encodings jointly distinguish all required distances, allowing one retrieval rule to select either the next source token or the end marker. In contrast, we prove a width-independent impossibility result for copying under sequential finite-precision softmax accumulation. It applies to transformers whose only positional input is an additive attention bias that eventually becomes constant, including NoPE and a recursive implementation of ALiBi. Once an identical-token run exceeds the resulting…