Copy-Paste Language Models

While large language models (LLMs) can solve advanced reasoning problems in seconds, we show that even frontier models fail to perform a much simpler operation: exactly copying an input string that lies well within their context windows. We attribute this failure to positional encodings in Transformer architectures, whose inductive bias favors copying through a shortcut based on matching local contexts rather than carefully locating the corresponding input positions. To address this issue, we introduce 2D-RoPE, which organizes text into a 2D grid rather than a 1D sequence and assigns each token a row ID and a column ID. Under this view, copying becomes simply retrieving input tokens at a fixed column offset, which makes the task easy to learn. In synthetic copy experiments, shallow Transformers with 2D-RoPE achieve perfect copying at input lengths hundreds of times longer than those seen during training, whereas standard positional encodings fall far behind. We further show that the advantage of 2D-RoPE language models on copy tasks consistently holds in large-scale pretraining on DCLM with model sizes up to 1.4B parameters. Overall, our results suggest that viewing text in 2D can benefit language modeling, and we hope this encourages future work to further explore the potential of 2D positional encodings.

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 saturation threshold, further repetitions leave the logits unchanged. If this threshold grows sublinearly with $N$, these models cannot both complete a long all-identical copy and stop correctly, a pattern resembling the termination errors of frontier LLMs. In synthetic copying experiments, baseline transformer models fail on long repeated strings even within the training range. Trained VO models, by contrast, generalize beyond the training lengths with near-perfect accuracy up to length $\approx 5005$, the selected primes' period product.

Large language models (LLMs) reliably perform entity copying, in which a model copies tokens referring to an entity, termed entity tokens, from the prompt into its output to answer a question. Although entity copying is straightforward for most LLMs, existing research does not provide a systematic account of which layers specialize in this fundamental task or how other tokens in the same sequence, termed context tokens, influence the model's ability to copy the entity tokens. To address these questions, we conduct experiments on Qwen3-8B using two novel methods: genie-in-a-bottle, which controls exactly which layers can participate in an entity-copying task, and attention lobotomy, which cuts off specific tokens' attention to entity tokens without affecting the remaining attention distribution. We find that two distinct groups of layers in the second half of the model are both necessary and sufficient for entity copying. Moreover, in addition to the decoding position's attention to entity tokens, context tokens' attention to entity tokens also proves necessary for copying the exact tokens, even though context tokens do not store entity information themselves unless they satisfy particular semantic properties. Our findings establish the critical role of late layers in entity copying under the guidance of context tokens, calling for future work on how models propagate and consume entity information.