Separators Make Carry Propagation Learnable:The Geometry of Latent Carry in a Multiplication Transformer
Transformers asked to multiply multi-digit numbers in a single forward pass often fail, and interpretability studies of pretrained language models find arithmetic solved by input-range heuristics rather than by an explicit carry. We train small Llama-style transformers from scratch on 4x4 multiplication without chain of thought and find that the input format is decisive: inserting a space token between digits raises exact-match accuracy from 1% to 89%. Output positions are learned in carry-chain order, with the middle digits, which have the longest-range dependencies, learned last. Inside the model, the separator token that predicts each digit (its prediction slot) encodes the carry-in as...
| Authors | Sama Satariyan, Raphael Cousin, G{é}rard Biau |
|---|---|
| Primary category | cs.LG |
| Published | 5 October 2026 |
| Last updated at source | 5 October 2026 |
Popularity, last 2 days
0 now. Counts as reported by the source, snapshotted daily by Silytics.
Silytics shows public metadata from arXiv and links to the original. Information may be incomplete or out of date. Last refreshed 17 October 2026. Licenses and terms of the original apply to the work itself. Not financial, legal or professional advice.