# Trace Reconstruction with Language Models

arXiv: https://arxiv.org/abs/2507.12927 · HTML: https://mlsanity.com/paper/2507.12927/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 30 references that are in the map.
- First posted on arXiv 17 Jul 2025.

## Builds on (most cited first, 3 of 3)

- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Optimal mean-based algorithms for trace reconstruction](https://mlsanity.com/paper/1612.03148/) (2016)
- [Single-Read Reconstruction for DNA Data Storage Using Transformers](https://mlsanity.com/paper/2109.05478/) (2021)

## Abstract (arXiv)

The general trace reconstruction problem seeks to recover an original sequence from its noisy copies independently corrupted by insertions, deletions, and substitutions. This problem arises in applications such as DNA data storage, a promising storage medium due to its high information density and longevity. However, errors introduced during DNA synthesis, storage, and sequencing require correction through algorithms and codes, with trace reconstruction often used as part of data retrieval. In this work, we propose TReconLM, a decoder-only transformer that solves trace reconstruction as a next-token prediction task. TReconLM outperforms state-of-the-art trace reconstruction algorithms, including prior deep-learning approaches, recovering a substantially higher fraction of sequences without error. We pretrain on synthetic data generated from a simple error model and fine-tune on real-world data to adapt to technology-specific error patterns. Code is available at https://github.com/MLI-lab/TReconLM.