# Structure Development in List-Sorting Transformers

arXiv: https://arxiv.org/abs/2501.18666 · HTML: https://mlsanity.com/paper/2501.18666/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jan 2025.

## Built on by (most cited first, 4 of 4)

- [The Loss Kernel: A Geometric Probe for Deep Learning Interpretability](https://mlsanity.com/paper/2509.26537/) (2025)
- [Influence Dynamics and Stagewise Data Attribution](https://mlsanity.com/paper/2510.12071/) (2025)
- [Compressibility Measures Complexity: Minimum Description Length Meets Singular Learning Theory](https://mlsanity.com/paper/2510.12077/) (2025)
- [Modes of Sequence Models and Learning Coefficients](https://mlsanity.com/paper/2504.18048/) (2025)

## Abstract (arXiv)

We study how a one-layer attention-only transformer develops relevant structures while learning to sort lists of numbers. At the end of training, the model organizes its attention heads in two main modes that we refer to as vocabulary-splitting and copy-suppression. Both represent simpler modes than having multiple heads handle overlapping ranges of numbers. Interestingly, vocabulary-splitting is present regardless of whether we use weight decay, a common regularization technique thought to drive simplification, supporting the thesis that neural networks naturally prefer simpler solutions. We relate copy-suppression to a mechanism in GPT-2 and investigate its functional role in our model. Guided by insights from a developmental analysis of the model, we identify features in the training data that drive the model's final acquired solution. This provides a concrete example of how the training data shape the internal organization of transformers, paving the way for future studies that could help us better understand how LLMs develop their internal structures.