In this paper, I introduce the retrieval problem, a simple yet common reasoning task that can be solved only by transformers with a minimum number of layers, which grows logarithmically with the input size. I empirically show that large language models can solve the task under different prompting formulations without any fine-tuning. To understand how transformers solve the retrieval problem, I train several transformers on a minimal formulation. Successful learning occurs only under the presence of an implicit curriculum. I uncover the learned mechanisms by studying the attention maps in the trained transformers. I also study the training process, uncovering that attention heads always emerge in a specific sequence guided by the implicit curriculum.
@article{arxiv.2411.12118,
title = {Mechanism and Emergence of Stacked Attention Heads in Multi-Layer Transformers},
author = {Tiberiu Musat},
journal= {arXiv preprint arXiv:2411.12118},
year = {2025}
}