# Mapping the Edge of Chaos: Fractal-Like Boundaries in The Trainability of Decoder-Only Transformer Models

arXiv: https://arxiv.org/abs/2501.04286 · HTML: https://mlsanity.com/paper/2501.04286/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 13 references that are in the map.
- First posted on arXiv 8 Jan 2025.

## Builds on (most cited first, 5 of 5)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Large Batch Optimization for Deep Learning: Training BERT in 76 minutes](https://mlsanity.com/paper/1904.00962/) (2019)
- [The boundary of neural network trainability is fractal](https://mlsanity.com/paper/2402.06184/) (2024)

## Built on by (most cited first, 1 of 1)

- [Revisiting Deep Information Propagation: Fractal Frontier and Finite-size Effects](https://mlsanity.com/paper/2508.03222/) (2025)

## Abstract (arXiv)

In the realm of fractal geometry, intricate structures emerge from simple iterative processes that partition parameter spaces into regions of stability and instability. Likewise, training large language models involves iteratively applying update functions, such as Adam, where even slight hyperparameter adjustments can shift the training process from convergence to divergence. Recent evidence from miniature neural networks suggests that the boundary separating these outcomes displays fractal characteristics. Building on these insights, this study extends them to medium-sized, decoder-only transformer architectures by employing a more consistent convergence measure and examining the learning rate hyperparameter landscape for attention and fully connected layers. The results show that the trainability frontier is not a simple threshold; rather, it forms a self-similar yet seemingly random structure at multiple scales, with statistically consistent and repeating patterns. Within this landscape, a region of stable convergence is surrounded by a complex chaotic border, illustrating the sensitive nature of the underlying training dynamics.