As artificial intelligence models have exploded in scale and capability, understanding of their internal mechanisms remains a critical challenge. Inspired by the success of dynamical systems approaches in neuroscience, here we propose a novel framework for studying computations in deep learning systems. We focus on the residual stream (RS) in transformer models, conceptualizing it as a dynamical system evolving across layers. We find that activations of individual RS units exhibit strong continuity across layers, despite the RS being a non-privileged basis. Activations in the RS accelerate and grow denser over layers, while individual units trace unstable periodic orbits. In reduced-dimensional spaces, the RS follows a curved trajectory with attractor-like dynamics in the lower layers. These insights bridge dynamical systems theory and mechanistic interpretability, establishing a foundation for a "neuroscience of AI" that combines theoretical rigor with large-scale data analysis to advance our understanding of modern neural networks.
View on arXiv@article{fernando2025_2502.12131,
title={ Transformer Dynamics: A neuroscientific approach to interpretability of large language models },
author={ Jesseba Fernando and Grigori Guitchounts },
journal={arXiv preprint arXiv:2502.12131},
year={ 2025 }
}