Unification of Symmetries Inside Neural Networks: Transformer,
  Feedforward and Neural ODE
Koji Hashimoto Yuji Hirono Akiyoshi Sannai
Understanding the inner workings of neural networks, including transformers,
remains one of the most challenging puzzles in machine learning. This study
introduces a novel approach by applying the principles of gauge symmetries, a
key concept in physics, to neural network architectures. By regarding model
functions as physical observables, we find that parametric redundancies of
various machine learning models can be interpreted as gauge symmetries. We
mathematically formulate the parametric redundancies in neural ODEs, and find
that their gauge symmetries are given by spacetime diffeomorphisms, which play
a fundamental role in Einstein's theory of gravity. Viewing neural ODEs as a
continuum version of feedforward neural networks, we show that the parametric
redundancies in feedforward neural networks are indeed lifted to
diffeomorphisms in neural ODEs. We further extend our analysis to transformer
models, finding natural correspondences with neural ODEs and their gauge
symmetries. The concept of gauge symmetries sheds light on the complex behavior
of deep learning models through physics and provides us with a unifying
perspective for analyzing various machine learning architectures.