Unification of Symmetries Inside Neural Networks: Transformer, Feedforward and Neural ODE
This work offers a foundational physics-based framework for analyzing neural network architectures, potentially benefiting researchers in machine learning and theoretical physics.
The study tackled the challenge of understanding neural networks by applying gauge symmetries from physics to interpret parametric redundancies in models like neural ODEs, feedforward networks, and transformers, revealing connections to spacetime diffeomorphisms and providing a unifying perspective.
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.