  The exponential moving average (EMA) is a commonly used statistic for
providing stable estimates of stochastic quantities in deep learning
optimization. Recently, EMA has seen considerable use in generative models,
where it is computed with respect to the model weights, and significantly
improves the stability of the inference model during and after training. While
the practice of weight averaging at the end of training is well-studied and
known to improve estimates of local optima, the benefits of EMA over the course
of training is less understood. In this paper, we derive an explicit connection
between EMA and a damped harmonic system between two particles, where one
particle (the EMA weights) is drawn to the other (the model weights) via an
idealized zero-length spring. We then leverage this physical analogy to analyze
the effectiveness of EMA, and propose an improved training algorithm, which we
call BELAY. Finally, we demonstrate theoretically and empirically several
advantages enjoyed by BELAY over standard EMA.
