The Edge of Orthogonality: A Simple View of What Makes BYOL Tick
This work provides theoretical insights into a key problem in unsupervised learning for researchers, though it is incremental as it builds on existing methods.
The authors tackled the problem of explaining why self-predictive unsupervised learning methods like BYOL avoid collapse, using simple linear algebra to show that the optimal linear predictor is near-orthogonal, and proposed closed-form predictor variants that outperform standard BYOL with top-1 linear accuracy on ImageNet at 100 and 300 epochs.
Self-predictive unsupervised learning methods such as BYOL or SimSiam have shown impressive results, and counter-intuitively, do not collapse to trivial representations. In this work, we aim at exploring the simplest possible mathematical arguments towards explaining the underlying mechanisms behind self-predictive unsupervised learning. We start with the observation that those methods crucially rely on the presence of a predictor network (and stop-gradient). With simple linear algebra, we show that when using a linear predictor, the optimal predictor is close to an orthogonal projection, and propose a general framework based on orthonormalization that enables to interpret and give intuition on why BYOL works. In addition, this framework demonstrates the crucial role of the exponential moving average and stop-gradient operator in BYOL as an efficient orthonormalization mechanism. We use these insights to propose four new \emph{closed-form predictor} variants of BYOL to support our analysis. Our closed-form predictors outperform standard linear trainable predictor BYOL at $100$ and $300$ epochs (top-$1$ linear accuracy on ImageNet).