The Standard Deviation in VICReg Buys a Safety Margin

Overview & Synopsis

VICReg prevents collapse with a hinge on the standard deviation of each embedding dimension, and its authors argue from the gradient that a hinge on the variance would fail. To our knowledge, this claim has not been tested experimentally. We test it in a controlled setting (ResNet-18, CIFAR-10 and CIFAR-100), changing only the hinge and sweeping its weight $μ$ over five orders of magnitude. At the default weight ($μ= 1$), the two hinges reach the same linear-probe accuracy on CIFAR-10 (about 89.5%). Both collapse below a threshold weight, but the standard-deviation hinge's threshold is 35-130$\times$ lower. CIFAR-100 shows a consistent gap. In training, the variance hinge's gradient fades as the feature variance shrinks, while the standard-deviation hinge's does not until that variance is very small. The standard-deviation hinge therefore buys a safety margin: it keeps training at weights far below the point where the variance hinge collapses.