In probabilistic contrastive learning, a shared temperature is commonly interpreted as a shared similarity scale, but this interpretation does not hold for high-dimensional distributional class representations. We study the exact von Mises-Fisher (vMF) probabilistic score used by ProCo when representation dimension and …
How accurate must a numerical approximation be within a learning system? Primitive error alone cannot answer this question: errors of the same magnitude can have very different consequences for losses, predictions, and gradients at different learning states. We study this question through the learning objective itself. …
Differentiable learning typically assumes that the scalar objective evaluated in the forward pass and the gradient supplied to the optimizer in the backward pass describe the same mathematical object. We show that this correspondence can fail when probabilistic objectives rely on finite special-function recurrences, cu …