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Standard softmax and cross-entropy have two numerical bugs, and the fix removes the Slingshot effect and stops students drifting from the teacher

AspireAI community · Google DeepMind (arXiv)
Google DeepMind's Jonathan Barron, Dan Gnanapragasam and Michael Tschannen document two real numerical bugs in the standard implementations of softmax, log-softmax and cross-entropy. The first, Softmax Collapse, rounds the target logit's gradient to zero when that logit is much larger than the others, so gradients no longer sum to zero. The second, Softmax Cancellation, occurs when student logits are close to teacher logits and produces non-zero gradients even when student and teacher logits are equal. The fix is a small change to how log-softmax, softmax and cross-entropy are implemented, and the reported effects are not cosmetic: it eliminates the previously observed Slingshot phenomenon, speeds up grokking with weight decay, prevents accuracy collapse without weight decay, and stops student networks drifting away from the teacher during distillation. The paper also shows that after memorisation, logit growth is bounded by an equilibrium between weight decay and Adam's epsilon. The limitation is that this is a numerical-correctness argument demonstrated on the authors' own experiments rather than a broad benchmark of production training runs.
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