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About this paper
Jonathan T. Barron, Dan Gnanapragasam, Michael Tschannen
Authors rewrite softmax, log-softmax, and cross-entropy to preserve gradients lost at high confidence or when student and teacher outputs nearly match, addressing Softmax Collapse and Softmax Cancellation without higher-precision casting. In an fp32 grokking experiment, test accuracy fell from 61% to 23% with standard cross-entropy, while fixed cross-entropy reached 85%; these results are specific, and studied extremes are uncommon in large-scale training.
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