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The success of the Adam optimizer on a wide array of architectures has madeit the default in settings where stochastic gradient descent (SGD) performspoorly. However, our theoretical understanding of this discrepancy is lagging,preventing the development of significant improvements on either algorithm.Recent work advances the hypothesis that Adam and other heuristics likegradient clipping outperform SGD on language tasks because the distribution ofthe error induced by sampling has heavy tails. This suggests that Adamoutperform SGD because it uses a more robust gradient estimate. We evaluatethis hypothesis by varying the batch size, up to the entire dataset, to controlfor stochasticity. We present evidence that stochasticity and heavy-tailednoise are not major factors in the performance gap between SGD and Adam.Rather, Adam performs better as the batch size increases, while SGD is lesseffective at taking advantage of the reduction in noise. This raises thequestion as to why Adam outperforms SGD in the full-batch setting. Throughfurther investigation of simpler variants of SGD, we find that the behavior ofAdam with large batches is similar to sign descent with momentum.

Noise Is Not the Main Factor Behind the Gap Between SGD and Adam on Transformers, but Sign Descent Might Be