Why Adaptive Optimizers Underestimate Rare Tokens
In the softmax output layer, a rare token receives a small positive logit gradient on most steps and a much larger negative gradient on the few steps when it is the target. SGD simply adds these contributions. Coordinate-wise adaptive methods such as Adam, RMSProp, and sign descent instead divide each update by a running estimate of its magnitude, and that estimate is largest immediately after the token appears. This imbalance has two effects. At the level of the whole output layer, we characterize which optimizers preserve the mean output embedding: every method whose update is linear in past gradients does, as do Kronecker-factored and orthogonalized methods such as Shampoo and Muon. Ad...
| Authors | Sangsidhya Kar |
|---|---|
| Primary category | cs.LG |
| Published | 29 September 2026 |
| Last updated at source | 29 September 2026 |
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