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Why Transformers Need Adam: A Hessian Perspective

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arxiv 2402.16788 v4 pith:4FLOZH33 submitted 2024-02-26 cs.LG cs.AI

Why Transformers Need Adam: A Hessian Perspective

classification cs.LG cs.AI
keywords adamheterogeneityperformstransformersworseblockblockshessian
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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SGD performs worse than Adam by a significant margin on Transformers, but the reason remains unclear. In this work, we provide an explanation through the lens of Hessian: (i) Transformers are "heterogeneous": the Hessian spectrum across parameter blocks vary dramatically, a phenomenon we call "block heterogeneity"; (ii) Heterogeneity hampers SGD: SGD performs worse than Adam on problems with block heterogeneity. To validate (i) and (ii), we check various Transformers, CNNs, MLPs, and quadratic problems, and find that SGD can perform on par with Adam on problems without block heterogeneity, but performs worse than Adam when the heterogeneity exists. Our initial theoretical analysis indicates that SGD performs worse because it applies one single learning rate to all blocks, which cannot handle the heterogeneity among blocks. This limitation could be ameliorated if we use coordinate-wise learning rates, as designed in Adam.

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