Why it matters

Sophia claimed AdamW improvement. Understanding shapes optimizer choice.

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The architecture

Sample Hessian occasionally.

Diagonal preconditioner from Hessian.

Clip step for stability.

Sophia structureHessian sampleoccasionallyDiagonal precond1/h_iClipped stepfor stabilityEfficient by using diagonal + occasional Hessian sampling
Sophia.
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How it works end to end

Hutchinson estimator for diagonal Hessian.

Update Hessian every k steps.

Clip: prevent extreme steps.