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NN.Proofs.Autograd.Tape.Nodes.Losses.MSE

Mean-Squared Error #

Tape node and Fréchet derivative proof for scalar mean-squared error.

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noncomputable def Proofs.Autograd.TapeNodes.mseLoss {Γ : List Spec.Shape} {s : Spec.Shape} (yhat target : Idx Γ s) :
Node Γ Spec.Shape.scalar

Mean-squared-error loss node: c * ‖yhat - target‖^2, with c = 1 / Spec.meanDenom s.

For nonempty shapes this is the usual 1 / Spec.Shape.size s. For the empty shape case, the scalar loss API is totalized with denominator 1, matching Spec.mseSpec and the IR evaluator.

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    noncomputable def Proofs.Autograd.TapeNodes.mseLossFderiv {Γ : List Spec.Shape} {s : Spec.Shape} (yhat target : Idx Γ s) :
    NodeFDerivCorrect (mseLoss yhat target)

    NodeFDerivCorrect for mse_loss.

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