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Enable use of pseudoinverse in computation of preconditioners #11
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…de (pip install -e .)
…g DistributedShampoo and GraftingType
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The derivations presented in the Adagrad paper provide a principled justification for the use of _pseudo_inverses in the computation of the preconditioner matrices whenever these are not full-rank.
This PR allows for the use of pseudoinverses in Shampoo and (diagonal) Adagrad-like methods (including Adagrad, Adam, RMSProp).
This PR also enables the computation of a preconditioner matrix at the very first iteration (
start_preconditioning_step=0
), even in conjunction with aprecondition_frequency != 1
. Previous behaviour (#10 ) led to no updates taking place for the firstprecondition_frequency
steps since the preconditioner and inverse preconditioner tensors were initialized with zeros.