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Meta-learning that uses implicit gradient have provided an excitingalternative to standard techniques which depend on the trajectory of the innerloop training. Implicit meta-learning (IML), however, require computing$2^{nd}$ order gradients, particularly the Hessian which is impractical tocompute for modern deep learning models. Various approximations for the Hessianwere proposed but a systematic comparison of their compute cost, stability,generalization of solution found and estimation accuracy were largelyoverlooked. In this study, we start by conducting a systematic comparativeanalysis of the various approximation methods and their effect whenincorporated into IML training routines. We establish situations wherecatastrophic forgetting is exhibited in IML and explain their cause in terms ofthe inability of the approximations to estimate the curvature at convergencepoints. Sources of IML training instability are demonstrated and remedied. Adetailed analysis of the effeciency of various inverse Hessian-vector productapproximation methods is also provided. Subsequently, we use the insightsgained to propose and evaluate a novel semi-supervised learning algorithm thatlearns to inductively weigh consistency regularization losses. We show howtraining a "Confidence Network" to extract domain specific features can learnto up-weigh useful images and down-weigh out-of-distribution samples. Resultsoutperform the baseline FixMatch performance.

On Training Implicit Meta-Learning With Applications to Inductive Weighing in Consistency Regularization