  Meta-learning that uses implicit gradient have provided an exciting
alternative to standard techniques which depend on the trajectory of the inner
loop training. Implicit meta-learning (IML), however, require computing
$2^{nd}$ order gradients, particularly the Hessian which is impractical to
compute for modern deep learning models. Various approximations for the Hessian
were proposed but a systematic comparison of their compute cost, stability,
generalization of solution found and estimation accuracy were largely
overlooked. In this study, we start by conducting a systematic comparative
analysis of the various approximation methods and their effect when
incorporated into IML training routines. We establish situations where
catastrophic forgetting is exhibited in IML and explain their cause in terms of
the inability of the approximations to estimate the curvature at convergence
points. Sources of IML training instability are demonstrated and remedied. A
detailed analysis of the effeciency of various inverse Hessian-vector product
approximation methods is also provided. Subsequently, we use the insights
gained to propose and evaluate a novel semi-supervised learning algorithm that
learns to inductively weigh consistency regularization losses. We show how
training a "Confidence Network" to extract domain specific features can learn
to up-weigh useful images and down-weigh out-of-distribution samples. Results
outperform the baseline FixMatch performance.
