Utilizing task-invariant knowledge acquired from related tasks as prior information, meta-learning offers a principled approach to learning a new task with limited data records. Sample-efficient adaptation of this prior information is a major challenge facing meta-learning, and plays an important role because it facilitates training the sought task-specific model with just a few optimization steps. Past works deal with this challenge through preconditioning that speeds up convergence of the per-task training. Though effective in representing locally quadratic loss curvatures, simple linear preconditioning can be hardly potent with complex loss geometries. Instead of relying on a quadratic distance metric, the present contribution copes with complex loss metrics by learning a versatile distance-generating function, which induces a nonlinear mirror map to effectively capture and optimize a wide range of loss geometries. With suitable parameterization, this generating function is effected by an expressive neural network that is provably a valid distance. Analytical results establish convergence of not only the proposed method, but also all meta-learning approaches based on preconditioning. To attain gradient norm less than $ε$, the convergence rate of $\mathcal{O}(ε^{-2})$ is on par with standard gradient-based meta-learning methods. Numerical tests on few-shot learning datasets demonstrate the superior empirical performance of the novel algorithm, as well as its rapid per-task convergence, which markedly reduces the number of adaptation steps, hence also accommodating large-scale meta-learning models.

The pretraining-fine-tuning paradigm has been the de facto strategy for transfer learning in modern language modeling. With the understanding that task adaptation in LMs is often a function of parameters shared across tasks, we argue that a more surgical approach to regularization needs to exist for smoother transfer learning. Towards this end, we investigate how the pretraining loss landscape is affected by these task-sensitive parameters through an information-theoretic lens. We then leverage the findings from our investigations to devise a novel approach to dropout for improved model regularization and better downstream generalization. This approach, named guided dropout, is both task & architecture agnostic and adds no computational overhead to the fine-tuning process. Through empirical evaluations, we showcase that our approach to regularization yields consistently better performance, even in scenarios of data paucity, compared to standardized baselines.

Utilizing task-invariant prior knowledge extracted from related tasks, meta-learning is a principled framework that empowers learning a new task especially when data records are limited. A fundamental challenge in meta-learning is how to quickly "adapt" the extracted prior in order to train a task-specific model within a few optimization steps. Existing approaches deal with this challenge using a preconditioner that enhances convergence of the per-task training process. Though effective in representing locally a quadratic training loss, these simple linear preconditioners can hardly capture complex loss geometries. The present contribution addresses this limitation by learning a nonlinear mirror map, which induces a versatile distance metric to enable capturing and optimizing a wide range of loss geometries, hence facilitating the per-task training. Numerical tests on few-shot learning datasets demonstrate the superior expressiveness and convergence of the advocated approach.