Model-agnostic meta-learning (MAML) is one of the most successful meta-learning algorithms. It has a bi-level optimization structure where the outer-loop process learns a shared initialization and the inner-loop process optimizes task-specific weights. Although MAML relies on the standard gradient descent in the inner-loop, recent studies have shown that controlling the inner-loop's gradient descent with a meta-learned preconditioner can be beneficial. Existing preconditioners, however, cannot simultaneously adapt in a task-specific and path-dependent way. Additionally, they do not satisfy the Riemannian metric condition, which can enable the steepest descent learning with preconditioned gradient. In this study, we propose Geometry-Adaptive Preconditioned gradient descent (GAP) that can overcome the limitations in MAML; GAP can efficiently meta-learn a preconditioner that is dependent on task-specific parameters, and its preconditioner can be shown to be a Riemannian metric. Thanks to the two properties, the geometry-adaptive preconditioner is effective for improving the inner-loop optimization. Experiment results show that GAP outperforms the state-of-the-art MAML family and preconditioned gradient descent-MAML (PGD-MAML) family in a variety of few-shot learning tasks. Code is available at: https://github.com/Suhyun777/CVPR23-GAP.

Since the introduction of deep learning, a wide scope of representation properties, such as decorrelation, whitening, disentanglement, rank, isotropy, and mutual information, have been studied to improve the quality of representation. However, manipulating such properties can be challenging in terms of implementational effectiveness and general applicability. To address these limitations, we propose to regularize von Neumann entropy (VNE) of representation. First, we demonstrate that the mathematical formulation of VNE is superior in effectively manipulating the eigenvalues of the representation autocorrelation matrix. Then, we demonstrate that it is widely applicable in improving state-of-the-art algorithms or popular benchmark algorithms by investigating domain-generalization, meta-learning, self-supervised learning, and generative models. In addition, we formally establish theoretical connections with rank, disentanglement, and isotropy of representation. Finally, we provide discussions on the dimension control of VNE and the relationship with Shannon entropy. Code is available at: https://github.com/jaeill/CVPR23-VNE.

In this study, we propose AID-Purifier that can boost the robustness of adversarially-trained networks by purifying their inputs. AID-Purifier is an auxiliary network that works as an add-on to an already trained main classifier. To keep it computationally light, it is trained as a discriminator with a binary cross-entropy loss. To obtain additionally useful information from the adversarial examples, the architecture design is closely related to the information maximization principle where two layers of the main classification network are piped into the auxiliary network. To assist the iterative optimization procedure of purification, the auxiliary network is trained with AVmixup. AID-Purifier can be also used together with other purifiers such as PixelDefend for an extra enhancement. Because input purification has been studied relative less when compared to adversarial training or gradient masking, we conduct extensive attack experiments to validate AID-Purifier’s robustness. The overall results indicate that the best performing adversarially-trained networks can be enhanced further with AID-Purifier. The code is available in https://github.com/yelobean/AIDPurifier.