FORML: A Riemannian Hessian-free Method for Meta-learning on Stiefel Manifolds

• URL: http://arxiv.org/abs/2402.18605v2
• Date: Fri, 31 May 2024 21:34:33 GMT
• Title: FORML: A Riemannian Hessian-free Method for Meta-learning on Stiefel Manifolds
• Authors: Hadi Tabealhojeh, Soumava Kumar Roy, Peyman Adibi, Hossein Karshenas,
• Abstract summary: This paper introduces a Hessian-free approach that uses a first-order approximation of derivatives on the Stiefel manifold. Our method significantly reduces the computational load and memory footprint.
• Score: 4.757859522106933
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Meta-learning problem is usually formulated as a bi-level optimization in which the task-specific and the meta-parameters are updated in the inner and outer loops of optimization, respectively. However, performing the optimization in the Riemannian space, where the parameters and meta-parameters are located on Riemannian manifolds is computationally intensive. Unlike the Euclidean methods, the Riemannian backpropagation needs computing the second-order derivatives that include backward computations through the Riemannian operators such as retraction and orthogonal projection. This paper introduces a Hessian-free approach that uses a first-order approximation of derivatives on the Stiefel manifold. Our method significantly reduces the computational load and memory footprint. We show how using a Stiefel fully-connected layer that enforces orthogonality constraint on the parameters of the last classification layer as the head of the backbone network, strengthens the representation reuse of the gradient-based meta-learning methods. Our experimental results across various few-shot learning datasets, demonstrate the superiority of our proposed method compared to the state-of-the-art methods, especially MAML, its Euclidean counterpart.

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