Curvature-adaptive meta-learning for fast adaptation to manifold data

Zhi Gao, Yuwei Wu, Mehrtash T. Harandi, Yunde Jia

Research output: Contribution to journalArticleResearchpeer-review


Meta-learning methods are shown to be effective in quickly adapting a model to novel tasks. Most existing meta-learning methods represent data and carry out fast adaptation in Euclidean space. In fact, data of real-world applications usually resides in complex and various Riemannian manifolds. In this paper, we propose a curvature-adaptive meta-learning method that achieves fast adaptation to manifold data by producing suitable curvature. Specifically, we represent data in the product manifold of multiple constant curvature spaces and build a product manifold neural network as the base-learner. In this way, our method is capable of encoding complex manifold data into discriminative and generic representations. Then, we introduce curvature generation and curvature updating schemes, through which suitable product manifolds for various forms of data manifolds are constructed via few optimization steps. The curvature generation scheme identifies task-specific curvature initialization, leading to a shorter optimization trajectory. The curvature updating scheme automatically produces appropriate learning rate and search direction for curvature, making a faster and more adaptive optimization paradigm compared to hand-designed optimization schemes. Experimental results on few-shot classification, few-shot regression, and reinforcement learning tasks show the benefits of our method.

Original languageEnglish
Number of pages18
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Publication statusAccepted/In press - 5 Apr 2022


  • Adaptation models
  • Constant Curvature Space
  • Curvature
  • Data models
  • Geometry
  • Manifold Data
  • Manifolds
  • Meta-Learning
  • Neural networks
  • Optimization
  • Product Manifold
  • Task analysis

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