# Riemannian Geometric-based Meta Learning

arXiv: https://arxiv.org/abs/2503.10993 · HTML: https://mlsanity.com/paper/2503.10993/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 35 references that are in the map.
- First posted on arXiv 14 Mar 2025.

## Builds on (most cited first, 24 of 24)

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Learning to Compare: Relation Network for Few-Shot Learning](https://mlsanity.com/paper/1711.06025/) (2017)
- [Meta-Learning in Neural Networks: A Survey](https://mlsanity.com/paper/2004.05439/) (2020)
- [Meta-Learning with Implicit Gradients](https://mlsanity.com/paper/1909.04630/) (2019)
- [Towards Out-Of-Distribution Generalization: A Survey](https://mlsanity.com/paper/2108.13624/) (2021)
- [Fundamentals of Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) Network](https://mlsanity.com/paper/1808.03314/) (2018)
- [Few-Shot Learning with Graph Neural Networks](https://mlsanity.com/paper/1711.04043/) (2017)
- [How to train your MAML](https://mlsanity.com/paper/1810.09502/) (2018)
- [Probabilistic Model-Agnostic Meta-Learning](https://mlsanity.com/paper/1806.02817/) (2018)
- [Meta-Learning: A Survey](https://mlsanity.com/paper/1810.03548/) (2018)
- [Bayesian Model-Agnostic Meta-Learning](https://mlsanity.com/paper/1806.03836/) (2018)
- [Task-Agnostic Meta-Learning for Few-shot Learning](https://mlsanity.com/paper/1805.07722/) (2018)
- [Manopt, a Matlab toolbox for optimization on manifolds](https://mlsanity.com/paper/1308.5200/) (2013)
- [Orthogonal Deep Neural Networks](https://mlsanity.com/paper/1905.05929/) (2019)
- [Advances and Challenges in Meta-Learning: A Technical Review](https://mlsanity.com/paper/2307.04722/) (2023)
- [Building Deep Networks on Grassmann Manifolds](https://mlsanity.com/paper/1611.05742/) (2016)
- [Torchmeta: A Meta-Learning library for PyTorch](https://mlsanity.com/paper/1909.06576/) (2019)
- [Optimization Techniques on Riemannian Manifolds](https://mlsanity.com/paper/1407.5965/) (2014)
- [Meta-learning approaches for few-shot learning: A survey of recent advances](https://mlsanity.com/paper/2303.07502/) (2023)
- [Variational Metric Scaling for Metric-Based Meta-Learning](https://mlsanity.com/paper/1912.11809/) (2019)
- [Simple algorithms for optimization on Riemannian manifolds with constraints](https://mlsanity.com/paper/1901.10000/) (2019)
- [Meta-learning in healthcare: A survey](https://mlsanity.com/paper/2308.02877/) (2023)
- [A Constraint Dissolving Approach for Nonsmooth Optimization over the Stiefel Manifold](https://mlsanity.com/paper/2205.10500/) (2022)
- [Riemannian Stochastic Proximal Gradient Methods for Nonsmooth Optimization over the Stiefel Manifold](https://mlsanity.com/paper/2005.01209/) (2020)

## Abstract (arXiv)

Meta-learning, or "learning to learn," aims to enable models to quickly adapt to new tasks with minimal data. While traditional methods like Model-Agnostic Meta-Learning (MAML) optimize parameters in Euclidean space, they often struggle to capture complex learning dynamics, particularly in few-shot learning scenarios. To address this limitation, we propose Stiefel-MAML, which integrates Riemannian geometry by optimizing within the Stiefel manifold, a space that naturally enforces orthogonality constraints. By leveraging the geometric structure of the Stiefel manifold, we improve parameter expressiveness and enable more efficient optimization through Riemannian gradient calculations and retraction operations. We also introduce a novel kernel-based loss function defined on the Stiefel manifold, further enhancing the model's ability to explore the parameter space. Experimental results on benchmark datasets--including Omniglot, Mini-ImageNet, FC-100, and CUB--demonstrate that Stiefel-MAML consistently outperforms traditional MAML, achieving superior performance across various few-shot learning tasks. Our findings highlight the potential of Riemannian geometry to enhance meta-learning, paving the way for future research on optimizing over different geometric structures.