# Scalable Bayesian Meta-Learning through Generalized Implicit Gradients

arXiv: https://arxiv.org/abs/2303.17768 · HTML: https://mlsanity.com/paper/2303.17768/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 38 references that are in the map.
- First posted on arXiv 31 Mar 2023.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [On First-Order Meta-Learning Algorithms](https://mlsanity.com/paper/1803.02999/) (2018)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Meta-Learning with Implicit Gradients](https://mlsanity.com/paper/1909.04630/) (2019)
- [Meta-Learning with Differentiable Convex Optimization](https://mlsanity.com/paper/1904.03758/) (2019)
- [Bilevel Programming for Hyperparameter Optimization and Meta-Learning](https://mlsanity.com/paper/1806.04910/) (2018)
- [Meta-learning with differentiable closed-form solvers](https://mlsanity.com/paper/1805.08136/) (2018)
- [Meta-SGD: Learning to Learn Quickly for Few-Shot Learning](https://mlsanity.com/paper/1707.09835/) (2017)
- [Bayesian Model-Agnostic Meta-Learning](https://mlsanity.com/paper/1806.03836/) (2018)
- [Recasting Gradient-Based Meta-Learning as Hierarchical Bayes](https://mlsanity.com/paper/1801.08930/) (2018)
- [Practical Gauss-Newton Optimisation for Deep Learning](https://mlsanity.com/paper/1706.03662/) (2017)
- [Generalization in Reinforcement Learning by Soft Data Augmentation](https://mlsanity.com/paper/2011.13389/) (2020)
- [On the Convergence Theory of Gradient-Based Model-Agnostic Meta-Learning Algorithms](https://mlsanity.com/paper/1908.10400/) (2019)
- [Meta-Learning with Warped Gradient Descent](https://mlsanity.com/paper/1909.00025/) (2019)
- [Sharp-MAML: Sharpness-Aware Model-Agnostic Meta Learning](https://mlsanity.com/paper/2206.03996/) (2022)
- [Uncertainty in Model-Agnostic Meta-Learning using Variational Inference](https://mlsanity.com/paper/1907.11864/) (2019)
- [Is Bayesian Model-Agnostic Meta Learning Better than Model-Agnostic Meta Learning, Provably?](https://mlsanity.com/paper/2203.03059/) (2022)

## Built on by (most cited first, 4 of 4)

- [MetaDiff: Meta-Learning with Conditional Diffusion for Few-Shot Learning](https://mlsanity.com/paper/2307.16424/) (2023)
- [Meta-Learning with Versatile Loss Geometries for Fast Adaptation Using Mirror Descent](https://mlsanity.com/paper/2312.13486/) (2023)
- [Learnable Loss Geometries with Mirror Descent for Scalable and Convergent Meta-Learning](https://mlsanity.com/paper/2509.02418/) (2025)
- [Binomial Gradient-Based Meta-Learning for Enhanced Meta-Gradient Estimation](https://mlsanity.com/paper/2604.13263/) (2026)

## Abstract (arXiv)

Meta-learning owns unique effectiveness and swiftness in tackling emerging tasks with limited data. Its broad applicability is revealed by viewing it as a bi-level optimization problem. The resultant algorithmic viewpoint however, faces scalability issues when the inner-level optimization relies on gradient-based iterations. Implicit differentiation has been considered to alleviate this challenge, but it is restricted to an isotropic Gaussian prior, and only favors deterministic meta-learning approaches. This work markedly mitigates the scalability bottleneck by cross-fertilizing the benefits of implicit differentiation to probabilistic Bayesian meta-learning. The novel implicit Bayesian meta-learning (iBaML) method not only broadens the scope of learnable priors, but also quantifies the associated uncertainty. Furthermore, the ultimate complexity is well controlled regardless of the inner-level optimization trajectory. Analytical error bounds are established to demonstrate the precision and efficiency of the generalized implicit gradient over the explicit one. Extensive numerical tests are also carried out to empirically validate the performance of the proposed method.