# Few-Shot Learning by Dimensionality Reduction in Gradient Space

arXiv: https://arxiv.org/abs/2206.03483 · HTML: https://mlsanity.com/paper/2206.03483/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 61 references that are in the map.
- First posted on arXiv 7 Jun 2022.

## Builds on (most cited first, 30 of 31)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [Learning to Compare: Relation Network for Few-Shot Learning](https://mlsanity.com/paper/1711.06025/) (2017)
- [On First-Order Meta-Learning Algorithms](https://mlsanity.com/paper/1803.02999/) (2018)
- [Meta-Learning in Neural Networks: A Survey](https://mlsanity.com/paper/2004.05439/) (2020)
- [Learning to learn by gradient descent by gradient descent](https://mlsanity.com/paper/1606.04474/) (2016)
- [Meta-SGD: Learning to Learn Quickly for Few-Shot Learning](https://mlsanity.com/paper/1707.09835/) (2017)
- [Measuring the Intrinsic Dimension of Objective Landscapes](https://mlsanity.com/paper/1804.08838/) (2018)
- [Rapid Learning or Feature Reuse? Towards Understanding the Effectiveness of MAML](https://mlsanity.com/paper/1909.09157/) (2019)
- [Few-Shot Learning via Embedding Adaptation with Set-to-Set Functions](https://mlsanity.com/paper/1812.03664/) (2018)
- [High-dimensional dynamics of generalization error in neural networks](https://mlsanity.com/paper/1710.03667/) (2017)
- [Gradient Descent Happens in a Tiny Subspace](https://mlsanity.com/paper/1812.04754/) (2018)
- [Revisiting Natural Gradient for Deep Networks](https://mlsanity.com/paper/1301.3584/) (2013)
- [Multimodal Model-Agnostic Meta-Learning via Task-Aware Modulation](https://mlsanity.com/paper/1910.13616/) (2019)
- [Meta-Learning with Warped Gradient Descent](https://mlsanity.com/paper/1909.00025/) (2019)
- [The Singular Values of Convolutional Layers](https://mlsanity.com/paper/1805.10408/) (2018)
- [Meta-Curvature](https://mlsanity.com/paper/1902.03356/) (2019)
- [Towards Learning Universal, Regional, and Local Hydrological Behaviors via Machine-Learning Applied to Large-Sample Datasets](https://mlsanity.com/paper/1907.08456/) (2019)
- [Generalization bounds for deep convolutional neural networks](https://mlsanity.com/paper/1905.12600/) (2019)
- [Universal Representation Learning from Multiple Domains for Few-shot Classification](https://mlsanity.com/paper/2103.13841/) (2021)
- [Few-shot Domain Adaptation by Causal Mechanism Transfer](https://mlsanity.com/paper/2002.03497/) (2020)
- [On Generalization Bounds of a Family of Recurrent Neural Networks](https://mlsanity.com/paper/1910.12947/) (2019)
- [Cross-Domain Few-Shot Learning by Representation Fusion](https://mlsanity.com/paper/2010.06498/) (2020)
- [Fast Adaptation with Linearized Neural Networks](https://mlsanity.com/paper/2103.01439/) (2021)
- [Modular Meta-Learning with Shrinkage](https://mlsanity.com/paper/1909.05557/) (2019)
- [Continuous-time system identification with neural networks: Model structures and fitting criteria](https://mlsanity.com/paper/2006.02915/) (2020)
- [How many degrees of freedom do we need to train deep networks: a loss landscape perspective](https://mlsanity.com/paper/2107.05802/) (2021)
- [On the adaptation of recurrent neural networks for system identification](https://mlsanity.com/paper/2201.08660/) (2022)

## Built on by (most cited first, 8 of 8)

- [Does SGD really happen in tiny subspaces?](https://mlsanity.com/paper/2405.16002/) (2024)
- [Parameter Efficient Fine-tuning via Explained Variance Adaptation](https://mlsanity.com/paper/2410.07170/) (2024)
- [Fine-tuning Happens in Tiny Subspaces: Exploring Intrinsic Task-specific Subspaces of Pre-trained Language Models](https://mlsanity.com/paper/2305.17446/) (2023)
- [SymbolicAI: A framework for logic-based approaches combining generative models and solvers](https://mlsanity.com/paper/2402.00854/) (2024)
- [A Layer Selection Approach to Test Time Adaptation](https://mlsanity.com/paper/2404.03784/) (2024)
- [Identifying Policy Gradient Subspaces](https://mlsanity.com/paper/2401.06604/) (2024)
- [PMSS: Pretrained Matrices Skeleton Selection for LLM Fine-tuning](https://mlsanity.com/paper/2409.16722/) (2024)
- [PARMESAN: Parameter-Free Memory Search and Transduction for Dense Prediction Tasks](https://mlsanity.com/paper/2403.11743/) (2024)

## Abstract (arXiv)

We introduce SubGD, a novel few-shot learning method which is based on the recent finding that stochastic gradient descent updates tend to live in a low-dimensional parameter subspace. In experimental and theoretical analyses, we show that models confined to a suitable predefined subspace generalize well for few-shot learning. A suitable subspace fulfills three criteria across the given tasks: it (a) allows to reduce the training error by gradient flow, (b) leads to models that generalize well, and (c) can be identified by stochastic gradient descent. SubGD identifies these subspaces from an eigendecomposition of the auto-correlation matrix of update directions across different tasks. Demonstrably, we can identify low-dimensional suitable subspaces for few-shot learning of dynamical systems, which have varying properties described by one or few parameters of the analytical system description. Such systems are ubiquitous among real-world applications in science and engineering. We experimentally corroborate the advantages of SubGD on three distinct dynamical systems problem settings, significantly outperforming popular few-shot learning methods both in terms of sample efficiency and performance.