# Meta-Learning with Warped Gradient Descent

arXiv: https://arxiv.org/abs/1909.00025 · HTML: https://mlsanity.com/paper/1909.00025/

## Key facts

- Cited by 98 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Aug 2019.

## Built on by (most cited first, 30 of 98)

- [Transformers learn in-context by gradient descent](https://mlsanity.com/paper/2212.07677/) (2022)
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- [FedBABU: Towards Enhanced Representation for Federated Image Classification](https://mlsanity.com/paper/2106.06042/) (2021)
- [A Comprehensive Survey of Few-shot Learning: Evolution, Applications, Challenges, and Opportunities](https://mlsanity.com/paper/2205.06743/) (2022)
- [Investigating Bi-Level Optimization for Learning and Vision from a Unified Perspective: A Survey and Beyond](https://mlsanity.com/paper/2101.11517/) (2021)
- [RotoGrad: Gradient Homogenization in Multitask Learning](https://mlsanity.com/paper/2103.02631/) (2021)
- [Towards Gradient-based Bilevel Optimization with Non-convex Followers and Beyond](https://mlsanity.com/paper/2110.00455/) (2021)
- [Learning a Universal Template for Few-shot Dataset Generalization](https://mlsanity.com/paper/2105.07029/) (2021)
- [Self-Destructing Models: Increasing the Costs of Harmful Dual Uses of Foundation Models](https://mlsanity.com/paper/2211.14946/) (2022)
- [Layerwise Optimization by Gradient Decomposition for Continual Learning](https://mlsanity.com/paper/2105.07561/) (2021)
- [Generalizing to New Physical Systems via Context-Informed Dynamics Model](https://mlsanity.com/paper/2202.01889/) (2022)
- [Powerpropagation: A sparsity inducing weight reparameterisation](https://mlsanity.com/paper/2110.00296/) (2021)
- [Meta-Learning with Task-Adaptive Loss Function for Few-Shot Learning](https://mlsanity.com/paper/2110.03909/) (2021)
- [Meta-Learning with Fewer Tasks through Task Interpolation](https://mlsanity.com/paper/2106.02695/) (2021)
- [Bootstrapped Meta-Learning](https://mlsanity.com/paper/2109.04504/) (2021)
- [LLMs are Greedy Agents: Effects of RL Fine-tuning on Decision-Making Abilities](https://mlsanity.com/paper/2504.16078/) (2025)
- [MetaDiff: Meta-Learning with Conditional Diffusion for Few-Shot Learning](https://mlsanity.com/paper/2307.16424/) (2023)
- [Understanding Cross-Domain Few-Shot Learning Based on Domain Similarity and Few-Shot Difficulty](https://mlsanity.com/paper/2202.01339/) (2022)
- [Learning Domain Invariant Prompt for Vision-Language Models](https://mlsanity.com/paper/2212.04196/) (2022)
- [Learning where to learn: Gradient sparsity in meta and continual learning](https://mlsanity.com/paper/2110.14402/) (2021)
- [Introducing Symmetries to Black Box Meta Reinforcement Learning](https://mlsanity.com/paper/2109.10781/) (2021)
- [Continual Object Detection: A review of definitions, strategies, and challenges](https://mlsanity.com/paper/2205.15445/) (2022)
- [Meta-Learning Sparse Compression Networks](https://mlsanity.com/paper/2205.08957/) (2022)
- [Retrieval-Augmented Decision Transformer: External Memory for In-context RL](https://mlsanity.com/paper/2410.07071/) (2024)
- [Self-Supervision Can Be a Good Few-Shot Learner](https://mlsanity.com/paper/2207.09176/) (2022)
- [Offline Model-Based Optimization via Policy-Guided Gradient Search](https://mlsanity.com/paper/2405.05349/) (2024)
- [Model-based Meta Reinforcement Learning using Graph Structured Surrogate Models](https://mlsanity.com/paper/2102.08291/) (2021)
- [Few-Shot Learning Meets Transformer: Unified Query-Support Transformers for Few-Shot Classification](https://mlsanity.com/paper/2208.12398/) (2022)
- [Adaptive Poincar'e Point to Set Distance for Few-Shot Classification](https://mlsanity.com/paper/2112.01719/) (2021)
- [Eliminating Meta Optimization Through Self-Referential Meta Learning](https://mlsanity.com/paper/2212.14392/) (2022)

## Abstract (arXiv)

Learning an efficient update rule from data that promotes rapid learning of new tasks from the same distribution remains an open problem in meta-learning. Typically, previous works have approached this issue either by attempting to train a neural network that directly produces updates or by attempting to learn better initialisations or scaling factors for a gradient-based update rule. Both of these approaches pose challenges. On one hand, directly producing an update forgoes a useful inductive bias and can easily lead to non-converging behaviour. On the other hand, approaches that try to control a gradient-based update rule typically resort to computing gradients through the learning process to obtain their meta-gradients, leading to methods that can not scale beyond few-shot task adaptation. In this work, we propose Warped Gradient Descent (WarpGrad), a method that intersects these approaches to mitigate their limitations. WarpGrad meta-learns an efficiently parameterised preconditioning matrix that facilitates gradient descent across the task distribution. Preconditioning arises by interleaving non-linear layers, referred to as warp-layers, between the layers of a task-learner. Warp-layers are meta-learned without backpropagating through the task training process in a manner similar to methods that learn to directly produce updates. WarpGrad is computationally efficient, easy to implement, and can scale to arbitrarily large meta-learning problems. We provide a geometrical interpretation of the approach and evaluate its effectiveness in a variety of settings, including few-shot, standard supervised, continual and reinforcement learning.