# Negative Inner-Loop Learning Rates Learn Universal Features

arXiv: https://arxiv.org/abs/2203.10185 · HTML: https://mlsanity.com/paper/2203.10185/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 12 references that are in the map.
- First posted on arXiv 18 Mar 2022.

## Builds on (most cited first, 9 of 9)

- [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)
- [On First-Order Meta-Learning Algorithms](https://mlsanity.com/paper/1803.02999/) (2018)
- [Meta-SGD: Learning to Learn Quickly for Few-Shot Learning](https://mlsanity.com/paper/1707.09835/) (2017)
- [Rapid Learning or Feature Reuse? Towards Understanding the Effectiveness of MAML](https://mlsanity.com/paper/1909.09157/) (2019)
- [What makes ImageNet good for transfer learning?](https://mlsanity.com/paper/1608.08614/) (2016)
- [Unraveling Meta-Learning: Understanding Feature Representations for Few-Shot Tasks](https://mlsanity.com/paper/2002.06753/) (2020)
- [Meta-learning with negative learning rates](https://mlsanity.com/paper/2102.00940/) (2021)

## Built on by (most cited first, 1 of 1)

- [CCoMAML: Efficient Cattle Identification Using Cooperative Model-Agnostic Meta-Learning](https://mlsanity.com/paper/2509.11219/) (2025)

## Abstract (arXiv)

Model Agnostic Meta-Learning (MAML) consists of two optimization loops: the outer loop learns a meta-initialization of model parameters that is shared across tasks, and the inner loop task-specific adaptation step. A variant of MAML, Meta-SGD, uses the same two loop structure, but also learns the learning-rate for the adaptation step. Little attention has been paid to how the learned learning-rate of Meta-SGD affects feature reuse. In this paper, we study the effect that a learned learning-rate has on the per-task feature representations in Meta-SGD. The learned learning-rate of Meta-SGD often contains negative values. During the adaptation phase, these negative learning rates push features away from task-specific features and towards task-agnostic features. We performed several experiments on the Mini-Imagenet dataset. Two neural networks were trained, one with MAML, and one with Meta-SGD. The feature quality for both models was tested as follows: strip away the linear classification layer, pass labeled and unlabeled samples through this encoder, classify the unlabeled samples according to their nearest neighbor. This process was performed: 1) after training and using the meta-initialization parameters; 2) after adaptation, and validated on that task; and 3) after adaptation, and validated on a different task. The MAML trained model improved on the task it was adapted to, but had worse performance on other tasks. The Meta-SGD trained model was the opposite; it had worse performance on the task it was adapted to, but improved on other tasks. This confirms the hypothesis that Meta-SGD's negative learning rates cause the model to learn task-agnostic features rather than simply adapt to task specific features.