# Learning by Examples Based on Multi-level Optimization

arXiv: https://arxiv.org/abs/2109.10824 · HTML: https://mlsanity.com/paper/2109.10824/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 41 of its 68 references that are in the map.
- First posted on arXiv 22 Sep 2021.

## Builds on (most cited first, 30 of 41)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [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)
- [A Closer Look at Few-shot Classification](https://mlsanity.com/paper/1904.04232/) (2019)
- [Meta-Learning with Latent Embedding Optimization](https://mlsanity.com/paper/1807.05960/) (2018)
- [Meta-Learning with Differentiable Convex Optimization](https://mlsanity.com/paper/1904.03758/) (2019)
- [TADAM: Task dependent adaptive metric for improved few-shot learning](https://mlsanity.com/paper/1805.10123/) (2018)
- [Dynamic Few-Shot Visual Learning without Forgetting](https://mlsanity.com/paper/1804.09458/) (2018)
- [Meta-SGD: Learning to Learn Quickly for Few-Shot Learning](https://mlsanity.com/paper/1707.09835/) (2017)
- [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)
- [A Baseline for Few-Shot Image Classification](https://mlsanity.com/paper/1909.02729/) (2019)
- [Few-Shot Learning via Embedding Adaptation with Set-to-Set Functions](https://mlsanity.com/paper/1812.03664/) (2018)
- [Learning to Propagate Labels: Transductive Propagation Network for Few-shot Learning](https://mlsanity.com/paper/1805.10002/) (2018)
- [SimpleShot: Revisiting Nearest-Neighbor Classification for Few-Shot Learning](https://mlsanity.com/paper/1911.04623/) (2019)
- [Learning Fine-grained Image Similarity with Deep Ranking](https://mlsanity.com/paper/1404.4661/) (2014)
- [Boosting Few-Shot Visual Learning with Self-Supervision](https://mlsanity.com/paper/1906.05186/) (2019)
- [Few-Shot Image Recognition by Predicting Parameters from Activations](https://mlsanity.com/paper/1706.03466/) (2017)
- [Online Learning Rate Adaptation with Hypergradient Descent](https://mlsanity.com/paper/1703.04782/) (2017)
- [Generative Teaching Networks: Accelerating Neural Architecture Search by Learning to Generate Synthetic Training Data](https://mlsanity.com/paper/1912.07768/) (2019)
- [Prototype Rectification for Few-Shot Learning](https://mlsanity.com/paper/1911.10713/) (2019)
- [Embedding Propagation: Smoother Manifold for Few-Shot Classification](https://mlsanity.com/paper/2003.04151/) (2020)
- [Few-Shot Learning Through an Information Retrieval Lens](https://mlsanity.com/paper/1707.02610/) (2017)
- [Empirical Bayes Transductive Meta-Learning with Synthetic Gradients](https://mlsanity.com/paper/2004.12696/) (2020)

## Abstract (arXiv)

Learning by examples, which learns to solve a new problem by looking into how similar problems are solved, is an effective learning method in human learning. When a student learns a new topic, he/she finds out exemplar topics that are similar to this new topic and studies the exemplar topics to deepen the understanding of the new topic. We aim to investigate whether this powerful learning skill can be borrowed from humans to improve machine learning as well. In this work, we propose a novel learning approach called Learning By Examples (LBE). Our approach automatically retrieves a set of training examples that are similar to query examples and predicts labels for query examples by using class labels of the retrieved examples. We propose a three-level optimization framework to formulate LBE which involves three stages of learning: learning a Siamese network to retrieve similar examples; learning a matching network to make predictions on query examples by leveraging class labels of retrieved similar examples; learning the ``ground-truth'' similarities between training examples by minimizing the validation loss. We develop an efficient algorithm to solve the LBE problem and conduct extensive experiments on various benchmarks where the results demonstrate the effectiveness of our method on both supervised and few-shot learning.