# A contrastive rule for meta-learning

arXiv: https://arxiv.org/abs/2104.01677 · HTML: https://mlsanity.com/paper/2104.01677/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 130 references that are in the map.
- First posted on arXiv 4 Apr 2021.

## Builds on (most cited first, 30 of 46)

- [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)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [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)
- [Surrogate Gradient Learning in Spiking Neural Networks](https://mlsanity.com/paper/1901.09948/) (2019)
- [Learning to learn by gradient descent by gradient descent](https://mlsanity.com/paper/1606.04474/) (2016)
- [Meta-Learning with Implicit Gradients](https://mlsanity.com/paper/1909.04630/) (2019)
- [Learning to Learn without Forgetting by Maximizing Transfer and Minimizing Interference](https://mlsanity.com/paper/1810.11910/) (2018)
- [Meta-Learning with Latent Embedding Optimization](https://mlsanity.com/paper/1807.05960/) (2018)
- [Tune: A Research Platform for Distributed Model Selection and Training](https://mlsanity.com/paper/1807.05118/) (2018)
- [BatchEnsemble: An Alternative Approach to Efficient Ensemble and Lifelong Learning](https://mlsanity.com/paper/2002.06715/) (2020)
- [Neural Processes](https://mlsanity.com/paper/1807.01622/) (2018)
- [How to train your MAML](https://mlsanity.com/paper/1810.09502/) (2018)
- [Optimizing Millions of Hyperparameters by Implicit Differentiation](https://mlsanity.com/paper/1911.02590/) (2019)
- [Continual learning with hypernetworks](https://mlsanity.com/paper/1906.00695/) (2019)
- [Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagation](https://mlsanity.com/paper/1602.05179/) (2016)
- [Hyperparameter optimization with approximate gradient](https://mlsanity.com/paper/1602.02355/) (2016)
- [Truncated Back-propagation for Bilevel Optimization](https://mlsanity.com/paper/1810.10667/) (2018)
- [Meta-Learning Representations for Continual Learning](https://mlsanity.com/paper/1905.12588/) (2019)
- [SuperSpike: Supervised learning in multi-layer spiking neural networks](https://mlsanity.com/paper/1705.11146/) (2017)
- [Long short-term memory and learning-to-learn in networks of spiking neurons](https://mlsanity.com/paper/1803.09574/) (2018)
- [Recasting Gradient-Based Meta-Learning as Hierarchical Bayes](https://mlsanity.com/paper/1801.08930/) (2018)
- [Deep Bayesian Bandits Showdown: An Empirical Comparison of Bayesian Deep Networks for Thompson Sampling](https://mlsanity.com/paper/1802.09127/) (2018)

## Built on by (most cited first, 14 of 14)

- [Dataset Distillation with Convexified Implicit Gradients](https://mlsanity.com/paper/2302.06755/) (2023)
- [Holomorphic Equilibrium Propagation Computes Exact Gradients Through Finite Size Oscillations](https://mlsanity.com/paper/2209.00530/) (2022)
- [Energy-based learning algorithms for analog computing: a comparative study](https://mlsanity.com/paper/2312.15103/) (2023)
- [Learning where to learn: Gradient sparsity in meta and continual learning](https://mlsanity.com/paper/2110.14402/) (2021)
- [Beyond backpropagation: bilevel optimization through implicit differentiation and equilibrium propagation](https://mlsanity.com/paper/2205.03076/) (2022)
- [Bottom-up and top-down approaches for the design of neuromorphic processing systems: Tradeoffs and synergies between natural and artificial intelligence](https://mlsanity.com/paper/2106.01288/) (2021)
- [Making Scalable Meta Learning Practical](https://mlsanity.com/paper/2310.05674/) (2023)
- [The least-control principle for local learning at equilibrium](https://mlsanity.com/paper/2207.01332/) (2022)
- [Agnostic Physics-Driven Deep Learning](https://mlsanity.com/paper/2205.15021/) (2022)
- [Quantum Equilibrium Propagation: Gradient-Descent Training of Quantum Systems](https://mlsanity.com/paper/2406.00879/) (2024)
- [Improving equilibrium propagation without weight symmetry through Jacobian homeostasis](https://mlsanity.com/paper/2309.02214/) (2023)
- [Predicting Flat-Fading Channels via Meta-Learned Closed-Form Linear Filters and Equilibrium Propagation](https://mlsanity.com/paper/2110.00414/) (2021)
- [Learning to Learn with Contrastive Meta-Objective](https://mlsanity.com/paper/2410.05975/) (2024)
- [Predicting Multi-Antenna Frequency-Selective Channels via Meta-Learned Linear Filters based on Long-Short Term Channel Decomposition](https://mlsanity.com/paper/2203.12715/) (2022)

## Abstract (arXiv)

Humans and other animals are capable of improving their learning performance as they solve related tasks from a given problem domain, to the point of being able to learn from extremely limited data. While synaptic plasticity is generically thought to underlie learning in the brain, the precise neural and synaptic mechanisms by which learning processes improve through experience are not well understood. Here, we present a general-purpose, biologically-plausible meta-learning rule which estimates gradients with respect to the parameters of an underlying learning algorithm by simply running it twice. Our rule may be understood as a generalization of contrastive Hebbian learning to meta-learning and notably, it neither requires computing second derivatives nor going backwards in time, two characteristic features of previous gradient-based methods that are hard to conceive in physical neural circuits. We demonstrate the generality of our rule by applying it to two distinct models: a complex synapse with internal states which consolidate task-shared information, and a dual-system architecture in which a primary network is rapidly modulated by another one to learn the specifics of each task. For both models, our meta-learning rule matches or outperforms reference algorithms on a wide range of benchmark problems, while only using information presumed to be locally available at neurons and synapses. We corroborate these findings with a theoretical analysis of the gradient estimation error incurred by our rule.