# Flexible Phase Dynamics for Bio-Plausible Contrastive Learning

arXiv: https://arxiv.org/abs/2302.12431 · HTML: https://mlsanity.com/paper/2302.12431/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 48 references that are in the map.
- First posted on arXiv 24 Feb 2023.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [The Forward-Forward Algorithm: Some Preliminary Investigations](https://mlsanity.com/paper/2212.13345/) (2022)
- [Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagation](https://mlsanity.com/paper/1602.05179/) (2016)
- [Stochastic model-based minimization of weakly convex functions](https://mlsanity.com/paper/1803.06523/) (2018)
- [Mini-batch Stochastic Approximation Methods for Nonconvex Stochastic Composite Optimization](https://mlsanity.com/paper/1308.6594/) (2013)
- [Local plasticity rules can learn deep representations using self-supervised contrastive predictions](https://mlsanity.com/paper/2010.08262/) (2020)
- [Holomorphic Equilibrium Propagation Computes Exact Gradients Through Finite Size Oscillations](https://mlsanity.com/paper/2209.00530/) (2022)
- [The Predictive Forward-Forward Algorithm](https://mlsanity.com/paper/2301.01452/) (2023)
- [Equilibrium Propagation with Continual Weight Updates](https://mlsanity.com/paper/2005.04168/) (2020)
- [Kernelized information bottleneck leads to biologically plausible 3-factor Hebbian learning in deep networks](https://mlsanity.com/paper/2006.07123/) (2020)
- [The least-control principle for local learning at equilibrium](https://mlsanity.com/paper/2207.01332/) (2022)

## Built on by (most cited first, 4 of 4)

- [Self-Contrastive Forward-Forward Algorithm](https://mlsanity.com/paper/2409.11593/) (2024)
- [Brain-Inspired Machine Intelligence: A Survey of Neurobiologically-Plausible Credit Assignment](https://mlsanity.com/paper/2312.09257/) (2023)
- [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)

## Abstract (arXiv)

Many learning algorithms used as normative models in neuroscience or as candidate approaches for learning on neuromorphic chips learn by contrasting one set of network states with another. These Contrastive Learning (CL) algorithms are traditionally implemented with rigid, temporally non-local, and periodic learning dynamics that could limit the range of physical systems capable of harnessing CL. In this study, we build on recent work exploring how CL might be implemented by biological or neurmorphic systems and show that this form of learning can be made temporally local, and can still function even if many of the dynamical requirements of standard training procedures are relaxed. Thanks to a set of general theorems corroborated by numerical experiments across several CL models, our results provide theoretical foundations for the study and development of CL methods for biological and neuromorphic neural networks.