# Normative framework for deriving neural networks with multi-compartmental neurons and non-Hebbian plasticity

arXiv: https://arxiv.org/abs/2302.10051 · HTML: https://mlsanity.com/paper/2302.10051/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 115 references that are in the map.
- First posted on arXiv 20 Feb 2023.

## Builds on (most cited first, 27 of 27)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Dendritic cortical microcircuits approximate the backpropagation algorithm](https://mlsanity.com/paper/1810.11393/) (2018)
- [Towards deep learning with segregated dendrites](https://mlsanity.com/paper/1610.00161/) (2016)
- [Eigenvalue and Generalized Eigenvalue Problems: Tutorial](https://mlsanity.com/paper/1903.11240/) (2019)
- [A Hebbian/Anti-Hebbian Neural Network for Linear Subspace Learning: A Derivation from Multidimensional Scaling of Streaming Data](https://mlsanity.com/paper/1503.00669/) (2015)
- [Why do similarity matching objectives lead to Hebbian/anti-Hebbian networks?](https://mlsanity.com/paper/1703.07914/) (2017)
- [Neuroscience-inspired online unsupervised learning algorithms](https://mlsanity.com/paper/1908.01867/) (2019)
- [Constrained Predictive Coding as a Biologically Plausible Model of the Cortical Hierarchy](https://mlsanity.com/paper/2210.15752/) (2022)
- [Dendritic predictive coding: A theory of cortical computation with spiking neurons](https://mlsanity.com/paper/2205.05303/) (2022)
- [Blind nonnegative source separation using biological neural networks](https://mlsanity.com/paper/1706.00382/) (2017)
- [A Hebbian/Anti-Hebbian Network Derived from Online Non-Negative Matrix Factorization Can Cluster and Discover Sparse Features](https://mlsanity.com/paper/1503.00680/) (2015)
- [Structured and Deep Similarity Matching via Structured and Deep Hebbian Networks](https://mlsanity.com/paper/1910.04958/) (2019)
- [A biologically plausible neural network for multi-channel Canonical Correlation Analysis](https://mlsanity.com/paper/2010.00525/) (2020)
- [Biologically plausible single-layer networks for nonnegative independent component analysis](https://mlsanity.com/paper/2010.12632/) (2020)
- [A biologically plausible neural network for Slow Feature Analysis](https://mlsanity.com/paper/2010.12644/) (2020)
- [A Normative and Biologically Plausible Algorithm for Independent Component Analysis](https://mlsanity.com/paper/2111.08858/) (2021)
- [Stochastic Approximation for Canonical Correlation Analysis](https://mlsanity.com/paper/1702.06818/) (2017)
- [An Online Riemannian PCA for Stochastic Canonical Correlation Analysis](https://mlsanity.com/paper/2106.07479/) (2021)
- [A simple normative network approximates local non-Hebbian learning in the cortex](https://mlsanity.com/paper/2010.12660/) (2020)
- [Neural optimal feedback control with local learning rules](https://mlsanity.com/paper/2111.06920/) (2021)
- [Interneurons accelerate learning dynamics in recurrent neural networks for statistical adaptation](https://mlsanity.com/paper/2209.10634/) (2022)
- [ODE-Inspired Analysis for the Biological Version of Oja's Rule in Solving Streaming PCA](https://mlsanity.com/paper/1911.02363/) (2019)
- [A Similarity-preserving Neural Network Trained on Transformed Images Recapitulates Salient Features of the Fly Motion Detection Circuit](https://mlsanity.com/paper/2102.05503/) (2021)
- [Adaptive whitening in neural populations with gain-modulating interneurons](https://mlsanity.com/paper/2301.11955/) (2023)
- [A biologically plausible neural network for local supervision in cortical microcircuits](https://mlsanity.com/paper/2011.15031/) (2020)
- [An online algorithm for contrastive Principal Component Analysis](https://mlsanity.com/paper/2211.07723/) (2022)
- [Neural circuits for dynamics-based segmentation of time series](https://mlsanity.com/paper/2104.11852/) (2021)

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

- [Adaptive whitening with fast gain modulation and slow synaptic plasticity](https://mlsanity.com/paper/2308.13633/) (2023)
- [Duality Principle and Biologically Plausible Learning: Connecting the Representer Theorem and Hebbian Learning](https://mlsanity.com/paper/2309.16687/) (2023)
- [Curl Descent: Non-Gradient Learning Dynamics with Sign-Diverse Plasticity](https://mlsanity.com/paper/2510.02765/) (2025)
- [Neuronal Temporal Filters as Normal Mode Extractors](https://mlsanity.com/paper/2401.03248/) (2024)

## Abstract (arXiv)

An established normative approach for understanding the algorithmic basis of neural computation is to derive online algorithms from principled computational objectives and evaluate their compatibility with anatomical and physiological observations. Similarity matching objectives have served as successful starting points for deriving online algorithms that map onto neural networks (NNs) with point neurons and Hebbian/anti-Hebbian plasticity. These NN models account for many anatomical and physiological observations; however, the objectives have limited computational power and the derived NNs do not explain multi-compartmental neuronal structures and non-Hebbian forms of plasticity that are prevalent throughout the brain. In this article, we unify and generalize recent extensions of the similarity matching approach to address more complex objectives, including a large class of unsupervised and self-supervised learning tasks that can be formulated as symmetric generalized eigenvalue problems or nonnegative matrix factorization problems. Interestingly, the online algorithms derived from these objectives naturally map onto NNs with multi-compartmental neurons and local, non-Hebbian learning rules. Therefore, this unified extension of the similarity matching approach provides a normative framework that facilitates understanding multi-compartmental neuronal structures and non-Hebbian plasticity found throughout the brain.