# Optimization theory of Hebbian/anti-Hebbian networks for PCA and whitening

arXiv: https://arxiv.org/abs/1511.09468 · HTML: https://mlsanity.com/paper/1511.09468/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Nov 2015.

## Built on by (most cited first, 2 of 2)

- [Hebbian Semi-Supervised Learning in a Sample Efficiency Setting](https://mlsanity.com/paper/2103.09002/) (2021)
- [Synaptic Plasticity Models and Bio-Inspired Unsupervised Deep Learning: A Survey](https://mlsanity.com/paper/2307.16236/) (2023)

## Abstract (arXiv)

In analyzing information streamed by sensory organs, our brains face challenges similar to those solved in statistical signal processing. This suggests that biologically plausible implementations of online signal processing algorithms may model neural computation. Here, we focus on such workhorses of signal processing as Principal Component Analysis (PCA) and whitening which maximize information transmission in the presence of noise. We adopt the similarity matching framework, recently developed for principal subspace extraction, but modify the existing objective functions by adding a decorrelating term. From the modified objective functions, we derive online PCA and whitening algorithms which are implementable by neural networks with local learning rules, i.e. synaptic weight updates that depend on the activity of only pre- and postsynaptic neurons. Our theory offers a principled model of neural computations and makes testable predictions such as the dropout of underutilized neurons.