# A simple normative network approximates local non-Hebbian learning in the cortex

arXiv: https://arxiv.org/abs/2010.12660 · HTML: https://mlsanity.com/paper/2010.12660/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Oct 2020.

## Built on by (most cited first, 6 of 6)

- [A Normative and Biologically Plausible Algorithm for Independent Component Analysis](https://mlsanity.com/paper/2111.08858/) (2021)
- [Interneurons accelerate learning dynamics in recurrent neural networks for statistical adaptation](https://mlsanity.com/paper/2209.10634/) (2022)
- [Normative framework for deriving neural networks with multi-compartmental neurons and non-Hebbian plasticity](https://mlsanity.com/paper/2302.10051/) (2023)
- [Beyond accuracy: generalization properties of bio-plausible temporal credit assignment rules](https://mlsanity.com/paper/2206.00823/) (2022)
- [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)

## Abstract (arXiv)

To guide behavior, the brain extracts relevant features from high-dimensional data streamed by sensory organs. Neuroscience experiments demonstrate that the processing of sensory inputs by cortical neurons is modulated by instructive signals which provide context and task-relevant information. Here, adopting a normative approach, we model these instructive signals as supervisory inputs guiding the projection of the feedforward data. Mathematically, we start with a family of Reduced-Rank Regression (RRR) objective functions which include Reduced Rank (minimum) Mean Square Error (RRMSE) and Canonical Correlation Analysis (CCA), and derive novel offline and online optimization algorithms, which we call Bio-RRR. The online algorithms can be implemented by neural networks whose synaptic learning rules resemble calcium plateau potential dependent plasticity observed in the cortex. We detail how, in our model, the calcium plateau potential can be interpreted as a backpropagating error signal. We demonstrate that, despite relying exclusively on biologically plausible local learning rules, our algorithms perform competitively with existing implementations of RRMSE and CCA.