# Learning efficient backprojections across cortical hierarchies in real time

arXiv: https://arxiv.org/abs/2212.10249 · HTML: https://mlsanity.com/paper/2212.10249/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 82 references that are in the map.
- First posted on arXiv 20 Dec 2022.

## Builds on (most cited first, 26 of 26)

- [Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagation](https://mlsanity.com/paper/1602.05179/) (2016)
- [Direct Feedback Alignment Provides Learning in Deep Neural Networks](https://mlsanity.com/paper/1609.01596/) (2016)
- [Difference Target Propagation](https://mlsanity.com/paper/1412.7525/) (2014)
- [Assessing the Scalability of Biologically-Motivated Deep Learning Algorithms and Architectures](https://mlsanity.com/paper/1807.04587/) (2018)
- [Dendritic cortical microcircuits approximate the backpropagation algorithm](https://mlsanity.com/paper/1810.11393/) (2018)
- [Deep Learning without Weight Transport](https://mlsanity.com/paper/1904.05391/) (2019)
- [How Auto-Encoders Could Provide Credit Assignment in Deep Networks via Target Propagation](https://mlsanity.com/paper/1407.7906/) (2014)
- [Towards an integration of deep learning and neuroscience](https://mlsanity.com/paper/1606.03813/) (2016)
- [Towards deep learning with segregated dendrites](https://mlsanity.com/paper/1610.00161/) (2016)
- [Eligibility Traces and Plasticity on Behavioral Time Scales: Experimental Support of neoHebbian Three-Factor Learning Rules](https://mlsanity.com/paper/1801.05219/) (2018)
- [A Theoretical Framework for Target Propagation](https://mlsanity.com/paper/2006.14331/) (2020)
- [Random feedback weights support learning in deep neural networks](https://mlsanity.com/paper/1411.0247/) (2014)
- [Towards Scaling Difference Target Propagation by Learning Backprop Targets](https://mlsanity.com/paper/2201.13415/) (2022)
- [Feedback alignment in deep convolutional networks](https://mlsanity.com/paper/1812.06488/) (2018)
- [Credit Assignment in Neural Networks through Deep Feedback Control](https://mlsanity.com/paper/2106.07887/) (2021)
- [Learning to solve the credit assignment problem](https://mlsanity.com/paper/1906.00889/) (2019)
- [Direct Feedback Alignment with Sparse Connections for Local Learning](https://mlsanity.com/paper/1903.02083/) (2019)
- [Single-phase deep learning in cortico-cortical networks](https://mlsanity.com/paper/2206.11769/) (2022)
- [Latent Equilibrium: A unified learning theory for arbitrarily fast computation with arbitrarily slow neurons](https://mlsanity.com/paper/2110.14549/) (2021)
- [Early Inference in Energy-Based Models Approximates Back-Propagation](https://mlsanity.com/paper/1510.02777/) (2015)
- [Biological credit assignment through dynamic inversion of feedforward networks](https://mlsanity.com/paper/2007.05112/) (2020)
- [The Yin-Yang dataset](https://mlsanity.com/paper/2102.08211/) (2021)
- [A Biologically Plausible Learning Rule for Deep Learning in the Brain](https://mlsanity.com/paper/1811.01768/) (2018)
- [Stochastic inference with spiking neurons in the high-conductance state](https://mlsanity.com/paper/1610.07161/) (2016)
- [Cortical microcircuits as gated-recurrent neural networks](https://mlsanity.com/paper/1711.02448/) (2017)
- [Ghost Units Yield Biologically Plausible Backprop in Deep Neural Networks](https://mlsanity.com/paper/1911.08585/) (2019)

## Built on by (most cited first, 8 of 8)

- [Brain-inspired learning in artificial neural networks: a review](https://mlsanity.com/paper/2305.11252/) (2023)
- [Is artificial consciousness achievable? Lessons from the human brain](https://mlsanity.com/paper/2405.04540/) (2024)
- [Backpropagation through space, time, and the brain](https://mlsanity.com/paper/2403.16933/) (2024)
- [Pretraining with Random Noise for Fast and Robust Learning without Weight Transport](https://mlsanity.com/paper/2405.16731/) (2024)
- [Deep Learning without Weight Symmetry](https://mlsanity.com/paper/2405.20594/) (2024)
- [Spike-based alignment learning solves the weight transport problem](https://mlsanity.com/paper/2503.02642/) (2025)
- [Can Local Learning Match Self-Supervised Backpropagation?](https://mlsanity.com/paper/2601.21683/) (2026)
- [A Variational Latent Equilibrium for Learning in Neuronal Circuits](https://mlsanity.com/paper/2603.09600/) (2026)

## Abstract (arXiv)

Models of sensory processing and learning in the cortex need to efficiently assign credit to synapses in all areas. In deep learning, a known solution is error backpropagation, which however requires biologically implausible weight transport from feed-forward to feedback paths. We introduce Phaseless Alignment Learning (PAL), a bio-plausible method to learn efficient feedback weights in layered cortical hierarchies. This is achieved by exploiting the noise naturally found in biophysical systems as an additional carrier of information. In our dynamical system, all weights are learned simultaneously with always-on plasticity and using only information locally available to the synapses. Our method is completely phase-free (no forward and backward passes or phased learning) and allows for efficient error propagation across multi-layer cortical hierarchies, while maintaining biologically plausible signal transport and learning. Our method is applicable to a wide class of models and improves on previously known biologically plausible ways of credit assignment: compared to random synaptic feedback, it can solve complex tasks with less neurons and learn more useful latent representations. We demonstrate this on various classification tasks using a cortical microcircuit model with prospective coding.