# Single-phase deep learning in cortico-cortical networks

arXiv: https://arxiv.org/abs/2206.11769 · HTML: https://mlsanity.com/paper/2206.11769/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 36 references that are in the map.
- First posted on arXiv 23 Jun 2022.

## Builds on (most cited first, 6 of 6)

- [Difference Target Propagation](https://mlsanity.com/paper/1412.7525/) (2014)
- [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)
- [GAIT-prop: A biologically plausible learning rule derived from backpropagation of error](https://mlsanity.com/paper/2006.06438/) (2020)
- [Latent Equilibrium: A unified learning theory for arbitrarily fast computation with arbitrarily slow neurons](https://mlsanity.com/paper/2110.14549/) (2021)
- [Cortico-cerebellar networks as decoupling neural interfaces](https://mlsanity.com/paper/2110.11501/) (2021)

## Built on by (most cited first, 19 of 19)

- [Hebbian Deep Learning Without Feedback](https://mlsanity.com/paper/2209.11883/) (2022)
- [How connectivity structure shapes rich and lazy learning in neural circuits](https://mlsanity.com/paper/2310.08513/) (2023)
- [Improving equilibrium propagation without weight symmetry through Jacobian homeostasis](https://mlsanity.com/paper/2309.02214/) (2023)
- [Learning efficient backprojections across cortical hierarchies in real time](https://mlsanity.com/paper/2212.10249/) (2022)
- [Leveraging dendritic properties to advance machine learning and neuro-inspired computing](https://mlsanity.com/paper/2306.08007/) (2023)
- [Multilevel Interpretability Of Artificial Neural Networks: Leveraging Framework And Methods From Neuroscience](https://mlsanity.com/paper/2408.12664/) (2024)
- [Counter-Current Learning: A Biologically Plausible Dual Network Approach for Deep Learning](https://mlsanity.com/paper/2409.19841/) (2024)
- [An Overlooked Role of Context-Sensitive Dendrites](https://mlsanity.com/paper/2408.11019/) (2024)
- [Beyond Attention: Toward Machines with Intrinsic Higher Mental States](https://mlsanity.com/paper/2505.06257/) (2025)
- [Augmenting learning in neuro-embodied systems through neurobiological first principles](https://mlsanity.com/paper/2407.04525/) (2024)
- [Improving the adaptive and continuous learning capabilities of artificial neural networks: Lessons from multi-neuromodulatory dynamics](https://mlsanity.com/paper/2501.06762/) (2025)
- [Scalable Machines with Intrinsic Higher Mental-State Dynamics](https://mlsanity.com/paper/2603.13453/) (2026)
- [Can Biologically Plausible Temporal Credit Assignment Rules Match BPTT for Neural Similarity? E-prop as an Example](https://mlsanity.com/paper/2506.06904/) (2025)
- [The role of gain neuromodulation in layer-5 pyramidal neurons](https://mlsanity.com/paper/2507.03222/) (2025)
- [Dis-inhibitory neuronal circuits can control the sign of synaptic plasticity](https://mlsanity.com/paper/2310.19614/) (2023)
- [Stimulus-to-Stimulus Learning in RNNs with Cortical Inductive Biases](https://mlsanity.com/paper/2409.13471/) (2024)
- [Single layer tiny Co4 outpaces GPT-2 and GPT-BERT](https://mlsanity.com/paper/2510.08404/) (2025)
- [A Cellular Doctrine of Morality: Intrinsic Active Precision and the Mind-Reality Overload Dilemma](https://mlsanity.com/paper/2605.01376/) (2026)
- [Ontology-constrained multi-LLM scoring of hypothesis support in the predictive processing literature](https://mlsanity.com/paper/2606.05206/) (2026)

## Abstract (arXiv)

The error-backpropagation (backprop) algorithm remains the most common solution to the credit assignment problem in artificial neural networks. In neuroscience, it is unclear whether the brain could adopt a similar strategy to correctly modify its synapses. Recent models have attempted to bridge this gap while being consistent with a range of experimental observations. However, these models are either unable to effectively backpropagate error signals across multiple layers or require a multi-phase learning process, neither of which are reminiscent of learning in the brain. Here, we introduce a new model, Bursting Cortico-Cortical Networks (BurstCCN), which solves these issues by integrating known properties of cortical networks namely bursting activity, short-term plasticity (STP) and dendrite-targeting interneurons. BurstCCN relies on burst multiplexing via connection-type-specific STP to propagate backprop-like error signals within deep cortical networks. These error signals are encoded at distal dendrites and induce burst-dependent plasticity as a result of excitatory-inhibitory top-down inputs. First, we demonstrate that our model can effectively backpropagate errors through multiple layers using a single-phase learning process. Next, we show both empirically and analytically that learning in our model approximates backprop-derived gradients. Finally, we demonstrate that our model is capable of learning complex image classification tasks (MNIST and CIFAR-10). Overall, our results suggest that cortical features across sub-cellular, cellular, microcircuit and systems levels jointly underlie single-phase efficient deep learning in the brain.