# Learning in Deep Networks under Dale's Constraint

arXiv: https://arxiv.org/abs/2608.06963 · HTML: https://mlsanity.com/paper/2608.06963/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 51 references that are in the map.
- First posted on arXiv 7 Aug 2026.

## Builds on (most cited first, 22 of 22)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [The Forward-Forward Algorithm: Some Preliminary Investigations](https://mlsanity.com/paper/2212.13345/) (2022)
- [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)
- [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)
- [Towards deep learning with segregated dendrites](https://mlsanity.com/paper/1610.00161/) (2016)
- [A Theoretical Framework for Target Propagation](https://mlsanity.com/paper/2006.14331/) (2020)
- [Towards Scaling Difference Target Propagation by Learning Backprop Targets](https://mlsanity.com/paper/2201.13415/) (2022)
- [Updates of Equilibrium Prop Match Gradients of Backprop Through Time in an RNN with Static Input](https://mlsanity.com/paper/1905.13633/) (2019)
- [Reverse Differentiation via Predictive Coding](https://mlsanity.com/paper/2103.04689/) (2021)
- [On the relationship between predictive coding and backpropagation](https://mlsanity.com/paper/2106.13082/) (2021)
- [Hebbian Semi-Supervised Learning in a Sample Efficiency Setting](https://mlsanity.com/paper/2103.09002/) (2021)
- [Constrained Predictive Coding as a Biologically Plausible Model of the Cortical Hierarchy](https://mlsanity.com/paper/2210.15752/) (2022)
- [Self-Contrastive Forward-Forward Algorithm](https://mlsanity.com/paper/2409.11593/) (2024)
- [Activation Relaxation: A Local Dynamical Approximation to Backpropagation in the Brain](https://mlsanity.com/paper/2009.05359/) (2020)
- [Tightening the Biological Constraints on Gradient-Based Predictive Coding](https://mlsanity.com/paper/2104.15137/) (2021)
- [Bidirectional predictive coding](https://mlsanity.com/paper/2505.23415/) (2025)
- [The computational and learning benefits of Daleian neural networks](https://mlsanity.com/paper/2210.05961/) (2022)
- [Symmetries constrain dynamics in a family of balanced neural networks](https://mlsanity.com/paper/1602.05092/) (2016)

## Abstract (arXiv)

Biologically plausible learning models aim to explain how neural circuits can implement effective learning under the constraints of real neurons. Although significant progress has been made, a major remaining challenge is that existing models often allow neurons or synapses to represent mixed-sign values, both positive and negative, in violation of a basic aspect of cortical circuitry -- Dale's constraint: biological neurons are either excitatory or inhibitory, but not both, and synapses cannot change sign. In this work, we address this discrepancy by introducing a biologically motivated neural architecture in which both neural activations and learning signals are represented by non-negative activity, and synapses have fixed sign, while still supporting backpropagation-like learning. Our approach uses two complementary interacting non-negative channels to represent positive and negative contributions, inspired by evidence of on-off representations in the brain. These channels are implemented through a simple neural circuit motif, which is repeated throughout the network in both bottom-up and top-down pathways. Combined with a local Hebbian learning rule, the resulting model propagates learning signals and updates weights using only local interactions between neurons. We show theoretically that our learning scheme can exactly recover the backpropagation update despite relying solely on non-negative error signals. Empirically, beyond satisfying stronger biological constraints, the on-off architecture learns efficient representations, yielding substantial gains over comparable vanilla networks on the Tiny ImageNet benchmark. These results demonstrate that effective learning can emerge from biologically plausible mechanisms without requiring mixed-sign signals, providing a step toward more realistic models of neural computation.