# Symmetries constrain dynamics in a family of balanced neural networks

arXiv: https://arxiv.org/abs/1602.05092 · HTML: https://mlsanity.com/paper/1602.05092/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Feb 2016.

## Built on by (most cited first, 1 of 1)

- [Learning in Deep Networks under Dale's Constraint](https://mlsanity.com/paper/2608.06963/) (2026)

## Abstract (arXiv)

We examine a family of random firing-rate neural networks in which we enforce the neurobiological constraint of Dale's Law --- each neuron makes either excitatory or inhibitory connections onto its post-synaptic targets. We find that this constrained system may be described as a perturbation from a system with non-trivial symmetries. We analyze the symmetric system using the tools of equivariant bifurcation theory, and demonstrate that the symmetry-implied structures remain evident in the perturbed system. In comparison, spectral characteristics of the network coupling matrix are relatively uninformative about the behavior of the constrained system.