# Feedforward Ordering in Neural Connectomes via Feedback Arc Minimization

arXiv: https://arxiv.org/abs/2506.13799 · HTML: https://mlsanity.com/paper/2506.13799/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 17 references that are in the map.
- First posted on arXiv 13 Jun 2025.

## Builds on (most cited first, 5 of 5)

- [The physics of brain network structure, function, and control](https://mlsanity.com/paper/1809.06441/) (2018)
- [Flow of Information in Feed-Forward Deep Neural Networks](https://mlsanity.com/paper/1603.06220/) (2016)
- [Feedback arcs and node hierarchy in directed networks](https://mlsanity.com/paper/1612.05347/) (2016)
- [Connectomic Constraints on Computation in Feedforward Networks of Spiking Neurons](https://mlsanity.com/paper/1402.4579/) (2014)
- [Minimum Weighted Feedback Arc Sets for Ranking from Pairwise Comparisons](https://mlsanity.com/paper/2412.16181/) (2024)

## Abstract (arXiv)

We present a suite of scalable algorithms for minimizing feedback arcs in large-scale weighted directed graphs, with the goal of revealing biologically meaningful feedforward structure in neural connectomes. Using the FlyWire Connectome Challenge dataset, we demonstrate the effectiveness of our ranking strategies in maximizing the total weight of forward-pointing edges. Our methods integrate greedy heuristics, gain-aware local refinements, and global structural analysis based on strongly connected components. Experiments show that our best solution improves the forward edge weight over previous top-performing methods. All algorithms are implemented efficiently in Python and validated using cloud-based execution on Google Colab Pro+.