# NeuroSteiner: A Graph Transformer for Wirelength Estimation

arXiv: https://arxiv.org/abs/2407.03792 · HTML: https://mlsanity.com/paper/2407.03792/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 27 references that are in the map.
- First posted on arXiv 4 Jul 2024.

## Builds on (most cited first, 10 of 10)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Recipe for a General, Powerful, Scalable Graph Transformer](https://mlsanity.com/paper/2205.12454/) (2022)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [Learning the Travelling Salesperson Problem Requires Rethinking Generalization](https://mlsanity.com/paper/2006.07054/) (2020)

## Abstract (arXiv)

A core objective of physical design is to minimize wirelength (WL) when placing chip components on a canvas. Computing the minimal WL of a placement requires finding rectilinear Steiner minimum trees (RSMTs), an NP-hard problem. We propose NeuroSteiner, a neural model that distills GeoSteiner, an optimal RSMT solver, to navigate the cost--accuracy frontier of WL estimation. NeuroSteiner is trained on synthesized nets labeled by GeoSteiner, alleviating the need to train on real chip designs. Moreover, NeuroSteiner's differentiability allows to place by minimizing WL through gradient descent. On ISPD 2005 and 2019, NeuroSteiner can obtain 0.3% WL error while being 60% faster than GeoSteiner, or 0.2% and 30%.