# DRESS: A Continuous Framework for Structural Graph Refinement

arXiv: https://arxiv.org/abs/2602.20833 · HTML: https://mlsanity.com/paper/2602.20833/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 21 references that are in the map.
- First posted on arXiv 24 Feb 2026.

## Builds on (most cited first, 8 of 8)

- [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)
- [Provably Powerful Graph Networks](https://mlsanity.com/paper/1905.11136/) (2019)
- [On the equivalence between graph isomorphism testing and function approximation with GNNs](https://mlsanity.com/paper/1905.12560/) (2019)
- [From Stars to Subgraphs: Uplifting Any GNN with Local Structure Awareness](https://mlsanity.com/paper/2110.03753/) (2021)
- [Equivariant Subgraph Aggregation Networks](https://mlsanity.com/paper/2110.02910/) (2021)
- [Dynamic Structural Similarity on Graphs](https://mlsanity.com/paper/1805.01419/) (2018)
- [High-Quality Disjoint and Overlapping Community Structure in Large-Scale Complex Networks](https://mlsanity.com/paper/1805.12238/) (2018)

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

- [Breaking Hard Isomorphism Benchmarks with DRESS](https://mlsanity.com/paper/2603.18582/) (2026)

## Abstract (arXiv)

We introduce DRESS, a deterministic, parameter-free framework that iteratively refines the structural similarity of edges in a graph to produce a canonical fingerprint: a real-valued edge vector, obtained by converging a non-linear dynamical system to its unique fixed point. The fingerprint is isomorphism-invariant by construction, numerically stable (strictly bounded, precision-preserving, and mathematically well-posed), fast and embarrassingly parallel to compute: DRESS total runtime is O(I · m · dmax) for I iterations to convergence, and convergence is guaranteed by Birkhoff contraction. We generalize the original equation to Motif-DRESS (arbitrary structural motifs) and Generalized-DRESS (abstract aggregation template), and introduce Delta-DRESS, which runs DRESS on each vertex-deleted subgraph to boost expressiveness. Delta-DRESS empirically separates all 7,983 graphs in a comprehensive Strongly Regular Graph benchmark, and on the tested CFI instances (k = 0,1,2,3), k-deletion (Deltak-DRESS) empirically matches the (k+2)-WL boundary.