# Flood and Echo Net: Algorithmically Aligned GNNs that Generalize

arXiv: https://arxiv.org/abs/2310.06970 · HTML: https://mlsanity.com/paper/2310.06970/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 38 references that are in the map.
- First posted on arXiv 10 Oct 2023.

## Builds on (most cited first, 25 of 25)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [Recipe for a General, Powerful, Scalable Graph Transformer](https://mlsanity.com/paper/2205.12454/) (2022)
- [On the Bottleneck of Graph Neural Networks and its Practical Implications](https://mlsanity.com/paper/2006.05205/) (2020)
- [How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks](https://mlsanity.com/paper/2009.11848/) (2020)
- [Generalization and Representational Limits of Graph Neural Networks](https://mlsanity.com/paper/2002.06157/) (2020)
- [What graph neural networks cannot learn: depth vs width](https://mlsanity.com/paper/1907.03199/) (2019)
- [Random Features Strengthen Graph Neural Networks](https://mlsanity.com/paper/2002.03155/) (2020)
- [On the equivalence between graph isomorphism testing and function approximation with GNNs](https://mlsanity.com/paper/1905.12560/) (2019)
- [What Can Neural Networks Reason About?](https://mlsanity.com/paper/1905.13211/) (2019)
- [From Local Structures to Size Generalization in Graph Neural Networks](https://mlsanity.com/paper/2010.08853/) (2020)
- [Rethinking the Expressive Power of GNNs via Graph Biconnectivity](https://mlsanity.com/paper/2301.09505/) (2023)
- [DropGNN: Random Dropouts Increase the Expressiveness of Graph Neural Networks](https://mlsanity.com/paper/2111.06283/) (2021)
- [Can You Learn an Algorithm? Generalizing from Easy to Hard Problems with Recurrent Networks](https://mlsanity.com/paper/2106.04537/) (2021)
- [The CLRS Algorithmic Reasoning Benchmark](https://mlsanity.com/paper/2205.15659/) (2022)
- [Approximation Ratios of Graph Neural Networks for Combinatorial Problems](https://mlsanity.com/paper/1905.10261/) (2019)
- [A Complete Expressiveness Hierarchy for Subgraph GNNs via Subgraph Weisfeiler-Lehman Tests](https://mlsanity.com/paper/2302.07090/) (2023)
- [Gophormer: Ego-Graph Transformer for Node Classification](https://mlsanity.com/paper/2110.13094/) (2021)
- [Pointer Graph Networks](https://mlsanity.com/paper/2006.06380/) (2020)
- [A Theoretical Comparison of Graph Neural Network Extensions](https://mlsanity.com/paper/2201.12884/) (2022)
- [Traffic4cast at NeurIPS 2022 -- Predict Dynamics along Graph Edges from Sparse Node Data: Whole City Traffic and ETA from Stationary Vehicle Detectors](https://mlsanity.com/paper/2303.07758/) (2023)
- [Deterministic subgraph detection in broadcast CONGEST](https://mlsanity.com/paper/1705.10195/) (2017)

## Built on by (most cited first, 2 of 2)

- [Learn to Jump: Adaptive Random Walks for Long-Range Propagation through Graph Hierarchies](https://mlsanity.com/paper/2509.01381/) (2025)
- [Fitting Every Hint Is Not Enough: Premature Floods in Recurrent Algorithmic Reasoners](https://mlsanity.com/paper/2610.14982/) (2026)

## Abstract (arXiv)

Most Graph Neural Networks follow the standard message-passing framework where, in each step, all nodes simultaneously communicate with each other. We want to challenge this paradigm by aligning the computation more closely to the execution of distributed algorithms and propose the Flood and Echo Net. A single round of a Flood and Echo Net consists of an origin node and a flooding phase followed by an echo phase. First, during the flooding, messages are sent from the origin and propagated outwards throughout the entire graph. Then, during the echo, the message flow reverses and messages are sent back towards the origin. As nodes are only sparsely activated upon receiving a message, this leads to a wave-like activation pattern that traverses the graph. Through these sparse but parallel activations, the Net becomes more expressive than traditional MPNNs which are limited by the 1-WL test and also is provably more efficient in terms of message complexity. Moreover, the mechanism's inherent ability to generalize across graphs of varying sizes positions it as a practical architecture for the task of algorithmic learning. We test the Flood and Echo Net on a variety of synthetic tasks and the SALSA-CLRS benchmark and find that the algorithmic alignment of the execution improves generalization to larger graph sizes.