---
title: "Convolutional Networks on Graphs for Learning Molecular"
description: "Predicting molecular properties with machine learning is hard because molecules vary in size and… 30 references, cited by 136 papers here."
authors: ["David Duvenaud", "Dougal Maclaurin", "Jorge Aguilera-Iparraguirre", "Rafael Gómez-Bombarelli", "Timothy Hirzel", "Alán Aspuru-Guzik", "Ryan P. Adams"]
year: 2015
venue: "arXiv:1509.09292"
source: "https://arxiv.org/abs/1509.09292"
doi: "10.48550/arxiv.1509.09292"
arxiv: "1509.09292"
licence: "CC BY 4.0 (arXiv)"
licence_url: "http://creativecommons.org/licenses/by/4.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/duvenaud-2015-convolutional-networks-graphs-learning-molecular/"
---
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# Convolutional Networks on Graphs for Learning Molecular Fingerprints

**Authors:** [David Duvenaud](https://md.research.elamur.ai/free/en/authors/david-duvenaud/), Dougal Maclaurin, Jorge Aguilera-Iparraguirre, Rafael Gómez-Bombarelli, Timothy Hirzel, Alán Aspuru-Guzik and Ryan P. Adams · **Year:** 2015 · **Venue:** arXiv:1509.09292 · **Licence:** [CC BY 4.0 (arXiv)](http://creativecommons.org/licenses/by/4.0/)

**Links:** [Publisher's page](https://arxiv.org/abs/1509.09292) · [PDF](https://arxiv.org/pdf/1509.09292) · [DOI 10.48550/arxiv.1509.09292](https://doi.org/10.48550/arxiv.1509.09292) · [arXiv 1509.09292](https://arxiv.org/abs/1509.09292) · [OpenAlex](https://openalex.org/W2173027866)

**Citations:** 857 citations (OpenAlex, 2026-10-14) · [136](https://md.research.elamur.ai/free/en/papers/duvenaud-2015-convolutional-networks-graphs-learning-molecular/cited-by/) in our library, of the 149,439 papers whose bibliographies we read

## Summary
Predicting molecular properties with machine learning is hard because molecules vary in size and structure, while most models expect fixed-length inputs. The usual workaround is to compute hand-designed circular fingerprints (ECFP) with existing software and feed these frozen vectors into a regressor or deep network. Duvenaud and colleagues instead make the fingerprint itself learnable. They treat a molecule as a graph, with atoms as nodes and bonds as edges, and rebuild the ECFP pipeline from differentiable parts. The hash becomes a single neural layer applied to an atom plus the sum of its neighbours. Bit-indexing becomes a softmax whose outputs are summed into the fingerprint. The whole pipeline can then be trained end to end with gradient descent. With large random weights the model behaves much like ECFP, and ECFP can be seen as a limiting special case of it. When trained, the neural fingerprints match or outperform standard ones on solubility, drug efficacy and photovoltaic efficiency tasks. They are also more compact and easier to interpret. The work is an early, influential step toward graph neural networks for chemistry.

## Key points
- Atom neighbourhoods are combined by summation rather than sorting, which gives permutation invariance simply and scales well. Each layer has a separate hidden weight matrix for each atom degree (up to 5 bonds in organic molecules).
- On the solubility dataset, with 2048-length fingerprints, pairwise distances from randomly weighted neural fingerprints correlate with ECFP distances at r = 0.823. Random networks with small weights already predict better than ECFP when paired with linear regression.
- Learned features are interpretable without manual effort:
  - For solubility, one feature captures hydrophilic R-OH groups and another captures non-polar repeated rings.
  - For the toxicity datasets SR-MMP and NR-AHR, features pick out sulphur attached to aromatic rings and polycyclic aromatic hydrocarbons.
- Learned features avoid the huge vectors of fixed fingerprints; earlier work needed about 43,000 dimensions.
- The model has two main limitations:
  - How far information travels across the graph is bounded by network depth.
  - It cannot yet distinguish stereoisomers.

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

## Institutions

- [Harvard University](https://md.research.elamur.ai/free/en/universities/harvard-university/) — University, Cambridge, United States · 126 works · 45,130 citations

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## Cite

Cite as: David Duvenaud, Dougal Maclaurin, Jorge Aguilera-Iparraguirre, Rafael Gómez-Bombarelli, Timothy Hirzel, Alán Aspuru-Guzik and Ryan P. Adams. 2015. Convolutional Networks on Graphs for Learning Molecular Fingerprints. arXiv:1509.09292.

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@misc{duvenaud2015convolutional,
  title = {{Convolutional Networks on Graphs for Learning Molecular Fingerprints}},
  author = {David Duvenaud, Dougal Maclaurin, Jorge Aguilera-Iparraguirre, Rafael Gómez-Bombarelli, Timothy Hirzel, Alán Aspuru-Guzik and Ryan P. Adams},
  year = {2015},
  doi = {10.48550/arxiv.1509.09292},
  eprint = {1509.09292},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.1509.09292}
}
```

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*Updated 2 November 2026*