# How Much Space Has Been Explored? Measuring the Chemical Space Covered by Databases and Machine-Generated Molecules

arXiv: https://arxiv.org/abs/2112.12542 · HTML: https://mlsanity.com/paper/2112.12542/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 67 references that are in the map.
- First posted on arXiv 22 Dec 2021.

## Builds on (most cited first, 21 of 21)

- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [MolGAN: An implicit generative model for small molecular graphs](https://mlsanity.com/paper/1805.11973/) (2018)
- [Graph Convolutional Policy Network for Goal-Directed Molecular Graph Generation](https://mlsanity.com/paper/1806.02473/) (2018)
- [GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generation](https://mlsanity.com/paper/2001.09382/) (2020)
- [GuacaMol: Benchmarking Models for De Novo Molecular Design](https://mlsanity.com/paper/1811.09621/) (2018)
- [Molecular Sets (MOSES): A Benchmarking Platform for Molecular Generation Models](https://mlsanity.com/paper/1811.12823/) (2018)
- [Molecular De Novo Design through Deep Reinforcement Learning](https://mlsanity.com/paper/1704.07555/) (2017)
- [Fr'echet ChemNet Distance: A metric for generative models for molecules in drug discovery](https://mlsanity.com/paper/1803.09518/) (2018)
- [Constrained Graph Variational Autoencoders for Molecule Design](https://mlsanity.com/paper/1805.09076/) (2018)
- [MARS: Markov Molecular Sampling for Multi-objective Drug Discovery](https://mlsanity.com/paper/2103.10432/) (2021)
- [Multi-Objective De Novo Drug Design with Conditional Graph Generative Model](https://mlsanity.com/paper/1801.07299/) (2018)
- [MolecularRNN: Generating realistic molecular graphs with optimized properties](https://mlsanity.com/paper/1905.13372/) (2019)
- [Differentiable Scaffolding Tree for Molecular Optimization](https://mlsanity.com/paper/2109.10469/) (2021)
- [A note on the triangle inequality for the Jaccard distance](https://mlsanity.com/paper/1612.02696/) (2016)
- [JANUS: Parallel Tempered Genetic Algorithm Guided by Deep Neural Networks for Inverse Molecular Design](https://mlsanity.com/paper/2106.04011/) (2021)
- [Artificial Intelligence in Drug Discovery: Applications and Techniques](https://mlsanity.com/paper/2106.05386/) (2021)
- [Generative Models for Automatic Chemical Design](https://mlsanity.com/paper/1907.01632/) (2019)
- [Generative chemistry: drug discovery with deep learning generative models](https://mlsanity.com/paper/2008.09000/) (2020)

## Built on by (most cited first, 27 of 27)

- [Exploring Chemical Space with Score-based Out-of-distribution Generation](https://mlsanity.com/paper/2206.07632/) (2022)
- [Discovering Many Diverse Solutions with Bayesian Optimization](https://mlsanity.com/paper/2210.10953/) (2022)
- [KL-Regularized Reinforcement Learning is Designed to Mode Collapse](https://mlsanity.com/paper/2510.20817/) (2025)
- [Re-evaluating Retrosynthesis Algorithms with Syntheseus](https://mlsanity.com/paper/2310.19796/) (2023)
- [A Prompt Log Analysis of Text-to-Image Generation Systems](https://mlsanity.com/paper/2303.04587/) (2023)
- [Drug Discovery with Dynamic Goal-aware Fragments](https://mlsanity.com/paper/2310.00841/) (2023)
- [Saturn: Sample-efficient Generative Molecular Design using Memory Manipulation](https://mlsanity.com/paper/2405.17066/) (2024)
- [ACEGEN: Reinforcement learning of generative chemical agents for drug discovery](https://mlsanity.com/paper/2405.04657/) (2024)
- [Lo-Hi: Practical ML Drug Discovery Benchmark](https://mlsanity.com/paper/2310.06399/) (2023)
- [Can LLMs Generate Diverse Molecules? Towards Alignment with Structural Diversity](https://mlsanity.com/paper/2410.03138/) (2024)
- [Challenges of Generating Structurally Diverse Graphs](https://mlsanity.com/paper/2409.18859/) (2024)
- [Measuring Diversity: Axioms and Challenges](https://mlsanity.com/paper/2410.14556/) (2024)
- [Pretraining Generative Flow Networks with Inexpensive Rewards for Molecular Graph Generation](https://mlsanity.com/paper/2503.06337/) (2025)
- [Diversity-Aware Reinforcement Learning for de novo Drug Design](https://mlsanity.com/paper/2410.10431/) (2024)
- [Toward Closed-loop Molecular Discovery via Language Model, Property Alignment and Strategic Search](https://mlsanity.com/paper/2512.09566/) (2025)
- [Evaluating machine learning models for predicting pesticide toxicity to honey bees](https://mlsanity.com/paper/2503.24305/) (2025)
- [Test-Time Training Scaling Laws for Chemical Exploration in Drug Design](https://mlsanity.com/paper/2501.19153/) (2025)
- [Diverse Mini-Batch Selection in Reinforcement Learning for Efficient Chemical Exploration in de novo Drug Design](https://mlsanity.com/paper/2506.21158/) (2025)
- [MolPILE -- large-scale, diverse dataset for molecular representation learning](https://mlsanity.com/paper/2509.18353/) (2025)
- [Sample Efficient Generative Optimization for Molecular Design](https://mlsanity.com/paper/2607.12488/) (2026)
- [A study of EHVI vs fixed scalarization for molecule design](https://mlsanity.com/paper/2507.13704/) (2025)
- [Look the Other Way: Designing 'Positive' Molecules with Negative Data via Task Arithmetic](https://mlsanity.com/paper/2507.17876/) (2025)
- [From Tokens to Blocks: A Block-Diffusion Perspective on Molecular Generation](https://mlsanity.com/paper/2601.21964/) (2026)
- [INDIBATOR: Diverse and Fact-Grounded Individuality for Multi-Agent Debate in Molecular Discovery](https://mlsanity.com/paper/2602.01815/) (2026)
- [Evaluating the Diversity of AI-Generated Content with Diversity Profiles](https://mlsanity.com/paper/2608.17731/) (2026)
- [Answer Probing-Guided Search for Diverse Solution Exploration of LLMs](https://mlsanity.com/paper/2608.30345/) (2026)
- [OPDiv: Optimal Selection of Top-K High-Scoring, Diverse Compounds](https://mlsanity.com/paper/2609.28665/) (2026)

## Abstract (arXiv)

Forming a molecular candidate set that contains a wide range of potentially effective compounds is crucial to the success of drug discovery. While most databases and machine-learning-based generation models aim to optimize particular chemical properties, there is limited literature on how to properly measure the coverage of the chemical space by those candidates included or generated. This problem is challenging due to the lack of formal criteria to select good measures of the chemical space. In this paper, we propose a novel evaluation framework for measures of the chemical space based on two analyses: an axiomatic analysis with three intuitive axioms that a good measure should obey, and an empirical analysis on the correlation between a measure and a proxy gold standard. Using this framework, we are able to identify #Circles, a new measure of chemical space coverage, which is superior to existing measures both analytically and empirically. We further evaluate how well the existing databases and generation models cover the chemical space in terms of #Circles. The results suggest that many generation models fail to explore a larger space over existing databases, which leads to new opportunities for improving generation models by encouraging exploration.