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Differentiable Scaffolding Tree for Molecular Optimization

Tianfan Fu, Wenhao Gao, Cao Xiao, Jacob Yasonik, Connor W. Coley, Jimeng Sun

TL;DR

This work tackles molecular optimization by introducing a differentiable scaffolding tree (DST) that renders substructure-level representations locally differentiable, enabling gradient-based optimization on discrete molecular graphs. A graph neural network serves as a surrogate oracle to guide DST updates, while a determinantal point process (DPP) ensures diversity among generated molecules. DST achieves sample-efficient optimization with improved interpretability, reducing online oracle usage compared to baselines. Experiments on ZINC 250K across multiple objectives show DST often outperforms state-of-the-art baselines in both objective scores and diversity, underscoring its potential for drug discovery and materials design.

Abstract

The structural design of functional molecules, also called molecular optimization, is an essential chemical science and engineering task with important applications, such as drug discovery. Deep generative models and combinatorial optimization methods achieve initial success but still struggle with directly modeling discrete chemical structures and often heavily rely on brute-force enumeration. The challenge comes from the discrete and non-differentiable nature of molecule structures. To address this, we propose differentiable scaffolding tree (DST) that utilizes a learned knowledge network to convert discrete chemical structures to locally differentiable ones. DST enables a gradient-based optimization on a chemical graph structure by back-propagating the derivatives from the target properties through a graph neural network (GNN). Our empirical studies show the gradient-based molecular optimizations are both effective and sample efficient. Furthermore, the learned graph parameters can also provide an explanation that helps domain experts understand the model output.

Differentiable Scaffolding Tree for Molecular Optimization

TL;DR

This work tackles molecular optimization by introducing a differentiable scaffolding tree (DST) that renders substructure-level representations locally differentiable, enabling gradient-based optimization on discrete molecular graphs. A graph neural network serves as a surrogate oracle to guide DST updates, while a determinantal point process (DPP) ensures diversity among generated molecules. DST achieves sample-efficient optimization with improved interpretability, reducing online oracle usage compared to baselines. Experiments on ZINC 250K across multiple objectives show DST often outperforms state-of-the-art baselines in both objective scores and diversity, underscoring its potential for drug discovery and materials design.

Abstract

The structural design of functional molecules, also called molecular optimization, is an essential chemical science and engineering task with important applications, such as drug discovery. Deep generative models and combinatorial optimization methods achieve initial success but still struggle with directly modeling discrete chemical structures and often heavily rely on brute-force enumeration. The challenge comes from the discrete and non-differentiable nature of molecule structures. To address this, we propose differentiable scaffolding tree (DST) that utilizes a learned knowledge network to convert discrete chemical structures to locally differentiable ones. DST enables a gradient-based optimization on a chemical graph structure by back-propagating the derivatives from the target properties through a graph neural network (GNN). Our empirical studies show the gradient-based molecular optimizations are both effective and sample efficient. Furthermore, the learned graph parameters can also provide an explanation that helps domain experts understand the model output.

Paper Structure

This paper contains 39 sections, 4 theorems, 44 equations, 13 figures, 7 tables, 2 algorithms.

Key Result

Theorem 1

Suppose Assumption assumption:moleculesize and assumption:submodular hold, we have the following relative improvement bound with the optimum where $Z_*$ is the local optimum found by DST -greedy, $X_*$ is the ideal optimal molecule, $X_0$ is an empty molecule, starting point of de novo molecule design. In molecule generation setting, a molecule is a local optimum when its objective value is maxim

Figures (13)

  • Figure 1: Illustration of the overall approach: During inference, we construct the corresponding scaffolding tree and differentiable scaffolding tree (DST ) for each molecule. We optimize each DST along its gradient back-propagated from the GNN and sample scaffolding trees from the optimized DST . After that, we assemble trees into molecules and diversify them for the next iteration.
  • Figure 2: Example of differentiable scaffolding tree. We show non-leaf nodes (grey), leaf nodes (yellow), expansion nodes (blue). The dashed nodes and edges are learnable, corresponding to nodes' identity and existence, respectively. $\widetilde{\mathbf{w}}$ and $\widetilde{\mathbf{A}}$ share the learnable parameters $\{\widehat{\mathbf{w}}_3, \widehat{\mathbf{w}}_4, \widehat{\mathbf{w}}_{5|3}, \widehat{\mathbf{w}}_{6|4}, \widehat{\mathbf{w}}_{7|1}, \widehat{\mathbf{w}}_{8|2} \}$.
  • Figure 3: Oracle efficiency test. Top-100 average score v.s. number of oracle calls.
  • Figure 4: Two steps in optimizing "QED+SA+JNK3+GSK3$\beta$".
  • Figure 5: All the substructures in the vocabulary set $\mathcal{S}$, drawn from ZINC 250K database sterling2015zinc. It includes atoms and single rings appearing more than 1000 times in the ZINC250K database.
  • ...and 8 more figures

Theorems & Definitions (19)

  • Definition 1: Oracle $\mathcal{O}$
  • Definition 2: Substructure
  • Definition 3: Scaffolding Tree $\mathcal{T}$
  • Definition 4
  • Definition 5
  • Definition 6
  • Definition 7
  • Definition 8
  • Definition 9
  • Definition 10: Neighborhood set
  • ...and 9 more