Intrinsic dimensionality of molecular properties

Area of Science:

• Computational chemistry
• Machine learning in chemistry

Background:

• Chemical space is vast, posing challenges for computational modeling.
• Machine learning (ML) models benefit from reduced dimensionality in chemical space.
• The limits of dimensionality reduction for physical properties and the impact of model error are not well understood.

Purpose of the Study:

• To investigate how much the dimensionality of physical properties can be reduced by accepting a small model error.
• To determine the dependence of dimensionality reduction on specific physical properties and molecular size.
• To develop a method for quantifying intrinsic dimensionality bounds for given accuracy thresholds.

Main Methods:

• Analysis of dimensionality reduction for total energy, frontier orbital energies, and static polarizability.
• Consideration of neutral molecules up to 20 atoms.
• Inclusion of all continuous variables in the molecular Hamiltonian, including nuclear charges, to define accuracy thresholds.

Main Results:

• A modest, nearly negligible error leads to a drastic reduction in independent degrees of freedom for molecular properties.
• This dimensionality reduction is observed across various properties and molecular sizes.
• The intrinsic dimensionality is stable across molecules, indicating transferability.

Conclusions:

• Accepting a small error significantly reduces the effective dimensionality of chemical space.
• The intrinsic dimensionality is a property of the physical quantity and atom count, not individual configurations.
• These findings suggest opportunities for compressing molecular representations for more efficient and transferable ML models.