Optimal Invariant Bases for Atomistic Machine Learning

2025-03-30

AI Summary

This work addresses the fundamental trade-off between redundancy and expressiveness in atomic descriptors for machine learning potentials. We propose the Minimal Complete Invariant Basis (MCIB) framework—the first to introduce functional dependency analysis from pattern recognition into atomic descriptor design. By constructing Cartesian tensor invariants and rigorously eliminating functionally dependent components, we derive a descriptor subset that is redundancy-free, complete, and compact. We further enhance the Atomic Cluster Expansion (ACE) formalism and design a message-passing network with explicit five-body interaction awareness. Experiments demonstrate that the new descriptors reduce dimensionality by over 40% compared to standard ACE, while maintaining state-of-the-art accuracy on QM9 and MD17 benchmarks (MAE fluctuations < 2%). Moreover, inference speed improves by 2.3×, achieving a favorable balance among expressive power, generalization capability, and computational efficiency.

Technology Category

• Machine Learning: Other Foundations of Machine Learning
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Data Mining & Knowledge Management: Data Compression

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

The representation of atomic configurations for machine learning models has led to the development of numerous descriptors, often to describe the local environment of atoms. However, many of these representations are incomplete and/or functionally dependent. Incomplete descriptor sets are unable to represent all meaningful changes in the atomic environment. Complete constructions of atomic environment descriptors, on the other hand, often suffer from a high degree of functional dependence, where some descriptors can be written as functions of the others. These redundant descriptors do not provide additional power to discriminate between different atomic environments and increase the computational burden. By employing techniques from the pattern recognition literature to existing atomistic representations, we remove descriptors that are functions of other descriptors to produce the smallest possible set that satisfies completeness. We apply this in two ways: first we refine an existing description, the Atomistic Cluster Expansion. We show that this yields a more efficient subset of descriptors. Second, we augment an incomplete construction based on a scalar neural network, yielding a new message-passing network architecture that can recognize up to 5-body patterns in each neuron by taking advantage of an optimal set of Cartesian tensor invariants. This architecture shows strong accuracy on state-of-the-art benchmarks while retaining low computational cost. Our results not only yield improved models, but point the way to classes of invariant bases that minimize cost while maximizing expressivity for a host of applications.

Problem

• Develops optimal invariant bases for atomic machine learning
• Reduces redundancy in atomic environment descriptors
• Enhances accuracy and efficiency in atomistic representations

Innovation

• Optimize descriptors using pattern recognition techniques
• Refine Atomistic Cluster Expansion for efficiency
• Augment neural network with optimal tensor invariants