Continuous Uniqueness and Novelty Metrics for Generative Modeling of Inorganic Crystals

To address pressing scientific challenges such as climate change, increasingly sophisticated generative artificial intelligence models are being developed that can efficiently sample the large chemical space of possible functional materials. These models can quickly sample new chemical compositions paired with crystal structures. They are typically evaluated using uniqueness and novelty metrics, which depend on a chosen crystal distance function. However, the most prevalent distance function has four limitations: it fails to quantify the degree of similarity between compounds, cannot distinguish compositional difference and structural difference, lacks Lipschitz continuity against shifts in atomic coordinates, and results in a uniqueness metric that is not invariant against the permutation of generated samples. In this work, we propose using two continuous distance functions to evaluate uniqueness and novelty, which theoretically overcome these limitations. Our experiments show that these distances reveal insights missed by traditional distance functions, providing a more reliable basis for evaluating and comparing generative models for inorganic crystals.

WILTing Trees: Interpreting the Distance Between MPNN Embeddings

We investigate the distance function learned by message passing neural networks (MPNNs) in specific tasks, aiming to capture the functional distance between prediction targets that MPNNs implicitly learn. This contrasts with previous work, which links MPNN distances on arbitrary tasks to structural distances on graphs that ignore task-specific information. To address this gap, we distill the distance between MPNN embeddings into an interpretable graph distance. Our method uses optimal transport on the Weisfeiler Leman Labeling Tree (WILT), where the edge weights reveal subgraphs that strongly influence the distance between embeddings. This approach generalizes two well-known graph kernels and can be computed in linear time. Through extensive experiments, we demonstrate that MPNNs define the relative position of embeddings by focusing on a small set of subgraphs that are known to be functionally important in the domain.