Semi-Supervised Learning for Molecular Graphs via Ensemble Consensus

Machine learning is transforming molecular sciences by accelerating property prediction, simulation, and the discovery of new molecules and materials. Acquiring labeled data in these domains is often costly and time-consuming, whereas large collections of unlabeled molecular data are readily available. Standard semi-supervised learning methods often rely on label-preserving augmentations, which are challenging to design in the molecular domain, where minor changes can drastically alter properties. In this work, we show that semi-supervised methods that rely on an ensemble consensus can boost predictive accuracy across a diverse range of molecular datasets, task types, and graph neural network architectures. We find that training with an ensemble consensus objective increases robustness in models and exhibits an effect similar to knowledge distillation; an individual member of an ensemble trained this way outperforms a full ensemble trained in a traditional supervised fashion in almost all cases. In addition, this type of semi-supervised training reduces calibration error.

Same Graph, Different Likelihoods: Calibration of Autoregressive Graph Generators via Permutation-Equivalent Encodings

Autoregressive graph generators define likelihoods via a sequential construction process, but these likelihoods are only meaningful if they are consistent across all linearizations of the same graph. Segmented Eulerian Neighborhood Trails (SENT), a recent linearization method, converts graphs into sequences that can be perfectly decoded and efficiently processed by language models, but admit multiple equivalent linearizations of the same graph. We quantify violations in assigned negative log-likelihood (NLL) using the coefficient of variation across equivalent linearizations, which we call Linearization Uncertainty (LU). Training transformers under four linearization strategies on two datasets, we show that biased orderings achieve lower NLL on their native order but exhibit expected calibration error (ECE) two orders of magnitude higher under random permutation, indicating that these models have learned their training linearization rather than the underlying graph. On the molecular graph benchmark QM9, NLL for generated graphs is negatively correlated with molecular stability (AUC $=0.43$), while LU achieves AUC $=0.85$, suggesting that permutation-based evaluation provides a more reliable quality check for generated molecules. Code is available at https://github.com/lauritsf/linearization-uncertainty

On Joint Regularization and Calibration in Deep Ensembles

Deep ensembles are a powerful tool in machine learning, improving both model performance and uncertainty calibration. While ensembles are typically formed by training and tuning models individually, evidence suggests that jointly tuning the ensemble can lead to better performance. This paper investigates the impact of jointly tuning weight decay, temperature scaling, and early stopping on both predictive performance and uncertainty quantification. Additionally, we propose a partially overlapping holdout strategy as a practical compromise between enabling joint evaluation and maximizing the use of data for training. Our results demonstrate that jointly tuning the ensemble generally matches or improves performance, with significant variation in effect size across different tasks and metrics. We highlight the trade-offs between individual and joint optimization in deep ensemble training, with the overlapping holdout strategy offering an attractive practical solution. We believe our findings provide valuable insights and guidance for practitioners looking to optimize deep ensemble models. Code is available at: https://github.com/lauritsf/ensemble-optimality-gap