Force-Aware Neural Tangent Kernels for Scalable and Robust Active Learning of MLIPs

Active learning for machine-learning interatomic potentials (MLIPs) must address several challenges to be practical: scaling to large candidate pools, leveraging energy-force supervision, and maintaining robustness when candidate pools are biased relative to the target distribution. In this work, we jointly address these challenges. We first introduce a linearly scaling acquisition framework based on chunked feature-space posterior-variance shortlisting. By avoiding materialisation of the candidate and train set kernels, this approach enables screening of ~200k structures within hours and applies broadly to acquisition strategies that score candidates based on molecular similarity metrics. We then extend the Neural Tangent Kernel (NTK) to a force-aware setting via mixed parameter-coordinate derivatives, yielding a force NTK and a joint energy-force NTK that provide natural similarity metrics for vector-field prediction. We demonstrate the effectiveness of the joint energy-force NTK on the OC20 dataset, where force-aware acquisition is crucial: it achieves the lowest energy and force MAE and RMSE across all metrics and distribution splits. Across T1x, PMechDB, and RGD benchmarks, our force NTK methods remain competitive with established baselines while being significantly more efficient than committee-based approaches. Under a controlled candidate-pool shift case study on T1x, acquisition based on pretrained MLIP embeddings and NTKs remains robust, whereas committee-based methods exhibit higher variance. Overall, these results show that a single pretrained MLIP can enable scalable, force-aware, and distribution-robust active learning for foundation-model fine-tuning.

Pretrained Model Representations as Acquisition Signals for Active Learning of MLIPs

Training machine learning interatomic potentials (MLIPs) for reactive chemistry is often bottlenecked by the high cost of quantum chemical labels and the scarcity of transition state configurations in candidate pools. Active learning (AL) can mitigate these costs, but its effectiveness hinges on the acquisition rule. We investigate whether the latent space of a pretrained MLIP already contains the information necessary for effective acquisition, eliminating the need for auxiliary uncertainty heads, Bayesian training and fine-tuning, or committee ensembles. We introduce two acquisition signals derived directly from a pretrained MACE potential: a finite-width neural tangent kernel (NTK) and an activation kernel built from hidden latent space features. On reactive-chemistry benchmarks, both kernels consistently outperform fixed-descriptor baselines, committee disagreement, and random acquisition, reducing the data required to reach performance targets by an average of 38% for energy error and 28% for force error. We further show that the pretrained model induces similarity spaces that preserve chemically meaningful structure and provide more reliable residual uncertainty estimates than randomly initialised or fixed-descriptor-based kernels. Our results suggest that pretraining aligns latent-space geometry with model error, yielding a practical and sufficient acquisition signal for reactive MLIP fine-tuning.

Integral Formulas for Vector Spherical Tensor Products

We derive integral formulas that simplify the Vector Spherical Tensor Product recently introduced by Xie et al., which generalizes the Gaunt tensor product to antisymmetric couplings. In particular, we obtain explicit closed-form expressions for the antisymmetric analogues of the Gaunt coefficients. This enables us to simulate the Clebsch-Gordan tensor product using a single Vector Spherical Tensor Product, yielding a $9\times$ reduction in the required tensor product evaluations. Our results enable efficient and practical implementations of the Vector Spherical Tensor Product, paving the way for applications of this generalization of Gaunt tensor products in $\mathrm{SO}(3)$-equivariant neural networks. Moreover, we discuss how the Gaunt and the Vector Spherical Tensor Products allow to control the expressivity-runtime tradeoff associated with the usual Clebsch-Gordan Tensor Products. Finally, we investigate low rank decompositions of the normalizations of the considered tensor products in view of their use in equivariant neural networks.