This paper proposes the Edge Complex Product Basis based on Generalized Asymmetric Contraction, a new formulation for many-body expansion that directly constructs higher-order interactions on edges through complex-valued equivariant multiplications and introduces Radial Rotary Complex Attention (RRA), which enhances extrapolation performance and surpasses existing attention vector formulations.
Abstract
In this paper, we provide a systematic investigation of SO(2) theory to machine learning interatomic potentials (MLIPs) and identify the limitations of conventional SO(2) Linear architectures relative to SO(3) Clebsch-Gordan Tensor Products (CGTP). Building on these insights, we propose direct Cartesian construction and recursive Clebsch-Gordan construction of Wigner D-matrices and introduce two novel interaction building blocks. First, we propose the Edge Complex Product Basis based on Generalized Asymmetric Contraction, a new formulation for many-body expansion that directly constructs higher-order interactions on edges through complex-valued equivariant multiplications. Second, we introduce Radial Rotary Complex Attention(RRA), which enhances extrapolation performance and surpasses existing attention vector formulations. We also introduce several improvements to the Atomic Cluster Expansion module. Building on these advances, we train our models on OMat24, sAlex, and MPTrj, and introduce TECE-OAM-RRA-1.0, which achieve state-of-the-art (SOTA) performance on the Matbench Discovery.
Transformer Atomic Cluster Expansion (TRACE) is introduced, an energy-conserving architecture that combines atomic cluster expansion density correlations with local multihead cross-attention that captures multi-species crystallization, liquid structures, phase diagrams, and chemical reactivity.
While machine-learning interatomic potentials (MLIPs) have successfully learned potential energy surfaces (PES) and atomic forces, many practical applications, such as vibrational analysis and transition state search, rely heavily on the PES Hessian. Yet, standard MLIPs tend to be trained on energy and forces alone, leaving Hessian information largely unexploited. Meanwhile, existing methods that explicitly incorporate the Hessian into training objectives require architectural modifications and introduce significant computational and memory overheads due to higher-order backpropagation. To address these limitations, we propose two Hessian-derived data augmentation schemes: isotropic Gaussian displacement (\textbf{UniAug}) and normal mode-weighted displacement (\textbf{ModeAug}). Both methods utilize simple Taylor expansions, achieving effective augmentation without altering training objectives or extending the autograd graph. This allows seamless, plug-and-play integration with existing architectures and training pipelines. Comprehensive evaluations across non-equilibrium and equilibrium datasets demonstrate that our approach enhances model accuracy while providing practical, task-specific guidelines.
This work proposes an operator-centric framework in which the external (nuclear) potential, expressed in an AO basis, serves as the model input and builds hierarchical, body-ordered representations of atomic configurations that closely mirror the principles underlying several popular atom-centered descriptors.
Jigyasa Nigam, T. Smidt, G. Dusson· Journal of Chemical Physics· 2 citations
Accurate benchmarking of intermolecular interaction energies is central to evaluating quantum chemical methods and guiding the development of reliable machine-learned interatomic potentials (MLIPs). We benchmark five MLIPs (AIMNet2(2023), AIMNet2(2025), MACE-OFF23(M), MACE-OMol, and UMA-S-OMol) across twenty-one datasets spanning hydrogen-bonded, dispersion- and pi-dominated, sigma-hole, ionic and charge transfer, and repulsive nonequilibrium interactions, with reference values at or near CCSD(T)/CBS accuracy. AIMNet2(2025) is a continually pretrained variant of AIMNet2(2023) that retains the original architecture but incorporates 3.8 million additional structures curated to improve noncovalent interactions (NCIs). AIMNet2(2025) improves on its predecessor across nearly all benchmark categories, with the largest gains in the hydrogen-bonded, sigma-hole, and repulsive regimes, while remaining competitive with the much larger MACE-OMol and UMA-S-OMol. The supramolecular S12L and L7 benchmarks show only marginal improvement: every evaluated MLIP exhibits large errors driven by a small number of pathological complexes. Two factors beyond intrinsic model quality significantly influence the reported performance. First, partial overlap between training and benchmark data, quantified here via systematic overlap detection, inflates apparent accuracy for all models, most strongly for those trained on OMol25. Second, differences in the DFT reference level used for MLIP training establish irreducible error floors, so superior benchmark performance may partly reflect closer proximity of the training functional to the CCSD(T)/CBS reference rather than stronger modeling capability. Sigma-hole interactions emerge as the category with the lowest training-benchmark overlap across all models and therefore provide the most discriminating test of true generalization. Meaningful MLIP evaluation must account for data provenance, reference theory consistency, and the distinction between interpolation and out-of-distribution generalization, particularly as standard NCI benchmark sets become absorbed into large-scale training datasets.
Rem3Di is introduced, a representation-learning framework that repurposes latent features from atomistic foundation models as transferable molecular descriptors for property prediction and virtual screening and provides a route from simulation-trained atomistic representations to transferable, chirality-aware molecular representations for chemical machine learning.
Steffen Wedig, Felix Burton, Rokas Elijošius et al.· 0 citations
Finding a low-rank approximation for the two-electron integral (ERI) tensor is a crucial step towards reducing the computational cost of many-body electronic structure methods. In recent years, a range of new tensor factorization techniques, like the so-called tensor-hypercontraction (THC) approach, have been developed to achieve this goal. Unfortunately, a systematic comparison of accuracy and efficiency of different THC construction algorithms is missing. In this work, we address this gap by benchmarking these techniques across a wide range of molecular systems. In addition to offering useful insights into the advantages and disadvantages of the different techniques, we provide reference implementations in the newly developed open-source library, PyTHC.
Niklas Paulicks, Johannes Tölle· 0 citations
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