Jean Philip Filling

Jean Philip Filling, Daniel Franzen, Michael Wand

We introduce a tensor-channel equivariant graph neural network for direct prediction of molecular polarizability tensors. Building on the efficient PaiNN architecture, we augment the hidden representation with explicit symmetric rank-2 tensor channels aligned with the decomposition of polarizability into isotropic and anisotropic components. In contrast to approaches that construct tensor outputs only at readout, our model propagates tensor structure throughout message passing using geometrically motivated tensor bases. This yields a target-aligned architecture for tensor-valued molecular prediction. On optimized QM7-X geometries, the proposed model achieves lower full-tensor and anisotropic error than both a PaiNN-style readout baseline and a dielectric MACE baseline under matched training conditions and at nearly identical parameter count. In this controlled setting, it also outperforms MACE while remaining substantially faster at inference. Ablation studies show that the gain does not arise from increased capacity alone, but from the combination of explicit tensor propagation and a traceless target parameterization matched to the anisotropic part of the polarizability tensor. Among the tensor bases considered, the strongest results are obtained from interactions between learned directional features, indicating that these are particularly effective for modeling molecular polarizability. Rotational equivariance tests further confirm that all compared models are numerically equivariant, so the observed improvements are attributable to better learning of the target tensor itself. Overall, our results show that for structured tensor-valued targets, propagating target-aligned tensor features can outperform both readout-only tensor construction and a more general higher-order equivariant model in the present training setting.

Daniel Franzen, Jean Philip Filling, Michael Wand

Group-convolutional neural networks (GCNNs) are among the most important methods for introducing symmetry as an inductive bias in deep learning: In each linear layer, GCNNs sample a transformation group $G$ densely and correlate data and filters in different poses (with suitable anti-aliasing for steerable GCNNs) to maintain equivariance with respect to $G$. Unfortunately, applying filters to many data items resulting from this sampling is expensive (even for translations alone, i.e., in ordinary CNNs), and costs grow exponentially with increasing degrees of freedom (such as translations and rotations in 3D), which often hinders practical applications. In this paper, we propose sampling in feature space, i.e., replacing geometrically dense samples with representative samples selected by feature similarity. This decouples geometric resolution from memory and processing costs during training and inference, providing a novel way to trade off computational effort and accuracy. Our main empirical finding is that a coarse feature-space sampling already preserves classification accuracy remarkably well, which permits precomputation based on geometric similarity, accelerating the training of equivariant 3D classifiers substantially.

Jean Philip Filling, Felix Post, Michael Wand et al.

We introduce a novel equivariant graph neural network (GNN) architecture designed to predict the tensorial response properties of molecules. Unlike traditional frameworks that focus on regressing scalar quantities and derive tensorial properties from their derivatives, our approach maintains $SO(3)$-equivariance through the use of local coordinate frames. Our GNN effectively captures geometric information by integrating scalar, vector, and tensor channels within a local message-passing framework. To assess the accuracy of our model, we apply it to predict the polarizabilities of molecules in the QM7-X dataset and show that tensorial message passing outperforms scalar message passing models. This work marks an advancement towards developing structured, geometry-aware neural models for molecular property prediction.