MARA: Continuous SE(3)-Equivariant Attention for Molecular Force Fields

Machine learning force fields (MLFFs) have become essential for accurate and efficient atomistic modeling. Despite their high accuracy, most existing approaches rely on fixed angular expansions, limiting flexibility in weighting local geometric interactions. We introduce Modular Angular-Radial Attention (MARA), a module that extends spherical attention -- originally developed for SO(3) tasks -- to the molecular domain and SE(3), providing an efficient approximation of equivariant interactions. MARA operates directly on the angular and radial coordinates of neighboring atoms, enabling flexible, geometrically informed, and modular weighting of local environments. Unlike existing attention mechanisms in SE(3)-equivariant architectures, MARA can be integrated in a plug-and-play manner into models such as MACE without architectural modifications. Across molecular benchmarks, MARA improves energy and force predictions, reduces high-error events, and enhances robustness. These results demonstrate that continuous spherical attention is an effective and generalizable geometric operator that increases the expressiveness, stability, and reliability of atomistic models.

Graph-Based Offline Signature Verification

Graphs provide a powerful representation formalism that offers great promise to benefit tasks like handwritten signature verification. While most state-of-the-art approaches to signature verification rely on fixed-size representations, graphs are flexible in size and allow modeling local features as well as the global structure of the handwriting. In this article, we present two recent graph-based approaches to offline signature verification: keypoint graphs with approximated graph edit distance and inkball models. We provide a comprehensive description of the methods, propose improvements both in terms of computational time and accuracy, and report experimental results for four benchmark datasets. The proposed methods achieve top results for several benchmarks, highlighting the potential of graph-based signature verification.

Offline Signature Verification by Combining Graph Edit Distance and Triplet Networks

Biometric authentication by means of handwritten signatures is a challenging pattern recognition task, which aims to infer a writer model from only a handful of genuine signatures. In order to make it more difficult for a forger to attack the verification system, a promising strategy is to combine different writer models. In this work, we propose to complement a recent structural approach to offline signature verification based on graph edit distance with a statistical approach based on metric learning with deep neural networks. On the MCYT and GPDS benchmark datasets, we demonstrate that combining the structural and statistical models leads to significant improvements in performance, profiting from their complementary properties.