Crystal structures are defined by the periodic arrangement of atoms in 3D space, inherently making them equivariant to SO(3) group. A fundamental requirement for crystal property prediction is that the model's output should remain invariant to arbitrary rotational transformations of the input structure. One promising strategy to achieve this invariance is to align the given crystal structure into a canonical orientation with appropriately computed rotations, or called frames. However, existing work either only considers a global frame or solely relies on more advanced local frames based on atoms' local structure. A global frame is too coarse to capture the local structure heterogeneity of the crystal, while local frames may inadvertently disrupt crystal symmetry, limiting their expressivity. In this work, we revisit the frame design problem for crystalline materials and propose a novel approach to construct expressive Symmetry-Preserving Frames, dubbed as SPFrame, for modeling crystal structures.

Crystal structures are defined by the periodic arrangement of atoms in 3D space, inherently making them equivariant to SO(3) group. A fundamental requirement for crystal property prediction is that the model's output should remain invariant to arbitrary rotational transformations of the input structure. One promising strategy to achieve this invariance is to align the given crystal structure into a canonical orientation with appropriately computed rotations, or called frames. However, existing work either only considers a global frame or solely relies on more advanced local frames based on atoms' local structure. A global frame is too coarse to capture the local structure heterogeneity of the crystal, while local frames may inadvertently disrupt crystal symmetry, limiting their expressivity. In this work, we revisit the frame design problem for crystalline materials and propose a novel approach to construct expressive {\bf S}ymmetry Preserving Frames, dubbed as SPFrame, for modeling crystal structures.

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.

We consider the task of predicting Hamiltonian matrices to accelerate electronic structure calculations, which plays an important role in physics, chemistry, and materials science. Motivated by the inherent relationship between the off-diagonal blocks of the Hamiltonian matrix and the SO(2) local frame, we propose a novel and efficient network, called QHNetV2, that achieves global SO(3) equivariance without the costly SO(3) Clebsch-Gordan tensor products. This is achieved by introducing a set of new efficient and powerful SO(2)-equivariant operations and performing all off-diagonal feature updates and message passing within SO(2) local frames, thereby eliminating the need of SO(3) tensor products. Moreover, a continuous SO(2) tensor product is performed within the SO(2) local frame at each node to fuse node features, mimicking the symmetric contraction operation. Extensive experiments on the large QH9 and MD17 datasets demonstrate that our model achieves superior performance across a wide range of molecular structures and trajectories, highlighting its strong generalization capability. The proposed SO(2) operations on SO(2) local frames offer a promising direction for scalable and symmetry-aware learning of electronic structures. Our code will be released as part of the AIRS library https://github.com/divelab/AIRS.

Equivariant neural networks offer strong inductive biases for learning from molecular and geometric data but often rely on specialized, computationally expensive tensor operations. We present a framework to transfers existing tensor field networks into the more efficient local canonicalization paradigm, preserving equivariance while significantly improving the runtime. Within this framework, we systematically compare different equivariant representations in terms of theoretical complexity, empirical runtime, and predictive accuracy. We publish the tensor frames package, a PyTorchGeometric based implementation for local canonicalization, that enables straightforward integration of equivariance into any standard message passing neural network.

Navigation is a fundamental capacity for mobile robots, enabling them to operate autonomously in complex and dynamic environments. Conventional approaches use probabilistic models to localize robots and build maps simultaneously using sensor observations. Recent approaches employ human-inspired learning, such as imitation and reinforcement learning, to navigate robots more effectively. However, these methods suffer from high computational costs, global map inconsistency, and poor generalization to unseen environments. This paper presents a novel method inspired by how humans perceive and navigate themselves effectively in novel environments. Specifically, we first build local frames that mimic how humans represent essential spatial information in the short term. Points in local frames are hybrid representations, including spatial information and learned features, so-called spatial-implicit local frames. Then, we integrate spatial-implicit local frames into the global topological map represented as a factor graph. Lastly, we developed a novel navigation algorithm based on Rapid-Exploring Random Tree Star (RRT*) that leverages spatial-implicit local frames and the topological map to navigate effectively in environments. To validate our approach, we conduct extensive experiments in real-world datasets and in-lab environments. We open our source code at https://github.com/tuantdang/simn}{https://github.com/tuantdang/simn.

--We introduce Corr2Distrib, the first correspondence-based method which estimates a 6D camera pose distribution from an RGB image, explaining the observations. Indeed, symmetries and occlusions introduce visual ambiguities, leading to multiple valid poses. While a few recent methods tackle this problem, they do not rely on local correspondences which, according to the BOP Challenge, are currently the most effective way to estimate a single 6DoF pose solution. Using correspondences to estimate a pose distribution is not straightforward, since ambiguous correspondences induced by visual ambiguities drastically decrease the performance of PnP . With Corr2Distrib, we turn these ambiguities into an advantage to recover all valid poses. Corr2Distrib first learns a symmetry-aware representation for each 3D point on the object's surface, characterized by a descriptor and a local frame. This representation enables the generation of 3DoF rotation hypotheses from single 2D-3D correspondences. Next, we refine these hypotheses into a 6DoF pose distribution using PnP and pose scoring. Our experimental evaluations on complex non-synthetic scenes show that Corr2Distrib outperforms state-of-the-art solutions for both pose distribution estimation and single pose estimation from an RGB image, demonstrating the potential of correspondences-based approaches.

Molecule inverse folding has been a long-standing challenge in chemistry and biology, with the potential to revolutionize drug discovery and material science. Despite specified models have been proposed for different small- or macro-molecules, few have attempted to unify the learning process, resulting in redundant efforts. Complementary to recent advancements in molecular structure prediction, such as RoseTTAFold All-Atom and AlphaFold3, we propose the unified model UniIF for the inverse folding of all molecules. We do such unification in two levels: 1) Data-Level: We propose a unified block graph data form for all molecules, including the local frame building and geometric feature initialization. 2) Model-Level: We introduce a geometric block attention network, comprising a geometric interaction, interactive attention and virtual long-term dependency modules, to capture the 3D interactions of all molecules. Through comprehensive evaluations across various tasks such as protein design, RNA design, and material design, we demonstrate that our proposed method surpasses state-of-the-art methods on all tasks. UniIF offers a versatile and effective solution for general molecule inverse folding.

In many applications of geometric deep learning, the choice of global coordinate frame is arbitrary, and predictions should be independent of the reference frame. In other words, the network should be equivariant with respect to rotations and reflections of the input, i.e., the transformations of O(d). We present a novel framework for building equivariant message passing architectures and modifying existing non-equivariant architectures to be equivariant. Our approach is based on local coordinate frames, between which geometric information is communicated consistently by including tensorial objects in the messages. Our framework can be applied to message passing on geometric data in arbitrary dimensional Euclidean space. While many other approaches for equivariant message passing require specialized building blocks, such as non-standard normalization layers or non-linearities, our approach can be adapted straightforwardly to any existing architecture without such modifications. We explicitly demonstrate the benefit of O(3)-equivariance for a popular point cloud architecture and produce state-of-the-art results on normal vector regression on point clouds.

We present MOTLEE, a distributed mobile multi-object tracking algorithm that enables a team of robots to collaboratively track moving objects in the presence of localization error. Existing approaches to distributed tracking make limiting assumptions regarding the relative spatial relationship of sensors, including assuming a static sensor network or that perfect localization is available. Instead, we develop an algorithm based on the Kalman-Consensus filter for distributed tracking that properly leverages localization uncertainty in collaborative tracking. Further, our method allows the team to maintain an accurate understanding of dynamic objects in the environment by realigning robot frames and incorporating frame alignment uncertainty into our object tracking formulation. We evaluate our method in hardware on a team of three mobile ground robots tracking four people. Compared to previous works that do not account for localization error, we show that MOTLEE is resilient to localization uncertainties, enabling accurate tracking in distributed, dynamic settings with mobile tracking sensors.