Related papers: A quatum inspired neural network for geometric mod…

The fundamental laws of physics are intrinsically geometric, dictating the evolution of systems through principles of symmetry and conservation. While modern machine learning offers powerful tools for modeling complex dynamics from data,…

Graph data often exhibits complex geometric heterogeneity, where structures with varying local curvature, such as tree-like hierarchies and dense communities, coexist within a single network. Existing geometric GNNs, which embed graphs into…

Diffusion generative models have emerged as a powerful framework for addressing problems in structural biology and structure-based drug design. These models operate directly on 3D molecular structures. Due to the unfavorable scaling of…

This work provides an architecture that incorporates depth and tactile information to create rich and accurate 3D models useful for robotic manipulation tasks. This is accomplished through the use of a 3D convolutional neural network (CNN).…

Most state-of-the-art Graph Neural Networks (GNNs) can be defined as a form of graph convolution which can be realized by message passing between direct neighbors or beyond. To scale such GNNs to large graphs, various neighbor-, layer-, or…

The standard cosmological model with cold dark matter posits a hierarchical formation of structures. We introduce topological neural networks (TNNs), implemented as message-passing neural networks on higher-order structures, to effectively…

Quantum many-body physics simulation has important impacts on understanding fundamental science and has applications to quantum materials design and quantum technology. However, due to the exponentially growing size of the Hilbert space…

Group equivariance (e.g. SE(3) equivariance) is a critical physical symmetry in science, from classical and quantum physics to computational biology. It enables robust and accurate prediction under arbitrary reference transformations. In…

Quantum Neural Networks (QNNs) are suggested as one of the quantum algorithms which can be efficiently simulated with a low depth on near-term quantum hardware in the presence of noises. However, their performance highly relies on choosing…

Most Graph Neural Networks (GNNs) propagate messages by treating node embeddings as holistic feature vectors, implicitly assuming uniform relevance across feature dimensions. This limits their ability to selectively transmit informative…

Incorporating inductive biases into ML models is an active area of ML research, especially when ML models are applied to data about the physical world. Equivariant Graph Neural Networks (GNNs) have recently become a popular method for…

Graph neural networks (GNNs) have a message-passing framework in which vector messages are exchanged between graph nodes and updated using feedforward layers. The inclusion of distributed message-passing in the GNN architecture makes them…

We propose Scalable Message Passing Neural Networks (SMPNNs) and demonstrate that, by integrating standard convolutional message passing into a Pre-Layer Normalization Transformer-style block instead of attention, we can produce…

Graph Neural Networks (GNNs) have gained popularity in various learning tasks, with successful applications in fields like molecular biology, transportation systems, and electrical grids. These fields naturally use graph data, benefiting…

A fundamental computation for statistical inference and accurate decision-making is to compute the marginal probabilities or most probable states of task-relevant variables. Probabilistic graphical models can efficiently represent the…

Accurately simulating soft tissue deformation is crucial for surgical training, pre-operative planning, and real-time haptic feedback systems. While physics-based models such as the finite element method (FEM) provide high-fidelity results,…

Graph neural networks (GNNs) are commonly divided into message-passing neural networks (MPNNs) and spectral graph neural networks, reflecting two largely separate research traditions in machine learning and signal processing. This paper…

Spatial networks are networks whose graph topology is constrained by their embedded spatial space. Understanding the coupled spatial-graph properties is crucial for extracting powerful representations from spatial networks. Therefore,…

We introduce tensor field neural networks, which are locally equivariant to 3D rotations, translations, and permutations of points at every layer. 3D rotation equivariance removes the need for data augmentation to identify features in…

Graph neural networks (GNNs) are widely used as surrogates for costly experiments and first-principles simulations to study the behavior of compounds at atomistic scale, and their architectural complexity is constantly increasing to enable…