相关论文: Grounding Continuous Representations in Geometry: …

Advances in neural operators have introduced discretization invariant surrogate models for PDEs on general geometries, yet many approaches struggle to encode local geometric structure and variable domains efficiently. We introduce enf2enf,…

Recently, Conditional Neural Fields (NeFs) have emerged as a powerful modelling paradigm for PDEs, by learning solutions as flows in the latent space of the Conditional NeF. Although benefiting from favourable properties of NeFs such as…

Deep learning has transformed computational imaging, but traditional pixel-based representations limit their ability to capture continuous, multiscale details of objects. Here we introduce a novel Local Conditional Neural Fields (LCNF)…

Convolutional Neural Networks (CNN) have been successful in processing data signals that are uniformly sampled in the spatial domain (e.g., images). However, most data signals do not natively exist on a grid, and in the process of being…

Many scientific problems require to process data in the form of geometric graphs. Unlike generic graph data, geometric graphs exhibit symmetries of translations, rotations, and/or reflections. Researchers have leveraged such inductive bias…

Although recent efforts have extended Neural Radiance Fields (NeRF) into LiDAR point cloud synthesis, the majority of existing works exhibit a strong dependence on precomputed poses. However, point cloud registration methods struggle to…

Fairness in machine learning is increasingly critical, yet standard approaches often treat data as static points in a high-dimensional space, ignoring the underlying generative structure. We posit that sensitive attributes (e.g., race,…

Neural fields (NeFs) have recently emerged as a versatile method for modeling signals of various modalities, including images, shapes, and scenes. Subsequently, a number of works have explored the use of NeFs as representations for…

Neural networks that process the parameters of other neural networks find applications in domains as diverse as classifying implicit neural representations, generating neural network weights, and predicting generalization errors. However,…

Applications of machine learning techniques for materials modeling typically involve functions known to be equivariant or invariant to specific symmetries. While graph neural networks (GNNs) have proven successful in such tasks, they…

We introduce Equivariant Neural Eikonal Solvers, a novel framework that integrates Equivariant Neural Fields (ENFs) with Neural Eikonal Solvers. Our approach employs a single neural field where a unified shared backbone is conditioned on…

In recent years, Neural Fields (NFs) have emerged as an effective tool for encoding diverse continuous signals such as images, videos, audio, and 3D shapes. When applied to 3D data, NFs offer a solution to the fragmentation and limitations…

Incorporating Euclidean symmetries (e.g. rotation equivariance) as inductive biases into graph neural networks has improved their generalization ability and data efficiency in unbounded physical dynamics modeling. However, in various…

Machine-learning (ML) force fields enable large-scale simulations with near-first-principles accuracy at substantially reduced computational cost. Recent work has extended ML force-field approaches to adiabatic dynamical simulations of…

Conditional Random Field (CRF) and recurrent neural models have achieved success in structured prediction. More recently, there is a marriage of CRF and recurrent neural models, so that we can gain from both non-linear dense features and…

Equivariant machine learning is an approach for designing deep learning models that respect the symmetries of the problem, with the aim of reducing model complexity and improving generalization. In this paper, we focus on an extension of…

This paper presents a novel framework for non-linear equivariant neural network layers on homogeneous spaces. The seminal work of Cohen et al. on equivariant $G$-CNNs on homogeneous spaces characterized the representation theory of such…

Graph Neural Networks (GNN) can capture the geometric properties of neural representations in EEG data. Here we utilise those to study how reinforcement-based motor learning affects neural activity patterns during motor planning, leveraging…

Equivariance is a nice property to have as it produces much more parameter efficient neural architectures and preserves the structure of the input through the feature mapping. Even though some combinations of transformations might never…

Learning to reason about relations and dynamics over multiple interacting objects is a challenging topic in machine learning. The challenges mainly stem from that the interacting systems are exponentially-compositional, symmetrical, and…