相关论文: Group Equivariant Conditional Neural Processes

Motivated by objects such as electric fields or fluid streams, we study the problem of learning stochastic fields, i.e. stochastic processes whose samples are fields like those occurring in physics and engineering. Considering general…

Recent advances in deep learning and Transformers have driven major breakthroughs in robotics by employing techniques such as imitation learning, reinforcement learning, and LLM-based multimodal perception and decision-making. However,…

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…

Incorporating group symmetries via equivariance into neural networks has emerged as a robust approach for overcoming the efficiency and data demands of modern deep learning. While most existing approaches, such as group convolutions and…

In Reinforcement Learning (RL), Convolutional Neural Networks(CNNs) have been successfully applied as function approximators in Deep Q-Learning algorithms, which seek to learn action-value functions and policies in various environments.…

In many real-world applications of regression, conditional probability estimation, and uncertainty quantification, exploiting symmetries rooted in physics or geometry can dramatically improve generalization and sample efficiency. While…

Convolutional Neural Networks (CNNs) traditionally encode translation equivariance via the convolution operation. Generalization to other transformations has recently received attraction to encode the knowledge of the data geometry in group…

We present group equivariant capsule networks, a framework to introduce guaranteed equivariance and invariance properties to the capsule network idea. Our work can be divided into two contributions. First, we present a generic routing by…

Reductive Lie Groups, such as the orthogonal groups, the Lorentz group, or the unitary groups, play essential roles across scientific fields as diverse as high energy physics, quantum mechanics, quantum chromodynamics, molecular dynamics,…

The ability to generalize compositionally is key to understanding the potentially infinite number of sentences that can be constructed in a human language from only a finite number of words. Investigating whether NLP models possess this…

Group equivariant neural networks have proven effective in modelling a wide range of tasks where the data lives in a classical geometric space and exhibits well-defined group symmetries. However, these networks are not suitable for learning…

The effectiveness of neural processes (NPs) in modelling posterior prediction maps -- the mapping from data to posterior predictive distributions -- has significantly improved since their inception. This improvement can be attributed to two…

Group invariant and equivariant Multilayer Perceptrons (MLP), also known as Equivariant Networks, have achieved remarkable success in learning on a variety of data structures, such as sequences, images, sets, and graphs. Using tools from…

This paper proposes a method to construct pretext tasks for self-supervised learning on group equivariant neural networks. Group equivariant neural networks are the models whose structure is restricted to commute with the transformations on…

Equivariant neural networks, whose hidden features transform according to representations of a group G acting on the data, exhibit training efficiency and an improved generalisation performance. In this work, we extend group invariant and…

The translation equivariance of convolutions can make convolutional neural networks translation equivariant or invariant. Equivariance to other transformations (e.g. rotations, affine transformations, scalings) may also be desirable as soon…

Convolutional neural networks have been extremely successful in the image recognition domain because they ensure equivariance to translations. There have been many recent attempts to generalize this framework to other domains, including…

We develop a theory of category-equivariant neural networks (CENNs) that unifies group/groupoid-equivariant networks, poset/lattice-equivariant networks, graph and sheaf neural networks. Equivariance is formulated as naturality in a…

Steerable convolutional neural networks (CNNs) provide a general framework for building neural networks equivariant to translations and transformations of an origin-preserving group $G$, such as reflections and rotations. They rely on…

Euclidean deep learning is often inadequate for addressing real-world signals where the representation space is irregular and curved with complex topologies. Interpreting the geometric properties of such feature spaces has become paramount…