Related papers: Group Equivariant Capsule Networks
Capsule networks are a recently developed class of neural networks that potentially address some of the deficiencies with traditional convolutional neural networks. By replacing the standard scalar activations with vectors, and by…
Quantum neural network architectures that have little-to-no inductive biases are known to face trainability and generalization issues. Inspired by a similar problem, recent breakthroughs in machine learning address this challenge by…
In recent years, deep learning techniques have shown great success in various tasks related to inverse problems, where a target quantity of interest can only be observed through indirect measurements by a forward operator. Common approaches…
Capsule networks are a recently proposed type of neural network shown to outperform alternatives in challenging shape recognition tasks. In capsule networks, scalar neurons are replaced with capsule vectors or matrices, whose entries…
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…
Capsule networks are a type of neural network that identify image parts and form the instantiation parameters of a whole hierarchically. The goal behind the network is to perform an inverse computer graphics task, and the network parameters…
Although group convolutional networks are able to learn powerful representations based on symmetry patterns, they lack explicit means to learn meaningful relationships among them (e.g., relative positions and poses). In this paper, we…
Learning invariant representations has been the long-standing approach to self-supervised learning. However, recently progress has been made in preserving equivariant properties in representations, yet do so with highly prescribed…
Capsule networks are recently proposed as an alternative to modern neural network architectures. Neurons are replaced with capsule units that represent specific features or entities with normalized vectors or matrices. The activation of…
Capsule network (CapsNet) was introduced as an enhancement over convolutional neural networks, supplementing the latter's invariance properties with equivariance through pose estimation. CapsNet achieved a very decent performance with a…
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…
The set of functions parameterized by a linear fully-connected neural network is a determinantal variety. We investigate the subvariety of functions that are equivariant or invariant under the action of a permutation group. Examples of such…
Transformation groups, such as translations or rotations, effectively express part of the variability observed in many recognition problems. The group structure enables the construction of invariant signal representations with appealing…
The rising adoption of machine learning in high energy physics and lattice field theory necessitates the re-evaluation of common methods that are widely used in computer vision, which, when applied to problems in physics, can lead to…
To effectively classify graph instances, graph neural networks need to have the capability to capture the part-whole relationship existing in a graph. A capsule is a group of neurons representing complicated properties of entities, which…
We provide a general self-attention formulation to impose group equivariance to arbitrary symmetry groups. This is achieved by defining positional encodings that are invariant to the action of the group considered. Since the group acts on…
A capsule is a group of neurons whose activity vector represents the instantiation parameters of a specific type of entity such as an object or an object part. We use the length of the activity vector to represent the probability that the…
We investigate the relation between end-to-end equivariance and layerwise equivariance in deep neural networks. We prove the following: For a network whose end-to-end function is equivariant with respect to group actions on the input and…
Equivariance has been a long-standing concern in various fields ranging from computer vision to physical modeling. Most previous methods struggle with generality, simplicity, and expressiveness -- some are designed ad hoc for specific data…
Previous work on symmetric group equivariant neural networks generally only considered the case where the group acts by permuting the elements of a single vector. In this paper we derive formulae for general permutation equivariant layers,…