Related papers: Learning Equivariant Functions via Quadratic Forms
For functional data lying on an unknown nonlinear low-dimensional space, we study manifold learning and introduce the notions of manifold mean, manifold modes of functional variation and of functional manifold components. These constitute…
We prove two results on convex subsets of Euclidean spaces invariant under an orthogonal group action. First, we show that invariant spectrahedra admit an equivariant spectrahedral description, i.e., can be described by an equivariant…
The principle of translation equivariance (if an input image is translated an output image should be translated by the same amount), led to the development of convolutional neural networks that revolutionized machine vision. Other…
We study the problem of learning an unknown function using random feature models. Our main contribution is an exact asymptotic analysis of such learning problems with Gaussian data. Under mild regularity conditions for the feature matrix,…
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,…
In machine learning datasets with symmetries, the paradigm for backward compatibility with symmetry-breaking has been to relax equivariant architectural constraints, engineering extra weights to differentiate symmetries of interest.…
Clifford Group Equivariant Neural Networks (CGENNs) leverage Clifford algebras and multivectors as an alternative approach to incorporating group equivariance to ensure symmetry constraints in neural representations. In principle, this…
Humans develop certain cognitive abilities to recognize objects and their transformations without explicit supervision, highlighting the importance of unsupervised representation learning. A fundamental challenge in unsupervised…
In this work, we present a mathematical formulation for machine learning of (1) functions on symmetric matrices that are invariant with respect to the action of permutations by conjugation, and (2) functions on point clouds that are…
Group Equivariant Convolutions (GConvs) enable convolutional neural networks to be equivariant to various transformation groups, but at an additional parameter and compute cost. We investigate the filter parameters learned by GConvs and…
Many classes of images exhibit rotational symmetry. Convolutional neural networks are sometimes trained using data augmentation to exploit this, but they are still required to learn the rotation equivariance properties from the data.…
We give an alternative method to obtain normal forms of reversible equivariant vector fields. We adapt the classical method using tools from invariant theory to establish formulae that take symmetries into account as a starting point.…
We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to…
Optimizing and certifying the positivity of polynomials are fundamental primitives across mathematics and engineering applications, from dynamical systems to operations research. However, solving these problems in practice requires large…
In the current framework of Geometric Quantum Machine Learning, the canonical method for constructing a variational ansatz that respects the symmetry of some group action is by forcing the circuit to be equivariant, i.e., to commute with…
Many machine learning tasks involve learning functions that are known to be invariant or equivariant to certain symmetries of the input data. However, it is often challenging to design neural network architectures that respect these…
Designing equivariance as an inductive bias into deep-nets has been a prominent approach to build effective models, e.g., a convolutional neural network incorporates translation equivariance. However, incorporating these inductive biases…
Extensive work has demonstrated that equivariant neural networks can significantly improve sample efficiency and generalization by enforcing an inductive bias in the network architecture. These applications typically assume that the domain…
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…
Efficient transfer learning algorithms are key to the success of foundation models on diverse downstream tasks even with limited data. Recent works of Basu et al. (2023) and Kaba et al. (2022) propose group averaging (equitune) and…