Related papers: Machine learning and invariant theory
Applications of machine learning tools to problems of physical interest are often criticized for producing sensitivity at the expense of transparency. To address this concern, we explore a data planing procedure for identifying combinations…
Equivariant neural networks have shown improved performance, expressiveness and sample complexity on symmetrical domains. But for some specific symmetries, representations, and choice of coordinates, the most common point-wise activations,…
Embedding molecular symmetries into machine-learning models is key for efficient learning of chemico-physical scalar properties, but little evidence on how to extend the same strategy to tensorial quantities exists. Here we formulate a…
Recent work has shown the utility of developing machine learning models that respect the structure and symmetries of eigenvectors. These works promote sign invariance, since for any eigenvector v the negation -v is also an eigenvector.…
State-of-the-art deep learning systems often require large amounts of data and computation. For this reason, leveraging known or unknown structure of the data is paramount. Convolutional neural networks (CNNs) are successful examples of…
Human reasoning involves recognising common underlying principles across many examples. The by-products of such reasoning are invariants that capture patterns such as "if someone went somewhere then they are there", expressed using…
It is widely believed that engineering a model to be invariant/equivariant improves generalisation. Despite the growing popularity of this approach, a precise characterisation of the generalisation benefit is lacking. By considering the…
This paper studies separating invariants: mappings on $D$ dimensional domains which are invariant to an appropriate group action, and which separate orbits. The motivation for this study comes from the usefulness of separating invariants in…
Fixed point lattice actions are designed to have continuum classical properties unaffected by discretization effects and reduced lattice artifacts at the quantum level. They provide a possible way to extract continuum physics with coarser…
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…
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 kinematics of many mechanical systems encountered in robotics and other fields, such as single-bearing attitude estimation and SLAM, are naturally posed on homogeneous spaces: That is, their state lies in a smooth manifold equipped with…
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…
We explain equivariant neural networks, a notion underlying breakthroughs in machine learning from deep convolutional neural networks for computer vision to AlphaFold 2 for protein structure prediction, without assuming knowledge of…
We find the complete equivalence group of a class of (1+1)-dimensional second-order evolution equations, which is infinite-dimensional. The equivariant moving frame methodology is invoked to construct, in the regular case of the…
Success of machine learning (ML) in the modern world is largely determined by abundance of data. However at many industrial and scientific problems, amount of data is limited. Application of ML methods to data-scarce scientific problems can…
Geometric Invariant Theory gives a method for constructing quotients for group actions on algebraic varieties which in many cases appear as moduli spaces parametrizing isomorphism classes of geometric objects (vector bundles, polarized…
Nonlinear models and optimization methods have successfully tackled a rapidly growing set of problems in recent years. Indeed, a relatively small toolbox of such models and methods can provide sufficient performance across a large landscape…
In this article we introduce powerful tools and techniques from invariant theory to free analysis. This enables us to study free maps with involution. These maps are free noncommutative analogs of real analytic functions of several…
Training fair machine learning models, aiming for their interpretability and solving the problem of domain shift has gained a lot of interest in the last years. There is a vast amount of work addressing these topics, mostly in separation.…