Related papers: Identifying the Group-Theoretic Structure of Machi…
We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We use fully connected neural networks to model the symmetry transformations and the corresponding…
Recent work has applied supervised deep learning to derive continuous symmetry transformations that preserve the data labels and to obtain the corresponding algebras of symmetry generators. This letter introduces two improved algorithms…
We introduce a machine-learning approach (denoted Symmetry Seeker Neural Network) capable of automatically discovering discrete symmetry groups in physical systems. This method identifies the finite set of parameter transformations that…
Symmetry is a fundamental tool in the exploration of a broad range of complex systems. In machine learning symmetry has been explored in both models and data. In this paper we seek to connect the symmetries arising from the architecture of…
Identifying symmetries in data sets is generally difficult, but knowledge about them is crucial for efficient data handling. Here we present a method how neural networks can be used to identify symmetries. We make extensive use of the…
What are the symmetries of a dataset? Whereas the symmetries of an individual data element can be characterized by its invariance under various transformations, the symmetries of an ensemble of data elements are ambiguous due to Jacobian…
The problem of detecting and quantifying the presence of symmetries in datasets is useful for model selection, generative modeling, and data analysis, amongst others. While existing methods for hard-coding transformations in neural networks…
Symmetry is one of the most central concepts in physics, and it is no surprise that it has also been widely adopted as an inductive bias for machine-learning models applied to the physical sciences. This is especially true for models…
Physical theories grounded in mathematical symmetries are an essential component of our understanding of a wide range of properties of the universe. Similarly, in the domain of machine learning, an awareness of symmetries such as rotation…
Quantum information processing in the presence of continuous symmetry is of wide importance and exhibits many novel physical and mathematical phenomena. SU(d) is a continuous group of particular interest since it represents a fundamental…
Learning disentangled representations is a key step towards effectively discovering and modelling the underlying structure of environments. In the natural sciences, physics has found great success by describing the universe in terms of…
Knowing the symmetries of a polyhedron can be very useful for the analysis of its structure as well as for practical polyhedral computations. In this note, we study symmetry groups preserving the linear, projective and combinatorial…
Symmetry in differential equations reveals invariances and offers a powerful means to reduce model complexity. Lie group analysis characterizes these symmetries through infinitesimal generators, which provide a local, linear criterion for…
Symmetry detection can improve various machine learning tasks. In the context of continuous symmetry detection, current state of the art experiments are limited to detecting affine transformations. Under the manifold assumption, we outline…
Recent work has used deep learning to derive symmetry transformations, which preserve conserved quantities, and to obtain the corresponding algebras of generators. In this letter, we extend this technique to derive sparse representations of…
Symmetry-based disentangled representation learning leverages the group structure of environment transformations to uncover the latent factors of variation. Prior approaches to symmetry-based disentanglement have required strong prior…
We consider the problem of learning a function respecting a symmetry from among a class of symmetries. We develop a unified framework that enables symmetry discovery across a broad range of subgroups including locally symmetric, dihedral…
Symmetries (transformations by group actions) are present in many datasets, and leveraging them holds considerable promise for improving predictions in machine learning. In this work, we aim to understand when and how deep networks -- with…
If supersymmetric particles are discovered, an important problem will be to determine how supersymmetry has been broken. At collider energies, supersymmetry breaking can be parameterised by soft supersymmetry breaking parameters. Several…
Testing whether data breaks symmetries of interest can be important to many fields. This paper describes a simple way that machine learning algorithms (whose outputs have been appropriately symmetrised) can be used to detect symmetry…