相关论文: Identifying the Group-Theoretic Structure of Machi…

We introduce group crosscoders, an extension of crosscoders that systematically discover and analyse symmetrical features in neural networks. While neural networks often develop equivariant representations without explicit architectural…

We introduce a sub-symmetry of a differential system as an infinitesimal transformation of a subset of the system that leaves the subset invariant on the solution set of the entire system. We discuss the geometrical meaning and properties…

In recent years, skeleton-based action recognition has become a popular 3D classification problem. State-of-the-art methods typically first represent each motion sequence as a high-dimensional trajectory on a Lie group with an additional…

We develop a new unsupervised symmetry learning method that starts with raw data and provides the minimal generator of an underlying Lie group of symmetries, together with a symmetry-equivariant representation of the data, which turns the…

These are introductory notes on symmetries in quantum field theory and how they apply to particle physics. The notes cover the fundamentals of group theory, their representations, Lie groups, and Lie algebras, along with an elaborate…

We study the global symmetries of the $\mathbb{Z}_2$-orbifold of N=4 Super-Yang-Mills theory and its marginal deformations. The process of orbifolding to obtain an N=2 theory would appear to break the $\mathrm{SU}(4)$ R-symmetry down to…

We propose a framework to understand the unprecedented performance and robustness of deep neural networks using field theory. Correlations between the weights within the same layer can be described by symmetries in that layer, and networks…

We propose a modular, data-driven framework for jointly learning unknown functional mappings and discovering the underlying one-parameter symmetry subgroup governing the data. Unlike conventional geometric deep learning methods that assume…

Symmetry is a powerful tool for finding analytical solutions to differential equations, both partial and ordinary, via the similarity variables or via the invariance of the equation under group transformations. It is the largest group of…

Symmetry is present throughout nature and continues to play an increasingly central role in physics and machine learning. Fundamental symmetries, such as Poincar\'{e} invariance, allow physical laws discovered in laboratories on Earth to be…

We introduce the group-equivariant autoencoder (GE-autoencoder) -- a deep neural network (DNN) method that locates phase boundaries by determining which symmetries of the Hamiltonian have spontaneously broken at each temperature. We use…

Physical symmetries provide a strong inductive bias for constructing functions to analyze data. In particular, this bias may improve robustness, data efficiency, and interpretability of machine learning models. However, building machine…

Learning from unordered sets is a fundamental learning setup, recently attracting increasing attention. Research in this area has focused on the case where elements of the set are represented by feature vectors, and far less emphasis has…

Symmetries play a central role in physics, organizing dynamics, constraining interactions, and determining the effective number of physical degrees of freedom. In parallel, modern artificial intelligence methods have demonstrated a…

Deep metric learning has yielded impressive results in tasks such as clustering and image retrieval by leveraging neural networks to obtain highly discriminative feature embeddings, which can be used to group samples into different classes.…

Structural defects within amorphous packings of symmetric particles can be characterized using a machine learning approach that incorporates structure functions of radial distances and angular arrangement. This yields a scalar field,…

Continuous symmetries and their breaking play a prominent role in contemporary physics. Effective low-energy field theories around symmetry breaking states explain diverse phenomena such as superconductivity, magnetism, and the mass of…

This paper is a study of the Lie groups of point symmetries admitted by a system describing a non-stationary planar flow of an ideal plastic material. For several types of forces involved in the system, the infinitesimal generators which…

Spectral Embedding (SE) has often been used to map data points from non-linear manifolds to linear subspaces for the purpose of classification and clustering. Despite significant advantages, the subspace structure of data in the original…

Computational methods that automatically extract knowledge from data are critical for enabling data-driven materials science. A reliable identification of lattice symmetry is a crucial first step for materials characterization and…