SymmetryLens: A new candidate paradigm for unsupervised symmetry learning via locality and equivariance
We develop a new, unsupervised symmetry learning method that starts with raw data, and gives the minimal (discrete) generator of an underlying Lie group of symmetries, together with a symmetry equivariant representation of the data. The method is able to learn the pixel translation operator from a dataset with only an approximate translation symmetry, and can learn quite different types of symmetries which are not apparent to the naked eye, equally well. The method is based on the formulation of an information-theoretic loss function that measures both the degree to which the dataset is symmetric under a given candidate symmetry, and also, the degree of locality of the samples in the dataset with respect to this symmetry. We demonstrate that this coupling between symmetry and locality, together with a special optimization technique developed for entropy estimation, results in a highly stable system that gives reproducible results. The symmetry actions we consider are group representations, however, we believe the approach has the potential to be generalized to more general, nonlinear actions of non-commutative Lie groups.
Code (0)
등록된 구현이 없습니다.
Tasks
TranslationSimilar Papers 제목 키워드 기반
Blind Recovery of Latent Domains via Unsupervised Symmetry Discovery
Primary motivation in blind inverse problems is to recover signals of interest from corrupted observations without knowing the obfuscating mechanism. Blind deconvolution is a prominent approach when the corruption is con…
Concurrence of Symmetry Breaking and Nonlocality Phase Transitions in Diffusion Models
Diffusion models undergo a phase transition in a critical time window during generation dynamics, with two complementary diagnoses of criticality. The symmetry breaking picture views the critical window as when trajector…
The Locality and Symmetry of Positional Encodings
Positional Encodings (PEs) are used to inject word-order information into transformer-based language models. While they can significantly enhance the quality of sentence representations, their specific contribution to la…
SentenceMulti-Sample Consensus Driven Unsupervised Normal Estimation for 3D Point Clouds
Deep normal estimators have made great strides on synthetic benchmarks. Unfortunately, their performance dramatically drops on the real scan data since they are supervised only on synthetic datasets. The point-wise annot…
Mechanisms for spontaneous symmetry breaking in developing visual cortex
For the brain to recognize local orientations within images, neurons must spontaneously break the translation and rotation symmetry of their response functions -- an archetypal example of unsupervised learning. The domin…