Neural Group Actions
We introduce an algorithm for designing Neural Group Actions, collections of deep neural network architectures which model symmetric transformations satisfying the laws of a given finite group. This generalizes involutive neural networks $\mathcal{N}$, which satisfy $\mathcal{N}(\mathcal{N}(x))=x$ for any data $x$, the group law of $\mathbb{Z}_2$. We show how to optionally enforce an additional constraint that the group action be volume-preserving. We conjecture, by analogy to a universality result for involutive neural networks, that generative models built from Neural Group Actions are universal approximators for collections of probabilistic transitions adhering to the group laws. We demonstrate experimentally that a Neural Group Action for the quaternion group $Q_8$ can learn how a set of nonuniversal quantum gates satisfying the $Q_8$ group laws act on single qubit quantum states.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Bridging or Breaking: Impact of Intergroup Interactions on Religious Polarization
While exposure to diverse viewpoints may reduce polarization, it can also have a backfire effect and exacerbate polarization when the discussion is adversarial. Here, we examine the question whether intergroup interactio…
Meta-LearningProxemics and Permeability of the Pedestrian Group
People tend to walk in groups, and interactions with those groups have a significant impact on crowd behavior and pedestrian traffic dynamics. Social norms can be seen as unwritten rules regulating people interactions in…
Structural Recurrent Neural Network (SRNN) for Group Activity Analysis
A group of persons can be analyzed at various semantic levels such as individual actions, their interactions, and the activity of the entire group. In this paper, we propose a structural recurrent neural network (SRNN) t…
Learning Group Actions In Disentangled Latent Image Representations
Modeling group actions on latent representations enables controllable transformations of high-dimensional image data. Prior works applying group-theoretic priors or modeling transformations typically operate in the high-…
Identifying Group Anchors in Real-World Group Interactions Under Label Scarcity
Group interactions occur in various real-world contexts, e.g., co-authorship, email communication, and online Q&A. In each group, there is often a particularly significant member, around whom the group is formed. Example…