论文标题
神经群体的行动
Neural Group Actions
论文作者
论文摘要
我们介绍了一种用于设计神经群体动作的算法，深度神经网络体系结构的集合，这些算法模拟了满足给定有限群体定律的对称转换。这概括了涉及的神经网络$ \ MATHCAL {n} $，它满足$ \ MATHCAL {n}（\ MATHCAL {n}（x）（x）（x））= x $，用于任何数据$ x $，$ \ mathbb {z} _2 _2 $的组定律。我们展示了如何可选地强制执行一个额外的限制，即组动作具有数量的保留。我们以类似于涉及的神经网络的通用结果的猜想，由神经群体作用构建的生成模型是遵守群体定律的概率过渡的通用近似值。我们在实验上证明，针对四元组的神经群体行动$ q_8 $可以学习如何满足单个量子量子状态的$ q_8 $组法律的一组非额量子门。
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.
