Invariance has recently proven to be a powerful inductive bias in machine learning models. One such class of predictive or generative models are tensor networks. We introduce a new numerical algorithm to construct a basis of tensors that are invariant under the action of normal matrix representations of an arbitrary discrete group. This method can be up to several orders of magnitude faster than previous approaches. The group-invariant tensors are then combined into a group-invariant tensor train network, which can be used as a supervised machine learning model. We applied this model to a protein binding classification problem, taking into account problem-specific invariances, and obtained prediction accuracy in line with state-of-the-art deep learning approaches.

翻译：不变性最近已被证明是机器学习模型中一种强大的归纳偏置。张量网络是其中一类预测或生成模型。我们提出了一种新的数值算法，用于构造在任意离散群的正规矩阵表示作用下不变的张量基。该方法可以比先前方法快数个数量级。这些群不变张量随后被组合成一个群不变张量列网络，可用作监督机器学习模型。我们将该模型应用于蛋白质结合分类问题，考虑了问题特定的不变性，并获得了与最先进深度学习方法相一致的预测精度。