In this article, we propose a topological model to encode partial equivariance in neural networks. To this end, we introduce a class of operators, called P-GENEOs, that change data expressed by measurements, respecting the action of certain sets of transformations, in a non-expansive way. If the set of transformations acting is a group, then we obtain the so-called GENEOs. We then study the spaces of measurements, whose domains are subject to the action of certain self-maps, and the space of P-GENEOs between these spaces. We define pseudo-metrics on them and show some properties of the resulting spaces. In particular, we show how such spaces have convenient approximation and convexity properties.

翻译：本文提出了一种拓扑模型，用于编码神经网络中的部分等变性。为此，我们引入了一类算子，称为P-GENEOs，它们以一种非扩张的方式处理由测量值表示的数据，同时尊重特定变换集合的作用。若所作用的变换集合构成群，则我们所获得的即为GENEOs。随后，我们研究了定义域受到特定自映射作用的测量空间，以及这些空间之间的P-GENEOs空间。我们在其上定义了伪度量，并展示了由此所得空间的一些性质。特别地，我们揭示了这些空间如何具备良好的逼近与凸性性质。