This work introduces E3x, a software package for building neural networks
that are equivariant with respect to the Euclidean group $\mathrm{E}(3)$,
consisting of translations, rotations, and reflections of three-dimensional
space. Compared to ordinary neural networks, $\mathrm{E}(3)$-equivariant models
promise benefits whenever input and/or output data are quantities associated
with three-dimensional objects. This is because the numeric values of such
quantities (e.g. positions) typically depend on the chosen coordinate system.
Under transformations of the reference frame, the values change predictably,
but the underlying rules can be difficult to learn for ordinary machine
learning models. With built-in $\mathrm{E}(3)$-equivariance, neural networks
are guaranteed to satisfy the relevant transformation rules exactly, resulting
in superior data efficiency and accuracy. The code for E3x is available from
this https URL

这项工作介绍了 E3x，这是一个用于构建神经网络的软件包，它对于欧几里得群 E (3) 是等变的，包括三维空间的平移、旋转和反射。与普通的神经网络相比，E (3) 等变模型在输入和 / 或输出数据为与三维对象相关的量时具有优势。因为这些量的数值值（例如位置）通常取决于所选的坐标系。在参考坐标系的变换下，值会发生可预测的变化，但对于普通的机器学习模型来说，学习这些基本规则可能会很困难。内置 E (3) 等变性后，神经网络保证完全符合相关的变换规则，从而具有卓越的数据效率和准确性。E3x 的代码可以从此 https URL 获得。