Recent equivariant models have shown significant progress in not just chemical property prediction, but as surrogates for dynamical simulations of molecules and materials. Many of the top performing models in this category are built within the framework of tensor products, which preserves equivariance by restricting interactions and transformations to those that are allowed by symmetry selection rules. Despite being a core part of the modeling process, there has not yet been much attention into understanding what information persists in these equivariant representations, and their general behavior outside of benchmark metrics. In this work, we report on a set of experiments using a simple equivariant graph convolution model on the QM9 dataset, focusing on correlating quantitative performance with the resulting molecular graph embeddings. Our key finding is that, for a scalar prediction task, many of the irreducible representations are simply ignored during training -- specifically those pertaining to vector ($l=1$) and tensor quantities ($l=2$) -- an issue that does not necessarily make itself evident in the test metric. We empirically show that removing some unused orders of spherical harmonics improves model performance, correlating with improved latent space structure. We provide a number of recommendations for future experiments to try and improve efficiency and utilization of equivariant features based on these observations.

翻译：近年来，等变模型不仅在化学性质预测方面取得显著进展，而且已成为分子和材料动力学模拟的替代模型。该领域中许多性能最优的模型均构建在张量积框架内，该框架通过将相互作用和变换限制在对称选择规则允许的范围内来保持等变性。尽管这是建模过程的核心部分，但人们对这些等变表示中持续存在的信息及其在基准指标之外的一般行为尚未给予足够关注。在本研究中，我们报告了在QM9数据集上使用简单等变图卷积模型进行的一系列实验，重点关注定量性能与所得分子图嵌入之间的相关性。我们的关键发现是：对于标量预测任务，训练过程中许多不可约表示被完全忽略——特别是涉及矢量（$l=1$）和张量（$l=2$）的表示——这一问题在测试指标中未必显现。我们通过实验证明，移除部分未使用的球谐函数阶次可提升模型性能，这与潜在空间结构的改善相关。基于这些观察，我们为未来实验提出若干建议，以尝试提高等变特征的效率和利用率。