We introduce group crosscoders, an extension of crosscoders that systematically discover and analyse symmetrical features in neural networks. While neural networks often develop equivariant representations without explicit architectural constraints, understanding these emergent symmetries has traditionally relied on manual analysis. Group crosscoders automate this process by performing dictionary learning across transformed versions of inputs under a symmetry group. Applied to InceptionV1's mixed3b layer using the dihedral group $\mathrm{D}_{32}$, our method reveals several key insights: First, it naturally clusters features into interpretable families that correspond to previously hypothesised feature types, providing more precise separation than standard sparse autoencoders. Second, our transform block analysis enables the automatic characterisation of feature symmetries, revealing how different geometric features (such as curves versus lines) exhibit distinct patterns of invariance and equivariance. These results demonstrate that group crosscoders can provide systematic insights into how neural networks represent symmetry, offering a promising new tool for mechanistic interpretability.

本研究针对神经网络中对称特征的手动分析问题，提出了群交叉编码器的创新方法，旨在自动发现和分析对称特征。通过在输入的变换版本中执行字典学习，本方法能够揭示特征的可解释性聚类，并显著改进了特征的不变性和复合性分析，展示了其在神经网络对称性代表性分析中的潜在影响。

用于对称机制分析的群交叉编码器