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.

Recent work on sparse autoencoders (SAEs) has shown promise in extracting interpretable features from neural networks and addressing challenges with polysemantic neurons caused by superposition. In this paper, we apply SAEs to the early vision layers of InceptionV1, a well-studied convolutional neural network, with a focus on curve detectors. Our results demonstrate that SAEs can uncover new interpretable features not apparent from examining individual neurons, including additional curve detectors that fill in previous gaps. We also find that SAEs can decompose some polysemantic neurons into more monosemantic constituent features. These findings suggest SAEs are a valuable tool for understanding InceptionV1, and convolutional neural networks more generally.

Methods for model explainability have become increasingly critical for testing the fairness and soundness of deep learning. Concept-based interpretability techniques, which use a small set of human-interpretable concept exemplars in order to measure the influence of a concept on a model's internal representation of input, are an important thread in this line of research. In this work we show that these explainability methods can suffer the same vulnerability to adversarial attacks as the models they are meant to analyze. We demonstrate this phenomenon on two well-known concept-based interpretability methods: TCAV and faceted feature visualization. We show that by carefully perturbing the examples of the concept that is being investigated, we can radically change the output of the interpretability method. The attacks that we propose can either induce positive interpretations (polka dots are an important concept for a model when classifying zebras) or negative interpretations (stripes are not an important factor in identifying images of a zebra). Our work highlights the fact that in safety-critical applications, there is need for security around not only the machine learning pipeline but also the model interpretation process.

In neuroscience, a tuning dimension is a stimulus attribute that accounts for much of the activation variance of a group of neurons. These are commonly used to decipher the responses of such groups. While researchers have attempted to manually identify an analogue to these tuning dimensions in deep neural networks, we are unaware of an automatic way to discover them. This work contributes an unsupervised framework for identifying and interpreting "tuning dimensions" in deep networks. Our method correctly identifies the tuning dimensions of a synthetic Gabor filter bank and tuning dimensions of the first two layers of InceptionV1 trained on ImageNet.