  We present an approach for analyzing grouping information contained within a
neural network's activations, permitting extraction of spatial layout and
semantic segmentation from the behavior of large pre-trained vision models.
Unlike prior work, our method conducts a holistic analysis of a network's
activation state, leveraging features from all layers and obviating the need to
guess which part of the model contains relevant information. Motivated by
classic spectral clustering, we formulate this analysis in terms of an
optimization objective involving a set of affinity matrices, each formed by
comparing features within a different layer. Solving this optimization problem
using gradient descent allows our technique to scale from single images to
dataset-level analysis, including, in the latter, both intra- and inter-image
relationships. Analyzing a pre-trained generative transformer provides insight
into the computational strategy learned by such models. Equating affinity with
key-query similarity across attention layers yields eigenvectors encoding scene
spatial layout, whereas defining affinity by value vector similarity yields
eigenvectors encoding object identity. This result suggests that key and query
vectors coordinate attentional information flow according to spatial proximity
(a `where' pathway), while value vectors refine a semantic category
representation (a `what' pathway).
