Linear probes for Othello board states factor into tensor-product structure with square and color embeddings composed by a binding matrix, from which the linear probes can be directly recovered.
Taken together, these works suggest that linear probes may sometimes only recover local readouts of a richer underlying structure
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Tensor Product Representation Probes Reveal Shared Structure Across Linear Directions
Linear probes for Othello board states factor into tensor-product structure with square and color embeddings composed by a binding matrix, from which the linear probes can be directly recovered.