The authors identify a binding subspace via a Hessian-based algorithm that approximates the model's second-order structure. Interchange interventions projecting activations into the top 50 singular vectors (out of 5120 dimensions) successfully swap binding information between entities across all 40 layers. The subspace, computed on two-entity contexts, generalizes to three-entity contexts, enabling swaps 0-1, 0-2, and 1-2. Random subspaces of all dimensions fail, and Distributed Alignment Search (DAS) succeeds only for the 0-1 swap but not 1-2.
Evidence
interventional
Key metric
Top 50 dimensions (out of 5120) sufficient for all three pairwise binding swaps in 3-entity contexts; random subspaces fail at all dimensions tested
Caveat
The 50-dim subspace may contain spurious non-binding directions; the binding similarity metric does not clearly discriminate between the second and third entities in qualitative plots.