Localist alignment achieves ~0.51 IIA on MoNLI tasks, near chance performance

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• Best localist alignment achieves IIA of 0.73 on hierarchical equality Both Equality Relations in Layer 1finding0.833
  Shows localist alignment fails to capture the distributed structure found by DAS.
• Localist Alignment Baselinemethod0.793
  Baseline that finds the axis-aligned orthogonal matrix closest to the learned distributed rotation, assuming disjoint neuron groups.
• Over 80% IIA achieved using complex non-linear alignment maps on randomly initialised MLPs in hierarchical equality taskfinding0.777
  Demonstrates that high IIA can be obtained even when model cannot solve the task
• Brute-force search achieves maximum IIA of 0.60 on MoNLI tasksfinding0.747
  DAS substantially outperforms brute-force search on MoNLI across all models.
• Near-perfect IIA can be achieved on randomly initialised models that cannot solve the task, suggesting causal alignment does not require task capabilityclaim0.747
  Empirical support for vacuousness of unrestricted causal abstraction
• Is a mutual nearest-neighbor alignment score of 0.16 indicative of strong alignment with remaining gap being noise, or does it signify poor alignment with major differences left to explain?question0.743
  Open question the authors leave unresolved about interpreting the magnitude of their alignment measurements
• Cross-modal language-vision alignment reaches a maximum of approximately 0.16 on mutual nearest-neighbor metric in Figure 3, well below the theoretical maximum of 1finding0.743
  Quantitative bound on observed alignment; raises the open question of whether this gap reflects noise or real misalignment
• Algorithm 1: Finding Localist Alignment Matrixmethod0.740
  Algorithm that extracts a localist (axis-aligned) approximation from any learned orthogonal rotation matrix for baseline comparison.