CKA shows a very weak trend of alignment between models even within modality, compared to mutual k-NN which shows stronger trends

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• As number of nearest neighbors k decreases in CKNNA metric, cross-modal alignment trend becomes more pronounced across both models and tasksfinding0.865
  Shows cross-modal alignment is primarily local rather than global
• Spearman's rank correlation among different alignment metrics (CKA, SVCCA, Mutual k-NN, CKNNA) over 78 vision models is high across variants, with all p-values below 2.24×10^-105finding0.786
  Validates robustness of alignment metric choice
• Correlative methods like RSA and CKA are insufficient for determining functional similarity between neural systems; causal methods are necessaryclaim0.781
  Central motivating claim of the paper; supported by empirical comparisons showing RSA/CKA miss Markovian differences detectable by MAS.
• CKA and RSA show potentially unintuitive (over-estimated) hidden state similarity for GRU-Transformer comparisons on Multi-Object taskfinding0.781
  Prior work shows transformers use anti-Markovian solutions; MAS correctly shows low IIA reflecting this, while RSA/CKA do not detect it.
• Alignment type is the only significant predictor of koan scores (p=0.006); architecture, parameter count, open/closed weights, MoE/dense are all non-significantfinding0.769
  Main statistical finding: what predicts scores is training approach, not size or architecture
• Does alignment type predict meta-cognitive style when models review consciousness research, as well as koan responses?question0.766
  Four frontier models reviewing the paper each responded in the mode their alignment type predicts; N=1, awaiting systematic study
• 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?question0.758
  Open question the authors leave unresolved about interpreting the magnitude of their alignment measurements
• The effect of alignment map ϕ complexity on IIA in causal abstraction is an analogue of the probing complexity–accuracy trade-offclaim0.758
  Authors connect their finding to the prior probing literature debate