Mutual k-Nearest Neighbor Alignment Metric

Primary alignment metric used in experiments; measures mean intersection of k-nearest neighbor sets between two kernels

Neighborhood — ranked by edge-count

Papers (1)

paper

The Platonic Representation Hypothesis
introducesuses

Findings (2)

finding

As number of nearest neighbors k decreases in CKNNA metric, cross-modal alignment trend becomes more pronounced across both models and tasks
supports
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^-105
supports
Validates robustness of alignment metric choice

Concepts (1)

concept

Representational Alignment
implements
Measure of similarity between the similarity structures (kernels) induced by two different representations

Methods (2)

method

Centered Kernel Alignment
extends
Standard alignment metric cited and compared against; measures global kernel similarity between representations
Centered Kernel Nearest-Neighbor Alignment
extends
Modified CKA metric that restricts cross-covariance to nearest neighbors; introduced in this paper's appendix

Related by similarity (8)

cosine ≥ 0.65 · no typed edge

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

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?question0.768
Open question the authors leave unresolved about interpreting the magnitude of their alignment measurements
What is the appropriate metric for measuring representational alignment, given active debate on merits and deficiencies of all proposed measures?question0.759
Open methodological question acknowledged as limitation
Mutual Information Cap on Alignmentconcept0.748
The theoretical cap on cross-modal alignment determined by mutual information between input signals and model capacity
Alignment Map (ϕ)concept0.742
The bijective function mapping DNN inner neurons to latent variables in causal abstraction; its complexity is the central variable studied
Alignmentconcept0.737
The goal of making model behavior match human values and intentions, often addressed during post-training.
Data-Centric Alignmentconcept0.734
Alignment approach that focuses on curating or modifying training data; the paper bridges this with interpretability methods.
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 1finding0.730
Quantitative bound on observed alignment; raises the open question of whether this gap reflects noise or real misalignment
Brute-Force Alignment Searchmethod0.725
Baseline method that exhaustively searches discrete spaces of localist alignments between high-level variables and neuron groups.