Similarity Metrics

shesha.sim provides extrinsic similarity metrics — measuring how well two representations align with each other. These are distinct from (and empirically uncorrelated with) the intrinsic stability metrics in the core module.

CKA

shesha.sim.cka() computes Centered Kernel Alignment. Invariant to orthogonal transformations and isotropic scaling; widely used for comparing neural network layers.

import shesha.sim as sim

similarity = sim.cka(layer_a, layer_b)
similarity_debiased = sim.cka(layer_a, layer_b, debiased=True)

Procrustes similarity

shesha.sim.procrustes_similarity() finds the best orthogonal alignment between two representations and returns the residual similarity. More sensitive to outliers than CKA (~6× more false alarms in stable regimes).

similarity = sim.procrustes_similarity(X, Y)

RDM similarity (sim module)

shesha.sim.rdm_similarity() is an RSA-style RDM correlation. Rank-based and robust to monotone transformations.

similarity = sim.rdm_similarity(X, Y, metric='cosine', method='spearman')