scripts/verify_cka.py

import numpy as np

from src.cka.compute import linear_cka, linear_cka_feature


def hsic_biased(k, l):
    h = np.eye(k.shape[0], dtype=k.dtype) - 1 / k.shape[0]
    return float(np.trace(k @ h @ l @ h))


def hsic_unbiased(k, l):
    m = k.shape[0]
    k_tilde = k.copy()
    l_tilde = l.copy()
    np.fill_diagonal(k_tilde, 0.0)
    np.fill_diagonal(l_tilde, 0.0)
    hsic_value = (
        (np.sum(k_tilde * l_tilde.T))
        + (np.sum(k_tilde) * np.sum(l_tilde) / ((m - 1) * (m - 2)))
        - (2 * np.sum(k_tilde @ l_tilde) / (m - 2))
    )
    hsic_value /= m * (m - 3)
    return float(hsic_value)


def ref_cka(a, b, unbiased=False):
    k = a @ a.T
    l = b @ b.T
    hsic_fn = hsic_unbiased if unbiased else hsic_biased
    hsic_kk = hsic_fn(k, k)
    hsic_ll = hsic_fn(l, l)
    hsic_kl = hsic_fn(k, l)
    return float(hsic_kl / (np.sqrt(hsic_kk * hsic_ll) + 1e-6))


def main():
    rng = np.random.default_rng(0)
    a = rng.standard_normal((64, 128)).astype(np.float64)
    b = rng.standard_normal((64, 128)).astype(np.float64)

    our_biased = linear_cka(a, b, unbiased=False)
    ref_biased = ref_cka(a, b, unbiased=False)

    our_unbiased = linear_cka(a, b, unbiased=True)
    ref_unbiased = ref_cka(a, b, unbiased=True)

    our_feature = linear_cka_feature(a, b)

    print("biased:", our_biased, ref_biased, "diff", abs(our_biased - ref_biased))
    print("unbiased:", our_unbiased, ref_unbiased, "diff", abs(our_unbiased - ref_unbiased))
    print("feature:", our_feature, ref_biased, "diff", abs(our_feature - ref_biased))


if __name__ == "__main__":
    main()