Generalization Bounds via Vector-Valued Lₚ Correlation Vα
Hamaneh et al.
A family of dependence measures \(V_\alpha\) that interpolates between total-variation and \(\chi^2\)-type generalisation bounds, and stays finite for heavy-tailed losses when \(\alpha > 2\).
Source published · In the Daily Brief of 23 October 2026
Filed under Learning theory, Probability
Information-theoretic generalisation bounds measure how much a randomised algorithm’s output depends on its training data, typically through mutual information or total variation, which behave differently in high dimensions. Hamaneh, Mojahedian and Yassaee study a one-parameter family \(V_\alpha\) of vector-valued \(L_p\) correlations whose bounds run from total variation at \(\alpha = 1\) to variance and \(\chi^2\) behaviour at \(\alpha = 2\).
For \(\alpha > 2\) the conjugate loss moment falls below two, so the bounds remain finite even when the loss variance is infinite. At \(\alpha = 2\) the bound reads as the spread of the output density across datasets, \(\int \sqrt{\mathrm{Var}_S[p(w \mid S)]}\,dw\). The whole family is invariant under smooth reparameterisations, and an adaptive density stability condition gives explicit rates for Gibbs posteriors under bounded losses.