Relation between feature halving times and explicit fairness criteria

Establish how the per-feature halving times derived for recursive diffusion-model training relate to explicit fairness criteria, including whether the loss of fragile or under-represented features can be quantitatively characterized in fairness terms.

Background

The theoretical analysis introduces feature-specific halving times that quantify how quickly recursive training erases information associated with different eigen-directions of the linear-response operator. The empirical metrics used in the paper, however, measure distributional distance rather than downstream utility or fairness.

The paper explicitly identifies the connection between these halving times and fairness criteria as unresolved. Resolving it would provide a principled way to assess whether recursive training disproportionately removes information relevant to protected or under-represented groups.