Generalized feature calibration for distinguishable features

Let $\mathcal{D}$ be a natural distribution over examples, let $n$ be the number of samples, let $\mathcal{F}$ be a family of interpolating models, and let $\varepsilon\geq0$. A partition $L$ is an $\varepsilon$-distinguishable feature when it can be learned with test success at least $1-\varepsilon$ by training a model from $\mathcal{F}$ on $n$ samples labeled by $L$. Feature Calibration. For every such $\mathcal{D},n,\mathcal{F},\varepsilon$, and every $\varepsilon_L$-distinguishable feature $L$, the distributions of the feature and classifier output and of the feature and true label are statistically close:

$$\underset{\substack{f\gets\operatorname{Train}_{\mathcal{F}}(\mathcal{D}^n)\x,y\sim\mathcal{D}}}{(L(x),f(x))}\approx_{\varepsilon}\underset{x,y\sim\mathcal{D}}{(L(x),y)}.$$

The conjecture extends feature calibration beyond explicitly supplied labels to any learnable partition, including features unrelated to the class label. The source presents it as a main conjecture, with no resolution supplied.