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Got rid of a one I don't know why it was there.

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Aner Zakobar
2026-07-03 01:10:25 +03:00
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content/method/method.tex
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@@ -695,7 +695,7 @@ of both classes.
\begin{proposition}[Gradient balance] \begin{proposition}[Gradient balance]
\label{prop:gradient-balance} \label{prop:gradient-balance}
Let $\mathcal{F}$ be any distribution family whose CDF estimator is translation-invariant, Let $\mathcal{F}$ be any distribution family whose CDF estimator is translation-invariant,
meaning $\hat{F}_k(t\,;\,\mathbf{s}+\delta\mathbf{1}) = \hat{F}_k(t-\delta\,;\,\mathbf{s})$ meaning $\hat{F}_k(t\,;\,\mathbf{s}+\delta) = \hat{F}_k(t-\delta\,;\,\mathbf{s})$
for all $\delta \in \mathbb{R}$. Then for any batch $\mathcal{B} = \mathcal{B}_0 \cup \mathcal{B}_1$: for all $\delta \in \mathbb{R}$. Then for any batch $\mathcal{B} = \mathcal{B}_0 \cup \mathcal{B}_1$:
\begin{equation} \begin{equation}
\sum_{\mathbf{x}_i \in \mathcal{B}_1} \sum_{\mathbf{x}_i \in \mathcal{B}_1}