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\begin{itemize}
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\item An estimate $\z_i^k$ of its optimal position $\z_i^*$,
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\item An estimate $\s_i^k$ of the aggregation function $\sigma(\z^k) = \frac{1}{N} \sum_{j=1}^{N} \phi_j(\z_j^k)$,
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\item An estimate $\v_i^k$ of the gradient with respect to the second argument of the loss $\sum_{j=1}^{N} \nabla_{[\sigma(\z^k)]} l_j(\z_j^k, \sigma(\z^k))$.
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\item An estimate $\v_i^k$ of the gradient with respect to the second argument of the loss $\frac{1}{N} \sum_{j=1}^{N} \nabla_{[\sigma(\z^k)]} l_j(\z_j^k, \sigma(\z^k))$.
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\end{itemize}
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The step is based on the centralized gradient method using the local estimates:
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8
src/year2/ethics-in-ai/module2/sections/_gen_ai.tex
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8
src/year2/ethics-in-ai/module2/sections/_gen_ai.tex
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\begin{remark}
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Transformative rule: Two purposes of a work:
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\begin{itemize}
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\item Original of the work (e.g., creative work)
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\item Training
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\end{itemize}
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It is allowed if the original and training reason is different.
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\end{remark}
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