1Cademy - Consider the following formula for a loss function used to train a model on ranked lists of outputs, where `N` is the number of items in a given list `Y`:<br><br>$\mathcal{L} = -\mathbb{E}\left[\frac{1}{N(N-1)}\sum_{\substack{\mathbf{y}_a\in Y, \mathbf{y}_b\in Y \\ \mathbf{y}_a\neq \mathbf{y}_b}} \log\Pr(\mathbf{y}_a \succ \mathbf{y}_b|\mathbf{x})\right]$<br><br>What is the primary analytical consequence of including the normalization term $\frac{1}{N(N-1)}$ in this calculation?

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Listwise Loss Formula from Accumulated Pairwise Comparisons

Multiple Choice

Consider the following formula for a loss function used to train a model on ranked lists of outputs, where N is the number of items in a given list Y:

$\mathcal{L} = -\mathbb{E}\left[\frac{1}{N(N-1)}\sum_{\substack{\mathbf{y}_a\in Y, \mathbf{y}_b\in Y \mathbf{y}_a\neq \mathbf{y}_b}} \log\Pr(\mathbf{y}_a \succ \mathbf{y}_b|\mathbf{x})\right]$

What is the primary analytical consequence of including the normalization term $\frac{1}{N(N-1)}$ in this calculation?

Updated 2025-09-28

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