Symbol σ

The passage around this formula

A reward model. A network is trained to assign a scalar to a prompt–response pair such that the preferred response scores higher. The near-universal choice is the Bradley–Terry model of paired comparisons, published in Biometrika in 1952 for ranking treatments in incomplete block designs [ 5 ] , which assumes each item has a latent scalar merit and that $P(y_A \text{ preferred to } y_B \mid x) = \sigma\!\left(r_\phi(x, y_A) - r_\phi(x, y_B)\right)$. with $\sigma$ the logistic function. Everything downstream inherits the assumptions in that line. Quality is one-dimensional. Preferences are transitive. Disagreement between raters is noise around a single underlying merit, not evidence of two different merits.

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