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smilesun committed Sep 18, 2024
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5 changes: 3 additions & 2 deletions docs/docIRM.md
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Expand Up @@ -7,9 +7,10 @@ where we use $\ell$ to denote the cross entropy for a classification task, and $

The idea of IRM is to choose classifier $w$ to be in the intersection of optimal classifiers for each domain $$d$$.

$$w \in {\argmin}_{\bar{w}} \ell^{(d)}(\bar{w} \circ \Phi) \quad \forall d$$
$$w \in {\arg\min}_{\bar{w}} \ell^{(d)}(\bar{w} \circ \Phi) \quad \forall d$$

regardless of feature extractor $$\Phi(\cdot)$$, this serves as a constraint on the choice of classifiers $w$.
regardless of feature extractor $\Phi(\cdot)$,
this serves as a constraint on the choice of classifiers $w$.

The feature extractor $\Phi(\cdot)$ then get optimized under this constraint.

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