Global average pooling (GAP) is a popular component in deep metric learning (DML) for aggregating features. Its effectiveness is often attributed to treating each feature vector as a distinct semantic entity and GAP as a combination of them. Albeit substantiated, such an explanation's algorithmic implications to learn generalizable entities to represent unseen classes, a crucial DML goal, remain unclear. To address this, we formulate GAP as a convex combination of learnable prototypes. We then show that the prototype learning can be expressed as a recursive process fitting a linear predictor to a batch of samples. Building on that perspective, we consider two batches of disjoint classes at each iteration and regularize the learning by expressing the samples of a batch with the prototypes that are fitted to the other batch. We validate our approach on 4 popular DML benchmarks.
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