The problem of long-tailed recognition (LTR) has received attention in recent years due to the fundamental power-law distribution of objects in the real-world. Most recent works in LTR use softmax classifiers that have a tendency to correlate classifier norm with the amount of training data for a given class. On the other hand, Prototype classifiers do not suffer from this shortcoming and can deliver promising results simply using Nearest-Class-Mean (NCM), a special case where prototypes are empirical centroids. However, the potential of Prototype classifiers as an alternative to softmax in LTR is relatively underexplored. In this work, we propose Prototype classifiers, which jointly learn prototypes that minimize average cross-entropy loss based on probability scores from distances to prototypes. We theoretically analyze the properties of Euclidean distance based prototype classifiers that leads to stable gradient-based optimization which is robust to outliers. We further enhance Prototype classifiers by learning channel-dependent temperature parameters to enable independent distance scales along each channel. Our analysis shows that prototypes learned by Prototype classifiers are better separated than empirical centroids. Results on four long-tailed recognition benchmarks show that Prototype classifier outperforms or is comparable to the state-of-the-art methods.

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