# G-softmax: Improving Intra-class Compactness and Inter-class Separability of Features

arXiv: https://arxiv.org/abs/1904.04317 · HTML: https://mlsanity.com/paper/1904.04317/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Apr 2019.

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## Abstract (arXiv)

Intra-class compactness and inter-class separability are crucial indicators to measure the effectiveness of a model to produce discriminative features, where intra-class compactness indicates how close the features with the same label are to each other and inter-class separability indicates how far away the features with different labels are. In this work, we investigate intra-class compactness and inter-class separability of features learned by convolutional networks and propose a Gaussian-based softmax (G-softmax) function that can effectively improve intra-class compactness and inter-class separability. The proposed function is simple to implement and can easily replace the softmax function. We evaluate the proposed G-softmax function on classification datasets (i.e., CIFAR-10, CIFAR-100, and Tiny ImageNet) and on multi-label classification datasets (i.e., MS COCO and NUS-WIDE). The experimental results show that the proposed G-softmax function improves the state-of-the-art models across all evaluated datasets. In addition, analysis of the intra-class compactness and inter-class separability demonstrates the advantages of the proposed function over the softmax function, which is consistent with the performance improvement. More importantly, we observe that high intra-class compactness and inter-class separability are linearly correlated to average precision on MS COCO and NUS-WIDE. This implies that improvement of intra-class compactness and inter-class separability would lead to improvement of average precision.