# Additive Orthant Loss for Deep Face Recognition
## 3 Orthant Loss
Although the accuracies of ArcCentFace and MagCentFace have increased compared to original ones, it can be seen that ArcOrthFace has the best accuracy in most benchmarks. Table 4 shows identification and verification results of various loss functions for MegaFace. Similar to the results in Table 3, it can be seen that the loss functions using Orthant loss improve identification and verification accuracies. It demonstrates that Orthant loss makes feature spaces distinguishable by improving the inter-class separability and the intra-class compactness. In addition, it shows that MagOrthFace has higher accuracy than MagFace, which demonstrates that Orthant loss can improve the distinguishability of adaptively learned feature spaces of MagFace. In Table 4, it is shown that MagCentFace further improves the distinguishability of the adaptively learned feature spaces compared to MagOrthFace. However, ArcOrthFace shows the highest identification and verification accuracies compared to all the other loss functions. ## 5 Conclusions

In this paper, we proposed an additive Orthant loss to improve the inter-class separability and the intra-class compactness. The Orthant loss uses the rescaled softplus function and an additive margin to move features away from the origin. In addition, the Orthant loss uses 1-bit quantization and element-wise operation to map features to an orthant of each class. Experimental results demonstrated that loss functions combined with Orthant loss improve the recognition accuracy in most benchmarks compared to original loss functions. In particular, we showed that the loss function combining ArcFace with Orthant loss has the best accuracy on MegaFace, a challenging test benchmark containing more than 1 million distractors. In conclusion, Orthant loss, combined with a softmax-based loss function, can improve the accuracy of deep face recognition by improving the intra-class compactness and the inter-class separability. We believe that the proposed Orthant loss can be used as a loss function in recognition systems using various human characteristics, e.g., fingerprint, iris, and palmprint, which will require a future study for each recognition system. Conceptualization, Y.S. ; methodology, Y.S. ; software, Y.S. ; investigation, Y.S. ; writing--original draft preparation, Y.S. ; writing--review and editing, N.Y.Y. ; supervision, N.Y.Y. ; project administration, Y.S. and N.Y.Y. ; funding acquisition, N.Y.Y. All authors have read and agreed to the published version of the manuscript. This work was supported by GIST Research Project grant funded by the GIST in 2022. Not applicable. The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results. ## References

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