ArcFace.md

ArcFace: Additive Angular Margin Loss for Deep Face Recognition (2019), Jiankang Deng et al.

contributors: @GitYCC

[paper] [code]

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• Method:

  • ArcFace Loss:
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• Margin Boundary: Norm-Softmax, SphereFace, CosFace and ArcFace

  • loss:

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    • Norm-Softmax: $m_1=1$, $m_2=0$, $m_3=0$
    • SphereFace: $m_1>1$, $m_2=0$, $m_3=0$
    • CosFace: $m_1=1$, $m_2=0$, $m_3>0$
    • ArcFace: $m_1=1$, $m_2>0$, $m_3=0$

  • equations of margin boundary

    • given two-class problem: $Class1$ and $Class2$
    • according to above loss function (4), the boundary is where two scores from $Class1$ and $Class2$ are equal. $$ For\ Class1,\ s\cdot(cos(m_1\theta_1+m_2)-m_3)=s\cdot cos(\theta_2) $$
    • Norm-Softmax: $cos\theta_1-cos\theta_2=0\Rightarrow \theta_1-\theta_2=0$
    • SphereFace: $cos(m_1\theta_1)-cos\theta_2=0\Rightarrow m_1\theta_1-\theta_2=0$
    • CosFace: $cos\theta_1-m_3-cos\theta_2=0\Rightarrow cos\theta_1-cos\theta_2-m_3=0$
    • ArcFace: $cos(\theta_1+m_2)-cos\theta_2=0\Rightarrow \theta_1-\theta_2+m_2=0$

  • figures of margin boundary

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    • ArcFace enhance the intra-class compactness and inter-class discrepancy.
    • Despite the numerical similarity between ArcFace and previous works, ArcFace has a better geometric attribute as the angular margin has the exact correspondence to the geodesic distance.

• Results

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