Imagem do filme "Ivan Vasilievich muda de profissão"

? , - . — , . . — , , , .

- .

(backbone) — , , , — , . InsightFace — Open Source .
(embedding) — , . 128 512. , 512. : . , , , — . , ( ) 1, — -1 ( 0).
Embedding- — , , ( ) .
— , ( ) , — , — . $W^TX + b$ , $X$ — ( ), $W$ — , $b$ — . softmax.

, , . — , , . — ( — ), — . .

: (metric learning) .

L o s s = \sum_{i = 0}^{N} [| | f_{i}^{a} - f_{i}^{p} | |_{2}^{2} - [| | f_{i}^{a} - f_{i}^{n} | |_{2}^{2} + α],

$Loss = \sum_{i=0}^N[||f_{i}^a - f_{i}^p||_{2}^2 - [||f_{i}^a - f_{i}^n||_{2}^2 + \alpha],$

$f^a$ — anchor, , ;
$f^p$ — positive, ;
$f^n$ — negative, ;
$\alpha$ — , .

, , $\alpha$ - .

, ( — ), , , embedding- .

Triplet Loss , “ ”, , , SotA , . , Triplet Loss (fine-tuning) . , .

, , , , , . :

Classificação

— , ( 512), — ( , ). — () , . , “ ” . : , , . . , :

: , , , . , . , , Triplet Loss — , , (hard sampling), .

— , , : Softmax Cross Entropy — . Softmax Loss.

Softmax Loss

Softmax, . :

$W$ — ()
$X$ — embedding-,
$b$ — bias,

, ( , embedding- ): $z =W^TX + b$ . Softmax( $\sigma$ ) :

σ (z)_{j} = \frac{e^{z_{j}}}{\sum_{i = 0}^{C} e^{z_{i}}}

$\sigma(z)_j = \frac{e^{z_j}} {\sum_{i=0}^C e^{z_i} }$

— Cross Entropy, Softmax Loss :

L_{S o f t m a x} = - \frac{1}{N} \sum_{i = 1}^{N} l o g \frac{e^{W_{y_{i}}^{T} x_{i} + b_{y_{i}}}}{\sum_{j = 1}^{C} e^{W_{j}^{T} x_{i} + b_{j}}},

$L_{Softmax} = - \frac {1}{N} \sum_{i=1}^N log\frac {e^{W^T_{y_i}x_i + b_{y_i}}}{\sum_{j=1}^C e^{W_j^Tx_i + b_j}},$

$y_i$ — . , , 42, 42- .

— , .

: $W^TX + b$ — : $b = 0$ , $W^TX$ . , . :

$X$ $F\times B$ , $B$ — ( ), $F$ — ( 512).
$W$ $F\times C$ , $C$ — .

$W^T$ $X$ $C\times B$ , .

, :

c o s (θ) = \frac{d o t (u, v)}{| | u | | | | v | |}

$cos(\theta) = \frac {dot(u,v)}{||u||||v||}$

, : — , . , , ( $||W_i|| = 1$ ), $X$ s (scale), :

W^{T} X = s * c o s (θ)

$W^TX = s*cos(\theta)$

A escala é o nosso primeiro de dois hiperparâmetros. Corrigir isso para todos os vetores leva ao fato de que agora eles estão localizados na hiperesfera. Em uma versão 2D, fica assim (uma cor - uma classe):

Imagem do artigo ArcFace , um exemplo de brinquedo para demonstração: cada classe é destacada com sua própria cor, cada ponto no círculo é uma imagem tirada separadamente, o vetor do meio de cada classe é conectado ao centro para maior clareza. Observe que as classes são conectadas "sem lacunas".

Vamos reescrever a perda de Softmax (agora chamada de perda de Softmax normalizada, N-Softmax) com estas observações em mente:

L_{N S o f t m a x} = - \frac{1}{N} \sum_{i = 1}^{N} l o g \frac{e^{s * c o s (θ_{y_{i}})}}{e^{s * c o s (θ_{y_{i}})} + \sum_{j = 1, j \neq y_{i}}^{C} e^{s * c o s (θ_{j})}}

$L_{N Softmax} = - \frac {1}{N} \sum_{i=1}^N log\frac {e^{s*cos(\theta_{y_i})}}{e^{s*cos(\theta_{y_i})} + \sum_{j=1, j\neq y_i}^C e^{s*cos(\theta_j)}}$

Dividimos a soma no denominador em dois termos para a conveniência de maiores explicações. Todas as principais funções de perda de reconhecimento facial são baseadas no N-Softmax.

Margin-Based Loss

, , — . softmax loss, . , (decision boundary), ( ). . ? () , . — (decision margin). — margin — , : scale — . 2D ( ArcFace):

— margin, — margin

, .

, margin ( $m$ ) :

. $cos(\theta)$ $cos(m*\theta)$ . : Large-Margin Softmax Loss SphereFace. , , Margin-based loss. :

$L_{S p h e r e F a c e} = - \frac{1}{N} \sum_{i = 1}^{N} l o g \frac{e^{s * c o s (m * θ_{y_{i}})}}{e^{s * c o s (m * θ_{y_{i}})} + \sum_{j = 1, j \neq y_{i}}^{C} e^{s * c o s (θ_{j})}}$
$L_{SphereFace} = - \frac {1}{N} \sum_{i=1}^N log\frac {e^{s*cos(m*\theta_{y_i})}}{e^{s*cos(m*\theta_{y_i})} + \sum_{j=1, j\neq y_i}^C e^{s*cos(\theta_j)}}$
margin . $cos(\theta)$ $cos(\theta) - m$ . : AM-Softmax CosFace , , , . :

$L_{C o s F a c e} = - \frac{1}{N} \sum_{i = 1}^{N} l o g \frac{e^{s * c o s (θ_{y_{i}}) - m}}{e^{s * c o s (θ_{y_{i}}) - m} + \sum_{j = 1, j \neq y_{i}}^{C} e^{s * c o s (θ_{j})}}$
$L_{CosFace} = - \frac {1}{N} \sum_{i=1}^N log\frac {e^{s*cos(\theta_{y_i}) - m}}{e^{s*cos(\theta_{y_i}) - m} + \sum_{j=1, j\neq y_i}^C e^{s*cos(\theta_j)}}$
margin : $cos(\theta)$ → $cos(\theta + m)$ . ArcFace. ArcFace :

$L_{C o s F a c e} = - \frac{1}{N} \sum_{i = 1}^{N} l o g \frac{e^{s * c o s (θ_{y_{i}} + m)}}{e^{s * c o s (θ_{y_{i}} + m)} + \sum_{j = 1, j \neq y_{i}}^{C} e^{s * c o s (θ_{j})}}$
$L_{CosFace} = - \frac {1}{N} \sum_{i=1}^N log\frac {e^{s*cos(\theta_{y_i}+m) }}{e^{s*cos(\theta_{y_i}+m) } + \sum_{j=1, j\neq y_i}^C e^{s*cos(\theta_j)}}$
, ArcFace AirFace. Margin , ArcFace, , ( $arccos(cos(\theta)) = \theta$ ). , , ( — ), , $\theta$ , $(\pi - 2\theta)/\pi$ , :

$L_{A i r F a c e} = - \frac{1}{N} \sum_{i = 1}^{N} l o g \frac{e^{s * (π - 2 (θ_{y_{i}} + m)) / π}}{e^{s * (π - 2 (θ_{y_{i}} + m)) / π} + \sum_{j = 1, j \neq y_{i}}^{C} e^{s * (π - 2 θ_{j}) / π}}$
$L_{AirFace} = - \frac {1}{N} \sum_{i=1}^N log\frac {e^{s*(\pi - 2(\theta_{y_i}+m))/\pi}}{e^{s*(\pi - 2(\theta_{y_i}+m))/\pi} + \sum_{j=1, j\neq y_i}^C e^{s*(\pi - 2\theta_j)/\pi}}$

margin — , — ( ArcFace).

Margin & Scale

- , , — scale (s) margin (m), . , AM Softmax $s = 30$ , $m = 0.35$ , ArcFace — $s = 64$ , a $m = 0.5$ , CosFace (, , AM Softmax) $s = 64$ , a $m = 0.35$ . , , “ ”, .

— AdaCos, — scale margin . :

Margin scale — , .
scale margin, margin scale.
scale .
— scale

2 20 , , Y — , , X — . , , , :

scale ( , , margin 0), — margin scale=30. , scale, “” , margin X. , — scale margin, - , ? AdaCos scale ( ). , : $s = \sqrt{2}*\ln{(C-1)}$ , $C$ — . s [10, 25], .

AdaCos — scale. , scale , . , , .

margin , , , ? . X , Y — ( N-softmax $cos(\theta)$ ):

: CosFace N-softmax , ArcFace — . SphereFace, $\frac {\pi}{margin}$ , $\frac{\pi}{3}$ . ArcFace — target logit, , , . , , ( $\frac{5\pi}{6}$ ). , (, ) , :
```
# cosine - cos(theta)
# phi - cos(theta + m)
# th - cos(math.pi - m)
# mm - sin(math.pi - m) * m
if easy_margin:
  phi = torch.where(cosine > 0, phi, cosine)  
else:
  phi = torch.where(cosine > th, phi, cosine - mm)
      
      

        
        
        
      

    
        
        
        
      
      

        
        
        
      

    
    
```
easy_margin , :

Easy margin , $\frac{\pi}{2}$ N-Softmax ( $cos(\theta)$ ), not easy margin . , , , $\frac{\pi}{2}$ , “”, , , .

, . — " " ArcFace. , ( 4 8 ):

Loss LFW MegaFace, Rank1 @ $10^6$ MegaFace, Tar @ Far $10^{-6}$

AM-Softmax/CosFace 99.33 0.9833 0.9841

ArcFace 99.83 0.9836 0.9848

SphereFace 99.42 0.9743 0.9766

( 3 ), LFW, — - :

Loss Resnet50-MSC MobileNet-MSC Resnet50-Casia MobileNet-Casia

AM-Softmax/CosFace 99.3 97.65 99.34 98.46

ArcFace 99.15 98.43 99.35 99.01

SphereFace 99.02 96.86 99.1 97.83

, ArcFace SotA .

. (margin) , . AM Softmax ( ) ArcFace ( ). , , , AirFace.

:

SphereFace https://arxiv.org/abs/1704.08063

AM Softmax https://arxiv.org/abs/1801.05599

CosFace https://arxiv.org/abs/1801.09414

ArcFace https://arxiv.org/abs/1801.07698

AirFace https://arxiv.org/abs/1907.12256

:

Deep Face Recognition: A Survey https://arxiv.org/abs/1804.06655

A Performance Evaluation of Loss Functions for Deep Face Recognition https://arxiv.org/abs/1901.05903

Seu rosto não é um rei! Funções de perda para problema de reconhecimento de rosto

Softmax Loss

Margin-Based Loss

Margin & Scale

:

:

More articles:

Loss	LFW	MegaFace, Rank1 @ $10^6$	MegaFace, Tar @ Far $10^{-6}$
AM-Softmax/CosFace	99.33	0.9833	0.9841
ArcFace	99.83	0.9836	0.9848
SphereFace	99.42	0.9743	0.9766

Loss	Resnet50-MSC	MobileNet-MSC	Resnet50-Casia	MobileNet-Casia
AM-Softmax/CosFace	99.3	97.65	99.34	98.46
ArcFace	99.15	98.43	99.35	99.01
SphereFace	99.02	96.86	99.1	97.83