Face Recognition in PyTorch

This project mainly contains various loss function and light neural network.

Light Neural Network

MobileNet-v3

EfficientNet

Loss function:

These functions addresses deep face recognition (FR) problem under open-set protocol, where ideal face features are expected to have smaller maximal intra-class distance than minimal inter-class distance under a suitably chosen met- ric space.

Softmax:

$L_{1}=-\frac{1}{N} \sum_{i=1}^{N} \log \frac{e^{W_{y_{i}}^{T} x_{i}+b_{y_{i}}}}{\sum_{j=1}^{n} e^{W_{j}^{T} x_{i}+b_{j}}}$

CenterLoss:

$\mathcal{L}_{C}=\frac{1}{2} \sum_{i=1}^{m}\left\|\boldsymbol{x}_{i}-\boldsymbol{c}_{y_{i}}\right\|_{2}^{2}$

L-Softmax:

$L_{i}=-\log \left(\frac{e^{\left\|\boldsymbol{W}_{y_{i}}\right\|\left\|\boldsymbol{x}_{i}\right\| \psi\left(\theta_{y_{i}}\right)}}{e^{\left\|\boldsymbol{W}_{y_{i}}\right\|\left\|\boldsymbol{x}_{i}\right\| \psi\left(\theta_{y_{i}}\right)}+\sum_{j \neq y_{i}} e^{\left\|\boldsymbol{W}_{j}\right\|\left\|\boldsymbol{x}_{i}\right\| \cos \left(\theta_{j}\right)}}\right)$

where
$\psi(\theta)=\left\{\begin{array}{ll} \cos (m \theta), & 0 \leq \theta \leq \frac{\pi}{m} \\ \mathcal{D}(\theta), \quad \frac{\pi}{m}<\theta \leq \pi \end{array}\right.$

Calculate phi(theta) and k:
$\psi(\theta)=(-1)^{k} \cos (m \theta)-2 k, \quad \theta \in\left[\frac{k \pi}{m}, \frac{(k+1) \pi}{m}\right]$

Calculate cos(m * theta):
$\begin{aligned} \cos \left(m \theta_{y_{i}}\right) &=C_{m}^{0} \cos ^{m}\left(\theta_{y_{i}}\right)-C_{m}^{2} \cos ^{m-2}\left(\theta_{y_{i}}\right)\left(1-\cos ^{2}\left(\theta_{y_{i}}\right)\right) \\ &+C_{m}^{4} \cos ^{m-4}\left(\theta_{y_{i}}\right)\left(1-\cos ^{2}\left(\theta_{y_{i}}\right)\right)^{2}+\cdots \\ &(-1)^{n} C_{m}^{2 n} \cos ^{m-2 n}\left(\theta_{y_{i}}\right)\left(1-\cos ^{2}\left(\theta_{y_{i}}\right)\right)^{n}+\cdots \end{aligned}$

Angular-Softmax:

$L_{\text {modified }}=\frac{1}{N} \sum_{i}-\log \left(\frac{e^{\left\|\boldsymbol{x}_{i}\right\| \cos \left(\theta_{y_{i}, i}\right)}}{\sum_{j} e^{\left\|\boldsymbol{x}_{i}\right\| \cos \left(\theta_{j, i}\right)}}\right)$

$L_{\mathrm{ang}}=\frac{1}{N} \sum_{i}-\log \left(\frac{e^{\left\|\boldsymbol{x}_{i}\right\| \cos \left(m \theta_{y_{i}, i}\right)}}{e^{\left\|\boldsymbol{x}_{i}\right\| \cos \left(m \theta_{y_{i}, i}\right)}+\sum_{j \neq y_{i}} e^{\left\|\boldsymbol{x}_{i}\right\| \cos \left(\theta_{j, i}\right)}}\right)$

$L_{\text {ang }}=\frac{1}{N} \sum_{i}-\log \left(\frac{e^{\left\|\boldsymbol{x}_{i}\right\| \psi\left(\theta_{y_{i}}, i\right)}}{e^{\left\|\boldsymbol{x}_{i}\right\| \psi\left(\theta_{y_{i}, i}\right)}+\sum_{j \neq y_{i}} e^{\left\|\boldsymbol{x}_{i}\right\| \cos \left(\theta_{j, i}\right)}}\right)$

Cosine-Softmax:

$L_{l m c}=\frac{1}{N} \sum_{i}-\log \frac{e^{s\left(\cos \left(\theta_{y_{i}, i}\right)-m\right)}}{e^{s\left(\cos \left(\theta_{y_{i}, i}\right)-m\right)}+\sum_{j \neq y_{i}} e^{s \cos \left(\theta_{j, i}\right)}}$

where,

$\begin{aligned} W &=\frac{W^{*}}{\left\|W^{*}\right\|} \\ x &=\frac{x^{*}}{\left\|x^{*}\right\|} \\ \cos \left(\theta_{j}, i\right) &=W_{j}^{T} x_{i} \end{aligned}$

ArcFace:

$L_{4}=-\frac{1}{N} \sum_{i=1}^{N} \log \frac{e^{s\left(\cos \left(m_{1} \theta_{y_{i}}+m_{2}\right)-m_{3}\right)}}{e^{s\left(\cos \left(m_{1} \theta_{y_{i}}+m_{2}\right)-m_{3}\right)}+\sum_{j=1, j \neq y_{i}}^{n} e^{s \cos \theta_{j}}}$

Reference

https://github.com/MuggleWang/CosFace_pytorch/blob/master/layer.py

ArcFace: Additive Angular Margin Loss for Deep Face Recognition

SphereFace: Deep Hypersphere Embedding for Face Recognition

A Discriminative Feature Learning Approach for Deep Face Recognition

CosFace: Large Margin Cosine Loss for Deep Face Recognition

Large-Margin Softmax Loss for Convolutional Neural Networks

EfficientNet

MobileNet-v3

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README.md

Face Recognition in PyTorch

This project mainly contains various loss function and light neural network.

Light Neural Network

Loss function:

Reference

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README.md

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Face Recognition in PyTorch

This project mainly contains various loss function and light neural network.

Light Neural Network

Loss function:

Reference