Face Identification

A 1 x 1 Convolution is a convolution with some special properties in that it can be used for dimensionality reduction, efficient low dimensional embeddings, and applying non-linearity after convolutions. It maps an input pixel with all its channels to an output pixel which can be squeezed to a desired output depth. It can be viewed as an MLP looking at a particular pixel location. Image Credit: http://deeplearning.ai

Global Average Pooling is a pooling operation designed to replace fully connected layers in classical CNNs. The idea is to generate one feature map for each corresponding category of the classification task in the last mlpconv layer. Instead of adding fully connected layers on top of the feature maps, we take the average of each feature map, and the resulting vector is fed directly into the softmax layer. One advantage of global average pooling over the fully connected layers is that it is more native to the convolution structure by enforcing correspondences between feature maps and categories. Thus the feature maps can be easily interpreted as categories confidence maps. Another advantage is that there is no parameter to optimize in the global average pooling thus overfitting is avoided at this layer. Furthermore, global average pooling sums out the spatial information, thus it is more robust to spatial translations of the input.

A Focal Loss function addresses class imbalance during training in tasks like object detection. Focal loss applies a modulating term to the cross entropy loss in order to focus learning on hard misclassified examples. It is a dynamically scaled cross entropy loss, where the scaling factor decays to zero as confidence in the correct class increases. Intuitively, this scaling factor can automatically down-weight the contribution of easy examples during training and rapidly focus the model on hard examples. Formally, the Focal Loss adds a factor $(1 - p\_{t})^\gamma$ to the standard cross entropy criterion. Setting $\gamma>0$ reduces the relative loss for well-classified examples ($p\_{t}>.5$), putting more focus on hard, misclassified examples. Here there is tunable focusing parameter $\gamma \ge 0$. $$ {\text{FL}(p\_{t}) = - (1 - p\_{t})^\gamma \log\left(p\_{t}\right)} $$

RetinaNet is a one-stage object detection model that utilizes a focal loss function to address class imbalance during training. Focal loss applies a modulating term to the cross entropy loss in order to focus learning on hard negative examples. RetinaNet is a single, unified network composed of a backbone network and two task-specific subnetworks. The backbone is responsible for computing a convolutional feature map over an entire input image and is an off-the-shelf convolutional network. The first subnet performs convolutional object classification on the backbone's output; the second subnet performs convolutional bounding box regression. The two subnetworks feature a simple design that the authors propose specifically for one-stage, dense detection. We can see the motivation for focal loss by comparing with two-stage object detectors. Here class imbalance is addressed by a two-stage cascade and sampling heuristics. The proposal stage (e.g., Selective Search, EdgeBoxes, DeepMask, RPN) rapidly narrows down the number of candidate object locations to a small number (e.g., 1-2k), filtering out most background samples. In the second classification stage, sampling heuristics, such as a fixed foreground-to-background ratio, or online hard example mining (OHEM), are performed to maintain a manageable balance between foreground and background. In contrast, a one-stage detector must process a much larger set of candidate object locations regularly sampled across an image. To tackle this, RetinaNet uses a focal loss function, a dynamically scaled cross entropy loss, where the scaling factor decays to zero as confidence in the correct class increases. Intuitively, this scaling factor can automatically down-weight the contribution of easy examples during training and rapidly focus the model on hard examples. Formally, the Focal Loss adds a factor $(1 - p\_{t})^\gamma$ to the standard cross entropy criterion. Setting $\gamma>0$ reduces the relative loss for well-classified examples ($p\_{t}>.5$), putting more focus on hard, misclassified examples. Here there is tunable focusing parameter $\gamma \ge 0$. $$ {\text{FL}(p\_{t}) = - (1 - p\_{t})^\gamma \log\left(p\_{t}\right)} $$

ArcFace, or Additive Angular Margin Loss, is a loss function used in face recognition tasks. The softmax is traditionally used in these tasks. However, the softmax loss function does not explicitly optimise the feature embedding to enforce higher similarity for intraclass samples and diversity for inter-class samples, which results in a performance gap for deep face recognition under large intra-class appearance variations. The ArcFace loss transforms the logits $W^{T}\_{j}x\_{i} = || W\_{j} || \text{ } || x\_{i} || \cos\theta\_{j}$, where $\theta\_{j}$ is the angle between the weight $W\_{j}$ and the feature $x\_{i}$. The individual weight $ || W\_{j} || = 1$ is fixed by $l\_{2}$ normalization. The embedding feature $ ||x\_{i} ||$ is fixed by $l\_{2}$ normalization and re-scaled to $s$. The normalisation step on features and weights makes the predictions only depend on the angle between the feature and the weight. The learned embedding features are thus distributed on a hypersphere with a radius of $s$. Finally, an additive angular margin penalty $m$ is added between $x\_{i}$ and $W\_{y\_{i}}$ to simultaneously enhance the intra-class compactness and inter-class discrepancy. Since the proposed additive angular margin penalty is equal to the geodesic distance margin penalty in the normalised hypersphere, the method is named ArcFace: $$ L\_{3} = -\frac{1}{N}\sum^{N}\_{i=1}\log\frac{e^{s\left(\cos\left(\theta\_{y\_{i}} + m\right)\right)}}{e^{s\left(\cos\left(\theta\_{y\_{i}} + m\right)\right)} + \sum^{n}\_{j=1, j \neq y\_{i}}e^{s\cos\theta\_{j}}} $$ The authors select face images from 8 different identities containing enough samples (around 1,500 images/class) to train 2-D feature embedding networks with the softmax and ArcFace loss, respectively. As the Figure shows, the softmax loss provides roughly separable feature embedding but produces noticeable ambiguity in decision boundaries, while the proposed ArcFace loss can obviously enforce a more evident gap between the nearest classes. Other alternatives to enforce intra-class compactness and inter-class distance include Supervised Contrastive Learning.

Some object detection datasets contain an overwhelming number of easy examples and a small number of hard examples. Automatic selection of these hard examples can make training more effective and efficient. OHEM, or Online Hard Example Mining, is a bootstrapping technique that modifies SGD to sample from examples in a non-uniform way depending on the current loss of each example under consideration. The method takes advantage of detection-specific problem structure in which each SGD mini-batch consists of only one or two images, but thousands of candidate examples. The candidate examples are subsampled according to a distribution that favors diverse, high loss instances.