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SphereFaceLoss

SphereFace: Deep Hypersphere Embedding for Face Recognition

losses.SphereFaceLoss(num_classes, embedding_size, margin=4, scale=1,
    *, weight_regularizer=None, weight_reg_weight=1.0, weight_init_func=None, **options)

Equation:

\[ L_i = -\log\left(\frac{e^{\lVert \mathbf{x}_i \rVert \psi(\theta_{y_i})}}{e^{\lVert \mathbf{x}_i \rVert \psi(\theta_{y_i})} + \sum_{j \neq y_i} e^{\lVert \mathbf{x}_i \rVert \cos(\theta_j)}}\right) \]

with \(\psi\) as in LargeMarginSoftmaxLoss. The weight vectors are L2-normalized, so only the embedding norm scales the logits.

Implementation notes: The paper's annealing with a decreasing \(\lambda\) is not implemented. Every logit is multiplied by scale. With an indices_tuple, each embedding's loss is multiplied by its miner weight. get_logits(embeddings) returns the logits with \(\cos\theta_j\) in place of \(\psi\); see classification logits. This loss derives from LargeMarginSoftmaxLoss and BaseProxyLoss.

Example:

import torch
from pytorch_metric_learning import losses

loss_func = losses.SphereFaceLoss(num_classes=10, embedding_size=128)
optimizer = torch.optim.SGD(loss_func.parameters(), lr=0.01)
embeddings = torch.randn(32, 128, requires_grad=True)
labels = torch.randint(0, 10, (32,))
loss = loss_func(embeddings, labels)
loss.backward()
optimizer.step()

Parameters:

  • num_classes: The number of classes in the training set. Labels must be in 0..num_classes - 1.
  • embedding_size: The size of the embeddings passed to the loss.
  • margin: The integer angular margin \(m\). A value that is not an int raises TypeError, and a value below 1 raises ValueError. The paper uses 4.
  • scale: A multiplier of every logit. The paper uses 1.
  • weight_regularizer, weight_reg_weight, weight_init_func: See learnable weight arguments. The class weights are weight, shaped (num_classes, embedding_size) and initialized with torch.nn.init.normal_. Include loss_func.parameters() in an optimizer.

Default distance:

  • CosineSimilarity(). This is the only compatible distance; another distance class raises TypeError.

Default reducer:

Reducer input:

  • loss: One loss per embedding, indexed by embedding position.