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# pylint: disable=E0611,E0401
import tensorflow.keras.backend as K
# ALPHA = 0.2 # used in FaceNet https://arxiv.org/pdf/1503.03832.pdf
ALPHA = 0.1 # used in Deep Speaker.
def batch_cosine_similarity(x1, x2):
# https://en.wikipedia.org/wiki/Cosine_similarity
# 1 = equal direction ; -1 = opposite direction
dot = K.squeeze(K.batch_dot(x1, x2, axes=1), axis=1)
# as values have have length 1, we don't need to divide by norm (as it is 1)
return dot
def deep_speaker_loss(y_true, y_pred, alpha=ALPHA):
# y_true is not used. we respect this convention:
# y_true.shape = (batch_size, embedding_size) [not used]
# y_pred.shape = (batch_size, embedding_size)
# EXAMPLE:
# _____________________________________________________
# ANCHOR 1 (512,)
# ANCHOR 2 (512,)
# POS EX 1 (512,)
# POS EX 2 (512,)
# NEG EX 1 (512,)
# NEG EX 2 (512,)
# _____________________________________________________
split = K.shape(y_pred)[0] // 3
anchor = y_pred[0:split]
positive_ex = y_pred[split:2 * split]
negative_ex = y_pred[2 * split:]
# If the loss does not decrease below ALPHA then the model does not learn anything.
# If all anchor = positive = negative (model outputs the same vector always).
# Then sap = san = 1. and loss = max(alpha,0) = alpha.
# On the contrary if anchor = positive = [1] and negative = [-1].
# Then sap = 1 and san = -1. loss = max(-1-1+0.1,0) = max(-1.9, 0) = 0.
sap = batch_cosine_similarity(anchor, positive_ex)
san = batch_cosine_similarity(anchor, negative_ex)
loss = K.maximum(san - sap + alpha, 0.0)
total_loss = K.mean(loss)
return total_loss
if __name__ == '__main__':
import numpy as np
print(deep_speaker_loss(alpha=0.1, y_true=0, y_pred=np.array([[0.9], [1.0], [-1.0]])))
print(deep_speaker_loss(alpha=1, y_true=0, y_pred=np.array([[0.9], [1.0], [-1.0]])))
print(deep_speaker_loss(alpha=2, y_true=0, y_pred=np.array([[0.9], [1.0], [-1.0]])))
print('--------------')
print(deep_speaker_loss(alpha=2, y_true=0, y_pred=np.array([[0.6], [1.0], [0.0]])))
print(deep_speaker_loss(alpha=1, y_true=0, y_pred=np.array([[0.6], [1.0], [0.0]])))
print(deep_speaker_loss(alpha=0.1, y_true=0, y_pred=np.array([[0.6], [1.0], [0.0]])))
print(deep_speaker_loss(alpha=0.2, y_true=0, y_pred=np.array([[0.6], [1.0], [0.0]])))
print('--------------')
print(deep_speaker_loss(alpha=2, y_true=0, y_pred=np.array([[0.9], [1.0], [-1.0]])))
print(deep_speaker_loss(alpha=1, y_true=0, y_pred=np.array([[0.9], [1.0], [-1.0]])))
print(deep_speaker_loss(alpha=0.1, y_true=0, y_pred=np.array([[0.9], [1.0], [-1.0]])))
print(deep_speaker_loss(alpha=0.2, y_true=0, y_pred=np.array([[0.9], [1.0], [-1.0]])))
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