def test_single_label(self):
"""Test single label, which is the same with `NpairsLoss`."""
nml_obj = npairs.NpairsMultilabelLoss()
# batch size = 4, hidden size = 2
y_true = tf.constant(
[[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]],
dtype=tf.int64)
# features of anchors
f = tf.constant([[1.0, 1.0], [1.0, -1.0], [-1.0, 1.0], [-1.0, -1.0]],
dtype=tf.float32)
# features of positive samples
fp = tf.constant([[1.0, 1.0], [1.0, -1.0], [-1.0, 1.0], [-1.0, -1.0]],
dtype=tf.float32)
# similarity matrix
y_pred = tf.matmul(f, fp, transpose_a=False, transpose_b=True)
loss = nml_obj(y_true, y_pred)
# Loss = 1/4 * \sum_i log(1 + \sum_{j != i} exp(f_i*fp_j^T-f_i*f_i^T))
# Compute loss for i = 0, 1, 2, 3 without multiplier 1/4
# i = 0 => log(1 + sum([exp(-2), exp(-2), exp(-4)])) = 0.253846
# i = 1 => log(1 + sum([exp(-2), exp(-4), exp(-2)])) = 0.253846
# i = 2 => log(1 + sum([exp(-2), exp(-4), exp(-2)])) = 0.253846
# i = 3 => log(1 + sum([exp(-4), exp(-2), exp(-2)])) = 0.253846
# Loss = (0.253856 + 0.253856 + 0.253856 + 0.253856) / 4 = 0.253856
self.assertAllClose(loss, 0.253856)
# Test sparse tensor
y_true = tf.sparse.from_dense(y_true)
loss = nml_obj(y_true, y_pred)
self.assertAllClose(loss, 0.253856)
def test_multilabel():
nml_obj = npairs.NpairsMultilabelLoss()
# batch size = 4, hidden size = 2
y_true = tf.constant(
[[1, 1, 0, 0], [0, 1, 1, 0], [0, 0, 1, 1], [0, 0, 0, 1]], dtype=tf.int64
)
# features of anchors
f = tf.constant(
[[1.0, 1.0], [1.0, -1.0], [-1.0, 1.0], [-1.0, -1.0]], dtype=tf.float32
)
# features of positive samples
fp = tf.constant(
[[1.0, 1.0], [1.0, -1.0], [-1.0, 1.0], [-1.0, -1.0]], dtype=tf.float32
)
# similarity matrix
y_pred = tf.matmul(f, fp, transpose_a=False, transpose_b=True)
loss = nml_obj(y_true, y_pred)
# Loss = \sum_i log(1 + \sum_{j != i} exp(f_i*fp_j^T-f_i*f_i^T))
# Because of multilabel, the label matrix is normalized so that each
# row sums to one. That's why the multiplier before log exists.
# Compute loss for i = 0, 1, 2, 3 without multiplier 1/4
# i = 0 => 2/3 * log(1 + sum([exp(-2), exp(-2), exp(-4)])) +
# 1/3 * log(1 + sum([exp(2) , exp(0) , exp(-2)])) = 0.920522
# i = 1 => 1/4 * log(1 + sum([exp(2) , exp(-2), exp(0) ])) +
# 1/2 * log(1 + sum([exp(-2), exp(-4), exp(-2)])) +
# 1/4 * log(1 + sum([exp(2) , exp(4) , exp(2) ])) = 1.753856
# i = 2 => 1/4 * log(1 + sum([exp(2) , exp(4) , exp(2) ])) +
# 1/2 * log(1 + sum([exp(-2), exp(-4), exp(-2)])) +
# 1/4 * log(1 + sum([exp(0) , exp(-2), exp(2) ])) = 1.753856
# i = 4 => 1/2 * log(1 + sum([exp(-2), exp(0) , exp(2) ])) +
# 1/2 * log(1 + sum([exp(-4), exp(-2), exp(-2)])) = 1.253856
# Loss = (0.920522 + 1.753856 + 1.753856 + 1.253856) / 4 = 1.420522
np.testing.assert_allclose(loss, 1.420522, rtol=1e-06, atol=1e-06)
# Test sparse tensor
y_true = tf.sparse.from_dense(y_true)
loss = nml_obj(y_true, y_pred)
np.testing.assert_allclose(loss, 1.420522, rtol=1e-06, atol=1e-06)
def config(self):
nml_obj = npairs.NpairsMultilabelLoss(name="nml")
self.assertEqual(nml_obj.name, "nml")
self.assertEqual(nml_obj.reduction, tf.keras.losses.Reduction.NONE)
def config():
nml_obj = npairs.NpairsMultilabelLoss(name="nml")
assert nml_obj.name == "nml"
assert nml_obj.reduction == tf.keras.losses.Reduction.NONE
