Model with normalized binary cross entropy loss does not converge-CodePudding

The

Here is my implementation:

import tensorflow as tf from keras.utils import losses_utils class NormalizedBinaryCrossentropy(tf.keras.losses.Loss): def __init__( self, from_logits=False, label_smoothing=0.0, axis=-1, reduction=tf.keras.losses.Reduction.NONE, name="normalized_binary_crossentropy", **kwargs ): super().__init__( reduction=reduction, name=name ) self.from_logits = from_logits self._epsilon = tf.keras.backend.epsilon() def call(self, target, logits): if tf.is_tensor(logits) and tf.is_tensor(target): logits, target = losses_utils.squeeze_or_expand_dimensions( logits, target ) logits = tf.convert_to_tensor(logits) target = tf.cast(target, logits.dtype) if self.from_logits: logits = tf.math.sigmoid(logits) logits = tf.clip_by_value(logits, self._epsilon, 1.0 - self._epsilon) numer = target * tf.math.log(logits) (1 - target) * tf.math.log(1 - logits) denom = - (tf.math.log(logits) tf.math.log(1 - logits)) return - numer / denom def get_config(self): config = super().get_config() config.update({"from_logits": self._from_logits}) return config

I'm using this loss to train a binary classifier (CTR predictor), but loss of the model does not decrease and ROC-AUC remains at ~0.49-0.5. To verify the implementation of numerator, I tried training by removing the denominator and it's working fine.

# Example Usage labels = np.array([[0], [1], [0], [0], [0]]).astype(np.int64) logits = np.array([[-1.024], [2.506], [1.43], [0.004], [-2.0]]).astype(np.float64) tf_nce = NormalizedBinaryCrossentropy( reduction=tf.keras.losses.Reduction.NONE, from_logits=True ) tf_nce(labels, logits) #<tf.Tensor: shape=(5, 1), dtype=float64, numpy= # array([[0.18737159], # [0.02945536], # [0.88459308], # [0.50144269], # [0.05631594]])>

I checked manually with some extremes and that loss doesn't hit nans or 0s.

Can anyone help me in debugging why the model is not able to converge on this loss? Is there something wrong with my understanding of the loss function or implementation?

Edit 1: Model architecture is a Multi-Gate Mixture-of-Experts with 6 tasks. All 6 tasks are binary classification and losses from all tasks are added together to get final loss.

CodePudding user response：

One thing which is mentioned in the paper as described above is that the Norm of the loss should be inclusively in between [0 ~ 1] but as your loss is violating this condition of Normalized Binary Cross Entropy and the other reason is you are dividing by the wrong denominator, you have to divide it by the Cross-Entropy of your logits for this take the BinaryCrossEntropy() of your logits. so, these can be the reasons that your function is not decreasing... I have made some changes to your code that satisfy this Norm Property...

import tensorflow as tf from keras.utils import losses_utils class NormalizedBinaryCrossentropy(tf.keras.losses.Loss): def __init__( self, from_logits=False, label_smoothing=0.0, axis=-1, reduction=tf.keras.losses.Reduction.NONE, name="normalized_binary_crossentropy", **kwargs ): super().__init__( reduction=reduction, name=name ) self.from_logits = from_logits self._epsilon = tf.keras.backend.epsilon() def call(self, target, logits): if tf.is_tensor(logits) and tf.is_tensor(target): logits, target = losses_utils.squeeze_or_expand_dimensions( logits, target ) logits = tf.convert_to_tensor(logits) target = tf.cast(target, logits.dtype) logits = tf.clip_by_value(logits, self._epsilon, 1.0 - self._epsilon) if self.from_logits: numer = tf.keras.losses.binary_crossentropy(target, logits,from_logits=True)[:,tf.newaxis] denom = -( tf.math.log(logits) tf.math.log(1 - logits)) return numer * denom / tf.reduce_sum(denom) else: logits = tf.nn.log_softmax(logits) num = - tf.math.reduce_sum(tf.multiply(target, logits), axis=1) denom = -tf.math.reduce_sum(logits, axis=1) return num / denom def get_config(self): config = super().get_config() config.update({"from_logits": self._from_logits}) return config

I have updated the solution, there are two ways for computing the BCE if your logits are one-hot then set from_logit=False else set it True.

CodePudding user response：

I would try to avoid log-Sigmoid stability issues and try to implement the above model as a 2 class problem with Softmax Binary cross entropy..

The NormalizedCrossEntropy is defined as:

class NormalizedCrossEntropy(keras.layers.Layer): def __init__(self, num_classes): super(NormalizedCrossEntropy, self).__init__() self.num_classes = num_classes def call(self, pred, labels): pred = tf.nn.log_softmax(pred, axis=1,) label_one_hot = tf.one_hot(labels, self.num_classes) numer = -1 * tf.reduce_sum(label_one_hot * pred, axis=1) denom = -1* tf.reduce_sum(pred, axis=1) nce = numer/ denom return nce

Example usage:

NormalizedCrossEntropy(num_classes=2)(np.array([[-1.024, 0.5], [0.1, 2.506], [1, .0], [0., 1.], [-0.89, -2.0]]), np.array([0, 1, 0, 0, 0]) ) #array([0.89725673, 0.03348167, 0.19259584, 0.80740416, 0.16958274]