tensorflow gradients in eager mode return zeros

Question

The problem: I'm loading a simple VGG16 from a saved checkpoint. I want to generate the saliency for an image during inference. When i compute the gradients (of loss wrt input image) required for this, i get back all gradients as zero. Any ideas as to what I'm missing here is much appreciated!

tf version: tensorflow-2.0alpha-gpu

The model:

import tensorflow as tf
from tensorflow.keras.applications.vgg16 import VGG16 as KerasVGG16
from tensorflow.keras.models import Model
from tensorflow.keras.layers import Flatten, Dense

class VGG16(Model):

    def __init__(self, num_classes, use_pretrained=True):

        super(VGG16, self).__init__()
        self.num_classes = num_classes
        self.use_pretrained = use_pretrained

        if use_pretrained:
            self.base_model = KerasVGG16(weights='imagenet', include_top=False)
            for layer in self.base_model.layers:
                layer.trainable = False
        else:
            self.base_model = KerasVGG16(include_top=False)

        self.flatten1 = Flatten(name='flatten')
        self.dense1 = Dense(4096, activation='relu', name='fc1')
        self.dense2 = Dense(100, activation='relu', name='fc2')
        self.dense3 = Dense(self.num_classes, activation='softmax', name='predictions')

    def call(self, inputs):

        x = self.base_model(tf.cast(inputs, tf.float32))
        x = self.flatten1(x)
        x = self.dense1(x)
        x = self.dense2(x)
        x = self.dense3(x)
        return x

I train this model and save it to a checkpoint and load it back via:

model = VGG16(num_classes=2, use_pretrained=False)
checkpoint = tf.train.Checkpoint(net=model)
        status = checkpoint.restore(tf.train.latest_checkpoint('./my_checkpoint'))
status.assert_consumed()

I verify the weights are correctly loaded.

Get a test image

# load my image and make sure its float
img = tf.convert_to_tensor(image, dtype=tf.float64)
support_class = tf.convert_to_tensor(support_class, dtype=tf.float64)

Get the gradients:

with tf.GradientTape(persistent=True) as g_tape:
    g_tape.watch(img)
    #g_tape.watch(model.base_model.trainable_variables)
    #g_tape.watch(model.trainable_variables)
    loss = tf.losses.CategoricalCrossentropy()(support_class, model(img))    
    gradients_wrt_image = g_tape.gradient(loss,
                                    img, unconnected_gradients=tf.UnconnectedGradients.NONE)

When i inspect my gradients they are all zero! Any idea what am i missing? Thanks in advance!

Answer 1

The gradients are not zero, although they are very small:

def almost_equals(a, b, decimal=6):
    try:
        np.testing.assert_almost_equal(a, b, decimal=decimal)
    except AssertionError:
        return False
    return True

image = [abs(np.random.normal(size=(32, 32, 3))) for _ in range(20)]
label = [[0, 1] if i % 3 == 0 else [1, 0] for i in range(20)]
img = tf.convert_to_tensor(image, dtype=tf.float64)
support_class = tf.convert_to_tensor(label, dtype=tf.float64)
loss_fn = tf.losses.CategoricalCrossentropy()

with tf.GradientTape(persistent=True) as tape:
    tape.watch(img)
    softmaxed = model(img)
    loss = loss_fn(support_class, softmaxed)
    grads = tape.gradient(loss, img, unconnected_gradients=tf.UnconnectedGradients.NONE)
    # summing up all gradients with reduction over all dimension:
    print(tf.reduce_sum(grads, axis=None).numpy()) # 0.07137820225818814
    # comparing to zeros:
    zeros_like_grads = np.zeros_like(grads.numpy())  
    for decimal in range(10, 0, -1):
        print('decimal: {0}: {1}'.format(decimal,
                                         almost_equals(zeros_like_grads,
                                                       grads.numpy(),
                                                       decimal=decimal)))
# decimal: 10: False
# decimal: 9: False
# decimal: 8: False
# decimal: 7: False
# decimal: 6: False
# decimal: 5: False
# decimal: 4: False
# decimal: 3: True
# decimal: 2: True
# decimal: 1: True

As you can see, only starting at decimal=3 it starts to return True .

Answer 2

So, it turns out there is nothing wrong with the network. The problem is related the behavior of the softmax activation that i use in my final Dense layer. I didn't consider the fact that very confident predictions from the softmax (eg one of my predictions [[1.0000000e+00 1.9507678e-25]]) would make gradients zero (theoretically very close to zero but practically, zero). A useful thread that discuss this and how to counter it: https://github.com/keras-team/keras/issues/5881

My solution : turn off the softmax activation when i want to compute gradients wrt input image