I am trying to write a custom training loop for a variational autoencoder (VAE) that consists of two separate tf.keras.Model objects. The objective of this VAE is multi-class classification. As usual, the outputs of the encoder model are fed as inputs to the decoder model. The decoder is a recurrent decoder. Also as usual, two loss functions are involved in the VAE: reconstruction loss (categorical cross entropy) and latent loss. The inspiration for my current architecture is based on a pytorch implementation at this github.
Problem: Whenever I calculate the gradients using tape.gradient(loss, decoder.trainable_weights) for the decoder model, the returned list has only NoneType objects for each element. I assume I am making some mistake with the use of the reconstruction_tensor, which is near the bottom of the code I have written below. Since I need to have the iterative decoding process, how can I use something like the reconstruction_tensor without returning a list of NoneType elements for gradients? You may run the code using this colab notebook if you wish.
To further clarify what the tensors in this problem look like, I shall illustrate the original input, the zeros tensor to which predicted 'tokens' will be assigned, and a single update of the zeroes tensor based on the predicted 'tokens' from the decoder:
Example original input tensor of shape (batch_size, max_seq_length, num_classes):
_ _ _ _ _ _ _ _
| | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | |
| | 0 1 0 0 | | 1 0 0 0 | | 1 0 0 0 | |
|_ |_ 0 0 1 0 _| , |_ 0 0 0 1 _|, |_ 0 1 0 0 _| _|
Initial zeros tensor:
_ _ _ _ _ _ _ _
| | 0 0 0 0 | | 0 0 0 0 | | 0 0 0 0 | |
| | 0 0 0 0 | | 0 0 0 0 | | 0 0 0 0 | |
|_ |_ 0 0 0 0 _| , |_ 0 0 0 0 _|, |_ 0 0 0 0 _| _|
Example zeros tensor after a single iteration of the decoding loop:
_ _ _ _ _ _ _ _
| | 0.2 0.4 0.1 0.3 | | 0.1 0.2 0.6 0.1 | | 0.7 0.05 0.05 0.2 | |
| | 0 0 0 0 | | 0 0 0 0 | | 0 0 0 0 | |
|_ |_ 0 0 0 0 _| , |_ 0 0 0 0 _|, |_ 0 0 0 0 _| _|
Here is the code to reproduce the problem:
# Arbitrary data
batch_size = 3
max_seq_length = 3
num_classes = 4
original_inputs = tf.one_hot(tf.argmax((np.random.randn(batch_size, max_seq_length, num_classes)), axis=2), depth=num_classes)
latent_dims = 5 # Must be less than (max_seq_length * num_classes)
def sampling(inputs):
"""Reparametrization function. Used for Lambda layer"""
mus, log_vars = inputs
epsilon = tf.keras.backend.random_normal(shape=tf.keras.backend.shape(mus))
z = mus + tf.keras.backend.exp(log_vars/2) * epsilon
return z
def latent_loss_fxn(mus, log_vars):
"""Return latent loss for means and log variance."""
return -0.5 * tf.keras.backend.mean(1. + log_vars - tf.keras.backend.exp(log_vars) - tf.keras.backend.pow(mus, 2))
class DummyEncoder(tf.keras.Model):
def __init__(self, latent_dimension):
"""Define the hidden layer (bottleneck) and sampling layers"""
super().__init__()
self.hidden = tf.keras.layers.Dense(units=32)
self.dense_mus = tf.keras.layers.Dense(units=latent_dimension)
self.dense_log_vars = tf.keras.layers.Dense(units=latent_dimension)
self.sampling = tf.keras.layers.Lambda(function=sampling)
def call(self, inputs):
"""Define forward computation that outputs z, mu, log_var of input."""
dense_projection = self.hidden(inputs)
mus = self.dense_mus(dense_projection)
log_vars = self.dense_log_vars(dense_projection)
z = self.sampling([mus, log_vars])
return z, mus, log_vars
class DummyDecoder(tf.keras.Model):
def __init__(self, num_classes):
"""Define GRU layer and the Dense output layer"""
super().__init__()
self.gru = tf.keras.layers.GRU(units=1, return_sequences=True, return_state=True)
self.dense = tf.keras.layers.Dense(units=num_classes, activation='softmax')
def call(self, x, hidden_states=None):
"""Define forward computation"""
outputs, h_t = self.gru(x, hidden_states)
# The purpose of this computation is to use the unnormalized log
# probabilities from the GRU to produce normalized probabilities via
# the softmax activation function in the Dense layer
reconstructions = self.dense(outputs)
return reconstructions, h_t
# Instantiate the models
encoder_model = DummyEncoder(latent_dimension=5)
decoder_model = DummyDecoder(num_classes=num_classes)
# Instantiate reconstruction loss function
cce_loss_fxn = tf.keras.losses.CategoricalCrossentropy()
# Begin tape
with tf.GradientTape(persistent=True) as tape:
# Flatten the inputs for the encoder
reshaped_inputs = tf.reshape(original_inputs, shape=(tf.shape(original_inputs)[0], -1))
# Encode the input
z, mus, log_vars = encoder_model(reshaped_inputs, training=True)
# Expand dimensions of z so it meets recurrent decoder requirements of
# (batch, timesteps, features)
z = tf.expand_dims(z, axis=1)
################################
# SUSPECTED CAUSE OF PROBLEM
################################
# A tensor that will be modified based on model outputs
reconstruction_tensor = tf.Variable(tf.zeros_like(original_inputs))
################################
# END SUSPECTED CAUSE OF PROBLEM
################################
# A decoding loop to iteratively generate the next token (i.e., outputs)...
# in the sequence
hidden_states = None
for ith_token in range(max_seq_length):
# Reconstruct the ith_token for a given sample in the batch
reconstructions, hidden_states = decoder_model(z, hidden_states, training=True)
# Reshape the reconstructions to allow assigning to reconstruction_tensor
reconstructions = tf.squeeze(reconstructions)
# After the loop is done iterating, this tensor is the model's prediction of the
# original inputs. Therefore, after a single iteration of the loop,
# a single token prediction for each sample in the batch is assigned to
# this tensor.
reconstruction_tensor = reconstruction_tensor[:, ith_token,:].assign(reconstructions)
# Calculates losses
recon_loss = cce_loss_fxn(original_inputs, reconstruction_tensor)
latent_loss = latent_loss_fxn(mus, log_vars)
loss = recon_loss + latent_loss
# Calculate gradients
encoder_gradients = tape.gradient(loss, encoder_model.trainable_weights)
decoder_gradients = tape.gradient(loss, decoder_model.trainable_weights)
# Release tape
del tape
# Inspect gradients
print('Valid Encoder Gradients:', not(None in encoder_gradients))
print('Valid Decoder Gradients:', not(None in decoder_gradients), ' -- ', decoder_gradients)
>>> Valid Encoder Gradients: True
>>> Valid Decoder Gradients: False -- [None, None, None, None, None]
Found a 'solution' to my problem:
There must be some problem with the use of a tf.Variable in the GradientTape() context manager. While I do not know what that problem is, by replacing the reconstructions_tensor with a list, appending to that list during decoding iterations, and then stacking the list, gradients can be computed without a problem. The colab notebook reflects the changes. See code snippet below for the fix:
....
....
with tf.GradientTape(persistent=True) as tape:
....
....
# FIX
reconstructions_tensor = []
hidden_states = None
for ith_token in range(max_seq_length):
# Reconstruct the ith_token for a given sample in the batch
reconstructions, hidden_states = decoder_model(z, hidden_states, training=True)
# Reshape the reconstructions
reconstructions = tf.squeeze(reconstructions)
# FIX
# Appending to the list which will eventually be stacked
reconstructions_tensor.append(reconstructions)
# FIX
# Stack the reconstructions along axis=1 to get same result as previous assignment with zeros tensor
reconstructions_tensor = tf.stack(reconstructions_tensor, axis=1)
....
....
# Successful gradient computations and subsequent optimization of models
# ....
Edit 1:
I don't think this 'solution' ideal if one has a model that can be run in graph mode. My limited understanding is that graph mode does not do well with python objects such as list.