pythontensorflowloss-functionregularizedgradienttape# TensorFlow: Calculating gradients of regularization loss terms dependent on model input and output

# Overview

## Question

My model is an encoder that has input `Z`

and output `x`

.

I'm trying to use a `total_loss`

that has both traditional supervised learning and regularization term(s). I have additional functions (outside the network) that use the input `Z`

and the predicted output `x_pred`

to calculate their respective regularization terms to include in the loss calculation.

```
# Custom training function within model class
def train_step(self, Z, x):
# Define loss object
loss_object = tf.keras.losses.MeanSquaredError()
with tf.GradientTape() as tape:
# Get encoder output
x_pred = self.encoder(Z)
# Calculate traditional supervised learning data loss
data_loss = loss_object(x, x_pred)
# Calculate regularization terms
x_hat, Z_pred = calc_reg_terms(x_pred, Z) # physics-informed function
# Calculate respective regularization losses
loss_x = loss_object(x, x_hat)
loss_z = loss_object(Z, Z_pred)
"""<Additional Code>"""
```

**What is the correct method for calculating the gradient of my total_loss?**

In the past, I've tried simply adding all the loss terms together, then taking the gradient of the summed loss.

```
### PAST METHOD ###
# Calculate total loss
total_loss = data_loss + a * loss_x + b * loss_z # a,b -> set hyperparameters
# Get gradients
grads = tape.gradient(total_loss, self.trainable_weights)
```

However, since my `loss_x`

and `loss_z`

are defined outside the encoder, I fear that these losses act more as a bias to the `total_loss`

calculation because **the model is actually performing worse when these losses are added** to `data_loss`

. The `data_loss`

term has a clear connection to the trainable weights of the encoder, making for a clear gradient calculation, but the same cannot easily be said for my regularization loss terms.

**NOTE:** Tracking each of these three losses during training shows that `data_loss`

can decrease with each passing training epoch, but both `loss_x`

and `loss_z`

tend to plateau early on during training, hence the fear they act more as an unwanted bias to the `total_loss`

.

**What is the proper way to then calculate the gradients with the data_loss, loss_x, and loss_z terms?**

Solution

Thanks for the clarification in your comment, it makes sense.

Your code looks correct to me -- that is the general approach. Calculate `total_loss = data_reconstruction_loss + constant * regularization_loss`

, then calculate the gradient on the `total_loss`

, and backpropagate. A simple way to make sure that it's working without doing a full hyperparameter sweep is to set `a=0`

and `b=0`

, then gradually increase `a`

from some very small value (e.g., `a=1E-10`

) to a large value (e.g., `a=1`

). You can take big steps, but you should see your train and validation loss change as you sweep across values of `a`

. You can then repeat the same process with `b`

. If everything works out, continue to the hyperparameter sweep.

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