How to prevent backpropagation after compiling a keras model?

I have a multi output model such as this

       input
         |
      hidden
         |
        / \
       /   \
output1    output2

I can train this model by model.train_on_batch(input=input,output=[output1,output2]) but at some particulat stage in my training I want to train only one branch (output2) of this model and prevent backpropogation from output1. I initally tried passing a None value in the model model.train_on_batch(input=input,output=[None,output2]) but its showing

AttributeError: 'NoneType' object has no attribute 'shape'

Then I tried passing a NaN arrays of output1 shape model.train_on_batch(input=input,output=[Nan_array,output2]) then the loss becomes NaN. How can I train only one branch in a multi output keras model and prevent backpropogation in the other?

Edit

I was trying to find a solution to this problem and came across K.stop_gradient function. I tried to stop backpropogaion in a one output model like this

import numpy as np
from keras.models import Sequential
from keras.layers import Dense, Dropout
import keras.backend as K

def loss(y_true, y_pred):
    return K.stop_gradient(y_pred)
    
# Generate dummy data
x_train = np.random.random((10, 20))
y_train = np.random.randint(2, size=(10, 1))
x_test = np.random.random((10, 20))
y_test = np.random.randint(2, size=(10, 1))

model = Sequential()
model.add(Dense(64, input_dim=20, activation='relu'))
model.add(Dropout(0.5))
model.add(Dense(64, activation='relu'))
model.add(Dropout(0.5))
model.add(Dense(1, activation='sigmoid'))

model.compile(loss=loss,
              optimizer='rmsprop',
              metrics=['accuracy'])

model.fit(x_train, y_train,
          epochs=1,
          batch_size=128)

score = model.evaluate(x_test, y_test, batch_size=128)

But gets this error

ValueError: Tried to convert 'x' to a tensor and failed. Error: None values not supported.

Solution

You can create two Model objects with sharing weights. The first model optimizes on output=[output1, output2], while the second model only contains the branch of output2. If you call train_on_batch on the second model, the weights in branch 1 will not be updated.

For example,

x = Input(shape=(32,))
hidden = Dense(32)(x)
output1 = Dense(1)(hidden)
output2 = Dense(1)(hidden)

model = Model(x, [output1, output2])
model.compile(loss='mse', optimizer='adam')

model_only2 = Model(x, output2)
model_only2.compile(loss='mse', optimizer='adam')

X = np.random.rand(2, 32)
y1 = np.random.rand(2)
y2 = np.random.rand(2)

# verify: all the weights will change if we train on `model`
w0 = model.get_weights()
model.train_on_batch(X, [y1, y2])
w1 = model.get_weights()
print([np.allclose(x, y) for x, y in zip(w0, w1)])
# => [False, False, False, False, False, False]

# verify: branch 1 will not change if we train on `model_only2`
model_only2.train_on_batch(X, y2)
w2 = model.get_weights()
print([np.allclose(x, y) for x, y in zip(w1, w2)])
# => [False, False, True, True, False, False]