Derivative in loss function in Keras

Question

I want to make following loss function in keras:

Loss = mse + double_derivative(y_pred,x_train)

I am not able to incorporate the derivative term. I have tried K.gradients(K.gradients(y_pred,x_train),x_train) but it does not help.

I am getting error message:

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

def _loss_tensor(y_true, y_pred,x_train):
    l1 = K.mean(K.square(y_true - y_pred), axis=-1)
    sigma = 0.01
    lamda = 3
    term = K.square(sigma)*K.gradients(K.gradients(y_pred,x_train),x_train)
    l2 = K.mean(lamda*K.square(term),axis=-1)
    return l1+l2

def loss_func(x_train):
        def loss(y_true,y_pred):
            return _loss_tensor(y_true,y_pred,x_train)
        return loss

def create_model_neural(learning_rate, num_layers,
                 num_nodes, activation):

    model_neural = Sequential()

    x_train = model_neural.add(Dense(num_nod, input_dim=num_input, activation=activation))

    for i in range(num_layers-1):
        model_neural.add(Dense(num_nodes,activation=activation,name=name))

    model_neural.add(Dense(1, activation=activation))

    optimizer = SGD(lr=learning_rate)
    model_loss = loss_func(x_train=x_train)

    model_neural.compile(loss=model_loss,optimizer=optimizer)

    return model_neural

Answer 1

The problem is that x_train is always None and keras can't take a derivative wrt None. And this is happening because model_neural.add(...) does not return anything.

I assume that x_train is the input that is passed to the network. In this case x_train should probably be another argument of create_model_neural or alternatively you can try model_neural.input tensor.