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Feed input to a keras model only to be accessed by a custom loss function

Is there a way to pass a feature to a keras model as an input only to be accessed by a custom loss function without affecting the model as an input feature? I only need the feature to calculate the loss, not to feed-forward through the hidden layers in the network. (Basically what I want is to feed the feature in as an input and extract it as it is as an output along with y_pred to be accessed in the loss function).
A worked example would be much appreciated.

If you are writing your custom loss, you could use pass the feature as an input, and then using a Lambda layer, you can make it bypass the network and directly concatenate at the end. Something like the following -
from tensorflow.keras import layers, Model, utils
inp = layers.Input((11,))
x = layers.Lambda(lambda x: x[:,:-1])(inp)
o2 = layers.Lambda(lambda x: x[:,-1:])(inp)
x = layers.Dense(20)(x)
x = layers.Dense(20)(x)
o1 = layers.Dense(1)(x)
out = layers.concatenate([o1, o2])
model = Model(inp, out)
def custom_loss(outputs, actuals):
...
utils.plot_model(model, show_shapes=True, show_layer_names=False)
Here the first 10 features are the ones you want to pass via the network, and the last feature is the one you just want as is, for the custom loss. The final output is going to just be a concatenation of your expected output for the first 10 features via the network + the untouched feature.
If you want to know how to write a custom loss, please check this excellent SO post that explains it.

Does Keras support if statements inside the model?

In my input_shape there is a variable x that goes from 0 to 100, and I want to separate the neural network such that for values smaller than 50 it uses some weights and for values bigger than 50 it uses other weights. I imagine something like this:
inputs = keras.Input(shape=(3,)) # let's say x is the first of the three variables
if inputs[0] < 50:
x = layers.Dense(10)(inputs)
output_small = layers.Dense(10)(x)
else:
x = layers.Dense(10)(inputs)
output_big = layers.Dense(10)(x)
model1 = keras.Model(inputs, output_small, name="small_values")
model2 = keras.Model(inputs, output_big, name="big_values")
I necessarily need the if inside the model because I later want to use output_small and output_big in a same Dense layer, therefore I can't run the two samples separately. Would this work or is it possible in another way using Keras? Otherwise is it possible using some other tool?

Yes you should be able to manage conditional branching and merging of layers in a model with functional API.
Link to guide on functional API: https://keras.io/guides/functional_api/

Constructing a keras model

I don't understand what's happening in this code:
def construct_model(use_imagenet=True):
# line 1: how do we keep all layers of this model ?
model = keras.applications.InceptionV3(include_top=False, input_shape=(IMG_SIZE, IMG_SIZE, 3),
weights='imagenet' if use_imagenet else None) # line 1: how do we keep all layers of this model ?
new_output = keras.layers.GlobalAveragePooling2D()(model.output)
new_output = keras.layers.Dense(N_CLASSES, activation='softmax')(new_output)
model = keras.engine.training.Model(model.inputs, new_output)
return model
Specifically, my confusion is, when we call the last constructor
model = keras.engine.training.Model(model.inputs, new_output)
we specify input layer and output layer, but how does it know we want all the other layers to stay?
In other words, we append the new_output layer to the pre-trained model we load in line 1, that is the new_output layer, and then in the final constructor (final line), we just create and return a model with a specified input and output layers, but how does it know what other layers we want in between?
Side question 1): What is the difference between keras.engine.training.Model and keras.models.Model?
Side question 2): What exactly happens when we do new_layer = keras.layers.Dense(...)(prev_layer)? Does the () operation return new layer, what does it do exactly?

This model was created using the Functional API Model
Basically it works like this (perhaps if you go to the "side question 2" below before reading this it may get clearer):
You have an input tensor (you can see it as "input data" too)
You create (or reuse) a layer
You pass the input tensor to a layer (you "call" a layer with an input)
You get an output tensor
You keep working with these tensors until you have created the entire graph.
But this hasn't created a "model" yet. (One you can train and use other things).
All you have is a graph telling which tensors go where.
To create a model, you define it's start end end points.
In the example.
They take an existing model: model = keras.applications.InceptionV3(...)
They want to expand this model, so they get its output tensor: model.output
They pass this tensor as the input of a GlobalAveragePooling2D layer
They get this layer's output tensor as new_output
They pass this as input to yet another layer: Dense(N_CLASSES, ....)
And get its output as new_output (this var was replaced as they are not interested in keeping its old value...)
But, as it works with the functional API, we don't have a model yet, only a graph. In order to create a model, we use Model defining the input tensor and the output tensor:
new_model = Model(old_model.inputs, new_output)
Now you have your model.
If you use it in another var, as I did (new_model), the old model will still exist in model. And these models are sharing the same layers, in a way that whenever you train one of them, the other gets updated as well.
Question: how does it know what other layers we want in between?
When you do:
outputTensor = SomeLayer(...)(inputTensor)
you have a connection between the input and output. (Keras will use the inner tensorflow mechanism and add these tensors and nodes to the graph). The output tensor cannot exist without the input. The entire InceptionV3 model is connected from start to end. Its input tensor goes through all the layers to yield an ouptut tensor. There is only one possible way for the data to follow, and the graph is the way.
When you get the output of this model and use it to get further outputs, all your new outputs are connected to this, and thus to the first input of the model.
Probably the attribute _keras_history that is added to the tensors is closely related to how it tracks the graph.
So, doing Model(old_model.inputs, new_output) will naturally follow the only way possible: the graph.
If you try doing this with tensors that are not connected, you will get an error.
Side question 1
Prefer to import from "keras.models". Basically, this module will import from the other module:
https://github.com/keras-team/keras/blob/master/keras/models.py
Notice that the file keras/models.py imports Model from keras.engine.training. So, it's the same thing.
Side question 2
It's not new_layer = keras.layers.Dense(...)(prev_layer).
It is output_tensor = keras.layers.Dense(...)(input_tensor).
You're doing two things in the same line:
Creating a layer - with keras.layers.Dense(...)
Calling the layer with an input tensor to get an output tensor
If you wanted to use the same layer with different inputs:
denseLayer = keras.layers.Dense(...) #creating a layer
output1 = denseLayer(input1) #calling a layer with an input and getting an output
output2 = denseLayer(input2) #calling the same layer on another input
output3 = denseLayer(input3) #again
Bonus - Creating a functional model that is equal to a sequential model
If you create this sequential model:
model = Sequential()
model.add(Layer1(...., input_shape=some_shape))
model.add(Layer2(...))
model.add(Layer3(...))
You're doing exactly the same as:
inputTensor = Input(some_shape)
outputTensor = Layer1(...)(inputTensor)
outputTensor = Layer2(...)(outputTensor)
outputTensor = Layer3(...)(outputTensor)
model = Model(inputTensor,outputTensor)
What is the difference?
Well, functional API models are totally free to be build anyway you want. You can create branches:
out1 = Layer1(..)(inputTensor)
out2 = Layer2(..)(inputTensor)
You can join tensors:
joinedOut = Concatenate()([out1,out2])
With this, you can create anything you want with all kinds of fancy stuff, branches, gates, concatenations, additions, etc., which you can't do with a sequential model.
In fact, a Sequential model is also a Model, but created for a quick use in models without branches.

There's this way of building a model from a pretrained one that you may build upon.
See https://keras.io/applications/#fine-tune-inceptionv3-on-a-new-set-of-classes:
base_model = InceptionV3(weights='imagenet', include_top=False)
x = base_model.output
x = GlobalAveragePooling2D()(x)
x = Dense(1024, activation='relu')(x)
predictions = Dense(200, activation='softmax')(x)
model = Model(inputs=base_model.input, outputs=predictions)
for layer in base_model.layers:
layer.trainable = False
model.compile(optimizer='rmsprop', loss='categorical_crossentropy')
Each time a layer is added by an op like "x=Dense(...", information about the computational graph is updated. You can type this interactively to see what it contains:
x.graph.__dict__
You can see there's all kinds of attributes, including about previous and next layers. These are internal implementation details and possibly change over time.

How to verify structure a neural network in keras model?

I'm new in Keras and Neural Networks. I'm writing a thesis and trying to create a SimpleRNN in Keras as it is illustrated below:
As it is shown in the picture, I need to create a model with 4 inputs + 2 outputs and with any number of neurons in the hidden layer.
This is my code:
model = Sequential()
model.add(SimpleRNN(4, input_shape=(1, 4), activation='sigmoid', return_sequences=True))
model.add(Dense(2))
model.compile(loss='mean_absolute_error', optimizer='adam')
model.fit(data, target, epochs=5000, batch_size=1, verbose=2)
predict = model.predict(data)
1) Does my model implement the graph?
2) Is it possible to specify connections between neurons Input and Hidden layers or Output and Input layers?
Explanation:
I am going to use backpropagation to train my network.
I have input and target values
Input is a 10*4 array and target is a 10*2 array which I then reshape:
input = input.reshape((10, 1, 4))
target = target.reshape((10, 1, 2))
It is crucial for to able to specify connections between neurons as they can be different. For instance, here you can have an example:

1) Not really. But I'm not sure about what exactly you want in that graph. (Let's see how Keras recurrent layers work below)
2) Yes, it's possible to connect every layer to every layer, but you can't use Sequential for that, you must use Model.
This answer may not be what you're looking for. What exactly do you want to achieve? What kind of data you have, what output you expect, what is the model supposed to do? etc...
1 - How does a recurrent layer work?
Documentation
Recurrent layers in keras work with an "input sequence" and may output a single result or a sequence result. It's recurrency is totally contained in it and doesn't interact with other layers.
You should have inputs with shape (NumberOrExamples, TimeStepsInSequence, DimensionOfEachStep). This means input_shape=(TimeSteps,Dimension).
The recurrent layer will work internally with each time step. The cycles happen from step to step and this behavior is totally invisible. The layer seems to work just like any other layer.
This doesn't seem to be what you want. Unless you have a "sequence" to input. The only way I know if using recurrent layers in Keras that is similar to you graph is when you have a segment of a sequence and want to predict the next step. If that's the case, see some examples by searching for "predicting the next element" in Google.
2 - How to connect layers using Model:
Instead of adding layers to a sequential model (which will always follow a straight line), start using the layers independently, starting from an input tensor:
from keras.layers import *
from keras.models import Model
inputTensor = Input(shapeOfYourInput) #it seems the shape is "(2,)", but we must see your data.
#A dense layer with 2 outputs:
myDense = Dense(2, activation=ItsAGoodIdeaToUseAnActivation)
#The output tensor of that layer when you give it the input:
denseOut1 = myDense(inputTensor)
#You can do as many cycles as you want here:
denseOut2 = myDense(denseOut1)
#you can even make a loop:
denseOut = Activation(ItsAGoodIdeaToUseAnActivation)(inputTensor) #you may create a layer and call it with the input tensor in just one line if you're not going to reuse the layer
#I'm applying this activation layer here because since we defined an activation for the dense layer and we're going to cycle it, it's not going to behave very well receiving huge values in the first pass and small values the next passes....
for i in range(n):
denseOut = myDense(denseOut)
This kind of usage allows you to create any kind of model, with branches, alternative ways, connections from anywhere to anywhere, provided you respect the shape rules. For a cycle like that, inputs and outputs must have the same shape.
At the end, you must define a model from one or many inputs to one or many outputs (you must have training data to match all inputs and outputs you choose):
model = Model(inputTensor,denseOut)
But notice that this model is static. If you want to change the number of cycles, you will have to create a new model.
In this case, it would be as simple as repeating the loop step denseOut = myDense(denseOut) and creating another model2=Model(inputTensor,denseOut).
3 - Trying to create something like the image below:
I am supposing C and F will participate in all iterations. If not,
Since there are four actual inputs, and we are going to treat them all separately, let's create 4 inputs instead, all like (1,).
Your input array should be divided in 4 arrays, all being (10,1).
from keras.models import Model
from keras.layers import *
inputA = Input((1,))
inputB = Input((1,))
inputC = Input((1,))
inputF = Input((1,))
Now the layers N2 and N3, that will be used only once, since C and F are constant:
outN2 = Dense(1)(inputC)
outN3 = Dense(1)(inputF)
Now the recurrent layer N1, without giving it the tensors yet:
layN1 = Dense(1)
For the loop, let's create outA and outB. They start as actual inputs and will be given to the layer N1, but in the loop they will be replaced
outA = inputA
outB = inputB
Now in the loop, let's do the "passes":
for i in range(n):
#unite A and B in one
inputAB = Concatenate()([outA,outB])
#pass through N1
outN1 = layN1(inputAB)
#sum results of N1 and N2 into A
outA = Add()([outN1,outN2])
#this is constant for all the passes except the first
outB = outN3 #looks like B is never changing in your image....
Now the model:
finalOut = Concatenate()([outA,outB])
model = Model([inputA,inputB,inputC,inputF], finalOut)

Keras regression multiple outputs

a question concerning keras regression with multiple outputs:
Could you explain the difference beteween this net:
two inputs -> two outputs
input = Input(shape=(2,), name='bla')
hidden = Dense(hidden, activation='tanh', name='bla')(input)
output = Dense(2, activation='tanh', name='bla')(hidden)
and: two single inputs -> two single outputs:
input = Input(shape=(2,), name='speed_input')
hidden = Dense(hidden_dim, activation='tanh', name='hidden')(input)
output = Dense(1, activation='tanh', name='bla')(hidden)
input_2 = Input(shape=(1,), name='angle_input')
hidden_2 = Dense(hidden_dim, activation='tanh', name='hidden')(input_2)
output_2 = Dense(1, activation='tanh', name='bla')(hidden_2)
model = Model(inputs=[speed_input, angle_input], outputs=[speed_output, angle_output])
They behave very similar. Other when I completly seperate them, then the two nets behave like they re supposed to.
And is it normal that two single output nets behave much more intelligible than a bigger one with two outputs, I didnt think the difference could be huge like I experienced.
Thanks a lot :)

This goes back to how neural networks operate. In your first model, each hidden neuron receives 2 input values (as it is a 'Dense' layer, the input propagates to every neuron). In your second model, you have twice as many neurons, but each of these only receive either speed_input or angle_input, and only works with that data instead of the entire data.
So, if speed_input and angle_input are 2 completely unrelated attributes, you'll likely see better performance from splitting the 2 models, since neurons aren't receiving what is basically noise input (they don't know that your outputs correspond to your inputs, they can only try to optimize your loss function). Essentially, you're creating 2 seperate models.
But in most cases, you want to feed the model relevant attributes that combine to draw a prediction. So splitting the model then would not make sense, since you're just stripping neccessary information away.