Adding unprocessed input to later layers in a neural network

I apologize if this is a bit of an open-ended question. I'm working in R, using the keras library; I'd like to train a neural network to approximate a function f(y, x) where I know that the true f is increasing in y (but not in x). y is a scalar, while x is a vector.

I need the estimate of f represented by the trained NN -- let's call it g -- to be increasing in y as well. My idea was to use non-negativity constraints on the weights of any node that has y among its ancestors; nodes that only process x have unconstrained weights so that non-monotonous responses to changes in x are possible.

How do I do this in keras? Well, one idea I had was to

1. process x in a number of suitable layers with unconstrained weights, and then
2. process the output of those layers (let's call it z) and y in further layers in which all weights are constrained to be non-negative.

Neither step is difficult in isolation, but what I'm having difficulty with is figuring out how to, in essence, feed a new input to the NN after other input has already been processed.

It's not as easy as splitting the whole NN in two, of course, i.e. gluing two NNs together. There is no single "right" z resulting from the initial processing of x; in fact I cannot even measure how "good" the intermediate result z is at all, I can only evaluate the overall response g(y, x) by comparing it to the known f(y, x) in my training data.

That said, perhaps there is an easy/straightforward way of architecting1 the NN in such a way that y passes the initial layers unprocessed and only gets used as an input in one of the later layers.

I've looked at the keras documentation as well as searched Google etc., but to no avail. I'm no expert on neural networks or any kind of statistical learning, nor on keras (much less TensorFlow and whatever else underlies it). I'd merely like to use this keras for my application needs, and could use a little not-too-technical help re: how to do the above.

Side note: I'm not too hung up on my specific approach. Ultimately, anything that gives me an NN for which g(y, x) is guaranteed to be increasing in y but not in x is fine with me.

Thank you!

1. I hope that's a word.

Answering myself, yes, this seems to be possible; however, the NN cannot be sequential, and in particular you cannot use keras_model_sequential(). Instead,

1. create two separate input layers using layer_input(shape = ..., name = "...") (name them x and y, say), and assign to e.g. input_x and input_y;
2. pipe the input layer for x into the desired processing layers with unconstrained weights, and assign the resulting "building block" of the NN to e.g. intermediate_z;
3. combine this building block and the input layer for y using layer_concatenate(inputs = list(intermediate_z, input_y)) and assign to e.g. output_f;
4. pipe this into further processing layers with constrained weights;
5. create the NN as keras_model(inputs = list(input_x, input_y), output = output_f);
6. compile the NN as usual using compile();
7. train the NN using fit(list("x" = train_x, "y" = train_y), train_f, ...) (where the names of the list elements correspond to the names you assigned to the input layers in step 1);
8. predict new values using predict((list("x" = new_x, "y" = new_y)).

I found this guide to the functional TensorFlow API helpful.