Keras: How to feed input directly into other hidden layers of the neural net than the first?

You didn't show which kind of model you use to me, but I assume that you initialized your model as Sequential. In a Sequential model you can only stack one layer after another - so adding a "short-cut" connection is not possible.

For this reason authors of Keras added option of building "graph" models. In this case you can build a graph (DAG) of your computations. It's a more complicated than designing a stack of layers, but still quite easy.

Check the documentation site to look for more details.

Provided your Keras's backend is Theano, you can do the following:

import theano
import numpy as np

d = Dense(1500, W_regularizer=l2(1e-3), activation='relu') # I've joined activation and dense layers, based on assumption you might be interested in post-activation values
model.add(d)
model.add(Dropout(0.5))
model.add(Dense(1))

c = theano.function([d.get_input(train=False)], d.get_output(train=False))
layer_input_data = np.random.random((1,20000)).astype('float32') # refer to d.input_shape to get proper dimensions of layer's input, in my case it was (None, 20000)
o = c(layer_input_data)