Understanding keras layer structure/notation

Question

I am trying to understand the following keras model:

in = keras.Input(shape = 76)

x = layers.Dense(80, activation='tanh')(in)
x = layers.Dense(70, activation='tanh')(x)
x = layers.Dense(60, activation='tanh')(x)
x = layers.Dense(50, activation='tanh')(x)
x = layers.Dense(40, activation='tanh')(x)
x = layers.Dense(30, activation='tanh')(x)
x = layers.Dense(20, activation='tanh')(x)
x = layers.Dense(10, activation='tanh')(x)

out = layers.Dense(1, activation='linear')(x)

model = keras.Model(in, out)

So in general, I would like to know what this model is doing. I also have two specific questions:

1. Is there a mismatch between in the input tensor (shape=76) and the first layer's units (shape=80)? What effect does a mismatch have if any? How can 76 inputs go into 80 nodes/units?

2. What is the purpose parentheses input at, for example "(in)" in the first Dense layer x = layers.Dense(80, activation='tanh')(in) or the "(x)" in x = layers.Dense(70, activation='tanh')(x) the second layer? I am not familiar with this type of notation in keras and I've looked everywhere online to for insight.

Thanks in advance!

Answer 1

1. You are missing the point that the shapes are only one dimension, whereas the second one is implicit. I guess, this image showing both dimensions would be more helpful. As you can see, the shape of the input is $N \times 4$ and it is multiplied by $W_1$ with shape $4 \times 5$, so the shapes match as to multiply matrices you need only the "touching" dimensions to match.

2. You are using the functional API. layers.Dense(80, activation='tanh') returns an anonymous function that can be called. You could write it as well like

mylayer = layers.Dense(80, activation='tanh')
mylayer(x)

You can easily verify it by calling callable(layers.Dense(80, activation='tanh')), that confirms that the output is a function.