How to tell a neural network that: "your i-th input is special" Assume that I have a fully connected network that takes in a vector containing 1025 elements. First 1024 elements are related to the input image of size 32 x 32 x 1, and the last element in the vector (1025-th element) is a control bit that I call it special input.
When this bit is zero, the network should predict if there is a cat in the image or not, and when this bit is one, it should predict if there is a dog in the image or not.
So how can I tell the network that your 1025-th element should be special to you and you should pay more attention to it?
Note that it's just an example and the real problem is more complex than this. So please don't bypass the goal of this question by using tricks special to this example. Any idea is appreciated.
Assume the image can contain objects of class $C_1 \dots C_c$. Assume a set of additional inputs that has a meaning of questions as &quot;contains the image a C_i or C_j or ... ?&quot;.
The main problem for the system is classify the image in classes $C_i$. Second problem is answer the implicit question proposed by the remainder inputs.
Thus, better combine two NNs:

first one an object recognizer, with input the image data.
second one a NN that will answer the question implicit in remainder bits, with inputs the output of previous NN and the &quot;question&quot; bits.

In concrete for the example that the question describe:

a NN to classify dog/cat from 32x32 image. Two outputs for probabilities of dog an cat. Or simply one binary output 0:&quot;is a dog&quot;, 1:&quot;is a cat&quot;.
a second NN with the &quot;1025&quot; binary input ( 0: &quot;look for dogs&quot;, 1: &quot;look for cats&quot;) and output from previous one. In this case, if everything is ok, it will infer the logic &quot;a==b&quot;: &quot;is a dog&quot; and &quot;look for dogs&quot; or &quot;is a cat&quot; and &quot;look for cats&quot;.

Note that if you try to solve the problem directly with a full-connected NN with all inputs (1025 in the example), you loss the possibility of use CNN and max-pooling layers, etc. Moreover, split decreases training times, join subjects increases them &quot;exponentially&quot;. Not a promising way.