I was doing some research about the simplest neural network that can model each logic gate. By simplest I mean:
- no bias if possible
- fewest number of layers
- fewest number of neurons in each layer
- no activation function if possible
Starting from a 1-neuron network with no bias, I came up with the following chart:
I noticed that all the "negated" gates, namely NOT, NOR, NAND, and XNOR need a bias. Also note those gates are the negations of IDENTITY, OR, AND and XOR respectively.
1) Is this observation true?
2) If it is, why does "negation" require a bias?
Rigorous proofs and intuitive explanations are both welcome.
Edit: since there seems to be some confusion about what architecture/type of network I am referring too, I am adding a link showing diagrams of what I have found are the corresponding "simplest neural networks":