Neural networks - input values

Question

I have a question that may be trivial but it's not described anywhere i've looked. I'm studying neural networks and everywhere i look there's some theory and some trivial example with some 0s and 1s as an input. I'm wondering: do i have to put only one value as an input value for one neuron, or can it be a vector of, let's say, 3 values (RGB colour for example)?

Answer 1

The above answers are technically correct, but don't explain the simple truth: there is never a situation where you'd need to give a vector of numbers to a single neuron.

From a practical standpoint this is because (as one of the earlier solutions has shown) you can just have a neuron for each number in a vector and then have all of those be the input to a single neuron. This should get you your desired behavior after training, as the second layer neuron can effectively make use of the entire vector.

From a mathematical standpoint, there is a fundamental theorem of coding theory that states that any vector of numbers can be represented as a single number. Thus, if you really don't want an extra layer of neurons, you could simply encode the RGB values into a single number and input that to the neuron. Though, this coding function would probably make most learning problems more difficult, so I doubt this solution would be worth it in most cases.

To summarize: artificial neural networks are used without giving a vector to an input unit, but lose no computational power because of this.