A counter question I would ask is why would you want to do it without using the toolbox when the facility is available?
A Neural Network (NN) can be expressed as a parametric equation, i.e., the relationship between inputs to an NN and its output can simply be described as an equation composed of weighted sums, followed by some form of activation (i.e., output of the weighted summation being passed through some form of an activation function - Sigmoid function for example). That is the basic architecture of an NN (many modifications or alternative forms can be explored), and the problem at hand now is estimating the right parameter values (weights) to give the correct outputs you want, which can be done through optimization (can formulate as a convex optimization problem). Then you try to optimize the parameters to the best you can by minimizing the residues between the NN outputs and actual output values in your training examples. That is how you train an NN.
I would suggest starting from the toolbox and generating the script for the NN you design. Once you have the script, you can make alterations and experiment and innovate as you wish by making alterations to the script. That is the most efficient way I see in getting the hang of coding NNs by hand, will save time rather than when attempting to write from scratch.
However, solving problems with NNs still does not contribute to the knowledge field as fundamental contributions as NNs are still 'black boxes' more or less. So in addition to solving problems with NNs, try to investigate deeper and answer the question "why a particular NN you designed works for the particular problem you addressed", and try to relate your NN architecture to some solid science. This is where looking into the script and hand-coding helps immensely I believe. That will enable your NN to go beyond the "black box" label and become a fundamental contribution to knowledge.
hi, does anyone through light, on working with NN code in MATLAB function to run the function onto Arduino via serial communication. (Real time simulation).
Firstly, you can use MATLAB's ANN toolbox to follow the proposed steps, then at the end you can generate a code in Matlab script or in C ++ which you can modify if necessary