Interpreting neurons in the neural network

Question

I have come up with a solution for a classification problem using neural networks. I have got the weight vectors for the same too. The data is 5 dimensional and there are 5 neurons in the hidden layer. Suppose neuron 1 has input weights w11, w12, ...w15 I have to explain the physical interpretation of these weights...like a combination of these weights, what does it represent in the problem.Does any such interpretation exist or is that the neuron has no specific interpretation as such?

Answer 1

A single neuron will not give you any interpretation, but looking at a combination of couple of neuron can tell you which pattern in your data is captured by that set of neurons (assuming your data is complicated enough to have multiple patterns and yet not too complicated that there is too many connections in the network).

Answer 2

The weights corresponding to neuron 1, in your case w11...w15, are the weights that map the 5 input features to that neuron. The weights quantify the extent to which each feature will effect its respective neuron (which is representing some higher dimensional feature, in turn). Each neuron is a matrix representation of these weights, usually after having an activation function applied.

The mathematical formula that determines the value of the neuron matrix is matrix multiplication of the feature matrix and the weight matrix, and using the loss function, which is most basically the sum of the square of the difference between the output from the matrix multiplication and the actual label.Stochastic Gradient Descent is then used to adjust the weight matrix's values to minimize the loss function.