Numerical Discrimination of the Generalisation Model from Learnt Weights in Neural Networks

Abstract

This research demonstrates a method of discriminating the numerical relationships of neural network layer inputs to the layer outputs established from the learnt weights and biases of a neural network's generalisation model. It is demonstrated with a mathematical form of a neural network rather than an image, speech or textual translation application as this provides clarity in the understanding gained from the generalisation model. It is also reliant on the input format but that format is not unlike an image pixel input format and as such the research is applicable to other applications too. The research results have shown that weight and biases can be used to discriminate the mathematical relationships between inputs and make discriminations of what mathematical operators are used between them in the learnt generalisation model. This may be a step towards gaining definitions and understanding for intractable problems that a Neural Network has generalised in a solution. For validating them, or as a mechanism for creating a model used as an alternative to traditional approaches, but derived from a neural network approach as a development tool for solving those problems. The demonstrated method was optimised using learning rate and the number of nodes and in this example achieves a low loss at 7.6e-6, a low Mean Absolute Error at 1e-3 with a high accuracy score of 1.0. But during the experiments a sensitivity to the number of epochs and the use of the random shuffle was discovered, and a comparison with an alternative shuffle using a non-random reordering demonstrated a lower but comparable performance, and is a subject for further research but demonstrated in this "decomposition" class architecture.