A conclusive answer to how neural networks work should be both descriptive and prescriptive. It should not only tell you how they work but give you new insights into how to train them or how to fix their errors.
For example, does your theory tell you how to initialize weights? How the weights in the NN were derived from specific training samples? If you removed a certain subset of training samples, how would the weights change? If the model makes a mistake, which neurons/layers are responsible? Which weights would have to change, and what training data would need to be added/removed to have the model learn better weights?
If you can't answer these sorts of questions, you can't really say you know how they work. Kind of like steam engines before Carnot, or Koch's principles in microbiology, a theory is often only as good as it can be operationalized.
For example, does your theory tell you how to initialize weights? How the weights in the NN were derived from specific training samples? If you removed a certain subset of training samples, how would the weights change? If the model makes a mistake, which neurons/layers are responsible? Which weights would have to change, and what training data would need to be added/removed to have the model learn better weights?
If you can't answer these sorts of questions, you can't really say you know how they work. Kind of like steam engines before Carnot, or Koch's principles in microbiology, a theory is often only as good as it can be operationalized.