The Question about Results.

[Longchao1047027852]

Hello, Sir! On the MNIST dataset, why is the result of my encrypted experiment 89.11%, which is obviously inconsistent with the 99% accuracy mentioned in the paper? What is the reason? Hope to hear from you!

[armandofln]

Sorry I missed your question all this time, I didn't notice. Just a quick disclaimer: this is an old project, and there's a lot of room for improvement, especially on the computational part of the neural network.

The encrypted experiment should yield EXACTLY the same accuracy as the plain neural network with integer numbers (the one in infere_plain.py). Even more, it should give exactly the same predictions (the actual vector in output), number by number. If this is the case and you want to increase the accuracy, I suggest playing around with the precision parameter. Try increasing it, but remember not to overdo it: it is necessary that during the whole inference no computation exceeds t/2.

As I wrote in the other question posted to me in this repository, it is possible that this constraint is a bit too restrictive. Maybe it is possible that in reality it's enough to require that during the encrypted inference phase q/2 is not exceeded, and only after decryption took place is necessary that no number must exceed t/2. However, this is just a speculation that came to my mind now, and I'm not sure about it, it should be tested.

Also note that the accuracy of the plain neural network should be slightly lower than the accuracy of the normal network (the one with floating point numbers).

If there is a discrepancy between the prediction vector of the plain network and the prediction vector of the encrypted network, it means that something went wrong during the inference phase in the encrypted network. Some number must have exceeded t/2 during the computation. This leads to a distortion of the result. In this case, you should choose a lower precision parameter.

Or, if you want a very high precision, or maybe you have a deeper neural network (with more than 5 layers like here), then the best solution should be to increase the subdivision of the parameter t via the Chinese remainder theorem. Instead of breaking it down into 5 numbers, try breaking it down into 6 numbers, 7 numbers or even more, so as to have a larger total t. However, consider that doing this, for cryptographic reasons, has a knock-on effect on the choice of all the other parameters of the homomorphic schemes.