Circom Circuits Library for Machine Learning

Disclaimer: This package is not affiliated with circom, circomlib, or iden3.

Description

• This repository contains a library of circuit templates.
• You can read more about the circom language in the circom documentation webpage.

Organisation

This respository contains 5 folders:

• circuits: it contains the implementation of different cryptographic primitives in circom language.
• test: tests.

Polynomial activation:

Inspired by Ali, R. E., So, J., & Avestimehr, A. S. (2020), circuit/Poly.circom has been addded as a template to implement f(x)=x**2+x as an alternative activation layer to ReLU. The non-polynomial nature of ReLU activation results in a large number of constraints per layer. By replacing ReLU with the polynomial activation f(n,x)=x**2+n*x, the number of constraints drastically decrease with a slight performance tradeoff. A parameter n is required when declaring the component to adjust for the scaling of floating-point weights and biases into integers. See below for more information.

Weights and biases scaling:

• Circom only accepts integers as signals, but Tensorflow weights and biases are floating-point numbers.
• In order to simulate a neural network in Circom, weights must be scaled up by 10**m times. The larger m is, the higher the precision.
• Subsequently, biases (if any) must be scaled up by 10**2m times or even more to maintain the correct output of the network.

An example is provided below.

Scaling example: mnist_poly

In models/mnist_poly.ipynb, a sample model of Conv2d-Poly-Dense layers was trained on the MNIST dataset. After training, the weights and biases must be properly scaled before inputting into the circuit:

• Pixel values ranged from 0 to 255. In order for the polynomial activation approximation to work, these input values were scaled to 0.000 to 0.255 during model training. But the original integer values were scaled by 10**6 times as input to the circuit
  • Overall scaled by 10**9 times
• Weights in the Conv2d layer were scaled by 10**9 times for higher precision. Subsequently, biases in the same layer must be scaled by (10**9)*(10**9)=10**18 times.
• The linear term in the polynomial activation layer would also need to be adjusted by 10**18 times in order to match the scaling of the quadratic term. Hence we performed the acitvation with f(x)=x**2+(10**18)*x.
• Weights in the Dense layer were scaled by 10**9 time for precision again.
• Biases in the Dense layer had been omitted for simplcity, since ArgMax layer is not affected by the biases. However, if the biases were to be included (for example in a deeper network as an intermediate layer), they would have to be scaled by (10**9)**5=10**45 times to adjust correctly.

We can easily see that a deeper network would have to sacrifice precision, due to the limitation that Circom works under a finite field of modulo p which is around 254 bits. As log(2**254)~76, we need to make sure total scaling do not aggregate to exceed 10**76 (or even less) times. On average, a network with l layers should be scaled by less than or equal to 10**(76//l) times.

TODO:

• add strides parameter to Conv2D and SumPooling2D