How do you perform a gradient based adversarial attack on an SVM based model?

Question

I have an SVM currently and want to perform a gradient based attack on it similar to FGSM discussed in Explaining And Harnessing Adversarial Examples.

I am struggling to actually calculate the gradient of the SVM cost function with respect to the input (I am assuming it needs to be w.r.t input).

Is there a way to avoid the maths (I am working in python if that helps?)

Answer 1

A way to avoid computing the SVM loss by hand is to use a differentiable programming framework, such as JAX. These frameworks will automatically calculate gradients using automatic differentiation.

If you can write down the SVM loss using numpy operations then you can use the framework's tools to get a function which evaluates the gradient with respect to any argument.

In JAX this would look like:

import jax
import jax.numpy as jnp
def hinge_loss(x, y, theta):
    # x is an nxd matrix, y is an nx1 matrix
    y_hat = model(x, theta) # returns nx1 matrix, model parameters theta
    return jnp.maximum(0, 1 - y_hat * y)

hinge_loss_grad = jax.grad(hinge_loss)
# hinge_loss_grad takes an x, y, theta and returns gradient of hinge loss wrt x