Hessian by DL toolbox

Hi there.

In my Matlab code, I am using customize training loop for my algorithm, so I am using forward and dlgradient to create my loss and gradient models, and then taking them by dlfeval.

I am going to ask you, is there any way to calculate the Hessian model of the objective function (in my case softmax cross entropy) in the training loop? Something similar dlgradent, lets say.

Thank you...

[Matt J]

Wouldn't the Hessian be impracticality large to store? How many learnable parameters do you have?

[MAHSA YOUSEFI]

3.500,000 parameters totally and a dataset with 50,000 samples. For sure, yes! It would be a large matrix.

In my Algorithm, I have a subsampled Hessian (10,000 samples) multiply by a vectore.

[MAHSA YOUSEFI]

Actually, if I find the way of computing Hessian, I can take some strategies to solve this problem, storing issue. I am going to do computations layer by layer. In this case, the size of Hessian matrix, depends on only to the number of that specific layter. So it would noy be too large if it is considered per layer.

Answer 1

[Anurag Ojha]

Hello Mahsa

You can use hessian function to find hessian matrix.

hessian(f,v) finds the Hessian matrix of the symbolic scalar function f with respect to vector v in Cartesian coordinates.

If we do not specify v, then hessian(f) finds the Hessian matrix of the scalar function f with respect to a vector constructed from all symbolic variables found in f.

Adding a example below

syms x y z
f = x*y + 2*z*x;
hessian(f,[x,y,z])

ans = 

Adding the MATLAB documentation link so that you can dive deeper:

• https://www.mathworks.com/help/symbolic/sym.hessian.html