Compute jacobian

I have a Module that computes a Tensor vector from a Tensor vector. I wish to compute the gradient of each output element with respect to each input element. In the Pytorch documentation, they show this can be done through the use of torch.autograd.functional.jacobian (see torch.autograd.functional.jacobian). I'm not sure the same can be done using TorchSharp.

I tried looping over the elements of the output tensor and doing a backward call:

for (int i = 0; i < output.Length; i++)
    output[i].backward(create_graph: false, retain_graph: true);

But even with retain_graph=true that results in the error:

System.Runtime.InteropServices.ExternalException: 'Trying to backward through the graph a second time (or directly access saved tensors after they have already been freed). Saved intermediate values of the graph are freed when you call .backward() or autograd.grad(). Specify retain_graph=True if you need to backward through the graph a second time or if you need to access saved tensors after calling backward.

Is there currently already a way to compute the jacobian of a function/module in TorchSharp? If not, can you suggest how I could get started on adding support for the above Pytorch functionality?

It's hard to say why you are getting the error without more code, but I believe that you're getting it because you're not calling zero_grad() after a first back-prop run.

I couldn't find anything in the native APIs for it, and it seems like it's all implemented in Python for PyTorch. It will take some time to figure out, but does not seem impossibly hard.

Source

A small code example:

var device = torch.cuda_is_available() ? torch.CPU : torch.CPU;

torch.Tensor x1 = torch.tensor(new double[,] { { 1.0, 3.0 }, { 2.0, 4.0 } }, device: device, requires_grad: true);
x1.retain_grad();

torch.Tensor intercepts = torch.tensor(new double[] { 1.0, 5.0 }, device: device, requires_grad: true);

torch.Tensor objectiveFunction(torch.Tensor x, torch.Tensor b)
{

    return torch.einsum("ij,j->i", x, b);
}
var example = objectiveFunction(x1, intercepts);
example[0].backward(retain_graph: true);
Console.WriteLine(string.Join(", ", x1.grad().data<double>().ToArray()));

x1.grad()?.zero_();
example.grad()?.zero_();
intercepts.grad()?.zero_();
example[1].backward(retain_graph: true);
Console.WriteLine(string.Join(", ", x1.grad().data<double>().ToArray()));

The first call of backward works like a charm, but the second fails. As you can see, using just a function of the input tensors, I cannot call zero_grad() anywhere, so I don't really know how to reset the gradients.

I also tried

torch.Tensor x1 = torch.tensor(new double[,] { { 1.0, 3.0, 2.0 }, { 2.0, 4.0, 3.0 } }, device: device, requires_grad: true);
x1.retain_grad();

torch.Tensor intercepts = torch.tensor(new double[] { 1.0, 5.0, 7.0 }, device: device, requires_grad: true);

torch.Tensor objectiveFunction(torch.Tensor x, torch.Tensor b)
{

    return torch.einsum("ij,j->i", x, b);
}
var example = objectiveFunction(x1, intercepts);

var jacobian = torch.autograd.grad(new torch.Tensor[] { example }, new torch.Tensor[] { intercepts }, new torch.Tensor[] { torch.tensor(new double[,] { { 1.0, 0.0 }, { 0.0, 1.0 } }) }, retain_graph: true);

which should return a tensor with the same data as x1, but this code returns the sum of x1 along the rows (i.e. [3, 7, 5]).

If not, can you suggest how I could get started on adding support for the above Pytorch functionality?

Hey, if you want to contribute the implementation, that would be awesome. The PyTorch jacobian and hessian functionality is implemented in Python, it seems, so that should be straight-forward (but it would take a while -- lots of code to translate). If not, I'll get to it sometime in December, probably.

https://pytorch.org/docs/stable/_modules/torch/autograd/functional.html#jacobian

How about Hessians? :-)

Sure, can implement those somewhere this week as well.

Navigation Menu

Repository navigation

Compute jacobian #1149

Metadata

Assignees

Labels

Type

Projects

Milestone

Relationships

Development

Compute jacobian #1149

Description

Activity

NiklasGustafsson commented on Nov 21, 2023

GeorgeS2019 commented on Nov 21, 2023

roelofsmn commented on Nov 22, 2023

roelofsmn commented on Nov 22, 2023

NiklasGustafsson commented on Nov 29, 2023

NiklasGustafsson commented on Jan 26, 2024

roelofsmn commented on Jan 29, 2024

Metadata

Metadata

Assignees

Labels

Type

Projects

Milestone

Relationships

Development

Issue actions