# Quick example¶

With NNGeometry, you can easily manipulate $$d \times d$$ matrices and $$d$$ vectors where $$d$$ is the number of parameter of your neural network, for modern neural networks where $$d$$ can be as big as $$10^8$$. These matrices include for instance:

• The Fisher Information Matrix (FIM) used in statistics, in the natural gradient algorithm, or as an approximate of the Hessian matrix in some applications.

• Posterior covariances in Bayesian Deep Learning.

You can also compute finite tangent kernels.

A naive computation of the FIM would require storing $$d \times d$$ scalars in memory. This is prohibitively large for modern neural network architectures, and a line of research has focused at finding lower memory intensive approximations specific to neural networks, such as KFAC, EKFAC, low-rank approximations, etc. This library proposes a common interface for manipulating these different approximations, called representations.

Let us now illustrate this by computing the FIM using the KFAC representation.

>>> F_kfac = FIM(model=model,
representation=PMatKFAC,
n_output=10,
variant='classif_logits',
device='cuda')
>>> print(F_kfac.trace())


Computing the FIM requires the following arguments:

• The torch.nn.Module model object is the PyTorch model used as our neural network.

• The torch.utils.data.DataLoader loader object is the dataloader that contains examples used for computing the FIM.

• The object.PMatKFAC PMatKFAC argument specifies which representation to use in order to store the FIM.

We will next define a vector in parameter space, by using the current value given by our model:

>>> v = PVector.from_model(model)


We can now compute the matrix-vector product $$F v$$ by simply calling:

>>> Fv = F_kfac.mv(v)


Note that switching from the object.PMatKFAC representation to any other representation such as object.PMatDense is as simple as passing representation=PMatDense when building the F_kfac object.

# More examples¶

More notebook examples can be found at https://github.com/tfjgeorge/nngeometry/tree/master/examples