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---
title: Automatic Differentiation
---
# Automatic Differentiation in EagerPy
EagerPy uses a functional approach to automatic differentiation. You first define a function that will then be differentiated with respect to its inputs. This function is then passed to `ep.value_and_grad` to evaluate both the function and its gradient. More generally, you can also use `ep.value_aux_and_grad` if your function has additional auxiliary outputs and `ep.value_and_grad_fn` if you want the gradient function without immediately evaluating it at some point `x`.
Using `ep.value_and_grad` for automatic differentiation in EagerPy:
```python
import torch
x = torch.tensor([1., 2., 3.])
# The following code works for any framework, not just Pytorch!
import eagerpy as ep
x = ep.astensor(x)
def loss_fn(x):
# this function takes and returns an EagerPy tensor
return x.square().sum()
print(loss_fn(x))
# PyTorchTensor(tensor(14.))
print(ep.value_and_grad(loss_fn, x))
# (PyTorchTensor(tensor(14.)), PyTorchTensor(tensor([2., 4., 6.])))
```
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