# Records operation history and defines formulas for differentiating ops.

Source:`R/autograd.R`

`autograd_function.Rd`

Every operation performed on Tensor's creates a new function object, that
performs the computation, and records that it happened. The history is
retained in the form of a DAG of functions, with edges denoting data
dependencies (input <- output). Then, when backward is called, the graph is
processed in the topological ordering, by calling `backward()`

methods of each
Function object, and passing returned gradients on to next Function's.

## Arguments

- forward
Performs the operation. It must accept a context

`ctx`

as the first argument, followed by any number of arguments (tensors or other types). The context can be used to store tensors that can be then retrieved during the backward pass. See AutogradContext for more information about context methods.- backward
Defines a formula for differentiating the operation. It must accept a context

`ctx`

as the first argument, followed by as many outputs ad`forward()`

returned (as a`list()`

). The names of the arguments don't matter and they are passed in the order in which they were returned by`forward()`

. The function should return a named list, where each argument is the gradient w.r.t the given output, and each element in the returned list should be the gradient w.r.t. the corresponding input. The context can be used to retrieve tensors saved during the forward pass. It also has an attribute`ctx$needs_input_grad`

as a named list of booleans representing whether each input needs gradient. E.g.,`backward()`

will have`ctx$needs_input_grad$input = TRUE`

if the`input`

argument to`forward()`

needs gradient computated w.r.t. the output. See AutogradContext for more information about context methods.

## Examples

```
if (torch_is_installed()) {
exp2 <- autograd_function(
forward = function(ctx, i) {
result <- i$exp()
ctx$save_for_backward(result = result)
result
},
backward = function(ctx, grad_output) {
list(i = grad_output * ctx$saved_variable$result)
}
)
}
```