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.

autograd_function(forward, backward)

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 did forward() return, and it should return a named list. 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) } ) }