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Adding operations to autograd requires implementing a new autograd_function for each operation. Recall that autograd_functionss are what autograd uses to compute the results and gradients, and encode the operation history. Every new function requires you to implement 2 methods:

  • forward() - the code that performs the operation. It can take as many arguments as you want, with some of them being optional, if you specify the default values. All kinds of R objects are accepted here. Tensor arguments that track history (i.e., with requires_grad=TRUE) will be converted to ones that don’t track history before the call, and their use will be registered in the graph. Note that this logic won’t traverse lists or any other data structures and will only consider Tensor’s that are direct arguments to the call. You can return either a single Tensor output, or a list of Tensors if there are multiple outputs. Also, please refer to the docs of autograd_function to find descriptions of useful methods that can be called only from forward().

  • backward() - gradient formula. It will be given as many Tensor arguments as there were outputs, with each of them representing gradient w.r.t. that output. It should return as many Tensors as there were Tensor's that required gradients in forward, with each of them containing the gradient w.r.t. its corresponding input.


It’s the user’s responsibility to use the special functions in the forward’s ctx properly in order to ensure that the new autograd_function works properly with the autograd engine.

  • save_for_backward() must be used when saving input or ouput of the forward to be used later in the backward.

  • mark_dirty() must be used to mark any input that is modified inplace by the forward function.

  • mark_non_differentiable() must be used to tell the engine if an output is not differentiable.


Below you can find code for a linear function:

linear <- autograd_function(
  forward = function(ctx, input, weight, bias = NULL) {
    ctx$save_for_backward(input = input, weight = weight, bias = bias)
    output <- input$mm(weight$t())
    if (!is.null(bias))
      output <- output + bias$unsqueeze(0)$expand_as(output)
  backward = function(ctx, grad_output) {
    s <- ctx$saved_variables
    grads <- list(
      input = NULL,
      weight = NULL,
      bias = NULL
    if (ctx$needs_input_grad$input)
      grads$input <- grad_output$mm(s$weight)
    if (ctx$needs_input_grad$weight)
      grads$weight <- grad_output$t()$mm(s$input)
    if (!is.null(s$bias) && ctx$needs_input_grad$bias)
      grads$bias <- grad_output$sum(dim = 0)

Here, we give an additional example of a function that is parametrized by non-Tensor arguments:

mul_constant <- autograd_function(
  forward = function(ctx, tensor, constant) {
    ctx$save_for_backward(constant = constant)
    tensor * constant
  backward = function(ctx, grad_output) {
    v <- ctx$saved_variables
      tensor = grad_output * v$constant
x <- torch_tensor(1, requires_grad = TRUE)
o <- mul_constant(x, 2)
#> torch_tensor
#>  2
#> [ CPUFloatType{1} ]