@ptrblck @fmassa
Problem: i need to save an “attribution” in tensor, and hope it can transform between forward and backward;
For example, we want save “local” in tensor and want this attribution can be transform both in forward and backward;
The forward works as expected, but the backward is not;  the print like:

output local: 1
output local: 2
grad_input local: 1
grad_input local: 1

Another interesting thing is: after add pdb.set_trace(), the backward also work as expected.
import pdb
import torch
from torch import nn
from torch.autograd import Function


class LinearFunction(Function):
    # Note that both forward and backward are @staticmethods
    @staticmethod
    # bias is an optional argument
    def forward(ctx, input, weight, bias=None):
        ctx.save_for_backward(input, weight, bias)
        output = input.mm(weight.t())
        if bias is not None:
            output += bias.unsqueeze(0).expand_as(output)
        if not hasattr(input, 'local'):
            output.local = 1
        else:
            output.local = input.local + 1
        print(f'output local: {output.local}')
        return output

    # This function has only a single output, so it gets only one gradient
    @staticmethod
    def backward(ctx, grad_output):
        input, weight, bias = ctx.saved_tensors
        grad_input = grad_weight = grad_bias = None

        if ctx.needs_input_grad[0]:
            grad_input = grad_output.mm(weight)
        if ctx.needs_input_grad[1]:
            grad_weight = grad_output.t().mm(input)
        if bias is not None and ctx.needs_input_grad[2]:
            grad_bias = grad_output.sum(0)
        # pdb.set_trace()  # NOTE: if add this line, it works as expected
        if not hasattr(grad_output, 'local'):
            grad_input.local = 1
        else:
            grad_input.local = grad_output.local + 1
        print(f'grad_input local: {grad_input.local}')
        return grad_input, grad_weight, grad_bias


class Linear(nn.Module):
    def __init__(self, input_features, output_features, bias=True):
        super(Linear, self).__init__()
        self.input_features = input_features
        self.output_features = output_features

        self.weight = nn.Parameter(torch.empty(output_features, input_features))
        if bias:
            self.bias = nn.Parameter(torch.empty(output_features))
        else:
            self.register_parameter('bias', None)

        # Not a very smart way to initialize weights
        self.weight.data.uniform_(-0.1, 0.1)
        if self.bias is not None:
            self.bias.data.uniform_(-0.1, 0.1)

    def forward(self, input):
        # See the autograd section for explanation of what happens here.
        return LinearFunction.apply(input, self.weight, self.bias)


if __name__ == '__main__':
    x = torch.randn((2, 4), requires_grad=True)
    y1 = Linear(input_features=4, output_features=3)(x)
    y2 = Linear(input_features=3, output_features=4)(y1)
    out = y2.sum()
    out.backward()