Flows the gradient from the output to the input. Returns two new tensors. Args: ctx : A_in : (B, L, D, N), X : (B, D, L, N) grad_output_in : (B, L, D, N) Returns: gradA : (B, L, D, N), gradX : (B, L, D, N)
(ctx, grad_output_in)
| 101 | |
| 102 | @staticmethod |
| 103 | def backward(ctx, grad_output_in): |
| 104 | """ |
| 105 | Flows the gradient from the output to the input. Returns two new tensors. |
| 106 | |
| 107 | Args: |
| 108 | ctx : A_in : (B, L, D, N), X : (B, D, L, N) |
| 109 | grad_output_in : (B, L, D, N) |
| 110 | |
| 111 | Returns: |
| 112 | gradA : (B, L, D, N), gradX : (B, L, D, N) |
| 113 | """ |
| 114 | |
| 115 | A_in, X = ctx.saved_tensors |
| 116 | |
| 117 | # clone tensors |
| 118 | A = A_in.clone() |
| 119 | # grad_output_in will be cloned with flip() |
| 120 | |
| 121 | # prepare tensors |
| 122 | A = A.transpose(2, 1) # (B, D, L, N) |
| 123 | A = torch.cat((A[:, :, :1], A[:, :, 1:].flip(2)), dim=2) |
| 124 | grad_output_b = grad_output_in.transpose(2, 1) |
| 125 | |
| 126 | # reverse parallel scan |
| 127 | grad_output_b = grad_output_b.flip(2) |
| 128 | PScan.pscan(A, grad_output_b) |
| 129 | grad_output_b = grad_output_b.flip(2) |
| 130 | |
| 131 | Q = torch.zeros_like(X) |
| 132 | Q[:, :, 1:].add_(X[:, :, :-1] * grad_output_b[:, :, 1:]) |
| 133 | |
| 134 | return Q.transpose(2, 1), grad_output_b.transpose(2, 1) |
| 135 | |
| 136 | |
| 137 | pscan = PScan.apply |