3 # Any copyright is dedicated to the Public Domain.
4 # https://creativecommons.org/publicdomain/zero/1.0/
6 # Written by Francois Fleuret <francois@fleuret.org>
10 ######################################################################
13 class PScan(torch.autograd.Function):
14 # Given A is NxTx1 and X is NxTxD, expands A and X in place in O(T),
15 # and O(log(T)) if not core-bounded, so that
18 # Y[:, t] = A[:, t] * Y[:, t-1] + X[:, t]
22 # Y[:, t] = A[:, t] * Y_init + X[:, t]
28 T = 2 * (A.size(1) // 2)
29 Aa = A[:, :T].view(A.size(0), T // 2, 2, -1, 1)
30 Xa = X[:, :T].view(X.size(0), T // 2, 2, -1, X.size(-1))
31 Xa[:, :, 1].add_(Aa[:, :, 1].mul(Xa[:, :, 0]))
32 Aa[:, :, 1].mul_(Aa[:, :, 0])
33 PScan.expand_(Aa[:, :, 1], Xa[:, :, 1])
34 Xa[:, 1:, 0].add_(Aa[:, 1:, 0].mul(Xa[:, :-1, 1]))
35 Aa[:, 1:, 0].mul_(Aa[:, :-1, 1])
37 X[:, -1].add_(A[:, -1].mul(X[:, -2]))
38 A[:, -1].mul_(A[:, -2])
44 T = 2 * (X.size(1) // 2)
45 Aa = A[:, -T:].view(A.size(0), T // 2, 2, -1, 1)
46 Xa = X[:, -T:].view(X.size(0), T // 2, 2, -1, X.size(-1))
47 Xa[:, :, 0].add_(Aa[:, :, 1].mul(Xa[:, :, 1]))
48 B = Aa[:, :, 0].clone()
49 B[:, 1:].mul_(Aa[:, :-1, 1])
50 PScan.acc_rev_(B, Xa[:, :, 0])
51 Xa[:, :-1, 1].add_(Aa[:, 1:, 0].mul(Xa[:, 1:, 0]))
53 X[:, 0].add_(A[:, 1].mul(X[:, 1]))
55 # A is NxT, X is NxTxD, Y_init is NxD
57 # returns Y of same shape as X, with
59 # Y[:, t] = A[:, 0] * Y_init + X[:, 0] if t == 0
60 # = A[:, t] * Y[:, t-1] + X[:, t] otherwise
63 def forward(ctx, A, X, Y_init):
64 ctx.A = A.unsqueeze(-1).clone()
65 ctx.Y_init = Y_init[:, None].clone()
66 ctx.A_star = ctx.A.clone()
67 ctx.X_star = X.clone()
68 PScan.expand_(ctx.A_star, ctx.X_star)
69 return ctx.A_star * ctx.Y_init + ctx.X_star
72 def backward(ctx, grad_output):
73 U = grad_output * ctx.A_star
75 R = grad_output.clone()
77 Q = ctx.Y_init.expand_as(ctx.X_star).clone()
78 Q[:, 1:].mul_(ctx.A_star[:, :-1]).add_(ctx.X_star[:, :-1])
79 return (Q * R).sum(-1), R, U.sum(dim=1)
84 ######################################################################
86 if __name__ == "__main__":
89 A = torch.rand(17, 12, 3)
90 X = torch.rand(17, 12, 3, 11)
91 Y_init = torch.rand(17, 3, 11)
92 Y = pscan(A, X, Y_init)
97 A = torch.rand(N, T, dtype=torch.float64).requires_grad_()
98 X = torch.randn(N, T, D, dtype=torch.float64).requires_grad_()
99 Y_init = torch.randn(N, D, dtype=torch.float64).requires_grad_()
101 # Iterative implementation
106 for k in range(A.size(1)):
107 y = A[:, k, None] * y + X[:, k]
112 gA_ref, gX_ref, gY_init_ref = torch.autograd.grad(
113 s, (A, X, Y_init), retain_graph=True
118 start_time = time.perf_counter()
119 for _ in range(1000):
120 Y = pscan(A, X, Y_init)
121 duration = time.perf_counter() - start_time
122 print(f"duration {duration}")
126 gA, gX, gY_init = torch.autograd.grad(s, (A, X, Y_init), retain_graph=True)
132 print((gA - gA_ref).norm())
133 print((gX - gX_ref).norm())
134 print((gY_init - gY_init_ref).norm())
136 Y1 = pscan(A[:, : T // 2], X[:, : T // 2], Y_init)
137 Y2 = pscan(A[:, T // 2 :], X[:, T // 2 :], Y1[:, -1])
139 print((Y - torch.cat([Y1, Y2], dim=1)).norm())