5 ######################################################################
12 for t in range(X.size(1)):
17 m = (W[:, t - 1] - 1 >= V[:, t]).long()
18 W[:, t] = m * (W[:, t - 1] - 1) + (1 - m) * V[:, t]
19 Y[:, t] = m * Y[:, t - 1] + (1 - m) * (
20 X[:, t] * (1 + dv) + Y[:, t - 1] * dv0
26 ######################################################################
30 return x.sigmoid() # (x >= 0).float() + (x - x.detach()) * (x < 0).float()
34 for t in range(X.size(1)):
39 m = (W - 1 - V[:, t]).sigmoid()
40 # m = hs(W - 1 - V[:, t])
41 W = m * (W - 1) + (1 - m) * V[:, t]
42 Y = m * Y + (1 - m) * X[:, t]
47 ######################################################################
54 T = 2 * (X.size(1) // 2)
56 Xf = X[:, :T].view(X.size(0), X.size(1) // 2, 2, X.size(2))
57 Vf = V[:, :T].view(V.size(0), V.size(1) // 2, 2)
59 # [:, :, 0] < [:, :, 1]
60 m = (Vf[:, :, 0] - s >= Vf[:, :, 1]).long()
61 Vf[:, :, 1] = m * (Vf[:, :, 0] - s) + (1 - m) * Vf[:, :, 1]
63 Xf[:, :, 1] = m * Xf[:, :, 0] + (1 - m) * Xf[:, :, 1]
65 pscan(Xf[:, :, 1], Vf[:, :, 1], s * 2)
67 # [:, :-1, 1] < [:, 1:, 0]
68 m = (Vf[:, :-1, 1] - s >= Vf[:, 1:, 0]).long()
69 Vf[:, 1:, 0] = m * (Vf[:, :-1, 1] - s) + (1 - m) * Vf[:, 1:, 0]
71 Xf[:, 1:, 0] = m * Xf[:, :-1, 1] + (1 - m) * Xf[:, 1:, 0]
75 m = (V[:, -2] - s >= V[:, -1]).long()
76 V[:, -1] = m * (V[:, -2] - s) + (1 - m) * V[:, -1]
78 X[:, -1] = m * X[:, -2] + (1 - m) * X[:, -1]
81 ######################################################################
84 def pscan_diff(X, V, s=1):
88 T = 2 * (X.size(1) // 2)
90 Xf = X[:, :T].view(X.size(0), X.size(1) // 2, 2, X.size(2))
91 Vf = V[:, :T].view(V.size(0), V.size(1) // 2, 2)
95 Xrf = Xr[:, :T].view(Xr.size(0), Xr.size(1) // 2, 2, Xr.size(2))
96 Vrf = Vr[:, :T].view(Vr.size(0), Vr.size(1) // 2, 2)
98 # [:, :, 0] < [:, :, 1]
99 dv0 = (Vf[:, :, 0] - Vf[:, :, 0].detach())[:, :, None]
100 dv = (Vf[:, :, 1] - Vf[:, :, 1].detach())[:, :, None]
101 m = (Vf[:, :, 0] - s >= Vf[:, :, 1]).long()
102 Vv = m * (Vf[:, :, 0] - s) + (1 - m) * Vf[:, :, 1]
104 Xx = m * Xf[:, :, 0] + (1 - m) * (Xf[:, :, 1] * (1 + dv) + Xf[:, :, 0] * dv0)
106 Xrf[:, :, 1], Vrf[:, :, 1] = pscan_diff(Xx, Vv, s * 2)
108 # [:, :-1, 1] < [:, 1:, 0]
109 dv0 = (Vrf[:, :-1, 1] - Vrf[:, :-1, 1].detach())[:, :, None]
110 dv = (Vf[:, 1:, 0] - Vf[:, 1:, 0].detach())[:, :, None]
111 m = (Vrf[:, :-1, 1] - s >= Vf[:, 1:, 0]).long()
112 Vrf[:, 1:, 0] = m * (Vrf[:, :-1, 1] - s) + (1 - m) * Vf[:, 1:, 0]
114 Xrf[:, 1:, 0] = m * Xrf[:, :-1, 1] + (1 - m) * (
115 Xf[:, 1:, 0] * (1 + dv) + Xrf[:, :-1, 1] * dv0
123 dx = X[:, -2] - X[:, -2].detach()
124 dv = (V[:, -1] - V[:, -1].detach())[:, None]
125 m = (V[:, -2] - s >= V[:, -1]).long()
126 Vr[:, -1] = m * (Vr[:, -2] - s) + (1 - m) * V[:, -1]
128 Xr[:, -1] = m * Xr[:, -2] + (1 - m) * (X[:, -1] * (1 + dv) + dx)
133 ######################################################################
135 if __name__ == "__main__":
140 torch.autograd.set_detect_anomaly(True)
143 X = torch.randn(N, T, D, dtype=torch.float64).requires_grad_()
144 V = torch.rand(N, T, dtype=torch.float64)
146 X0, V0 = baseline(X, V)
148 # print("########### X0 V0 ###########################################")
152 X1, V1 = pscan_diff(X, V)
154 # print("########### X V ############################################")
158 error = ((X0 - X1).abs().max() + (V0 - V1).abs().max()).item()
160 print("ERROR", error)
168 # print(torch.autograd.grad(s, X))
170 # with open("/tmp/v.dat", "w") as f:
172 # f.write(f"{V1[0,t].item()}\n")
174 Y = torch.randn(1, 1, D)
175 X = torch.randn(N, T, D) * 0.1
177 m = (torch.rand(N, T, 1).sort(dim=1).indices == 0).float()
178 X = (1 - m) * X + m * Y
179 V = torch.rand(N, T) # + 100* m.squeeze(dim=-1)
180 V = V.requires_grad_()
182 optimizer = torch.optim.SGD([V], lr=1e-1)
184 for k in range(1000):
185 X1, V1 = baseline(X, V)
186 loss = (X1 - Y).pow(2).mean()
187 print(k, loss.item())
188 optimizer.zero_grad()