X-Git-Url: https://fleuret.org/cgi-bin/gitweb/gitweb.cgi?p=pytorch.git;a=blobdiff_plain;f=pscan.py;h=891ec5578e118f48d8f5e933d3f4603e1703e9b1;hp=d009692a8062423a98b52cb2e4c2e93b35d8562b;hb=HEAD;hpb=ec688e5465818e2606e592b9aaf3ef4afb11cb3f

diff --git a/pscan.py b/pscan.py
index d009692..891ec55 100755
--- a/pscan.py
+++ b/pscan.py
@@ -1,74 +1,121 @@
 #!/usr/bin/env python
 
-import torch
-
-######################################################################
-
-
-def naive_rec(A, X, Y0):
-    Y = []
-    for t in range(X.size(1)):
-        if t == 0:
-            Y.append(A[:, t] * Y0 + X[:, t])
-        else:
-            Y.append(A[:, t] * Y[-1] + X[:, t])
+# Any copyright is dedicated to the Public Domain.
+# https://creativecommons.org/publicdomain/zero/1.0/
 
-    return torch.cat([y[:, None, :] for y in Y], dim=1)
+# Written by Francois Fleuret <francois@fleuret.org>
 
+import torch
 
 ######################################################################
 
-# A is NxTx1
-# X is NxTxD
-# Y0 is NxD
-#
-# Returns Y defined with
-#
-#           Y[:, 0] = A[:, 0] * Y0 + X[:,0]
-# for t > 0 Y[:, t] = A[:, t] * Y[:, t - 1] + X[:, t]
-
 
-def pscan_rec(A, X, Y0):
-    if X.size(1) % 2 == 1:
+class PScan(torch.autograd.Function):
+    # Given A is NxTx1 and X is NxTxD, expands A and X in place in O(T),
+    # and O(log(T)) if not core-bounded, so that
+    #
+    # Y[:, 0] = Y_init
+    # Y[:, t] = A[:, t] * Y[:, t-1] + X[:, t]
+    #
+    # can be computed as
+    #
+    # Y[:, t] = A[:, t] * Y_init + X[:, t]
+
+    @staticmethod
+    def expand(A, X):
+        if A.size(1) == 1:
+            return
+        T = 2 * (A.size(1) // 2)
+        Aa = A[:, :T].view(A.size(0), T // 2, 2, -1)
+        Xa = X[:, :T].view(X.size(0), T // 2, 2, -1)
+        Xa[:, :, 1].add_(Aa[:, :, 1].mul(Xa[:, :, 0]))
+        Aa[:, :, 1].mul_(Aa[:, :, 0])
+        PScan.expand(Aa[:, :, 1], Xa[:, :, 1])
+        Xa[:, 1:, 0].add_(Aa[:, 1:, 0].mul(Xa[:, :-1, 1]))
+        Aa[:, 1:, 0].mul_(Aa[:, :-1, 1])
+        if T < A.size(1):
+            X[:, -1].add_(A[:, -1].mul(X[:, -2]))
+            A[:, -1].mul_(A[:, -2])
+
+    # Computes inplace Y[:, s] = \sum_{t >= s} X[:, t]
+
+    @staticmethod
+    def accrev(X):
         if X.size(1) == 1:
-            return A[:, :1] * Y0[:, None] + X[:, :1]
-        else:
-            Y = pscan_rec(A[:, :-1], X[:, :-1], Y0)
-            return torch.cat([Y, A[:, -1:] * Y[:, -1:] + X[:, -1:]], dim=1)
-
-    A2 = A.reshape(A.size(0), A.size(1) // 2, 2, A.size(2))
-    X2 = X.reshape(X.size(0), X.size(1) // 2, 2, X.size(2))
+            return
+        T = 2 * (X.size(1) // 2)
+        Xa = X[:, -T:].view(X.size(0), T // 2, 2, -1)
+        Xa[:, :, 0].add_(Xa[:, :, 1])
+        PScan.accrev(Xa[:, :, 0])
+        Xa[:, :-1, 1].add_(Xa[:, 1:, 0])
+        if T < X.size(1):
+            X[:, 0].add_(X[:, 1])
+
+    # A is NxT, X is NxTxD, Y_init is NxD
+    #
+    # returns Y of same shape as X, with
+    #
+    # Y[:, t] = A[:, 0] * Y_init   + X[:, 0] if t == 0
+    #        = A[:, t] * Y[:, t-1] + X[:, t] otherwise
+
+    @staticmethod
+    def forward(ctx, A, X, Y_init):
+        ctx.A = A[:, :, None].clone()
+        ctx.Y_init = Y_init[:, None, :].clone()
+        ctx.A_star = A[:, :, None].clone()
+        ctx.X_star = X.clone()
+        PScan.expand(ctx.A_star, ctx.X_star)
+        return ctx.A_star * ctx.Y_init + ctx.X_star
+
+    @staticmethod
+    def backward(ctx, grad_output):
+        U = grad_output * ctx.A_star
+        R = U.clone()
+        PScan.accrev(R)
+        Q = ctx.Y_init / ctx.A
+        Q[:, 1:].add_(ctx.X_star[:, :-1] / ctx.A_star[:, 1:])
+        return (Q * R).sum(-1), R / ctx.A_star, U.sum(dim=1)
+
+
+pscan = PScan.apply
 
-    X_star = X2[:, :, 0].clone()
-    X_star[:, 1:] += A2[:, 1:, 0] * X2[:, :-1, 1]
+######################################################################
 
-    A_star = A2[:, :, 0].clone()
-    A_star[:, 1:] *= A2[:, :-1, 1]
+if __name__ == "__main__":
+    N, T, D = 2, 5, 3
 
-    Y_star = pscan_rec(A_star, X_star, Y0)[:, :, None]
+    A = torch.randn(N, T, dtype=torch.float64).requires_grad_()
+    X = torch.randn(N, T, D, dtype=torch.float64).requires_grad_()
+    Y_init = torch.randn(N, D, dtype=torch.float64).requires_grad_()
 
-    Y = torch.cat([Y_star, A2[:, :, 1, None] * Y_star + X2[:, :, 1, None]], dim=2)
+    # Iterative implementation
 
-    Y = Y.reshape(Y.size(0), -1, Y.size(-1))
+    y = Y_init
+    s = 0
 
-    return Y
+    for k in range(A.size(1)):
+        y = A[:, k, None] * y + X[:, k]
+        s = s + y
 
+    s = s.sum()
 
-######################################################################
+    gA_ref, gX_ref, gY_init_ref = torch.autograd.grad(
+        s, (A, X, Y_init), retain_graph=True
+    )
 
-N, T, D = 5, 29, 12
+    # parallel scan
 
-A = torch.rand(N, T, 1, dtype=torch.float64)
-X = torch.randint(10, (N, T, D), dtype=torch.float64)
-Y0 = torch.randint(10, (N, D), dtype=torch.float64)
+    Y = pscan(A, X, Y_init)
 
-naive_Y = naive_rec(A, X, Y0)
+    s = Y.sum()
 
-pscan_Y = pscan_rec(A, X, Y0)
+    gA, gX, gY_init = torch.autograd.grad(s, (A, X, Y_init), retain_graph=True)
 
-print((naive_Y - pscan_Y).pow(2).mean())
+    print((gA - gA_ref).norm())
+    print((gX - gX_ref).norm())
+    print((gY_init - gY_init_ref).norm())
 
-pscan_Y1 = pscan_rec(A[:, :15], X[:, :15], Y0)
-pscan_Y2 = pscan_rec(A[:, 15:], X[:, 15:], pscan_Y1[:, -1])
+    Y1 = pscan(A[:, : T // 2], X[:, : T // 2], Y_init)
+    Y2 = pscan(A[:, T // 2 :], X[:, T // 2 :], Y1[:, -1])
 
-print((naive_Y - torch.cat([pscan_Y1, pscan_Y2], dim=1)).pow(2).mean())
+    print((Y - torch.cat([Y1, Y2], dim=1)).norm())