X-Git-Url: https://fleuret.org/cgi-bin/gitweb/gitweb.cgi?p=pytorch.git;a=blobdiff_plain;f=pscan.py;h=891ec5578e118f48d8f5e933d3f4603e1703e9b1;hp=7b6cfc0ce21dc4938cd29437314daa9b5562a204;hb=HEAD;hpb=5e18a91ef9d1c1362a21b325425990e34ad18463

diff --git a/pscan.py b/pscan.py
index 7b6cfc0..891ec55 100755
--- a/pscan.py
+++ b/pscan.py
@@ -1,5 +1,10 @@
 #!/usr/bin/env python
 
+# Any copyright is dedicated to the Public Domain.
+# https://creativecommons.org/publicdomain/zero/1.0/
+
+# Written by Francois Fleuret <francois@fleuret.org>
+
 import torch
 
 ######################################################################
@@ -9,12 +14,12 @@ 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] = Y0
+    # Y[:, 0] = Y_init
     # Y[:, t] = A[:, t] * Y[:, t-1] + X[:, t]
     #
     # can be computed as
     #
-    # Y[:, t] = A[:, t] * Y0 + X[:, t]
+    # Y[:, t] = A[:, t] * Y_init + X[:, t]
 
     @staticmethod
     def expand(A, X):
@@ -46,23 +51,30 @@ class PScan(torch.autograd.Function):
         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, Y0):
+    def forward(ctx, A, X, Y_init):
         ctx.A = A[:, :, None].clone()
-        ctx.Y0 = Y0[:, 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.Y0 + 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.Y0 / ctx.A
+        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
+        return (Q * R).sum(-1), R / ctx.A_star, U.sum(dim=1)
 
 
 pscan = PScan.apply
@@ -70,33 +82,40 @@ pscan = PScan.apply
 ######################################################################
 
 if __name__ == "__main__":
-    # Iterative implementation
+    N, T, D = 2, 5, 3
 
-    A = torch.randn(1, 5, dtype=torch.float64).requires_grad_()
-    X = torch.randn(1, 5, 3, dtype=torch.float64).requires_grad_()
-    Y0 = torch.randn(1, 3, dtype=torch.float64).requires_grad_()
+    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 = Y0[:, None]
+    # Iterative implementation
+
+    y = Y_init
+    s = 0
 
     for k in range(A.size(1)):
         y = A[:, k, None] * y + X[:, k]
-        print(f"{k} -> {y}")
+        s = s + y
 
-    print(torch.autograd.grad(y.mean(), A, retain_graph=True))
-    print(torch.autograd.grad(y.mean(), X, retain_graph=True))
-    print(torch.autograd.grad(y.mean(), Y0, retain_graph=True))
+    s = s.sum()
 
-    print()
+    gA_ref, gX_ref, gY_init_ref = torch.autograd.grad(
+        s, (A, X, Y_init), retain_graph=True
+    )
 
     # parallel scan
 
-    Y = pscan(A, X, Y0)
+    Y = pscan(A, X, Y_init)
 
-    for k in range(A.size(1)):
-        print(f"{k} -> {Y[:,k]}")
+    s = Y.sum()
+
+    gA, gX, gY_init = torch.autograd.grad(s, (A, X, Y_init), retain_graph=True)
+
+    print((gA - gA_ref).norm())
+    print((gX - gX_ref).norm())
+    print((gY_init - gY_init_ref).norm())
 
-    y = Y[:, -1]
+    Y1 = pscan(A[:, : T // 2], X[:, : T // 2], Y_init)
+    Y2 = pscan(A[:, T // 2 :], X[:, T // 2 :], Y1[:, -1])
 
-    print(torch.autograd.grad(y.mean(), A, retain_graph=True))
-    print(torch.autograd.grad(y.mean(), X, retain_graph=True))
-    print(torch.autograd.grad(y.mean(), Y0, retain_graph=True))
+    print((Y - torch.cat([Y1, Y2], dim=1)).norm())