X-Git-Url: https://fleuret.org/cgi-bin/gitweb/gitweb.cgi?a=blobdiff_plain;f=pscan.py;h=891ec5578e118f48d8f5e933d3f4603e1703e9b1;hb=refs%2Fheads%2Fmaster;hp=f344200160cc1d8ccb4ae260e9ea5786c0af74fb;hpb=62f1bc82f6c8107960be0009603beb5b3e386a6a;p=pytorch.git

diff --git a/pscan.py b/pscan.py
index f344200..891ec55 100755
--- a/pscan.py
+++ b/pscan.py
@@ -1,69 +1,80 @@
 #!/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
 
 ######################################################################
 
-# 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[:, t] = A[:, t] * Y[:, t-1] + X[:, t]
-#
-# can be computed as
-#
-# Y[:, t] = A[:, t] * Y0 + X[:, t]
-
-
-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])
-    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]
-
-
-def accrev(X):
-    if X.size(1) == 1:
-        return
-    T = 2 * (X.size(1) // 2)
-    Xa = X[:, -T:].view(X.size(0), T // 2, 2, -1)
-    Xa[:, :, 0].add_(Xa[:, :, 1])
-    accrev(Xa[:, :, 0])
-    Xa[:, :-1, 1].add_(Xa[:, 1:, 0])
-    if T < X.size(1):
-        X[:, 0].add_(X[:, 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
+        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, 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()
-        expand(ctx.A_star, ctx.X_star)
-        return ctx.A_star * ctx.Y0 + ctx.X_star
+        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()
-        accrev(R)
-        Q = ctx.Y0 / ctx.A
+        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
+        return (Q * R).sum(-1), R / ctx.A_star, U.sum(dim=1)
 
 
 pscan = PScan.apply
@@ -71,29 +82,40 @@ pscan = PScan.apply
 ######################################################################
 
 if __name__ == "__main__":
-    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_()
+    N, T, D = 2, 5, 3
+
+    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()
 
-    Y = pscan(A, X, Y0)
+    gA_ref, gX_ref, gY_init_ref = torch.autograd.grad(
+        s, (A, X, Y_init), retain_graph=True
+    )
 
-    print()
+    # parallel scan
 
-    for k in range(A.size(1)):
-        print(f"{k} -> {Y[:,k]}")
+    Y = pscan(A, X, Y_init)
+
+    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())