import pscan
-
# X is /.../xTxD A is /.../xT Y_init is /.../xD
return Y
+def pscan_rgrad(grad_Y, A, X, Y_init, dim=-2, eps=1e-2):
+ with torch.no_grad():
+ s_A, s_X = 0, 0
+ for t in range(X.size(dim) - 1, 0, -1):
+ delta = (grad_Y[t] - s_A) / A[t].grad
+ s_A += A[t].grad * delta
+ A[t].grad = delta
+ delta = (grad_Y[t] - s_X) / X[t].grad
+ s_X += X[t].grad * delta
+ X[t].grad = delta
+
+
def pscan_shape(A, X, Y_init):
s = X.size()
A = A.reshape(-1, s[-2])
self.rec_K = X.new_zeros(N, R, T, DK)
# We start the recurrent sequences with optimizable
# initial values. No idea if it helps.
- self.rec_V[:, :, t0 - L : t0] = self.init_V_rec[None, :, :, :]
- self.rec_K[:, :, t0 - L : t0] = self.init_K_rec[None, :, :, :]
+ self.rec_V[:, :, t0 - L : t0, :] = self.init_V_rec[None, :, :, :]
+ self.rec_K[:, :, t0 - L : t0, :] = self.init_K_rec[None, :, :, :]
self.cache_Y = X.new_zeros(N, T, DM)
torch.einsum("ntc,hrc->nhrt", X, self.w_G) + self.b_G[None, :, :, None]
).sigmoid()
- # warnings.warn("softmax gating", RuntimeWarning)
+ # Clip the gating to avoid values greater than 1 when several
+ # heads hit the same row
- # G = (
- # torch.einsum("ntc,hrc->nhrt", X, self.w_G) + self.b_G[None, :, :, None]
- # ).softmax(dim=2)
+ G = G / G.sum(1, keepdim=True).clamp(min=1)
######################################################################
- # The "flashbacks"
- if self.training and self.proba_gate_dropout > 0.0:
- # This is a better implementation of "flashbacks".
+ def recurrence(G, V, K):
+ # We prepare the arguments for the parallel scan
- # G is NxHxExT where e is the caterpillar's row.
+ A = 1 - G.sum(1)
- warnings.warn("gate dropout", RuntimeWarning)
+ gated_V = torch.einsum("nhrt,nhtd->nrtd", G, V)
+ gated_K = torch.einsum("nhrt,nhtd->nrtd", G, K)
- kill = (
- torch.rand(G.size(), device=G.device) <= self.proba_gate_dropout
- ).float()
+ # We start from cached values, which matters in inference
- alpha = G / (1 - self.proba_gate_dropout)
+ init_rec_V = self.rec_V[:, :, t0 - L : t0]
+ init_rec_K = self.rec_K[:, :, t0 - L : t0]
- G = alpha * (1 - kill)
+ # Associative scan
- ######################################################################
- # Clip the gating to avoid values greater than 1 when several
- # heads hit the same row
+ # Here there is a trick: Since the stack at position t is
+ # computed by updating that at position t-L, the parallel
+ # scan operates with a period of L. To do so we split the
+ # sequence indexing in two axes, the second of size L, and
+ # run the parallel scan using the first as the sequence index.
- G = G / G.sum(1, keepdim=True).clamp(min=1)
-
- ######################################################################
- # Roll the gating indexes
-
- # warnings.warn("rotating barrel", RuntimeWarning)
+ A = A.unflatten(2, (-1, L))
+ gated_V = gated_V.unflatten(2, (-1, L))
+ gated_K = gated_K.unflatten(2, (-1, L))
- # r_barrel = torch.arange(R, device=G.device)[None, None, :, None]
- # t_barrel = torch.arange(t1 - t0, device=G.device)[None, None, None, :]
- # r_barrel = (r_barrel + (t_barrel + t0) // L) % R
- # G = G.gather(dim=2, index=r_barrel.expand_as(G))
+ next_V = pscan_dim(A, gated_V, init_rec_V, dim=2)
+ next_K = pscan_dim(A, gated_K, init_rec_K, dim=2)
- # We prepare the arguments for the parallel scan
+ next_V = next_V.flatten(2, 3)
+ next_K = next_K.flatten(2, 3)
- A = 1 - G.sum(1)
+ return next_V, next_K
- # warnings.warn("harmonic recurrence", RuntimeWarning)
- # har = torch.arange(t0, t1, device = G.device).float() + 1
- # A = har / (har + 1)
- # G = G / har
+ #################################################################
- gated_V = torch.einsum("nhrt,nhtd->nrtd", G, V)
- gated_K = torch.einsum("nhrt,nhtd->nrtd", G, K)
+ next_V, next_K = recurrence(G, V, K)
- # We start from cached values, which matters in inference
+ if self.training and self.proba_gate_dropout > 0.0:
+ # G is NxHxRxT where r is the caterpillar's row.
- init_rec_V = self.rec_V[:, :, t0 - L : t0]
- init_rec_K = self.rec_K[:, :, t0 - L : t0]
+ warnings.warn("gate dropout", RuntimeWarning)
- #################################################################
- # Associative scan
+ kill = (
+ torch.rand(G.size(), device=G.device) <= self.proba_gate_dropout
+ ).float()
- # Here there is a trick: Since the stack at position t is
- # computed by updating that at position t-L, the parallel
- # scan operates with a period of L. To do so we split the
- # sequence indexing in two axes, the second of size L, and
- # run the parallel scan using the first as the sequence index.
+ mask = 1 - kill
- A = A.unflatten(2, (-1, L))
- gated_V = gated_V.unflatten(2, (-1, L))
- gated_K = gated_K.unflatten(2, (-1, L))
+ masked_next_V, masked_next_K = recurrence(G * mask, V, K)
- next_V = pscan_dim(A, gated_V, init_rec_V, dim=2)
- next_K = pscan_dim(A, gated_K, init_rec_K, dim=2)
+ next_V = next_V.detach() + (masked_next_V - masked_next_V.detach()) / (
+ 1 - self.proba_gate_dropout
+ )
+ next_K = next_K.detach() + (masked_next_K - masked_next_K.detach()) / (
+ 1 - self.proba_gate_dropout
+ )
- self.rec_V[:, :, t0:t1] = next_V.flatten(2, 3)
- self.rec_K[:, :, t0:t1] = next_K.flatten(2, 3)
+ self.rec_V[:, :, t0:t1] = next_V
+ self.rec_K[:, :, t0:t1] = next_K
######################################################################
# compute the readout
projects / mygptrnn.git / blobdiff