######################################################################
 
 
-def baseline(X, V):
+def baseline1(X, V):
     Y = X.new(X.size())
     W = V.new(V.size())
+
     for t in range(X.size(1)):
         if t == 0:
             Y[:, t] = X[:, t]
             W[:, t] = V[:, t]
         else:
-            m = (V[:, t] >= W[:, t - 1] - 1).long()
-            Y[:, t] = m * X[:, t] + (1 - m) * Y[:, t - 1]
-            W[:, t] = m * V[:, t] + (1 - m) * (W[:, t - 1] - 1)
+            m = (W[:, t - 1] - 1 >= V[:, t]).long()
+            W[:, t] = m * (W[:, t - 1] - 1) + (1 - m) * V[:, t]
+            Y[:, t] = m * Y[:, t - 1] + (1 - m) * (
+                X[:, t] * (1 + dv) + Y[:, t - 1] * dv0
+            )
+
+    return Y, W
+
+
+######################################################################
+
+
+def hs(x):
+    return x.sigmoid()  # (x >= 0).float() + (x - x.detach()) * (x < 0).float()
+
+
+def baseline(X, V):
+    for t in range(X.size(1)):
+        if t == 0:
+            Y = X[:, t]
+            W = V[:, t]
+        else:
+            m = (W - 1 - V[:, t]).sigmoid()
+            # m = hs(W - 1 - V[:, t])
+            W = m * (W - 1) + (1 - m) * V[:, t]
+            Y = m * Y + (1 - m) * X[:, t]
 
     return Y, W
 
     Vrf = Vr[:, :T].view(Vr.size(0), Vr.size(1) // 2, 2)
 
     # [:, :, 0] < [:, :, 1]
-    dx = Xf[:, :, 1] - Xf[:, :, 1].detach()
+    dv0 = (Vf[:, :, 0] - Vf[:, :, 0].detach())[:, :, None]
     dv = (Vf[:, :, 1] - Vf[:, :, 1].detach())[:, :, None]
     m = (Vf[:, :, 0] - s >= Vf[:, :, 1]).long()
     Vv = m * (Vf[:, :, 0] - s) + (1 - m) * Vf[:, :, 1]
     m = m[:, :, None]
-    Xx = m * Xf[:, :, 0] + (1 - m) * (Xf[:, :, 1] * (1 + dv) + dx)
+    Xx = m * Xf[:, :, 0] + (1 - m) * (Xf[:, :, 1] * (1 + dv) + Xf[:, :, 0] * dv0)
 
     Xrf[:, :, 1], Vrf[:, :, 1] = pscan_diff(Xx, Vv, s * 2)
 
-    Xr[:, 0] = X[:, 0]
-    Vr[:, 0] = V[:, 0]
-
     # [:, :-1, 1] < [:, 1:, 0]
-    dx = Xf[:, 1:, 0] - Xf[:, 1:, 0].detach()
+    dv0 = (Vrf[:, :-1, 1] - Vrf[:, :-1, 1].detach())[:, :, None]
     dv = (Vf[:, 1:, 0] - Vf[:, 1:, 0].detach())[:, :, None]
     m = (Vrf[:, :-1, 1] - s >= Vf[:, 1:, 0]).long()
     Vrf[:, 1:, 0] = m * (Vrf[:, :-1, 1] - s) + (1 - m) * Vf[:, 1:, 0]
     m = m[:, :, None]
-    Xrf[:, 1:, 0] = m * Xrf[:, :-1, 1] + (1 - m) * (Xf[:, 1:, 0] * (1 + dv) + dx)
+    Xrf[:, 1:, 0] = m * Xrf[:, :-1, 1] + (1 - m) * (
+        Xf[:, 1:, 0] * (1 + dv) + Xrf[:, :-1, 1] * dv0
+    )
+
+    Xr[:, 0] = X[:, 0]
+    Vr[:, 0] = V[:, 0]
 
     if T < X.size(1):
         # [:, -2] < [:, -1]
-        dx = X[:, -1] - X[:, -1].detach()
+        dx = X[:, -2] - X[:, -2].detach()
         dv = (V[:, -1] - V[:, -1].detach())[:, None]
         m = (V[:, -2] - s >= V[:, -1]).long()
-        Vr[:, -1] = m * (V[:, -2] - s) + (1 - m) * V[:, -1]
+        Vr[:, -1] = m * (Vr[:, -2] - s) + (1 - m) * V[:, -1]
         m = m[:, None]
-        Xr[:, -1] = m * X[:, -2] + (1 - m) * (X[:, -1] * (1 + dv) + dx)
+        Xr[:, -1] = m * Xr[:, -2] + (1 - m) * (X[:, -1] * (1 + dv) + dx)
 
     return Xr, Vr
 
 
 if __name__ == "__main__":
     N = 1
-    T = 513
-    D = 2
+    T = 64
+    D = 128
 
-    X = torch.randn(N, T, D, dtype=torch.float64).requires_grad_()
-    V = torch.rand(N, T, dtype=torch.float64) * 10
+    torch.autograd.set_detect_anomaly(True)
 
-    X0, V0 = baseline(X, V)
+    for k in range(0):
+        X = torch.randn(N, T, D, dtype=torch.float64).requires_grad_()
+        V = torch.rand(N, T, dtype=torch.float64)
 
-    # print("########### X0 V0 ###########################################")
-    # print(V0)
-    # print(X0)
+        X0, V0 = baseline(X, V)
 
-    X1, V1 = pscan_diff(X, V)
+        # print("########### X0 V0 ###########################################")
+        # print(V0)
+        # print(X0)
 
-    # print("########### X V ############################################")
-    # print(V)
-    # print(X)
+        X1, V1 = pscan_diff(X, V)
 
-    print("ERROR", ((X0 - X1).abs().max() + (V0 - V1).abs().max()).item())
+        # print("########### X V ############################################")
+        # print(V)
+        # print(X)
 
-    exit(0)
+        error = ((X0 - X1).abs().max() + (V0 - V1).abs().max()).item()
+        if error > 0:
+            print("ERROR", error)
+            print(X0)
+            print(X1)
+            exit(0)
+
+    # exit(0)
 
     # s = X1.sum()
     # print(torch.autograd.grad(s, X))
     # f.write(f"{V1[0,t].item()}\n")
 
     Y = torch.randn(1, 1, D)
-    X = torch.randn(
-        N, T, D
-    )  # * 0.1 + (torch.rand(N,T,1).sort(dim=1).indices==0).float() * Y
-    V = torch.rand(N, T).requires_grad_()
+    X = torch.randn(N, T, D) * 0.1
+
+    m = (torch.rand(N, T, 1).sort(dim=1).indices == 0).float()
+    X = (1 - m) * X + m * Y
+    V = torch.rand(N, T)  # + 100* m.squeeze(dim=-1)
+    V = V.requires_grad_()
 
-    optimizer = torch.optim.SGD([V], lr=1e-2)
+    optimizer = torch.optim.SGD([V], lr=1e-1)
 
     for k in range(1000):
-        X1, V1 = X.clone(), V.clone()
-        pscan(X, V, X1, V1)
-        # X1=X1*(1+V1-V1.detach())[:,:,None]
-        loss = (X1[:, -1:] - Y).pow(2).mean()
+        X1, V1 = baseline(X, V)
+        loss = (X1 - Y).pow(2).mean()
         print(k, loss.item())
         optimizer.zero_grad()
         loss.backward()
 
         self.caterpillar_height = caterpillar_height
         self.attention_dropout = attention_dropout
 
-        self.gate_dropout_proba = args.gate_dropout_proba
-        self.gate_dropout_sync = args.gate_dropout_sync
-        self.gate_dropout_replace = args.gate_dropout_replace
-
         ######################################################################
 
-        self.w_G = randw(nb_heads, caterpillar_height, dim_model, factor=1e-3)
+        self.w_G = randw(nb_heads, caterpillar_height, dim_model)
         self.b_G = nn.Parameter(torch.full((nb_heads, caterpillar_height), 0.0))
 
         self.w_K = randw(nb_heads, dim_qk, dim_model)
         V = torch.einsum("ntc,hdc->nhtd", X, self.w_V)
         K = torch.einsum("ntc,hdc->nhtd", X, self.w_K)
 
-        # V, K = blanket(V), blanket(K)
-
         ######################################################################
         # Compute the recurrent state
 
 
         G = G / G.sum(1, keepdim=True).clamp(min=1)
 
-        # G_star = (1 - G).log().sum(1, keepdim=True).exp()
-
         ######################################################################
 
-        def recurrence(G, V, K):
-            # We prepare the arguments for the parallel scan
-
-            A = 1 - G.sum(dim=1)
-
-            gated_V = torch.einsum("nhrt,nhtd->nrtd", G, V)
-            gated_K = torch.einsum("nhrt,nhtd->nrtd", G, K)
-
-            # We start from cached values, which matters in inference
-
-            init_rec_V = self.rec_V[:, :, t0 - L : t0]
-            init_rec_K = self.rec_K[:, :, t0 - L : t0]
-
-            # 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.
-
-            A = A.unflatten(2, (-1, L))
-            gated_V = gated_V.unflatten(2, (-1, L))
-            gated_K = gated_K.unflatten(2, (-1, L))
-
-            next_V = pscan_dim(A, gated_V, init_rec_V, dim=2).flatten(2, 3)
-            next_K = pscan_dim(A, gated_K, init_rec_K, dim=2).flatten(2, 3)
+        A = 1 - G.sum(dim=1)
 
-            return next_V, next_K
+        gated_V = torch.einsum("nhrt,nhtd->nrtd", G, V)
+        gated_K = torch.einsum("nhrt,nhtd->nrtd", G, K)
 
-        #################################################################
+        # We start from cached values, which matters in inference
 
-        next_V, next_K = recurrence(G, V, K)
+        init_rec_V = self.rec_V[:, :, t0 - L : t0]
+        init_rec_K = self.rec_K[:, :, t0 - L : t0]
 
-        if self.training and self.gate_dropout_proba > 0.0:
-            # G is NxHxRxT where r is the caterpillar's 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.
 
-            warnings.warn("gate dropout", RuntimeWarning)
+        A = A.unflatten(2, (-1, L))
+        gated_V = gated_V.unflatten(2, (-1, L))
+        gated_K = gated_K.unflatten(2, (-1, L))
 
-            if self.gate_dropout_sync:
-                shape_kill = (N, 1, 1)
-            else:
-                shape_kill = (N, H, R)
-
-            # Pick a point in each of the NxHxR timeline and set this
-            # entry and the following to 1
-            kill = (
-                torch.rand(*shape_kill, t1 - t0, device=G.device).sort(dim=3).indices
-                == 0
-            ).cumsum(dim=3)
-
-            # Keep these mask for only some of the NxHxR
-            kill = kill * (
-                torch.rand(*shape_kill, 1, device=G.device) <= self.gate_dropout_proba
-            )
-
-            # The coefficient to keep are the complementary
-            mask = 1 - kill
-
-            masked_next_V, masked_next_K = recurrence(G * mask, V, K)
-
-            if self.gate_dropout_replace:
-                next_V = next_V.detach()
-                next_K = next_K.detach()
-
-            warnings.warn("the rescaling is probably a bad idea", RuntimeWarning)
-
-            next_V = next_V + (masked_next_V - masked_next_V.detach()) / (
-                1 - self.gate_dropout_proba
-            )
-            next_K = next_K + (masked_next_K - masked_next_K.detach()) / (
-                1 - self.gate_dropout_proba
-            )
+        next_V = pscan_dim(A, gated_V, init_rec_V, dim=2).flatten(2, 3)
+        next_K = pscan_dim(A, gated_K, init_rec_K, dim=2).flatten(2, 3)
 
         self.rec_V[:, :, t0:t1] = next_V
         self.rec_K[:, :, t0:t1] = next_K
             windowed_V,
         ).flatten(2)
 
-        # Compute the final output
-
-        # Y = blanket(Y)
-
         self.cache_Y[:, t0:t1] = Y @ self.w_O
 
         return BracketedSequence(self.cache_Y, t0, t1 - t0, bs.init_cache)
         dim_v,
         nb_heads=1,
         causal=False,
+        horizon=None,
         attention_dropout=0.0,
         logger=print,
         args=None,
             return nn.Parameter(torch.randn(*d) / math.sqrt(d[-1]))
 
         self.causal = causal
+        self.horizon = horizon
         self.attention_dropout = attention_dropout
         self.record_attention = False
 
                     torch.arange(x_q.size(1), device=q.device)[None, None, :, None]
                     < torch.arange(x_q.size(1), device=q.device)[None, None, None, :]
                 )
+
+                if self.horizon is not None:
+                    self.cache_attzero = torch.logical_or(
+                        self.cache_attzero,
+                        torch.arange(x_q.size(1), device=q.device)[None, None, :, None]
+                        >= torch.arange(x_q.size(1), device=q.device)[
+                            None, None, None, :
+                        ]
+                        + self.horizon,
+                    )
+
             a = a.masked_fill(
                 self.cache_attzero[
                     :, :, bs.first : bs.first + bs.nb, : bs.first + bs.nb
             "dumbrec",
             "kvrec",
             "caterpillar",
+            "attcat",
         }, f"Unknown attention operator {attention_layer}."
 
-        if attention_layer == "caterpillar":
+        if attention_layer == "caterpillar" or attention_layer == "attcat":
             assert nb_lines % caterpillar_height == 0
             self.caterpillar_length = nb_lines // caterpillar_height
             self.caterpillar_height = caterpillar_height
 
         def attlayer():
             if attention_layer == "mha":
-                return QKVAttention(
-                    dim_model=dim_model,
-                    dim_qk=dim_keys,
-                    dim_v=dim_model // nb_heads,
-                    nb_heads=nb_heads,
-                    causal=causal,
-                    attention_dropout=dropout,
-                    logger=logger,
-                    args=args,
+                return WithResidual(
+                    CacheWrapper(nn.LayerNorm((dim_model,))),
+                    QKVAttention(
+                        dim_model=dim_model,
+                        dim_qk=dim_keys,
+                        dim_v=dim_model // nb_heads,
+                        nb_heads=nb_heads,
+                        causal=causal,
+                        attention_dropout=dropout,
+                        logger=logger,
+                        args=args,
+                    ),
                 )
             elif attention_layer == "dumbrec":
-                return DumbRec(
-                    dim_model=dim_model,
-                    dim_qk=dim_keys,
-                    dim_v=dim_model // nb_heads,
-                    nb_heads=nb_heads,
-                    nb_lines=nb_lines,
-                    attention_dropout=dropout,
-                    logger=logger,
-                    args=args,
+                return WithResidual(
+                    CacheWrapper(nn.LayerNorm((dim_model,))),
+                    DumbRec(
+                        dim_model=dim_model,
+                        dim_qk=dim_keys,
+                        dim_v=dim_model // nb_heads,
+                        nb_heads=nb_heads,
+                        nb_lines=nb_lines,
+                        attention_dropout=dropout,
+                        logger=logger,
+                        args=args,
+                    ),
                 )
             elif attention_layer == "kvrec":
-                return KVRec(
-                    dim_model=dim_model,
-                    dim_qk=dim_keys,
-                    dim_v=dim_model // nb_heads,
-                    nb_heads=nb_heads,
-                    nb_lines=nb_lines,
-                    attention_dropout=dropout,
-                    logger=logger,
-                    args=args,
+                return WithResidual(
+                    CacheWrapper(nn.LayerNorm((dim_model,))),
+                    KVRec(
+                        dim_model=dim_model,
+                        dim_qk=dim_keys,
+                        dim_v=dim_model // nb_heads,
+                        nb_heads=nb_heads,
+                        nb_lines=nb_lines,
+                        attention_dropout=dropout,
+                        logger=logger,
+                        args=args,
+                    ),
                 )
             elif attention_layer == "caterpillar":
-                return Caterpillar(
-                    dim_model=dim_model,
-                    dim_qk=dim_keys,
-                    dim_v=dim_model // nb_heads,
-                    nb_heads=nb_heads,
-                    caterpillar_length=self.caterpillar_length,
-                    caterpillar_height=self.caterpillar_height,
-                    attention_dropout=dropout,
-                    logger=logger,
-                    args=args,
+                return WithResidual(
+                    CacheWrapper(nn.LayerNorm((dim_model,))),
+                    Caterpillar(
+                        dim_model=dim_model,
+                        dim_qk=dim_keys,
+                        dim_v=dim_model // nb_heads,
+                        nb_heads=nb_heads,
+                        caterpillar_length=self.caterpillar_length,
+                        caterpillar_height=self.caterpillar_height,
+                        attention_dropout=dropout,
+                        logger=logger,
+                        args=args,
+                    ),
+                )
+            elif attention_layer == "attcat":
+                return nn.Sequential(
+                    WithResidual(
+                        CacheWrapper(nn.LayerNorm((dim_model,))),
+                        QKVAttention(
+                            dim_model=dim_model,
+                            dim_qk=dim_keys,
+                            dim_v=dim_model // nb_heads,
+                            nb_heads=nb_heads,
+                            causal=causal,
+                            horizon=self.caterpillar_length,
+                            attention_dropout=dropout,
+                            logger=logger,
+                            args=args,
+                        ),
+                    ),
+                    WithResidual(
+                        CacheWrapper(nn.LayerNorm((dim_model,))),
+                        Caterpillar(
+                            dim_model=dim_model,
+                            dim_qk=dim_keys,
+                            dim_v=dim_model // nb_heads,
+                            nb_heads=nb_heads,
+                            caterpillar_length=self.caterpillar_length,
+                            caterpillar_height=self.caterpillar_height,
+                            attention_dropout=dropout,
+                            logger=logger,
+                            args=args,
+                        ),
+                    ),
                 )
             else:
                 raise ValueError(f"Unknown attention type {attention_layer}.")
 
         for b in range(nb_blocks):
             trunk_blocks += [
-                WithResidual(
-                    CacheWrapper(nn.LayerNorm((dim_model,))),
-                    attlayer(),
-                ),
+                attlayer(),
                 WithResidual(
                     CacheWrapper(
                         nn.LayerNorm((dim_model,)),