+####################
+
+
+class ProblemMixing(Problem):
+ def __init__(self, height=3, width=3, nb_time_steps=12, hard=False):
+ self.height = height
+ self.width = width
+ self.nb_time_steps = nb_time_steps
+ self.hard = hard
+
+ def start_random(self, nb):
+ y = torch.arange(self.height * self.width).reshape(1, -1).expand(nb, -1)
+
+ m = (torch.rand(y.size()).sort(dim=-1).indices < y.size(1) // 2).long()
+
+ y = (y * m + self.height * self.width * (1 - m)).reshape(
+ nb, self.height, self.width
+ )
+
+ return y
+
+ def start_error(self, x):
+ x = x.flatten(1)
+ u = torch.arange(self.height * self.width).reshape(1, -1)
+ m = ((x - u).abs() == 0).long()
+ d = (x - (m * u + (1-m) * self.height * self.width)).abs().sum(-1) + (
+ m.sum(dim=-1) != self.height * self.width // 2
+ ).long()
+ return d
+
+ def moves(self, x):
+ y = (
+ x[:, None, :, :]
+ .expand(-1, self.height * 2 + self.width * 2, -1, -1)
+ .clone()
+ )
+ k = 0
+
+ for i in range(self.height):
+ y[:, k, i, :] = y[:, k, i, :].roll(dims=-1, shifts=-1)
+ k += 1
+ y[:, k, i, :] = y[:, k, i, :].roll(dims=-1, shifts=1)
+ k += 1
+
+ for j in range(self.width):
+ y[:, k, :, j] = y[:, k, :, j].roll(dims=-1, shifts=-1)
+ k += 1
+ y[:, k, :, j] = y[:, k, :, j].roll(dims=-1, shifts=1)
+ k += 1
+
+ return y
+
+ def generate_sequences(self, nb):
+ x = self.start_random(nb)
+
+ seq = [x.flatten(1)]
+
+ for t in range(self.nb_time_steps - 1):
+ y = self.moves(x)
+ x = y[torch.arange(nb), torch.randint(y.size(1), (nb,))]
+ seq.append(x.flatten(1))
+
+ if self.hard:
+ seq.reverse()
+
+ seq = torch.cat(seq, dim=1)
+ return seq, seq.new_full(seq.size(), 1, dtype=torch.int64)
+
+ def compute_nb_correct(self, input, ar_mask, result):
+ a = [
+ x.reshape(result.size(0), self.height, self.width)
+ for x in result.split(self.height * self.width, dim=1)
+ ]
+ if self.hard:
+ a.reverse()
+
+ x = a[0]