add quaternion group

automata.py

@@ -122,7 +122,8 @@ class AutomatonSampler:
           data_config['random_length'] = 0
       self.random_length = data_config['random_length']
 
-      self.__info__ = "  - T (int): sequence length.\n" \
+      self.__info__ = \
+            "  - T (int): sequence length.\n" \
           + "  - random_length (int in {0, 1}): whether to randomly sample a length per sample.\n"
 
   def f(self, x):
@@ -602,6 +603,40 @@ class DihedralSampler(AutomatonSampler):
 
 
 
+class QuaternionSampler(AutomatonSampler):
+  def __init__(self, data_config):
+    super().__init__(data_config)
+
+    self.vocab_size = 8 # {-1, 1} x {1, i, j, k}
+    self.n_actions = 4  # {1, i, j, k}
+    self.transition_pos = [
+      0, 1, 2, 3,
+      1, 4, 3, 6,
+      2, 7, 4, 1,
+      3, 2, 5, 4,]
+    self.transition_neg = [(each+4)%8 for each in self.transition_pos]
+    self.transition = np.array(self.transition_pos + self.transition_neg)
+    self.transition = self.transition.reshape(-1, 4)
+
+    self.__info__ = "Quaternion group:\n" \
+        + "- Inputs: tokens in {0,1,2,3}, corresponding to 1,i,j,k.\n" \
+        + "- Labels: the state id; 8 states in total: 2 signs ({-1,1}) x 4 values ({1,i,j,k}).\n" \
+        + "- Config:\n" \
+         + self.__info__
+
+  def f(self, x):
+    curr_state = 0
+    states = []
+    for action_id in x:
+      curr_state = self.transition[curr_state, action_id]
+      states += curr_state,
+    return np.array(states).astype(np.int64)
+
+  def sample(self):
+    T = self.sample_length()
+    x = self.np_rng.choice(range(self.n_actions), size=T)
+    return x, self.f(x)
+
 
 dataset_map = {
   'abab': ABABSampler,
@@ -611,6 +646,7 @@ dataset_map = {
   'flipflop': FlipFlopSampler,
   'gridworld': GridworldSampler,
   'parity': ParitySampler,
+  'quaternion': QuaternionSampler,
   'symmetric': SymmetricSampler,
   # TODO: more datasets
   }