Add shuriken process: 3-state binary nonunifilar HMM

Implements the shuriken process as a new generative process with parameters p, r, u, v. Includes minimality determinant test and default Hydra config.
Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

Author: loren-ac

.gitignore

@@ -7,6 +7,7 @@ __pycache__/
 data/
 multirun/
 outputs/
+references/
 config.ini
 *temp*
 # MLflow tracking data

simplexity/generative_processes/transition_matrices.py

@@ -342,6 +342,51 @@ def tom_quantum(alpha: float, beta: float) -> jax.Array:
     return transition_matrices
 
 
+def shuriken(p: float = 0.72, r: float = 0.24, u: float = 0.36, v: float = 0.52) -> jax.Array:
+    """Creates transition matrices for the Shuriken Process.
+
+    A parameterized family of 3-state binary edge-emitting nonunifilar HMMs.
+
+    States: A, B, C
+    Alphabet: {0, 1}
+
+    Symbol-labeled transition matrices where T[x, i, j] = P(next_state=j, emit x | current_state=i):
+
+        T0 = [[u,   p-u, 0  ],    T1 = [[0,   0,   1-p],
+               [0,   v,   p-v],           [1-p, 0,   0  ],
+               [r,   0,   0  ]]           [0,   1-r, 0  ]]
+
+    The generator is minimal (all 3 hidden states are needed) when the minimality determinant
+    det(M) = -(p - r)^2 * (p - v) is nonzero, i.e. when p != r and p != v. Keeping these
+    differences large also improves numerical conditioning. The suggested parameter constraints
+        0 < r < p < 1, 0 < u < p, 0 < v < p
+    ensure minimality and that all matrix entries are non-negative.
+
+    Args:
+        p: P(emit 0) from states A and B. Also 1 - P(emit 1) from those states.
+        r: P(emit 0) from state C. Must differ from p for minimality.
+        u: P(emit 0, stay in A | state A). Controls the A/B split when emitting 0 from A.
+        v: P(emit 0, stay in B | state B). Must differ from p for minimality.
+
+    Returns:
+        Transition matrices of shape (2, 3, 3).
+    """
+    return jnp.array(
+        [
+            [
+                [u, p - u, 0],
+                [0, v, p - v],
+                [r, 0, 0],
+            ],
+            [
+                [0, 0, 1 - p],
+                [1 - p, 0, 0],
+                [0, 1 - r, 0],
+            ],
+        ]
+    )
+
+
 def zero_one_random(p: float) -> jax.Array:
     """Creates a transition matrix for the Zero One Random (Z1R) Process.
 
@@ -375,6 +420,7 @@ def zero_one_random(p: float) -> jax.Array:
     "mr_name": mr_name,
     "no_consecutive_ones": no_consecutive_ones,
     "rrxor": rrxor,
+    "shuriken": shuriken,
     "sns": sns,
     "zero_one_random": zero_one_random,
 }

tests/end_to_end/configs/generative_process/shuriken.yaml

@@ -0,0 +1,15 @@
+name: shuriken
+instance:
+  _target_: simplexity.generative_processes.builder.build_hidden_markov_model
+  process_name: shuriken
+  process_params:
+    p: 0.72
+    r: 0.24
+    u: 0.36
+    v: 0.52
+  device: ${device}
+
+base_vocab_size: ???
+bos_token: ???
+eos_token: null
+vocab_size: ???

tests/generative_processes/test_transition_matrices.py

@@ -17,6 +17,7 @@
     no_consecutive_ones,
     post_quantum,
     rrxor,
+    shuriken,
     sns,
     tom_quantum,
     zero_one_random,
@@ -204,6 +205,51 @@ def test_rrxor():
     assert jnp.allclose(stationary_distribution, jnp.array([2, 1, 1, 1, 1]) / 6)
 
 
+def test_shuriken():
+    """Test the shuriken transition matrices."""
+    transition_matrices = shuriken()
+    assert transition_matrices.shape == (2, 3, 3)
+    validate_hmm_transition_matrices(transition_matrices)
+
+
+def test_shuriken_custom_params():
+    """Test the shuriken transition matrices with custom parameters."""
+    transition_matrices = shuriken(p=0.8, r=0.3, u=0.4, v=0.5)
+    assert transition_matrices.shape == (2, 3, 3)
+    validate_hmm_transition_matrices(transition_matrices)
+
+
+def test_shuriken_minimality_determinant():
+    """Test that the minimality determinant matches the closed-form expression.
+
+    For pure states A=[1,0,0], B=[0,1,0], C=[0,0,1], construct
+    M = [[1, P(0|A), P(00|A)],
+         [1, P(0|B), P(00|B)],
+         [1, P(0|C), P(00|C)]]
+    and verify |det(M)| = (p-r)^2 * (p-v).
+
+    The nonzero determinant confirms that the three pure-state predictive distributions
+    are linearly independent, establishing that the model is minimal (3 states are needed).
+    """
+    p, r, u, v = 0.72, 0.24, 0.36, 0.52
+    transition_matrices = shuriken(p=p, r=r, u=u, v=v)
+    t0 = transition_matrices[0]
+
+    pure_states = jnp.eye(3)
+    p0 = jnp.sum(pure_states @ t0, axis=-1)
+    next_states = pure_states @ t0
+    next_states_normalized = next_states / p0[:, None]
+    p00 = p0 * jnp.sum(next_states_normalized @ t0, axis=-1)
+
+    m = jnp.stack([jnp.ones(3), p0, p00], axis=-1)
+    actual_abs_det = jnp.abs(jnp.linalg.det(m))
+    expected_abs_det = (p - r) ** 2 * (p - v)
+
+    assert jnp.isclose(actual_abs_det, expected_abs_det, atol=1e-6), (
+        f"Minimality determinant |det(M)|={actual_abs_det} != expected {expected_abs_det}"
+    )
+
+
 def test_sns():
     """Test the sns transition matrices."""
     transition_matrices = sns(p=0.5, q=0.5)