"""Level transition operator for constraint propagation between LADDER levels."""
from typing import Optional
import numpy as np
from mercurial.core.patterns import Constraints, Pattern
[docs]
class LevelTransitionOperator:
"""
Implements T_{i→j}[P] = Π_j ◦ Φ_{i→j} ◦ Π_i^{-1}[P]
where:
- Π_i projects onto level i degrees of freedom
- Φ_{i→j} is the constraint propagation map
"""
def __init__(self, coupling_strength: float = 0.1):
self.coupling = coupling_strength
[docs]
def project_to_level(
self, pattern: Pattern, target_level: int, current_level: Optional[int] = None
) -> np.ndarray:
"""
Π_j: Project pattern state variables to a different level's dimensionality.
Simplified: use linear interpolation/downsampling based on complexity ratio.
"""
# Estimate current level if not provided
if current_level is None:
from mercurial.hierarchy.complexity import ComplexityMeasure, LevelClassifier
measure = ComplexityMeasure()
comp = measure.compute(pattern.V)
current_level, _ = LevelClassifier.classify(comp)
# Level difference determines scaling factor
level_diff = target_level - current_level
# Exponential scaling of degrees of freedom (higher levels have more DOF)
scale_factor = 2.0**level_diff # heuristic
# Flatten pattern
flat = pattern.V.flatten()
new_size = max(1, int(len(flat) * scale_factor))
if new_size > len(flat):
# Upsample: interpolate
x_old = np.linspace(0, 1, len(flat))
x_new = np.linspace(0, 1, new_size)
projected = np.interp(x_new, x_old, flat)
else:
# Downsample: take every step
step = max(1, len(flat) // new_size)
projected = flat[::step][:new_size]
return projected
[docs]
def constraint_propagation(
self, source_state: np.ndarray, target_constraints: Constraints
) -> np.ndarray:
"""
Φ_{i→j}: Apply constraints from source to target.
Simplified: modify target state to satisfy source constraints.
"""
# Evaluate current constraint violations
violations = target_constraints.violation_norm(source_state)
if violations == 0:
return source_state
# Gradient descent to satisfy constraints (simplified)
# This is a placeholder – real implementation would use constraint satisfaction
new_state = source_state.copy()
learning_rate = 0.1 * self.coupling
for _ in range(5):
grad = np.zeros_like(new_state)
# Approximate gradient of constraint violation
eps = 1e-6
for i in range(len(new_state)):
perturb = np.zeros_like(new_state)
perturb[i] = eps
v_plus = new_state + perturb
v_minus = new_state - perturb
v_plus_viol = target_constraints.violation_norm(v_plus)
v_minus_viol = target_constraints.violation_norm(v_minus)
grad[i] = (v_plus_viol - v_minus_viol) / (2 * eps)
new_state -= learning_rate * grad
return new_state
[docs]
def apply_transition(
self,
source_pattern: Pattern,
target_level: int,
target_constraints: Constraints,
current_level: Optional[int] = None,
) -> Pattern:
"""
Apply T_{i→j} to source pattern, producing a pattern at target level.
"""
# Project to target level's state space
projected_state = self.project_to_level(source_pattern, target_level, current_level)
# Apply constraint propagation
constrained_state = self.constraint_propagation(projected_state, target_constraints)
# Create new pattern (simplified stability)
return Pattern(
constrained_state.reshape(-1, 1),
target_constraints,
source_pattern.R,
label=f"trans_{source_pattern.label}",
)