"""Bayesian perception as variational free energy minimization (MERCURIAL D)."""
from typing import Optional
import numpy as np
from mercurial.core.patterns import Pattern
[docs]
class VariationalPerception:
"""
Implements perception as pattern completion:
- Bottom‑up: sensory input constrains conscious state
- Top‑down: prior expectations bias interpretation
- Minimizes variational free energy F_perc = KL[q||p] - E_q[log p(s|h)]
"""
def __init__(self, prior_strength: float = 1.0, learning_rate: float = 0.1):
self.prior_strength = prior_strength
self.lr = learning_rate
[docs]
def free_energy(
self,
sensory_input: np.ndarray,
hidden_state: np.ndarray,
prior: Optional[np.ndarray] = None,
) -> float:
"""
F = ||sensory - hidden||^2 + β_prior ||hidden - prior||^2
This is a simplified Gaussian approximation.
"""
likelihood = np.linalg.norm(sensory_input - hidden_state) ** 2
if prior is not None:
prior_term = self.prior_strength * np.linalg.norm(hidden_state - prior) ** 2
else:
prior_term = 0.0
return likelihood + prior_term
[docs]
def infer_hidden_state(
self, sensory_input: np.ndarray, prior: Optional[np.ndarray] = None, max_iter: int = 20
) -> np.ndarray:
"""
Gradient descent on F to find the most likely hidden state (percept).
"""
if prior is not None:
hidden = prior.copy()
else:
hidden = sensory_input.copy()
for _ in range(max_iter):
grad = 2 * (hidden - sensory_input)
if prior is not None:
grad += 2 * self.prior_strength * (hidden - prior)
hidden -= self.lr * grad
return hidden
[docs]
def update_consciousness_from_reality(
self, consciousness_pattern: Pattern, reality_pattern: Pattern
) -> Pattern:
"""
Bottom‑up update: consciousness pattern is pulled toward reality pattern
via variational inference. This implements reality → consciousness causation.
"""
# Treat reality pattern as sensory input
sensory = reality_pattern.V
prior = consciousness_pattern.V
new_V = self.infer_hidden_state(sensory, prior)
return Pattern(
new_V,
consciousness_pattern.C,
consciousness_pattern.R,
label=f"{consciousness_pattern.label}_updated",
)