cognitive/docs/guides/pomdp_structure.md

POMDP Structure Guide

Overview

This guide explains our modular approach to representing Active Inference POMDPs using Obsidian's knowledge management capabilities.

Philosophy

Our approach combines:

1. Machine-readable matrix specifications
2. Human-readable documentation
3. Bidirectional linking for relationships
4. Version control for evolution
5. Visualization capabilities

Core Components

Matrix Specifications

Each POMDP matrix has its own specification:

• A_matrix - Perception (observation mapping)
• B_matrix - Transitions (dynamics)
• C_matrix - Preferences (goals)
• D_matrix - Priors (initial beliefs)
• E_matrix - Affordances (policies)

State Spaces

Fundamental spaces are defined separately:

• o_space - Observation space
• s_space - Hidden state space
• pi_space - Policy space

Machine Readability

YAML Frontmatter

---
type: matrix_spec
id: unique_identifier
matrix_type: perception
created: timestamp
modified: timestamp
tags: [matrix, type, active-inference]
related_spaces: [space1, space2]
---

Matrix Data Structure

matrix_data:
  format: numpy.ndarray
  dtype: float32
  initialization: method
  storage: path/to/data.npy

Constraints

constraints:
  - mathematical_property
  - dimensional_requirement
  - probability_constraint

Knowledge Integration

Bidirectional Links

• Matrix ↔ Space relationships
• Component dependencies
• Implementation references

Tag Taxonomy

• #matrix
• #state-space
• #active-inference
• #pomdp
• #generative-model

Computational Interface

Matrix Operations

from src.models.matrices import MatrixLoader

# Load matrix specification
A = MatrixLoader.load("A_matrix")

# Perform operations
result = A.update(observation)

State Space Interface

from src.models.spaces import StateSpace

# Initialize space
s_space = StateSpace.from_spec("s_space")

# Update beliefs
s_space.update_belief(evidence)

Visualization Pipeline

Matrix Visualization

1. Load specification from markdown
2. Read matrix data
3. Generate visualization
4. Export to desired format

Network Visualization

1. Extract relationship graph
2. Apply layout algorithm
3. Render interactive view
4. Enable exploration

Version Control

Matrix Evolution

• Track changes in specifications
• Version matrix data
• Document modifications
• Maintain history

Knowledge Base Updates

• Link updates
• Relationship changes
• Documentation evolution
• Implementation refinements

Integration Examples

Active Inference Implementation

class ActiveInferencePOMDP:
    def __init__(self, agent_spec: str):
        self.A = MatrixLoader.load("A_matrix")
        self.B = MatrixLoader.load("B_matrix")
        self.C = MatrixLoader.load("C_matrix")
        self.D = MatrixLoader.load("D_matrix")
        self.E = MatrixLoader.load("E_matrix")
        
    def infer_state(self, observation):
        """Perform state inference"""
        pass
    
    def select_policy(self):
        """Select optimal policy"""
        pass

Visualization Generation

class POMDPVisualizer:
    def __init__(self, agent_spec: str):
        self.spec = load_spec(agent_spec)
        
    def plot_matrices(self):
        """Generate matrix plots"""
        pass
    
    def plot_state_space(self):
        """Visualize state space"""
        pass

Best Practices

Specification Writing

1. Clear structure
2. Complete metadata
3. Explicit constraints
4. Comprehensive documentation

Knowledge Organization

1. Consistent naming
2. Meaningful links
3. Proper tagging
4. Regular updates

Implementation

1. Type checking
2. Constraint validation
3. Error handling
4. Performance optimization

Related Guides

• matrix_operations
• visualization_guide
• implementation_guide
• version_control

References

• active_inference_theory
• pomdp_formalism
• obsidian_usage
• git_workflow