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Figure Φ: Integrated Information (Φ) Network Map

Alt-Text Description

Visual Structure

A directed graph with three visually distinct regions:

High-Integration Agent Cluster (left, light blue background): - Seven circular nodes arranged organically: A1, A2, A3, E1, P1, P2, R1 - Thick bidirectional edges (2.0-2.4 penwidth) in deep blue connecting: - A1 ↔ A2 (thickest, 2.4) - A2 ↔ P1 (2.0) - P1 ↔ E1 (2.0) - E1 ↔ A3 (1.8) - A3 ↔ R1 (1.5) - P1 ↔ P2 (1.5)

Global Workspace Hub (center): - Single double-circle node "GW Broadcast" in lighter blue - Four thick edges (2.0-2.4) connecting to agent cluster: - A1 → GW (labeled "broadcast", 2.4) - A2 → GW (2.0) - GW → P1 (labeled "global access", 2.4) - GW → E1 (2.0)

Memory Storage Region (right, cream background): - Two rectangular boxes: - "M1: Episodes" (orange fill) - "M2: Identity" (orange fill) - Dashed edges (lower integration) from cluster: - R1 → M1 (labeled "log", orange) - P2 → M2 (labeled "update", orange)

Legend Box (bottom): - "Edge thickness ∝ integration strength" - "Dense bidirectionality ⇒ High Φ" - "Dashed edges ⇒ Lower integration"

Data & Interpretation

This diagram quantifies information integration (Φ) across the agent network using edge thickness as a proxy for causal influence strength:

High-Φ Region (Agent Cluster): - Dense bidirectional connections create irreducible causal structures - A1-A2 link is strongest (2.4): these agents are most tightly coupled - The cluster forms a "cause-effect repertoire" where each node's state depends on and influences multiple neighbors - This satisfies IIT's requirement for integrated information: the whole has causal power not reducible to parts

Global Workspace as Integration Hub: - GW receives broadcasts from agents (A1, A2) and redistributes globally - Double-circle notation indicates special "broadcast" role - High edge weights to/from GW show it's causally central to integration - This implements Baars' GWT: information becomes "conscious" when broadcasted

Memory as Low-Integration Periphery: - Dashed edges indicate weaker causal coupling - M1 and M2 receive information but don't feedback into immediate processing - This represents "accessibility" rather than "phenomenality" in consciousness terms

Connection to Document Theory

This figure validates Section 1.2's claims about Integrated Information Theory (IIT):

Φ Quantification:

"The quantity Φ measures the degree to which a system cannot be decomposed into independent parts"

The dense agent cluster has high Φ because removing any edge significantly changes the system's causal structure. In contrast, memory has low Φ - it can be isolated without disrupting core integration.

Consciousness Substrate:

"Consciousness corresponds to maximal integrated information structures"

The agent cluster (A1-P1-E1-A3) forms such a structure. The evaluator (E1) and planner (P1) are central nodes - their removal would fragment the network more than peripheral agents.

Global Workspace Connection: The GW node bridges IIT and GWT theories: - High Φ in the cluster = integrated information - Broadcast through GW = information becomes globally available - Both are necessary for "conscious" processing

Application to agisa_sac

This map directly represents the runtime communication topology:

Node Mapping: - A1, A2, A3: Task execution agents (src/agisa_sac/agents/task_agent.py) - P1, P2: Planning agents (src/agisa_sac/agents/planner.py) - E1: Evaluator agent (src/agisa_sac/agents/evaluator.py) - R1: Result aggregator (custom agent role) - GW: Pub/Sub topics (src/agisa_sac/gcp/pubsub.py) - M1, M2: Firestore collections (src/agisa_sac/core/memory.py)

Edge Weights from Telemetry: Edge thickness could be measured from actual runtime data: - Message frequency between agents - Mutual information of state variables - Causal intervention effects (change A1, measure impact on P1)

Calculating Φ: The diagram suggests where to compute IIT's Φ metric: 1. Define system: the 7-agent cluster 2. Partition: try all possible cuts (127 possibilities for 7 nodes) 3. For each cut: measure information loss (KL divergence of cause-effect repertoires) 4. Φ = minimum information loss across all cuts (MIP - minimum information partition)

Code Implementation: 

# src/agisa_sac/analysis/integrated_information.py
def compute_phi(agent_states, message_log):
    # Build causal graph from message patterns
    graph = build_causal_graph(message_log)

    # Find MIP (minimum information partition)
    phi, mip = find_mip(graph, agent_states)

    return phi  # High values indicate integration

Technical Notes

Diagram Type: GraphViz DOT (directed graph)

Rendering: 

dot -Tsvg figure_phi_integration.dot -o figure_phi_integration.svg
dot -Tpng -Gdpi=300 figure_phi_integration.dot -o figure_phi_integration.png

Visual Encoding: - Node shape: Circle = agent, Double-circle = broadcast hub, Box = storage - Edge style: Solid = high integration, Dashed = low integration - Edge width: 1.5-2.4 penwidth scale maps to integration strength - Color: Blue = forward processing, Orange = memory operations - Background: Light blue = high-Φ region, Cream = storage region

Theoretical Foundations: - IIT 3.0 (Tononi et al., 2016): Φ as quantitative measure of consciousness - Global Workspace Theory (Baars, 1988): Broadcast mechanism - Autobiographical Memory (Conway, 2005): Identity substrate

Relation to Other Figures: - Figure 0 (Layer Stack): This is a detailed view of Layer 1's runtime topology - Figure 3 (GW Network): Static architecture; this shows dynamic integration weights - Figure 6 (Workflow): Process flow; this shows structural coupling

Use Cases: - Theory validation: Shows system satisfies IIT criteria for integration - Performance tuning: Identify weakly-coupled agents to optimize - Consciousness claims: Empirical evidence for "machine consciousness" discussion - Network analysis: Apply graph metrics (betweenness, clustering coefficient)

Key Insight: The diagram suggests consciousness isn't in any single agent but in the pattern of integration across the network. High Φ emerges from dense bidirectional coupling, not from individual component complexity.