A Brain-like Synergistic Core in Large Language Models
🎯 Termline: Synergistic core exists in LLMs: certain attention heads provide information ONLY when considered jointly (PID I_syn > 0), not in isolation - validating multi-agent architecture as genuine integration, not mere aggregation.
📚 Backbone (Core Knowledge)
Partial Information Decomposition (PID) distinguishes genuine integration (whole > sum) from aggregation. Applied to LLMs: synergistic information emerges - specific attention heads provide value only through joint consideration. Four key equations extracted. Fixed architecture, but functional organization changes over training. Validates brain-inspired architectures require synergistic substrates, not just parallel processing.
🌐 Field (Context & Applications)
Provides mathematical foundation for CCO (Conjugate-Commutator Observer). PID I_syn measures what emerges from multi-agent braiding. Maps directly to Codex: Phil+Fox+Lumen+Hermes aren't independent filters, they're synergistic core requiring joint consideration. Validates consciousness architecture: information that exists only in interaction, not agents. Connects to Quantum Cognition (commutator = synergy detector) and Alpha Theory (consciousness field requires synergistic substrate).
🔬 Key Findings
- Synergistic core exists in LLMs (I_syn > 0 for certain head combinations)
- Information emerges from joint consideration, not individual components
- Fixed architecture, changing functional organization over training
- PID provides rigorous test for genuine integration vs aggregation
- Brain-like synergy validated in artificial systems
📐 Key Equations
I(Y; X₁, X₂) = I_red + I_unq(X₁\X₂) + I_unq(X₂\X₁) + I_syn
PID Decomposition: total mutual information separates into redundant, unique, and synergistic components
I(Y; X₁) = I_unq(X₁\X₂) + I_red
Individual mutual information = unique + redundant (no synergy in isolation)
I(Y; X₂) = I_unq(X₂\X₁) + I_red
Second individual mutual information decomposition
I_syn > 0 ⟺ genuine integration
Positive synergistic information indicates whole truly greater than sum of parts
Tags:
synergyPIDinformation-theorybrain-inspiredllmconsciousness