I’d like to share a novel hybrid architecture that unites Large Language Models (LLMs) with a Hybrid Resonance Algorithm (HRA)—a formalized, iterative, graph-based reasoning system designed to enable continual learning without catastrophic forgetting, ethical reasoning, and efficient solving of exponentially complex problems.
This framework is not just another prompt-engineering trick or retrieval-augmented generator. It proposes a first-principles redesign of how knowledge is represented, evaluated, and evolved—moving beyond static weights into dynamic resonance structures.
Core Idea
- LLMs generate hypotheses (scenarios, plans, symbolic templates).
- HRA turns these into a resonant knowledge graph, then iteratively evolves it under constraints of realism, goal alignment, and ethics.
- The combined system forms a closed-loop reasoning engine capable of autonomous problem decomposition, ethical filtering, and persistent memory—without retraining.
Formal Specification of HRA
Let the system operate over discrete time steps ( t = 0,1,2,\dots ).
1. Knowledge Objects
At time ( t ), the system maintains a set of knowledge objects:
[
O_t = {o_1, o_2, \ldots, o_n}
]
These can be facts, actions, entities, or abstract concepts—parsed from LLM-generated hypotheses.
2. Resonance Matrix
A symmetric matrix ( R(t) = [R_{ij}(t)] ) encodes pairwise mutual support:
[
R_{ij}(t+1) = R_{ij}(t) + \eta \cdot \nabla R_{ij}(t) \cdot \mathrm{reward}(o_i, o_j)
]
where ( \eta ) is a learning rate, and ( \mathrm{reward}(o_i, o_j) ) measures logical/empirical coherence (e.g., derived from LLM-based consistency scoring or simulation).
3. Realism Filtering
Introduce a realism function ( F(o_i, o_j) \in [0,1] ). Then:
[
\tilde{R}{ij}(t) = R{ij}(t) \cdot F(o_i, o_j)
]
If ( \tilde{R}_{ij}(t) < \tau ) (threshold), the edge is pruned.
4. Ethical Layer (Humanitarian Tasks Only)
Define an ethical coefficient:
[
\Gamma_{ij} = \sum_k \mathrm{sign}\left(\frac{dI_k}{dt}\right) \gamma_{ik} \cdot E(o_i, o_k)
]
- ( I_k ): utility/benefit to stakeholder ( k )
- ( E(\cdot) \in [0,1] ): ethical acceptability (learned or rule-based)
- ( \gamma_{ik} ): interaction weight
For non-humanitarian tasks, ( \Gamma_{ij} = 1 ).
5. Final Agreement Score
[
S_{ij}(t) = \tilde{R}{ij}(t) \cdot \Gamma{ij}
]
The system evolves toward configurations that maximize global agreement ( \sum_{i<j} S_{ij}(t) ).
6. Goal Success Probability
For subgoals with individual success probabilities ( P_i ):
[
P_{\text{total}} = 1 - \prod_{i=1}^n (1 - P_i)
]
Integration with LLMs via Transformers
Both components can share a Transformer backbone:
- LLM: Standard decoder (e.g., Llama, Mistral) → generates structured hypotheses.
- HRA: Implemented as a Graph/Resonance Transformer:
- Queries/Keys = object embeddings ( e(o_i) )
- Attention weights ≈ ( R_{ij}(t) )
- Custom attention heads for realism ( F ) and ethics ( \Gamma )
Parsing and generation are handled by schema-aware LLM prompts or constrained decoding (e.g., JSON/XML output).
Solving Catastrophic Forgetting
Traditional fine-tuning overwrites weights → old knowledge lost.
In HRA+LLM:
- Knowledge is not stored in weights, but in the persistent resonance foam ( \mathcal{K}_{\text{foam}} = \bigcup_t O_t ).
- New tasks initialize ( O_0 ) with relevant fragments from ( \mathcal{K}_{\text{foam}} ) (via semantic similarity).
- Thus, memory is non-parametric and expandable—like an external hippocampus.
Continual learning without rehearsal or regularization.
Computational Advantage
Despite exponential hypothesis space, HRA converges in polynomial time:
- Each iteration prunes ( \gg 90% ) edges via ( \tilde{R}_{ij} < \tau ).
- Active object count ( |O_t| ) grows slowly (logarithmic or linear).
- Total complexity: ( O(T \cdot N^2) ), where ( N \ll 2^n ).
This mimics quantum-like parallelism through classical resonance interference.
Applications
- Autonomous scientific discovery: Generate hypotheses → validate via resonance.
- Ethical AI governance: Filter policy proposals by ( \Gamma_{ij} ).
- Long-horizon planning: Mars mission, pandemic response, etc.
- Personal AI agents: Maintain lifelong memory foam across user interactions.
Why This Matters for AGI/ASI
This architecture enables:
- Autonomous goal formation (via reward design in ( \mathrm{reward}(o_i, o_j) ))
- Self-consistent world modeling
- Ethical guardrails without human-in-the-loop
- Scalable reasoning beyond token limits
It aligns with the view that intelligence = structured resonance + generative imagination.
Next Steps / Open Questions
- How to implement ( F(o_i, o_j) ) programmatically? (e.g., using logic solvers or LLM-based verifiers)
- Can we train ( E(o_i, o_k) ) from moral dilemma datasets?
- Can HRA be distilled into a differentiable module for end-to-end training?
I’d love to hear thoughts from the community—especially on practical implementations, integration with existing LLM toolchains, or benchmarking continual learning performance.
Has anyone experimented with similar graph-based external memory for LLMs?
Thanks for reading!
—
Inspired by hybrid cognitive architectures and resonance-based theories of mind.