Dual-Pathway Neuro-Symbolic Optimization via Spectral Structure Learning
Abstract: Conventional neuro-symbolic systems operate on fixed graphs, failing when faced with "out-of-distribution" logical paradoxes. DENSN treats logical frustration not as a terminal error, but as a generative signal for topological expansion. It introduces a Dual-Pathway architecture: minimizing tension via spectral diffusion in low-conflict regimes, and triggering Topological Structure Learning (TSL) to synthesize new Meta-Symbols in high-conflict regimes.
Read the Full Whitepaper (PDF)
Note: This repository serves as the reference implementation for the theory described in the paper. The core engine code will be released in the upcoming Alpha phase.
Optimization is not a monolithic process; it is a thermodynamic response to tension. DENSN splits this into two distinct pathways:
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Pathway A (Coherence): Triggered when
$\Psi < \Psi_{crit}$ . The system optimizes for modularity and consistency within the existing ontology, minimizing free energy via diffusion. -
Pathway B (Frustration): Triggered when
$\Psi \ge \Psi_{crit}$ (Persistent Singularity). The system recognizes the ontology is insufficient and forces Topological Structure Learning (TSL) to synthesize a new Meta-Symbol that resolves the paradox.
DENSN replaces heuristic solvers with a physics-based hybrid engine:
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Spectral Diffusion: Utilizes the Graph Laplacian (
$\Phi_{t+1} = (I - \kappa \mathcal{L})\Phi_t$ ) to diffuse "logical potential" across the graph structure. This allows the system to "feel" global topology before committing to discrete decisions. - Stochastic Collapse: A modified WalkSAT operator projects the continuous potential field back into discrete truth values, using the spectral gradient to avoid local minima.
To address the Symbol Grounding Problem, DENSN mathematically decouples Structural Truth from Semantic Meaning:
- The system learns a structure (
$f_{meta}$ ) to resolve a paradox. - It queries an Oracle (LLM) for a semantic label (
$L_{meta}$ ). - It injects a verification constraint (
$L_{meta} \leftrightarrow f_{meta}$ ) and measures the Global Tension Response ($\Delta \Psi$ ). - If
$\Delta \Psi$ spikes, the label is rejected as a hallucination. The semantic map must respect the structural territory.
The framework has been validated on both synthetic and real-world datasets:
- Biomedical Case Study (Ovarian Cancer): Ingested 579 atomic symbols from conflicting PubMed literature. The system successfully isolated the specific "Singular Contradiction" regarding Cisplatin vs. Carboplatin efficacy, separating it from the high-consensus background knowledge.
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Synthetic XOR Paradox: Demonstrated the ability to autonomously "invent" a Meta-Symbol to resolve an irreducible 3-constraint loop. The Conflict Cache escalated weights until TSL was triggered, reducing global tension from
$\Psi=16.0$ to$\Psi=0.0$ .
If you use this theory in your research, please cite the whitepaper:
@article{oboyle2025densn,
title={DENSN: Dual-Pathway Neuro-Symbolic Optimization via Spectral Structure Learning},
author={O'Boyle, Liam},
year={2025},
journal={Open Research Archive},
url={https://github.com/1-Liam/DENSN}
}This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
- You are free to: Share, copy, and redistribute the material in any medium or format.
- Under the following terms:
- Attribution: You must give appropriate credit, provide a link to the license, and indicate if changes were made.
- NonCommercial: You may not use the material for commercial purposes.
- NoDerivatives: If you remix, transform, or build upon the material, you may not distribute the modified material.
Commercial Inquiries: For commercial licensing, collaboration, or access to the production engine, please contact the author.
Author: Liam O'Boyle | Contact: liamoboyle0@gmail.com