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Adam-Ben-Khalifa/GIE-Whitepaper

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The Graph-Inference Engine (GIE)

A Neuro-Symbolic Architecture for Faithful Multi-Hop Reasoning via Differentiable Graph Traversal and Discrete DAG Extraction

Overview

This repository contains the complete whitepaper for the Graph-Inference Engine (GIE), a neuro-symbolic model that navigates and agentically evolves a continuous world-graph to resolve queries by outputting discrete Directed Acyclic Graph (DAG) reasoning traces.

๐Ÿ“„ [Read the full whitepaper โ†’](GIE_Whitepaper.md)

Key Contributions

PhaseInnovationMathematical Foundation
Phase 1Differentiable Graph TraversalNeural Bellman-Ford over learned semirings (NBFNet) + NOTEARS DAG extraction
Phase 2Hybrid RL TrainingGFlowNet Trajectory Balance with path-refined reward (reachability + parsimony + integrity)
Phase 3Agentic Graph EvolutionEdge Proposal Network + Sheaf Laplacian pre-filter + Datalog/PSL symbolic gatekeeper
Phase 4Reasoning Faithfulness MetricsCounterfactual Intervention Testing (CIT) + DAG-Consistency Index (DCI)
Phase 5Computational AdvantageO(kยทMยทdยฒ) linear vs O(kยฒยทtยฒยทdยฒ_model) quadratic; ~4,000ร— speedup at 20-hop

Architecture Diagram

Query Q โ†’ [Entity Grounding] โ†’ [NBFNet Traversal (T iterations)]
                                        โ†“
                              [Edge Relevance Scores ฯ€_q(e)]
                                        โ†“
                              [NOTEARS DAG Extraction] โ†’ D_Q
                                        โ†“
                    [Dead-End?] โ†’ YES โ†’ [Edge Proposal Network]
                        โ†“                      โ†“
                        NO              [Gatekeeper: Sheaf + Datalog + PSL]
                        โ†“                      โ†“
                  [Answer Decode]      [Expand G, Re-traverse]
                        โ†“                      โ†“
                    (v_answer, D_Q)  โ†โ†โ†โ†โ†โ†โ†โ†โ†โ†

Key References

  • โ€”NBFNet: Zhu et al. (2021) - Neural Bellman-Ford Networks. arXiv:2106.06935
  • โ€”GFlowNet TB: Malkin et al. (2022) - Trajectory Balance. arXiv:2201.13259
  • โ€”NOTEARS: Zheng et al. (2018) - DAGs with NO TEARS. arXiv:1803.01422
  • โ€”Knowledge Sheaves: Hansen & Ghrist (2021). arXiv:2110.03789
  • โ€”Faith and Fate: Dziri et al. (2024) - Limits of Transformers. arXiv:2305.18654
  • โ€”RFEval: Kim et al. (2026) - Reasoning Faithfulness. arXiv:2602.17053

Citation

bibtex
@techreport{gie2026,
  title={The Graph-Inference Engine: A Neuro-Symbolic Architecture for Faithful Multi-Hop Reasoning},
  year={2026},
  note={Technical whitepaper}
}