Adam-Ben-Khalifa/GIE-Whitepaper

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.

📄 Read the full whitepaper →

Key Contributions

Phase	Innovation	Mathematical Foundation
Phase 1	Differentiable Graph Traversal	Neural Bellman-Ford over learned semirings (NBFNet) + NOTEARS DAG extraction
Phase 2	Hybrid RL Training	GFlowNet Trajectory Balance with path-refined reward (reachability + parsimony + integrity)
Phase 3	Agentic Graph Evolution	Edge Proposal Network + Sheaf Laplacian pre-filter + Datalog/PSL symbolic gatekeeper
Phase 4	Reasoning Faithfulness Metrics	Counterfactual Intervention Testing (CIT) + DAG-Consistency Index (DCI)
Phase 5	Computational Advantage	O(k·M·d²) linear vs O(k²·t²·d²_model) quadratic; ~4,000× speedup at 20-hop

Architecture Diagram

Query Q → [Entity Grounding] → [NBFNet Traversal (T iterations)]
                                        ↓
                              [Edge Relevance Scores π_q(e)]
                                        ↓
                              [NOTEARS DAG Extraction] → D_Q
                                        ↓
                    [Dead-End?] → YES → [Edge Proposal Network]
                        ↓                      ↓
                        NO              [Gatekeeper: Sheaf + Datalog + PSL]
                        ↓                      ↓
                  [Answer Decode]      [Expand G, Re-traverse]
                        ↓                      ↓
                    (v_answer, D_Q)  ←←←←←←←←←←

Key References

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

Citation

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