ManifoldMind: Dynamic Hyperbolic Reasoning for Trustworthy Recommendations

2025-07-02

AI Summary

This work addresses key limitations in recommender systems—rigid semantic hierarchy modeling, inadequate uncertainty quantification, and opaque inference processes—by proposing the first hyperbolic geometric probabilistic model for trustworthy recommendation. Methodologically, it introduces adaptive-curvature probabilistic spherical embeddings, a curvature-aware semantic kernel function, and a soft multi-hop reasoning mechanism, enabling dynamic curvature optimization and explicit, interpretable reasoning path generation—overcoming constraints of fixed curvature and inflexible embeddings. Its primary contributions are: (i) the first integration of probabilistic modeling with dynamic curvature in hyperbolic space, enabling personalized uncertainty quantification and geometry-aware semantic exploration; and (ii) consistent improvements across four benchmark datasets in NDCG, recommendation diversity, and predictive calibration—demonstrating superior robustness and interpretability, especially under data sparsity and abstract user-item interactions.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Data Mining & Knowledge Management: Recommender Systems

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

We introduce ManifoldMind, a probabilistic geometric recommender system for exploratory reasoning over semantic hierarchies in hyperbolic space. Unlike prior methods with fixed curvature and rigid embeddings, ManifoldMind represents users, items, and tags as adaptive-curvature probabilistic spheres, enabling personalised uncertainty modeling and geometry-aware semantic exploration. A curvature-aware semantic kernel supports soft, multi-hop inference, allowing the model to explore diverse conceptual paths instead of overfitting to shallow or direct interactions. Experiments on four public benchmarks show superior NDCG, calibration, and diversity compared to strong baselines. ManifoldMind produces explicit reasoning traces, enabling transparent, trustworthy, and exploration-driven recommendations in sparse or abstract domains.

Problem

• Dynamic hyperbolic reasoning for trustworthy recommendations
• Personalized uncertainty modeling in hyperbolic space
• Multi-hop inference for diverse conceptual exploration

Innovation

• Adaptive-curvature probabilistic spheres modeling
• Curvature-aware semantic kernel for multi-hop inference
• Explicit reasoning traces for transparent recommendations