# ManifoldMind: Dynamic Hyperbolic Reasoning for Trustworthy Recommendations

arXiv: https://arxiv.org/abs/2507.02014 · HTML: https://mlsanity.com/paper/2507.02014/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 28 references that are in the map.
- First posted on arXiv 2 Jul 2025.

## Builds on (most cited first, 13 of 13)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation](https://mlsanity.com/paper/2002.02126/) (2020)
- [Neural Collaborative Filtering](https://mlsanity.com/paper/1708.05031/) (2017)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Neural Graph Collaborative Filtering](https://mlsanity.com/paper/1905.08108/) (2019)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Self-supervised Graph Learning for Recommendation](https://mlsanity.com/paper/2010.10783/) (2020)
- [Geoopt: Riemannian Optimization in PyTorch](https://mlsanity.com/paper/2005.02819/) (2020)
- [Continuous Hierarchical Representations with Poincar'e Variational Auto-Encoders](https://mlsanity.com/paper/1901.06033/) (2019)
- [Causal Disentangled Variational Auto-Encoder for Preference Understanding in Recommendation](https://mlsanity.com/paper/2304.07922/) (2023)
- [Causal Spherical Hypergraph Networks for Modelling Social Uncertainty](https://mlsanity.com/paper/2506.17840/) (2025)
- [CSRec: Rethinking Sequential Recommendation from A Causal Perspective](https://mlsanity.com/paper/2409.05872/) (2024)
- [Actionable Interpretability via Causal Hypergraphs: Unravelling Batch Size Effects in Deep Learning](https://mlsanity.com/paper/2506.17826/) (2025)

## Built on by (most cited first, 3 of 3)

- [RicciFlowRec: A Geometric Root Cause Recommender Using Ricci Curvature on Financial Graphs](https://mlsanity.com/paper/2508.09334/) (2025)
- [From News to Returns: A Granger-Causal Hypergraph Transformer on the Sphere](https://mlsanity.com/paper/2510.04357/) (2025)
- [GLANCE: Graph Logic Attention Network with Cluster Enhancement for Heterophilous Graph Representation Learning](https://mlsanity.com/paper/2507.18521/) (2025)

## Abstract (arXiv)

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.