# PersonaManifold: Revealing and Exploiting Curved Geometry in LLM Persona Representations

arXiv: https://arxiv.org/abs/2609.34571 · HTML: https://mlsanity.com/paper/2609.34571/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 36 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Builds on (most cited first, 17 of 17)

- [How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddings](https://mlsanity.com/paper/1909.00512/) (2019)
- [Scaling Synthetic Data Creation with 1,000,000,000 Personas](https://mlsanity.com/paper/2406.20094/) (2024)
- [Persona Vectors: Monitoring and Controlling Character Traits in Language Models](https://mlsanity.com/paper/2507.21509/) (2025)
- [InCharacter: Evaluating Personality Fidelity in Role-Playing Agents through Psychological Interviews](https://mlsanity.com/paper/2310.17976/) (2023)
- [Riemannian Continuous Normalizing Flows](https://mlsanity.com/paper/2006.10605/) (2020)
- [PersonaGym: Evaluating Persona Agents and LLMs](https://mlsanity.com/paper/2407.18416/) (2024)
- [Community Detection on Networks with Ricci Flow](https://mlsanity.com/paper/1907.03993/) (2019)
- [Consistently Simulating Human Personas with Multi-Turn Reinforcement Learning](https://mlsanity.com/paper/2511.00222/) (2025)
- [Evaluating Character Understanding of Large Language Models via Character Profiling from Fictional Works](https://mlsanity.com/paper/2404.12726/) (2024)
- [The Personality Illusion: Revealing Dissociation Between Self-Reports & Behavior in LLMs](https://mlsanity.com/paper/2509.03730/) (2025)
- [Character is Destiny: Can Role-Playing Language Agents Make Persona-Driven Decisions?](https://mlsanity.com/paper/2404.12138/) (2024)
- [Capturing Minds, Not Just Words: Enhancing Role-Playing Language Models with Personality-Indicative Data](https://mlsanity.com/paper/2406.18921/) (2024)
- [Personality Vector: Modulating Personality of Large Language Models by Model Merging](https://mlsanity.com/paper/2509.19727/) (2025)
- [PERSONA: Dynamic and Compositional Inference-Time Personality Control via Activation Vector Algebra](https://mlsanity.com/paper/2602.15669/) (2026)
- [MINDECHO: Role-Playing Language Agents for Key Opinion Leaders](https://mlsanity.com/paper/2407.05305/) (2024)
- [Dissecting Persona-Driven Reasoning in Language Models via Activation Patching](https://mlsanity.com/paper/2507.20936/) (2025)
- [Your Language Model Secretly Contains Personality Subnetworks](https://mlsanity.com/paper/2602.07164/) (2026)

## Abstract (arXiv)

Controlling persona in large language models (LLMs) at inference time is important for role-playing, personalized dialogue, and social simulation. Recent methods extract persona vectors from the model's activation space and apply Euclidean operations---addition, scaling, and linear interpolation---under the linear representation hypothesis. However, these methods themselves report systematic failures: non-orthogonal trait dimensions, asymmetric ceiling and resistance effects, and significant deviations in multi-trait composition, suggesting that the linear isotropic assumption does not hold. We propose PersonaManifold, a framework that models persona representations as points on a curved, low-dimensional Riemannian submanifold in activation space. We estimate the manifold's intrinsic geometry---local metric tensors, geodesic distances, and Ollivier-Ricci curvature---and introduce geodesic steering, which interpolates between personas along manifold geodesics rather than Euclidean straight lines. We also propose the Behavioral Similarity Triplet (BST) benchmark, which automatically generates situational questions grounded in six established psychological constructs and defines persona similarity through behavioral responses rather than self-report questionnaires. Experiments on three open-source LLMs show that persona activations form a manifold with heterogeneous curvature, geodesic distance predicts behavioral similarity more accurately than Euclidean alternatives with independent contributions from anisotropy and curvature, and geodesic steering produces more coherent intermediate personas on both our BST benchmark and external evaluations, with the advantage concentrated in high-deviation regions where the manifold deviates most from flatness.