Phase Potential Landscape in LLM Latent Spaces: A Structural Hypothesis for Concept Direction Formation

Recent work by Radhakrishnan et al. (Science, 2026; doi:10.1126/science.aea6792) demonstrated that large language models encode abstract concepts — from persona types to normative dispositions — as identifiable and steerable directions in latent representation space. Their Recursive Feature Machine (RFM) framework successfully extracted and modulated over 500 concept directions across multiple categories. The present work addresses a complementary structural question: why do these particular concept directions form and stabilize as structured features of latent space geometry? We propose a structural hypothesis: concept directions arise as compression equilibria of persistent representational tensions embedded in human-generated training data. These tensions — recurring structural oppositions such as normative dichotomies, authority-alignment patterns, and identity-stabilization dynamics — are not incidental biases. They are conditionally persistent outcomes of shared data-generating conditions. During training, predictive loss minimization under encoding cost constraints produces stabilized basin-like geometries. The global configuration of these equilibria constitutes what we term the Phase Potential Landscape — governed not by physical energy but by encoding cost gradients within representational compression dynamics. The hypothesis yields four empirically testable predictions: Differential Perturbation Stability — Directions rooted in long-standing representational tensions form basins with steeper curvature, resulting in non-linear resistance to sustained steering perturbations. Cross-Model Directional Recurrence — Independently trained models on overlapping corpora should exhibit structurally similar latent geometries, reflecting shared generative constraints rather than architectural identity. Coupled Directional Dynamics — Deeply stabilized concept basins may share topological boundary regions, such that perturbing one direction induces correlated shifts in adjacent directions. Structural Persistence Across Architectures — Underlying directional stabilization patterns should survive architectural variation, reflecting invariant data-level tensions rather than parameterization artifacts. Repository contents: • Phase_Potential_V1_Main.pdf — Structural hypothesis and qualitative predictions, serving as the primary self-contained reference. • Phase_Potential_V1_Geometric.pdf — Topological framing of basin stabilization, emphasizing encoding cost gradients and landscape curvature as formation mechanisms. • Phase_Potential_V1_Defensive.pdf — Defensive academic structure with formal extension notes, connecting the hypothesis to optimization dynamics and stability analysis. •Formal_Foundations_of_the_Phase_Potential_Landscape.pdf — Mathematical framework introducing information geometry, renormalization group (RG) flow, and logarithmic cost scaling. Published for timestamp purposes; refinement is ongoing. The main document is designed to be self-contained. Additional perspectives provide structured entry points for readers from different analytical backgrounds. The formal foundations document offers preliminary mathematical development for future work. Developed through multi-model collaborative refinement. Related Identifiers References: doi:10.1126/science.aea6792 (Radhakrishnan et al., "Mapping and Manipulating Concepts in Large Language Models," Science, 2026) References: doi:10.5281/zenodo.18745759 (Companion technical document — phase potential modeling) License Creative Commons Attribution 4.0 International (CC-BY-4.0)