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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2512.19086 |
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| _version_ | 1866908727462854656 |
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| author | Chae, Byung Gyu |
| author_facet | Chae, Byung Gyu |
| contents | Reentrant computation-recursive self-coupling in which a network continuously reinjects and reinterprets its own internal state-plays a central role in biological cognition but remains poorly characterized in neural network architectures. We introduce a minimal continuous-time formulation of a homeostatically regulated reentrant network (FHRN) and show that its population dynamics admit an exact reduction to a one-dimensional radial flow. This reduction reveals a dynamically fixed threshold for sustained reflective activity and enables a complete renormalization-group (RG) analysis of the reentry-homeostasis interaction. We derive a closed RG system for the parameters governing structural gain, homeostatic stiffness, and reentrant amplification, and show that all trajectories are attracted to a critical surface defined by $γρ=1$, where intrinsic leak and reentrant drive exactly balance. The resulting phase structure comprises quenched, reactive, and reflective regimes and exhibits a mean-field critical onset with universal scaling. Our results provide an RG-theoretic characterization of reflective computation and demonstrate how homeostatic fields stabilize deep reentrant transformations through scale-dependent self-regulation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19086 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Renormalization-Group Geometry of Homeostatically Regulated Reentry Networks Chae, Byung Gyu Computational Physics Reentrant computation-recursive self-coupling in which a network continuously reinjects and reinterprets its own internal state-plays a central role in biological cognition but remains poorly characterized in neural network architectures. We introduce a minimal continuous-time formulation of a homeostatically regulated reentrant network (FHRN) and show that its population dynamics admit an exact reduction to a one-dimensional radial flow. This reduction reveals a dynamically fixed threshold for sustained reflective activity and enables a complete renormalization-group (RG) analysis of the reentry-homeostasis interaction. We derive a closed RG system for the parameters governing structural gain, homeostatic stiffness, and reentrant amplification, and show that all trajectories are attracted to a critical surface defined by $γρ=1$, where intrinsic leak and reentrant drive exactly balance. The resulting phase structure comprises quenched, reactive, and reflective regimes and exhibits a mean-field critical onset with universal scaling. Our results provide an RG-theoretic characterization of reflective computation and demonstrate how homeostatic fields stabilize deep reentrant transformations through scale-dependent self-regulation. |
| title | Renormalization-Group Geometry of Homeostatically Regulated Reentry Networks |
| topic | Computational Physics |
| url | https://arxiv.org/abs/2512.19086 |