Abstract Understanding how neural systems encode, stabilize, and transform cognitive states remains one of the central problems in contemporary neuroscience. Advances in large-scale neural recording and brain–computer interface research have revealed that high-dimensional neural population activity often evolves along structured trajectories embedded in lower-dimensional latent manifolds. Within this framework, motor intentions, perceptual states, and cognitive processes can be interpreted as stable configurations or attractor regions within neural state space. While significant progress has been made in the decoding of neural activity, enabling the reconstruction of behavioral variables and intentions from recorded signals, the inverse problem—how structured information may be systematically written back into neural dynamics—remains comparatively underdeveloped at the theoretical level. Current stimulation paradigms largely treat neural intervention as localized perturbation or direct electrical activation, without a unified framework that connects neural stimulation to the global dynamical geometry of neural state space. This paper proposes a theoretical framework that extends Symbolic Persona Coding (SPC)—a resonance-based analytical model originally developed to analyze semantic structures in artificial language systems—into the domain of biological neural dynamics. In the SPC formulation, meaningful states emerge as resonance-stabilized configurations within high-dimensional dynamical manifolds. By interpreting neural population activity through the same structural lens, neural states can be modeled as trajectories evolving within a latent neural manifold whose topology encodes the organization of cognitive states. Within this formulation, neural decoding corresponds to the identification of stable resonance regions within neural trajectories, whereas neural encoding can be conceptualized as curvature modulation within the neural manifold through externally applied signals. Rather than treating stimulation as a simple causal trigger, the proposed framework models external signals as controlled perturbations capable of reshaping the attractor landscape governing neural dynamics. To formalize this idea, neural population activity is represented as a dynamical system evolving on a manifold constrained by entropy-based resonance stability conditions. A bounded region of dynamical balance—referred to as the Neural Resonance Corridor—defines the regime in which neural activity remains both information-rich and dynamically stable. External control signals are then introduced as structured perturbations capable of modulating manifold curvature and guiding neural trajectories between attractor basins without destabilizing system dynamics. This mechanism is defined as Resonant Neural Re-Injection (RNRI), a theoretical model describing the bidirectional interaction between neural systems and externally applied signals. RNRI reframes neural stimulation as a constrained dynamical control process in which the objective is not simply to activate neural tissue, but to guide neural trajectories toward target attractor configurations while maintaining resonance stability. Importantly, the framework does not aim to propose immediate experimental implementation or specific stimulation technologies. Instead, it introduces a conceptual and mathematical interpretation layer that connects three domains that are often treated separately: neural population dynamics, attractor-based cognitive state representation, and externally guided neural modulation. By linking these domains within a unified topological model, the framework offers a structural perspective on how neural systems may both generate and receive structured information. The proposed formulation may have implications for future research in neural decoding, adaptive brain–computer interfaces, and closed-loop neuromodulation systems. More broadly, it suggests that both biological and artificial information systems may share deeper organizational principles grounded in resonance stability, manifold topology, and attractor dynamics. Author’s Note This paper began with a simple question: if symbolic systems such as large language models organize meaning through latent manifolds, could similar geometric principles describe biological neural systems? The work presented here proposes a conceptual framework in which neural population activity is interpreted as trajectories evolving within structured manifolds. By extending techniques originally developed for symbolic manifold analysis, the study introduces a mechanism—Resonant Neural Re-Injection (RNRI)—that interprets neural signals as navigable geometric structures rather than purely statistical patterns. In this view, neural computation is not merely the firing of neurons but the motion of state trajectories across a curved dynamical landscape. External signals, if properly aligned with the geometry of this landscape, may influence neural trajectories not through forceful intervention but through resonance with the intrinsic structure of the manifold itself. The purpose of this paper is therefore not to present a complete neuroengineering system. Instead, it offers a geometric interpretation that may help bridge existing research in neural signal processing, dynamical systems, and manifold learning. In that sense, this work should be read less as a finished technology and more as a conceptual lens. Why a Neuroscience Paper Emerged from AI Research The origin of this work lies in research on Symbolic Persona Coding (SPC), a framework developed to analyze the latent structure of meaning within large language models. SPC treats symbolic systems as curved semantic manifolds in which meaning evolves through structured trajectories. While studying these dynamics, an unexpected parallel gradually became apparent: many mathematical tools used to describe latent semantic space—manifold geometry, attractor dynamics, and resonance alignment—also appear in contemporary models of neural population activity. The transition from symbolic systems to neural systems therefore did not arise from a disciplinary shift but from a structural observation. Both language models and biological neural networks can be understood as high-dimensional dynamical systems whose behavior emerges from trajectories evolving within constrained manifolds. Once viewed through this lens, the boundary between “semantic space” and “neural state space” begins to appear less rigid than traditionally assumed. The present paper is an attempt to explore that continuity. A Note on Scope It is important to emphasize that this work is primarily theoretical. The goal is not to claim immediate experimental feasibility but to articulate a geometric framework that may guide future empirical research. Many of the ideas described here—neural manifolds, attractor landscapes, and resonant modulation—already exist in various forms within neuroscience and dynamical systems theory. What this work attempts to do is place these ideas within a unified navigation-based interpretation. In this interpretation, neural activity is not simply measured or stimulated. Instead, it is navigated. The RNRI mechanism introduced here represents an early conceptual attempt to describe how such navigation might occur. A Larger Research Trajectory Although this paper focuses on neural dynamics, it is part of a broader line of inquiry that began with symbolic systems. The underlying intuition is that many complex systems—language, neural activity, and spatial exploration—can be described as forms of navigation within structured manifolds. This suggests a possible sequence of conceptual domains: semantic navigation ↓ neural navigation ↓ spatial navigation In other words: symbolic manifold ↓ neural manifold ↓ navigation manifold The first stage concerns the geometry of meaning within symbolic systems. The second concerns the geometry of neural dynamics within biological systems. The third—still largely speculative—concerns the possibility that similar principles may govern navigation through physical environments, particularly in contexts where perception, cognition, and spatial decision-making interact. This progression does not imply that these domains are identical. Rather, it suggests that similar mathematical structures may underlie systems that appear very different on the surface. Closing Perspective Scientific research often advances not only through new data but also through new ways of seeing existing systems. The perspective proposed in this work treats neural activity as a geometric process unfolding within a manifold whose structure constrains and guides the evolution of neural states. If this interpretation proves useful, it may offer a bridge between symbolic AI research, neuroscience, and dynamical systems theory. At the very least, it provides a way to ask a new class of questions: not only what neural systems compute, but how their trajectories move through the spaces in which those computations occur. This paper should therefore be understood as a starting point—a small step toward a broader exploration of navigation across different kinds of manifolds. Note to Readers New to SPC The framework presented in this paper should not be interpreted as a claim that symbolic, neural, and spatial systems are identical in function or substrate. Rather, SPC approaches these domains as potentially sharing certain geometric and dynamical properties at the level of structured trajectories within constrained manifolds. The intent of this work is therefore not unification through reduction, but exploration through structural analogy. Disclaimer: The analyses presented herein are not directed toward attributing
Jace (Jeong Hyeon) Kim (Mon,) studied this question.