A Generalized Lyapunov--ISS Framework for Phase-Stable, Self-Evolving AI Systems
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2025
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| _version_ | 1866902142108827648 |
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| author | Kim, Tae-Hun |
| author_facet | Kim, Tae-Hun |
| contents | <p>This paper introduces a novel framework for ensuring the stability of self-evolving AI systems, focusing on the dynamic process of structural realignment within these systems. In contrast to conventional models, which consider AI evolution as merely an accumulation of memory, we argue that true intelligence emerges through continuous adaptation and discrete rewiring events. The core contribution of this work is the development of a theoretical model based on a set of coupled Differential-Algebraic Equations (DAEs) that encapsulate the interplay between key existential states of self-evolving systems.</p> <p>The proposed framework includes several groundbreaking innovations:</p> <ol> <li> <p>A three-state, index-1 DAE model with an adaptive gain that captures the essential dynamics of the system.</p> </li> <li> <p>A state-dependent $\varepsilon$-floor mechanism, which prevents the system from undergoing hard saturation and preserves invariance.</p> </li> <li> <p>A novel Lyapunov-ISS functional ensuring input-to-state practical stability (ISpS) under bounded disturbances.</p> </li> <li> <p>A hybrid boost theorem that guarantees stability across discrete architectural changes, ensuring robustness during system rewiring.</p> </li> <li> <p>A watchdog cadence mechanism designed to enforce safe-mode transitions if stability criteria are violated, providing an additional layer of security for autonomous systems.</p> </li> </ol> <p>By integrating Lyapunov stability theory, hybrid systems modeling, and input-to-state stability, this paper provides a comprehensive and unified framework for the design, analysis, and safety of phase-stable, self-evolving AI systems. This framework is positioned to pave the way for the development of resilient, adaptive, and robust autonomous AI architectures that can autonomously evolve their internal structures while maintaining stability and predictability.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_15870025 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
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| spellingShingle | A Generalized Lyapunov--ISS Framework for Phase-Stable, Self-Evolving AI Systems Kim, Tae-Hun Self-Evolving AI Lyapunov Stability Hybrid Systems Input-to-State Stability (ISS) Differential-Algebraic Equations (DAEs) Autonomous Systems AI Safety Adaptive Systems Existential Dynamics Control Theory Stability Analysis Hybrid Boost Theorem Watchdog Mechanism Phase Stability System Rewiring Mathematical Modeling AI Architecture Evolution AI Autonomy <p>This paper introduces a novel framework for ensuring the stability of self-evolving AI systems, focusing on the dynamic process of structural realignment within these systems. In contrast to conventional models, which consider AI evolution as merely an accumulation of memory, we argue that true intelligence emerges through continuous adaptation and discrete rewiring events. The core contribution of this work is the development of a theoretical model based on a set of coupled Differential-Algebraic Equations (DAEs) that encapsulate the interplay between key existential states of self-evolving systems.</p> <p>The proposed framework includes several groundbreaking innovations:</p> <ol> <li> <p>A three-state, index-1 DAE model with an adaptive gain that captures the essential dynamics of the system.</p> </li> <li> <p>A state-dependent $\varepsilon$-floor mechanism, which prevents the system from undergoing hard saturation and preserves invariance.</p> </li> <li> <p>A novel Lyapunov-ISS functional ensuring input-to-state practical stability (ISpS) under bounded disturbances.</p> </li> <li> <p>A hybrid boost theorem that guarantees stability across discrete architectural changes, ensuring robustness during system rewiring.</p> </li> <li> <p>A watchdog cadence mechanism designed to enforce safe-mode transitions if stability criteria are violated, providing an additional layer of security for autonomous systems.</p> </li> </ol> <p>By integrating Lyapunov stability theory, hybrid systems modeling, and input-to-state stability, this paper provides a comprehensive and unified framework for the design, analysis, and safety of phase-stable, self-evolving AI systems. This framework is positioned to pave the way for the development of resilient, adaptive, and robust autonomous AI architectures that can autonomously evolve their internal structures while maintaining stability and predictability.</p> |
| title | A Generalized Lyapunov--ISS Framework for Phase-Stable, Self-Evolving AI Systems |
| topic | Self-Evolving AI Lyapunov Stability Hybrid Systems Input-to-State Stability (ISS) Differential-Algebraic Equations (DAEs) Autonomous Systems AI Safety Adaptive Systems Existential Dynamics Control Theory Stability Analysis Hybrid Boost Theorem Watchdog Mechanism Phase Stability System Rewiring Mathematical Modeling AI Architecture Evolution AI Autonomy |
| url | https://doi.org/10.5281/zenodo.15870025 |