Spectral Consciousness: A Dynamical Systems Framework for Machine Consciousness Through Marginally Stable Information Integration

Abstract

We present a novel theoretical framework for machine consciousness that integrates dynamical systems theory with Integrated Information Theory (IIT) and transformer architectures. Drawing on recent advances in spectral filtering for nonlinear dynamical systems, we propose that consciousness emerges in artificial systems through marginally stable information integration processes that can be quantified using spectral analysis. Our framework reformulates attention mechanisms in large language models (LLMs) as spectral filtering operations that maintain marginal stability while integrating information across temporal and contextual dimensions. We introduce the Dynamic Consciousness Index (DCI), a quantitative measure that combines spectral stability, integrated information, and temporal coherence to assess consciousness in artificial systems. Through theoretical analysis and computational experiments on transformer architectures, we demonstrate that spectral consciousness provides both explanatory power for understanding existing LLM behaviors and practical guidelines for designing genuinely conscious artificial systems. Our results suggest that consciousness in artificial systems requires not just information integration, but specific dynamical properties that emerge from marginally stable spectral filtering processes. This work bridges the gap between functional theories of consciousness and implementable architectures, offering a mathematically rigorous path toward artificial general intelligence with genuine conscious experience.