Derived Coefficients Interpretation Method

Modern AI systems remain powerful yet brittle: they perform im-pressively on benchmarks but struggle to sustain coherent, efficient, and safe long-term interaction with users. This work introduces the De-rived Coefficients Interpretation Method (DCIM), a quantum-inspired ramework that models each human–AI exchange as a trajectory through a structured conversational landscape rather than a flat series of text prompts. In DCIM, every dialogue is expressed as a state expanded in a low-dimensional basis of conversational operators, whose coefficients capture evolving intent, uncertainty, and salience across turns. Updating these coefficients dynamically—analogous to wavefunction evolution—DCIM allows the system to represent superposed or ambiguous user states while maintaining explicit safety constraints and resource-allocation rules at the protocol level. This approach provides a mathematically grounded method for managing contextual drift, identifying risk-relevant signals, and improving interpretability in complex interactions. Although developed for conversational AI, DCIM’s landscape-based formalism generalizes to any human–machine interface where states, updates, and constraints can be represented in a Hilbert-like structure.