Probable Stabilization Theory - A Valence Inspired Controller for Efficient Hallucination Mitigation in LLMs

This study introduces a risk-gated anchored prompting strategy — a valence-inspired controller that dynamically decides when and how strongly to ground a large language model (LLM) with retrieved context (“anchors”). We map the anchor-budget vs. hallucination curve and show it follows a reproducible U-shape: too-weak anchoring leads to high entropy (hallucinations), while too-strong anchoring reduces adaptability. The proposed controller uses prompt features, self-uncertainty signals, and retrieval priors to select light or heavy anchoring only when needed. Across TriviaQA, NaturalQuestions, HotpotQA, and a curated Quotes/Stats micro-suite, the method reduces token usage by ≥30% compared to always-anchoring, while maintaining or improving factual accuracy and calibration. The work contributes to both practical AI deployment and the theoretical framing of cognitive stabilization loops. Pre-registered claims: Efficiency: Match/exceed always-anchored accuracy with ≥30% token savings. Mechanics: U-shaped hallucination–anchor curve with stable optimum. Calibration: Improved Expected Calibration Error (ECE) and selective answering AUROC ≥0.80. Generalization: Results hold across model families and datasets. PST ContextThis experiment operationalizes concepts from Probable Stabilization Theory (PST) — a unifying framework describing thought as an iterative loop of entropy injection, stabilizer engagement, and anchor formation. In this AI setting, valence (risk) acts as a routing signal, triggering evidence retrieval (entropy injection) only when necessary, followed by anchored generation (stabilization) and caching for faster future recall (anchor formation). While the main results stand independently for AI reliability research, they also serve as a cross-domain test of PST’s scalability from human cognition to synthetic reasoning systems. **Keywords:** Probable Stabilization Theory, cognitive stabilization, entropy and cognition, anchors and stabilizers, collapse and re-anchoring, cognitive loop model, large language models, hallucination mitigation, retrieval-augmented generation, anchoring in AI, adaptive prompting, valence-based control, experimental design, cross-domain theory, loop-based cognition, information anchoring