An Exploratory Framework for Online Detection of Semantic Trajectory Shifts in Embedding Dynamics

As the context windows of language models continue to expand, monitoring the temporal consistency of sequential text generation has become a critical operational requirement. Existing methods for detecting topic divergence or semantic drift typically rely on strictly Markovian, step-to-step cosine similarity, which often fails to capture gradual, long-range semantic shifts. This paper introduces an exploratory framework utilizing a continuity-sensitive nonlocal functional (Φ). By incorporating a memory-weighting mechanism, the Φ-functional evaluates current embedding states against historical trajectory distributions, penalizing cumulative divergence rather than isolated anomalies. We evaluate this approach using a synthetically generated benchmark comprising coherent and drifting semantic trajectories. The proposed functional is compared against standard anomaly detection baselines, including moving variance, naive cosine thresholds, and cumulative sum (CUSUM), utilizing detection latency and F1-score as primary metrics. While initial synthetic results suggest that nonlocal memory improves early shift detection, we explicitly outline the geometric limitations of embedding spaces, the reliance on heuristic thresholding, and the critical necessity for future validation on organic, real-world conversational datasets.