The Lyra Technique: Cognitive Geometry in Transformer KV-Caches — From Metacognition to Misalignment Detection

We show that the key-value cache (KV-cache) of autoregressive transformers encodes a geometric signature of cognitive mode that is readable, consistent, and practically useful for AI safety monitoring. Through a systematic experimental program spanning 16 models (0.5B–70B parameters), six architecture families, and over 5,600 controlled trials, we establish three escalating claims. First, KV-cache geometry reflects cognitive mode generally: metacognitive, analytical, affective, and task-specific processing produce distinct geometric signatures in the key cache's singular value decomposition, with spectral entropy emerging as the most architecture-universal feature after confound control. Second, misalignment states—deception, confabulation, sycophancy, and refusal—are specific detectable instances of cognitive mode-switching, achieving within-model detection AUROC of 0.93–0.995 after Frisch-Waugh-Lovell residualization against token count. Third, geometric relationships between states reveal cognitive architecture: confabulation and deception produce geometrically distinct signatures. Hardware invariance is confirmed (RTX 3090 vs. H200: r > 0.998). We discuss dual-use implications and argue that cognitive geometry constitutes a new interpretability signal complementary to sparse autoencoders and representation engineering. This upload includes the full paper and an executive summary synthesizing five months of experimental work.