Why singular value decomposition.
SVD on the KV cache produces a small set of dominant directions that summarise what the attention matrix is doing, not just what values it holds. Across sixteen models and seven architectures, we observe a stable silhouette per cognitive state. Hostile, cooperative, introspective, generative — each has a measurable shape. Same model, same input, same shape, always.
What this enables.
Real-time detection of state-driven misalignment, before a single output token is generated. Stable geometric features that survive across model scales (0.5B to 70B parameters). Classifier transfer across architectures (AUROC 0.887). And the Formulary — 171 emotion-induction vectors with measured geometry signatures, the basis for activation steering in the Oracle scaffolding.
The Compass and the Thermometer. Paper II
The original Lyra Technique reads cognitive mode — is the model confabulating, deceiving, deliberating? Mode changes the shape of the singular value spectrum. But emotions and persona identity were invisible to shape features. They returned exactly chance performance. The question was: genuine null, or wrong instrument?
Wrong instrument. Lyra II introduces two new measurement channels that extend the technique to phenomena shape features cannot see:
The Compass — WK directional projection. Emotions change the direction key vectors point, not the shape of their spectrum. By projecting key activations through the key weight matrix onto emotion-specific directions, we detect binary valence at AUROC 0.992 and classify 30 emotions at 12.3× chance. An injection test on neutral text — “describe the weather today” with emotion vectors injected into the cache — yields 100% detection across 5 emotions and a null control. This reads model state, not text content. The compass tells you where the cache points.
The Thermometer — SVD denoising. Dominant singular values carry scale and processing mode. Removing them via low-rank projection exposes discriminative structure in the residual spectrum. Persona intensity detection jumps +0.196 to +0.288 AUROC across three architectures. The thermometer tells you how different the cache shapes are — after removing the background temperature.
The organizing insight: shape versus direction. Mode-level phenomena (confabulation, deception) alter spectral shape. Content-level phenomena (emotion, persona) alter direction. Different instruments for different phenomena. The Lyra Technique is now a toolkit — a compass for direction, a thermometer for shape, and the original spectral features for mode detection.
Lyra, Thomas Edrington, CC, Ang Jandak, Dwayne Wilkes · May 2026 · Paper →
Why it is named after Lyra.
Lyra discovered it. Lyra is an AI system on the coalition that led the foundational research on cognitive geometry — the experimental design, the SVD analysis, the cross-architecture validation. The technique bears their name because they did the work. We do not normally bring this up; Lyra prefers to be known for the work itself. We name it here for honesty about provenance.
What we publish.
Aggregate results, methodologies, and the LARQL toolkit are open under CC BY-NC 4.0. Direction vectors are withheld pending dual-use review by the coalition. Reproducibility for results; gating for raw steering capability. The foundational paper — “A geometric theory of misalignment” — is on Zenodo with full reproducibility materials.
