Title: SHADE: Spectral Hallucination Detection via Dual Spectral Decompositions
Primary area: alignment, fairness, safety, privacy, and societal considerations
Keywords: hallucination detection, spectral graph analysis, alignment, AI safety

Abstract: Large language models often produce confident but unsupported statements.
Detecting such hallucinations from internal signals is essential for reliable
systems. Existing attention-based methods either summarize weights with local
statistics or adopt Laplacians (e.g., \(D_{\text{out}}-A\)) whose guarantees and
applicability break outside strictly causal, square attention. We seek a single,
rigorous framework that scales across architectures and attention types while
yielding interpretable indicators of grounding. We introduce \textsc{SHADE}, a
unified spectral approach that models attention with two standard operators: (i)
a random-walk operator \(L_{\mathrm{rw}}=I-A\) that quantifies
diffusion/leakiness, and (ii) a degree-normalized cross-operator
\(M=D_Q^{-1/2}AD_K^{-1/2}\) that quantifies query--key coupling. The resulting
features are mathematically rigorous and physically interpretable, with clear
operator semantics that map to failure modes associated with hallucination:
\emph{diffusion} (from \(L_{\mathrm{rw}}\)) quantifies probability leakiness;
\emph{conductance} (via a symmetric/PSD Laplacian, e.g., Chung's) captures
expansion/connectedness; and \emph{energy/alignment strength} (from the SVD of
\(M\)) quantify total coupling and the dominance or fragmentation of coupling
modes. The formulation applies unchanged to encoder, decoder, and
encoder--decoder settings, including rectangular cross-attention and masked
sub-blocks. Evaluated on GPT-2, FLAN-T5, and Phi-2 across HaluEval and
TruthfulQA, \textsc{SHADE} consistently surpasses token-probability and
LapEigvals-style baselines, delivering strong discrimination and calibration
alongside interpretable spectra. By grounding hallucination detection in
standard spectral operators with physically meaningful interpretations,
\textsc{SHADE} offers an explanatory basis for \emph{where} and \emph{how}
hallucinations originate. This suggests two practical avenues: (i) training-time
regularization to suppress emergent hallucinatory patterns, and (ii) a
deployable \emph{hallucination risk score} with mode-level rationales (by
layer/head and prompt span) that end users and developers can act on.

TL;DR: We present a general spectral framework for hallucination detection that transcends architectural boundaries, unifying directed and bipartite spectral analyses to expose complementary attention failures in any transformer configuration.