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The paper introduces and validates the "truthfulness spectrum hypothesis," which posits that LLM representational spaces contain truth directions ranging from domain-general to domain-specific. They systematically evaluate probe generalization across five truth types, sycophantic/expectation-inverted lying, and honesty benchmarks, finding that linear probes generalize well across most domains but fail on specific types of lying. By analyzing probe geometry and using concept-erasure methods, the authors identify and characterize domain-general, domain-specific, and subset-specific truth directions, and demonstrate that domain-specific directions are more effective for causal steering, while post-training reshapes truth geometry, potentially contributing to sycophancy.
LLMs encode truthfulness along a spectrum from general principles to narrow domain expertise, and exploiting domain-specific truth representations is key to steering model behavior.
Large language models (LLMs) have been reported to linearly encode truthfulness, yet recent work questions this finding's generality. We reconcile these views with the truthfulness spectrum hypothesis: the representational space contains directions ranging from broadly domain-general to narrowly domain-specific. To test this hypothesis, we systematically evaluate probe generalization across five truth types (definitional, empirical, logical, fictional, and ethical), sycophantic and expectation-inverted lying, and existing honesty benchmarks. Linear probes generalize well across most domains but fail on sycophantic and expectation-inverted lying. Yet training on all domains jointly recovers strong performance, confirming that domain-general directions exist despite poor pairwise transfer. The geometry of probe directions explains these patterns: Mahalanobis cosine similarity between probes near-perfectly predicts cross-domain generalization (R^2=0.98). Concept-erasure methods further isolate truth directions that are (1) domain-general, (2) domain-specific, or (3) shared only across particular domain subsets. Causal interventions reveal that domain-specific directions steer more effectively than domain-general ones. Finally, post-training reshapes truth geometry, pushing sycophantic lying further from other truth types, suggesting a representational basis for chat models'sycophantic tendencies. Together, our results support the truthfulness spectrum hypothesis: truth directions of varying generality coexist in representational space, with post-training reshaping their geometry. Code for all experiments is provided in https://github.com/zfying/truth_spec.
