Lingtai: What Concept Geometry Reveals--and Does Not Reveal--About LLM Inference

Abstract:Observing what a large language model computes during autoregressive inference--online and without training probes--remains difficult. We introduce Lingtai, a training-free concept telemetry layer: at each generation step, residual states are projected onto a domain-specific bank of named concept anchors, constructed without labeled concept examples, outcome labels, gradient fitting, or activation-space optimization, producing a structured per-step concept-coordinate signal. Across code generation and grade-school mathematical reasoning, this signal exhibits a robust association with predictive uncertainty: the association survives problem-identity and token-position controls and is not attributable to a single token type, is not explained by a simple correct/incorrect mixture on GSM8K, and is not reproduced by matched random anchors; it is markedly weaker or direction-inconsistent in K-means and PCA projections. Two structures emerge: a recurring uncertainty-linked activity signal whose functional geometry is task-conditioned (distinct activity-entropy shapes on HumanEval, MBPP, and GSM8K), and an execution-specific trajectory identity with strong local inertia but weak re-instantiation invariance--under completion-only elastic alignment, corruption at k=32 (approximately a median quarter of the completion) on the matched re-execution subset still retrieves the archived episode at 62.0%, while a fresh execution retrieves it only 11.7-16.0% of the time. Finally, a matched audit finds no evidence that the scalar concept-activity signal used here supplies a stable correctness coordinate under the tested protocol; we therefore treat correctness as externally supplied. Telemetry adds 0.7-1.6% per-token decode overhead for the 161-anchor code implementation, with unchanged generated tokens.

15 pages, 4 figures, 7 tables. An earlier version was publicly released on Zenodo (DOI: https://doi.org/10.5281/zenodo.23068698)

Computation and Language (cs.CL)

arXiv:2610.00656 [cs.CL]

(or arXiv:2610.00656v1 [cs.CL] for this version)

https://doi.org/10.48550/arXiv.2610.00656 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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