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

arXiv: https://arxiv.org/abs/2610.00656 · HTML: https://mlsanity.com/paper/2610.00656/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 30 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Builds on (most cited first, 24 of 24)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Extracting Training Data from Large Language Models](https://mlsanity.com/paper/2012.07805/) (2020)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [Representation Engineering: A Top-Down Approach to AI Transparency](https://mlsanity.com/paper/2310.01405/) (2023)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Qwen2.5-Coder Technical Report](https://mlsanity.com/paper/2409.12186/) (2024)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [Probing Classifiers: Promises, Shortcomings, and Advances](https://mlsanity.com/paper/2102.12452/) (2021)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [Designing and Interpreting Probes with Control Tasks](https://mlsanity.com/paper/1909.03368/) (2019)
- [Gemma Scope: Open Sparse Autoencoders Everywhere All At Once on Gemma 2](https://mlsanity.com/paper/2408.05147/) (2024)
- [INSIDE: LLMs' Internal States Retain the Power of Hallucination Detection](https://mlsanity.com/paper/2402.03744/) (2024)
- [Scaling Monosemanticity: Extracting Interpretable Features from Claude 3 Sonnet](https://mlsanity.com/paper/2605.29358/) (2026)
- [OpenCoder: The Open Cookbook for Top-Tier Code Large Language Models](https://mlsanity.com/paper/2411.04905/) (2024)
- [LLM Internal States Reveal Hallucination Risk Faced With a Query](https://mlsanity.com/paper/2407.03282/) (2024)
- [The LLM Already Knows: Estimating LLM-Perceived Question Difficulty via Hidden Representations](https://mlsanity.com/paper/2509.12886/) (2025)
- [FastCAV: Efficient Computation of Concept Activation Vectors for Explaining Deep Neural Networks](https://mlsanity.com/paper/2505.17883/) (2025)

## Abstract (arXiv)

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.