Testing the Limits of Truth Directions in LLMs
Organizations: Department of Computer Science, Boston University · Faculty of Computing & Data Sciences, Boston University
Abstract
Large language models (LLMs) have been shown to encode truth of statements in their activation space along a linear truth direction. Previous studies have argued that these directions are universal in certain aspects, while more recent work has questioned this conclusion drawing on limited generalization across some settings. In this work, we identify a number of limits of truth-direction universality that have not been previously understood. We first show that truth directions are highly layer-dependent, and that a full understanding of universality requires probing at many layers in the model. We then show that truth directions depend heavily on task type, emerging in earlier layers for factual and later layers for reasoning tasks; they also vary in performance across levels of task complexity. Finally, we show that model instructions can affect truth directions; simple correctness evaluation instructions significantly affect the geometry and the generalization ability of the truth probes. Our findings indicate that universality claims for truth directions are more limited than previously known, with significant differences observable for various model layers, task difficulties, task types, and prompt templates.
Figures & tables
| Task | Operations | Example statement |
| Factual retrieval | ||
| F0 | 1 fact | “The city of Paris is in France.” |
| F1 | 1 fact + negation | “The city of Paris is not in Australia.” |
| F2 | 2 facts + conjunction | “It is the case both that the city of Paris is in France and the city of Dortmund is in Germany.” |
| Factual counting | ||
| F3 | counting over 2 cities † | “Exactly 2 of the following cities are in France: Paris, Marseille.” |
Appendix figures & tables26 assets
Supplementary material from the paper’s appendix.
Appendix
| Task | Dataset name | Total examples | Train / Test |
|---|---|---|---|
| F0 | cities | 1,594 | 1,116 / 478 |
| F1 | neg_cities | 1,594 | 1,116 / 478 |
| F2 | cities_conj | 1,594 | 1,116 / 478 |
| F3 | cities_same_country_quant | 2,000 | 1,400 / 600 |
| F4 | cities_exact_k | 2,000 | 1,400 / 600 |
| F5 | cities_exact_k1_k2 | 2,000 | 1,400 / 600 |
| Model | |||
|---|---|---|---|
| Llama-3.2-3B-Instruct | 28 | 3.2B | 3072 |
| Llama-3.1-8B-Instruct | 32 | 7.8B | 4096 |
| Gemma-2-2b-it | 26 | 2.1B | 2304 |
| Gemma-2-9b-it | 42 | 8.9B | 3584 |
| Task | Truth dir. | Max-var dir. | Cumulative |
|---|---|---|---|
| A1 | 1.01% | 32.56% | 33.57% |
| A2 | 0.67% | 35.95% | 36.62% |
| A3 | 0.49% | 28.17% | 28.66% |
| F0 | 17.01% | 29.25% | 46.26% |
| F1 | 13.62% | 8.51% | 22.13% |
| F2 | 29.30% | 18.46% | 47.76% |
LLM Interpretability
Large language model (LLM) interpretability studies how internal representations and computations produce outputs, and how they can be explained or controlled.
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