True and false statements are encoded asymmetrically, and LLM internal representations carry a third region distinct from both truth and falsehood
measured in 1 paper- Savcisens & Eliassi-Rad introduce sAwMIL, a multiclass probing framework (multiple-instance learning plus conformal prediction) that classifies statements as true, false, or neither directly from real LLMs' internal representations, and evaluate it across 16 real open-source LLMs (default and chat/instruct variants of Gemma, Gemma-2, Llama-3/3.1/3.2, two medical Llama-3 fine-tunes (Llama3-Med42-8B, Bio-Medical-Llama-3-8B), Mistral-7B-v0.3, and Qwen2.5-7B/14B). [savcisens-eliassi-rad-2026-trilemma-of-truth] - The learned is-true and is-false probe directions are not mirror images: their cosine similarity is not near -1 (Fig. 3), and the 2-column matrix of the two directions has rank 2 with effective rank 1.93 (sAwMIL) and 1.73 (multiclass SVM), which the authors read as the two directions spanning a low-dimensional subspace rather than one bidirectional truth axis. [savcisens-eliassi-rad-2026-trilemma-of-truth] - The authors also train an is-neither probe and conclude that, across the 16 models and three datasets, LLMs encode a third type of signal distinct from true and false; the 'neither' class is built from statements about synthetic entities (a proxy the authors flag as needing further validation), and all probes are linear. [savcisens-eliassi-rad-2026-trilemma-of-truth]