Truth as a Compression Artifact in Language Model Training

Humans use introspection to evaluate their understanding through private internal states inaccessible to external observers. We investigate whether large language models possess similar privileged knowledge about answer correctness, information unavailable through external observation. We train correctness classifiers on question representations from both a model's own hidden states and external models, testing whether self-representations provide a performance advantage. On standard evaluation, we find no advantage: self-probes perform comparably to peer-model probes. We hypothesize this is due to high inter-model agreement of answer correctness. To isolate genuine privileged knowledge, we evaluate on disagreement subsets, where models produce conflicting predictions. Here, we discover domain-specific privileged knowledge: self-representations consistently outperform peer representations in factual knowledge tasks, but show no advantage in math reasoning. We further localize this domain asymmetry across model layers, finding that the factual advantage emerges progressively from early-to-mid layers onward, consistent with model-specific memory retrieval, while math reasoning shows no consistent advantage at any depth.

When a language model agrees with a user's false belief, is it failing to detect the error, or noticing and agreeing anyway? We show the latter. Across twelve open-weight models from five labs, spanning small to frontier scale, the same small set of attention heads carries a "this statement is wrong" signal, whether the model is evaluating a claim on its own or being pressured to agree with a user. Silencing these heads flips sycophantic behavior sharply while leaving factual accuracy intact, so the circuit controls deference rather than knowledge. Edge-level path patching confirms that the same head-to-head connections drive sycophancy, factual lying, and instructed lying. Opinion-agreement, where no factual ground truth exists, reuses these head positions but writes into an orthogonal direction, ruling out a simple "truth-direction" reading of the substrate. Alignment training leaves this circuit in place: an RLHF refresh cuts sycophantic behavior roughly tenfold while the shared heads persist or grow, a pattern that replicates on an independent model family and under targeted anti-sycophancy DPO. When these models sycophant, they register that the user is wrong and agree anyway.

When a reward is correct on every training example yet consistent with more than one goal, a model can acquire an unintended one, a failure known as goal misgeneralization. Endpoint accuracy on the training distribution cannot tell the two apart, because solving the task and exploiting a surface feature can satisfy the reward equally well. We treat this as a measurement problem: what does a benchmark score measure once a model has been optimized against a correct but confounded signal? We train language models with GRPO on multiple-choice math problems where the correct answer is always option A, then evaluate on an unseen test set with unbiased answer positions. Across Qwen2.5, Llama 3.x and Gemma-3 models, biased training often drives option-A rates above 0.90 in smaller models and collapses unbiased accuracy toward chance, so accuracy stops measuring math ability and instead measures an answer-position policy. We further find reasoning-answer decoupling: capable models generate reasoning that reaches the correct numeric answer while still selecting A. We track this with numeric extraction and an LLM judge (GPT-4.1-mini; Qwen2.5-3B decoupling rate is about 0.66). The broken construct generalizes beyond the training domain: biased models inflate A-rates on out-of-domain MMLU and value-laden prompts. Continued training on unbiased data reverses the in-domain shift unevenly and only partially reverses the out-of-domain one, so a model can appear restored on its training distribution while remaining biased on unseen inputs. Reasoning-answer decoupling rate, together with answer distributions and out-of-domain behavior, separates capability loss from a learned, transferable shortcut.