Linear Probes Detect Task Format, Not Reasoning Mode in Language Model Hidden States

Large language models represent the same reasoning in vastly different surface forms -- English prose, Python code, mathematical notation -- yet whether they share a common internal substrate across these symbolic systems remains unknown. We introduce the TriForm Benchmark (18 concepts x 6 forms x 3 instances = 324 stimuli) and study five LLMs (1.6B-8B) across three architecture families. Using permutation-corrected RSA, cross-form probing, and activation patching, we find converging evidence for a Format-Agnostic Reasoning Subspace (FARS) in middle layers. We make FARS concrete: concept-centroid PCA extracts a 10-dimensional subspace that amplifies concept structure 3x while suppressing form information to near zero. Replacing only these 10 dimensions during cross-form patching preserves 90-96% of model output -- far exceeding both full activation replacement (44-56%) and variance-maximizing PCA (60-74%) -- while ablating them causes targeted disruption. FARS generalizes to held-out concepts and converges across architectures (CCA > 0.79 for all model pairs), providing within-modality evidence for the Platonic Representation Hypothesis. We further discover a declarative-procedural asymmetry: representations are far more compatible between prose and mathematics than between either and code, suggesting that the critical axis of divergence is not linguistic vs. formal but declarative vs. procedural.

We investigate whether open-source LLMs encode a linearly separable truthfulness signal in their hidden states, and at which network depth this signal is strongest. Across three $7$B--$8$B instruction-tuned models (Llama-3.1-8B, Mistral-7B, Qwen2.5-7B) loaded in $4$-bit NF4 quantization, we extract per-layer hidden states on four hallucination benchmarks (TruthfulQA, HaluEval-QA, FEVER, and a controlled synthetic set) and compare four detection approaches: linear and MLP probes, INSIDE EigenScore, self-consistency, and attention entropy. A linear probe on a single mid-network layer achieves $0.904$--$1.000$ AUROC on held-out splits, while sampling-based detectors do not exceed $0.541$ AUROC under the same protocol. The truthfulness signal is approximately linear: MLP probes rarely surpass linear probes by more than $0.01$ AUROC. Peak probing layers fall in a consistent band across model families on natural-language benchmarks -- blocks~$13$--$18$ of~$32$ for Llama and Mistral, and blocks~$19$--$25$ of~$28$ for Qwen. First-block attention entropy provides a complementary signal in knowledge-grounded settings ($0.866$--$0.941$ AUROC on HaluEval-QA) at no additional inference cost. The low discriminability of sampling methods under this protocol reflects a structural mismatch between paired-label evaluation and the information these methods access, rather than an inherent limitation of those methods. Code and data are released for full reproducibility on a single $8$,GB GPU.

Large language models often answer complex reasoning questions without revealing intermediate steps, raising whether they reason latently or complete patterns. We propose the Hidden CoT Detection Score (HCDS), a comparative behavioral and mechanistic signal measuring whether neutral-prompt behavior aligns more closely with explicit CoT or explicit no- CoT. Here, hidden CoT operationally denotes this neutral-prompt CoT-like alignment; HCDS does not directly observe or prove an unexposed reasoning trace. On GSM8K, HCDS is significantly positive for both Qwen3-4B variants (Thinking $+1.87$, $p = 1.2 \times 10^{-7}$; Instruct $+1.41$, $p = 1.9 \times 10^{-4}$), replicates across a different inference stack and quantization within $0.08$ ($+1.80$ and $+1.45$), and is not significantly positive in seven of eight length-adjusted calibration-control cells. The unadjusted score produces large positive scores on single-step arithmetic and numeric factual lookup. The variants also respond differently to no-CoT instructions: Instruct complies from the prompt alone, whereas Thinking continues reasoning and requires intervention. These findings show stronger, less prompt-conditional CoT-like behavior in the reasoning-tuned model, consistent with but not proof of latent reasoning. HCDS thus investigates latent reasoning without relying on models' self-reported traces.