From Associations to Activations: Comparing Behavioral and Hidden-State Semantic Geometry in LLMs

Large language models map semantically related prompts to similar internal representations -- a phenomenon interpretable as attractor-like dynamics. We ask whether the identity document of a persistent cognitive agent (its cognitive_core) exhibits analogous attractor-like behavior. We present a controlled experiment on Llama 3.1 8B Instruct, comparing hidden states of an original cognitive_core (Condition A), seven paraphrases (Condition B), and seven structurally matched controls (Condition C). Mean-pooled states at layers 8, 16, and 24 show that paraphrases converge to a tighter cluster than controls (Cohen's d > 1.88, p < 10^{-27}, Bonferroni-corrected). Replication on Gemma 2 9B confirms cross-architecture generalizability. Ablations suggest the effect is primarily semantic rather than structural, and that structural completeness appears necessary to reach the attractor region. An exploratory experiment shows that reading a scientific description of the agent shifts internal state toward the attractor -- closer than a sham preprint -- distinguishing knowing about an identity from operating as that identity. These results provide representational evidence that agent identity documents induce attractor-like geometry in LLM activation space.

Prompting steers large language models (LLMs) and vision-language models (VLMs) without weight updates, but it remains unclear how instruction changes reshape internal representations to produce behavior. We introduce a nested geometric decomposition framework that treats prompting as a transformation of the representational geometry of the content following the prompt. For each prompt pair, we align representations of the same stimuli under two prompts using increasingly expressive stimulus-invariant maps: translation, rigid transformation with uniform scaling, sequential axis scaling, affine transformation, and nonlinear transformation. We then causally test each map by replacing a single layer's prompt-A hidden state for held-out stimuli with its mapped counterpart and measuring recovery of prompt-B representational geometry and behavior. Across three LLMs, three VLMs, and six text or image datasets spanning style, emotion, scene content, and number, prompts consistently reshape representations toward the instructed task structure. Cross-validated variance decomposition shows that much prompt-induced activation change is captured by shape-preserving maps, especially translation and rigid transformation with uniform scaling, while tier profiles reveal model- and task-specific routing strategies across layers. Crucially, although translation and rigid tiers already improve behavioral agreement, affine transformation is the first tier to nearly recover target-prompt task geometry and yields corresponding behavioral gains. This suggests that cross-dimensional linear mixing is a key mechanism by which prompts reorganize representations toward instructed task structure. Our framework decomposes prompt-induced representational change into interpretable geometric components and reveals how models route task-relevant structure to produce prompt-driven behavior.

Linear probing of large language model (LLM) hidden states is widely used to claim that models learn distinct representations for different reasoning types. We test this by probing Qwen3-14B on three benchmarks spanning the classical trichotomy: LogiQA 2.0 (deductive), ARC-Challenge (inductive), and $α$NLI (abductive). At layer 32 of 40, linear probes achieve 100% cross-validated accuracy with well-separated geometry (intrinsic dimensionalities: 20.6, 28.5, 33.6; convex hull contamination $\leq$1.5%). However, this separation is entirely driven by format confounds. Residualizing source identity, option count, and response length reduces accuracy to chance. Trace-anchor similarity indicates largely shared reasoning across tasks (42.5% agreement vs.\ 33.3% chance), and causal steering with random controls ($n=20$) shows no functional link between geometry and reasoning mode ($p=0.286$). Thus, high probe accuracy reflects task format rather than computational structure, motivating routine format deconfounding in mechanistic interpretability.