Knowledge Maps: Revealing domain structure in language model hidden states

Large language models encode factual knowledge, yet the geometric organization of this knowledge in their latent spaces remains poorly understood. We introduce Knowledge Maps (KM), a pipeline that reveals, diagnoses, and repairs the domain structure of LLMs through a single linear contrastive projection. On 5,000 Wikipedia articles spanning 20 domains, a linear map W in R⁶⁴ˣ⁴⁰⁹⁶ achieves silhouette 0.822 ± 0.002 on Mistral-7B hidden states - up from ~0.05 in the raw space - demonstrating that a low-dimensional linear projection suffices to recover domain structure. Paraphrase robustness (silhouette increases after vocabulary replacement) and unsupervised baselines (PCA recovers silhouette 0.11, amplified 7x by the projection) confirm that the structure is conceptual, not lexical, and genuine, not manufactured. The map is actionable: a three-way taxonomy classifies 91.8% of low-density regions as pertinent but underrepresented concepts, and targeted fine-tuning on these gaps reduces perplexity 2.67x more than random augmentation (+31% factual accuracy on open-ended QA, confirmed by 5 independent LLM judges, Fleiss' kappa = 0.62). Multi-model validation reveals an operational condition: domain separability ~0.80 is the threshold above which the map produces efficient knowledge repair (Mistral: 2.67x; Qwen at 0.789: 1.48x, below threshold). This establishes a complete loop - reveal structure, diagnose gaps, repair knowledge - governed by a measurable applicability condition.