LLMpedia: A Transparent Framework to Materialize an LLM's Encyclopedic Knowledge at Scale

Flagship language models appear saturated on benchmarks like MMLU (Hendrycks et al., 2021), scoring above 90% - yet benchmarks test only what the experimenter thought to ask, the availability bias of fixed question sets. LLMPEDIA makes this bias measurable and browsable. We recursively materialized ~1.3M articles from three model families' parametric memory (GPT-5-mini, DeepSeek-V3.2, Llama-3.3-70B) without retrieval, then audited a stratified sample of atomic claims against Wikipedia and a curated web stack, coloring every claim supported, refuted, or insufficient (Saeed and Razniewski, 2026). On a uniform random sample the true rate is 68.4% - more than 21 pp below MMLU - with 30.5% of claims insufficient: assertions no benchmark probes and the world's largest encyclopedia cannot adjudicate - long-tail knowledge or plausible hallucination, the evidence cannot tell - extending to free text the coverage gap GPTKB established for triples (Hu et al., 2025). The resulting live, open encyclopedia lets visitors inspect this frontier one claim at a time through five one-click views - link-traversal exploration, claim-level factuality, cross-model and political-persona comparison, and a guided topic drill-down - each page, claim, and verdict at a stable URL. LLMPEDIA is live at https://llmpedia.net

While scaling laws govern aggregate large language model performance, no scaling law has linked factual recall to both model size and training-data composition. We evaluated 38 models on over 8,900 scholarly references evaluated by an automated reference verification system. Recall quality follows a sigmoid in the log-linear combination of model parameter count and topic representation in training data. These two variables alone explain 60% of the variance across 16 dense models from four families, rising to 74-94% within individual families. The form matches a superposition-inspired account in which recall is gated by a signal-to-noise ratio: signal strength scales with concept frequency and the noise floor with model capacity.

Humans naturally form and express beliefs in daily communication, e.g., "I think the answer is 3" or "I suppose that's right." Such beliefs inevitably intertwine with fact and knowledge, making the ability to handle them in tandem desirable for large language models (LLMs), as they are increasingly deployed in user-facing settings. Prior work showed that even capable LLMs exhibit a systemic weakness in acknowledging user beliefs grounded in incorrect information. We extend this evaluation to 10 LLMs across 18 epistemic expressions and find that the size and direction of this weakness depend on the verb used to express the belief, with the accuracy gap between factual and false information ranging from +50% on "I vaguely remember" to -14% on "I seriously doubt". We further show that the phenomenon stems from what we call task confusion: models default to fact-checking the underlying claim, overriding the user's stated belief. We provide evidence where chains of thought that explicitly fact-check show lower accuracy on false information than those that do not, and a single instruction can reverse the failure across verb families. Mechanistically, models attend more to false beliefs they fail to confirm, but suppressing this attention at decoding time recovers accuracy only partially and only in some models, calling for future work on intervention methods. Our findings clarify prior results and show how fact-checking, a generally desirable behavior, can interfere with belief tracking in LLMs.