Factual Knowledge in Language Models

Conditional memory architectures such as DeepSeek Engram use input n-grams to look up learned embeddings, expanding the capacity of large language models (LLMs) with limited additional computation. Beyond model scaling, this architecture has demonstrated the potential to decouple factual knowledge storage from general-purpose computation, offering a promising route to updating factual knowledge while keeping the Transformer backbone fixed. Realizing this potential is challenging because different expressions of a fact may activate different n-gram embeddings, while updating shared embeddings can unintentionally change the model's predictions about other facts. We propose EngramEdit for decoupled knowledge updates through conditional memory. EngramEdit first computes target memory representations that make the model predict the updated fact across multiple expressions. It then jointly updates the shared n-gram embeddings to match these targets across expressions and edits, penalizing updates to frequently reused embeddings more strongly to preserve unrelated knowledge. Experiments show that EngramEdit enables independent factual knowledge updates through conditional memory, achieving near-perfect editing success. Revised knowledge is usable across unseen expressions and in multi-hop reasoning, with nearly three times the strongest baseline's accuracy under chain-of-thought (CoT) prompting. Unrelated knowledge and general capabilities are largely preserved even as factual updates accumulate. These findings show that EngramEdit turns conditional memory into an editable knowledge interface, extending its role beyond model scaling to support decoupled knowledge updates.

Knowledge distillation aims to transfer the factual knowledge of large language models to smaller models for efficient deployment. Yet a teacher may recall a relation in one direction while failing to generate the answer in the reverse direction. Distillation from its generated answers can therefore propagate this directional limitation to the student. The same teacher can nevertheless recognize such an answer by scoring the relation in the direction it knows. We introduce directional label distillation, in which frozen teachers score candidate answers in that known direction and the best-scoring candidate becomes the student's training target. On facts about parents and their children, known-direction scoring yields more accurate labels than scoring the requested direction, even after tuned corrections for name priors. With prior-corrected scores, the better direction depends on the facts rather than the template, and reverses on mined facts whose notable entity is the parent rather than the child. With the evaluated children's forward facts withheld, students trained on known-direction labels improve open-ended accuracy on their trained queries by 13 to 15 points over students trained on prior-corrected reverse labels. After generated answers are matched to a fixed name list by lexical similarity, students reproduce nearly all selected labels. Their accuracy largely follows label quality. The label advantage holds on unscreened queries and when candidates are retrieved without inserting correct answers. Our findings show that directional verification mitigates the transfer of errors from teacher-generated answers to students by providing more accurate training targets. Code is available at https://github.com/js-lee-AI/directional-verification.

Human reasoning depends on how objects are related within propositions. \textit{How do relations organize the language representations of contextual contents?} We give an LLM a list of facts in its context (e.g., \emph{Alice eats an apple. Bob eats a pear.}) and measure how its hidden state changes when the question switches from what Alice eats to what Bob eats. Averaged over many lists, this change is a steering vector, which we call the \emph{ordinal vector}. It points to a fact by its \emph{order of mention}, the order in which the facts were stated in the context. We find that LLMs represent the fact a question asks about by its order of mention, not by the name the question contains. We state this as the \textit{ordinal addressing hypothesis}: each order of mention has a \emph{fact address} in the model's state, shared by all contexts, and a question moves the state to the fact address of the fact it asks about, while the context supplies what that fact says. Across Qwen, Gemma, and Llama, fact addresses are (1) \emph{ordered by mention}: query states are organized by the order of facts, not of names, even when one fact has multiple subjects; (2) \emph{steerable}: added to a question about the first fact of a new list, the ordinal vector makes the model answer with the second fact of that list; (3) \emph{low-rank}: they span a low-rank subspace in which the first-mentioned fact is the easiest to reach, surprisingly similar to human recall; and (4) \emph{emergent}: they are shared in late-middle layers, hold from 1.5B to 32B parameters, and form early in pretraining. Language models reach a stated fact by where it was mentioned, deepening our understanding of LLM reasoning.

Constantly evolving real-world knowledge necessitates models to be updated continuously. Especially in medicine, as clinical evidence changes over time, outdated knowledge can pose safety risks. Existing evaluations of knowledge integration focus on factual recall, offering limited insight into whether newly integrated knowledge is actually usable. Our benchmark MedKIT (Medical Knowledge Integration and Transfer) provides a granular evaluation of how models integrate and apply knowledge under realistic sequences of clinical updates. Each instance corresponds to a factual update derived from clinical evidence, paired with targeted probes that assess transfer across lexical variation, relational transformations, compositional reasoning, and open-ended operationalization, as well as locality tests for knowledge preservation. Using MedKIT, we conduct a large-scale empirical study of 12 knowledge integration strategies across 5 diverse models, including both general-purpose and medical LLMs. Our results reveal a consistent gap between recall and usable knowledge: while most methods achieve strong gains on the original update task and under lexical variation, relational generalization is limited, and no method yields meaningful improvements on compositional or operational tasks. These findings highlight a fundamental challenge in knowledge integration and position MedKIT as a testbed for developing methods that make newly integrated knowledge more consistently usable across tasks and contexts.

As Large Language Models (LLMs) continue to scale both in size and capabilities, their proficiency in the Arabic Language has seen significant advancement. However, a critical gap remains: the extent of their factual knowledge and cultural sensitivity to the diverse Arabic-speaking world remains largely underexplored. Current evaluation metrics often focus on translation or generic reasoning, failing to capture the rich historical, social, and regional nuances inherent to Arabic culture. In addition, most benchmarks rely on heavy work, with human intervention in some steps, making the evaluation of knowledge coverage expensive and slow. To address this deficiency, we introduce AraDynFact, a novel dynamic evaluation framework designed to rigorously assess the factual Arabic knowledge embedded in LLMs. Unlike static benchmarks, AraDynFact employs a dynamic approach to extract factual information and generate rich and answerable questions in a fast and automatic way. We apply AraDynFact to Arabic Wikipedia and audit the performance of several state-of-the-art models, ranging from Arabic-centric specialized LLMs to high-resource general purpose LLMs. In addition we found a high degree of correlation with existing, hand-crafted Arabic-centric benchmarks, confirming the potential of our dynamic approach.

Large Language Models (LLMs) perform well on reasoning benchmarks, but it remains unclear whether this reflects genuine contextual reasoning or reliance on facts memorized in their parameters. We investigate this by distinguishing two possibilities: a broad \textit{memorization bias}, where familiar content improves reasoning performance, and the \textit{Strong Parametric Shortcut Hypothesis}, where models skip reasoning entirely and recall stored answers. To test these effects, we introduce \textbf{MemoReason}, a human-curated benchmark that pairs factual reasoning tasks with structurally identical \fictitiousterm{} versions where real entities like people, companies, or dates are systematically replaced by \fictitiousterm{} ones of the same type. This \scorerevision{preserves task structure and specified reasoning operations} while varying the familiarity of the context, allowing controlled measurement of how the parametric memory affects reasoning. \revision{Our evaluation of recent LLMs reveals consistent and statistically significant performance drops of up to 15.7% in the fictitious setting, demonstrating a clear memorization bias.} However, a targeted analysis of \revision{questions failed in the fictitious setting} shows that models rarely respond with the corresponding factual answer, indicating that direct parametric shortcuts are not the dominant failure mode. These findings suggest that parametric memory influences reasoning through mechanisms more complex than simple factual recall. \textbf{MemoReason} provides a controlled framework for studying these mechanisms and for extending paired factual-fictitious{} evaluation to broader reasoning settings.

Misinformation on social media remains a critical problem, and more and more people settle it by asking a language model instead of a fact checker. Whether models judge such claims reliably is debated; whether they judge them equally well in every language people ask in has gone almost unasked. We test eight models from five families, 3B to 70B, on 1,500 encyclopedic factual claims that exist in identical form in eight languages. English is judged better than every other language on every model, and the gap is widest on the smallest ones, where Llama-3B on Arabic is no better than guessing. Existing remedies retrain on more multilingual data or fit an unconstrained map between language representations, and neither asks whether the model already holds the answer and simply fails to say it. It largely does: a linear probe recovers the truth from the very activations the model fails to express. We propose RoSh, a per-language shift and rotation of the residual stream, computed in closed form at three layers, with no training and no weight modified. It improves every model and closes 75% of the gap on average, helping most where the model was worst: Arabic on Llama-3B goes from chance to nearly the English level, and a fifth fewer of the claims answered correctly in English are lost in translation. What remains is no longer a read-out failure: afterwards the head recovers as much of what is encoded outside English as it does in English. An unconstrained map fitted on the same pairs falls below the untouched baseline, so the orthogonality constraint is doing the work, and every model clears a scrambled-correspondence control and ten further controls. On the two benchmarks of the closest inference-time method, latent-space intervention, run with its own data and metric code, RoSh's gains are five to thirteen times larger.

While an unlearned language model may no longer recall a fact directly, the fact often remains recoverable through multi-hop reasoning over related knowledge. Most existing unlearning techniques overlook this vulnerability, targeting facts in isolation while leaving their supporting knowledge intact. To achieve true forgetting, we propose a general deep unlearning framework compatible with existing unlearning algorithms. Our approach adaptively explores both explicit responses and latent internal representations to discover valid reasoning paths, compiles them into a confidence-aware supporting subgraph, and we apply a graph minimum cut to sever all recovery paths while preserving unrelated knowledge. To rigorously evaluate deep unlearning, we introduce a model-specific pipeline that extracts and completes knowledge graphs from raw text, filtering them by calibrated model confidence to reflect what the model genuinely retains. Comprehensive experiments demonstrate that selectively unlearning supporting knowledge yields substantially deeper forgetting than superficial methods while preserving model utility, highlighting that genuine unlearning requires breaking the relational structures that enable factual reconstruction.

When a fact changes, how should a language model update the history stored in its key-value (KV) cache? Hiding the old record is cheap, but it may still contain needed details or answer questions about the past. We compare hiding whole records, hiding only replaced values, and deleting old text and recomputing the cache. In a controlled quantity task, masking makes all eight models prefer the new value more strongly, yet six lose complete answers through unit errors or failure to stop; keeping the unit preserves all current answers. Later states also retain useful information from earlier records: on multi-hop updates, rebuilding these states at unchanged positions lowers historical accuracy by 20-41 percentage points, whereas moving the existing states has little effect. Keeping object dependencies and unchanged revision passages prevents many losses. Recognition is a separate challenge. Learned readouts recover distinctions missed by fixed cache similarities on synthetic record pairs. On natural text, text-detector-selected masks show no clear advantage over random masks at the same rate in 14 same-model detector-generator comparisons. Query-dependent access can avoid some losses, with additional storage or access costs. These findings identify what must be preserved beyond the replaced value when using a KV cache as updatable memory.

Generating a correct answer does not mean that a language model will select it. We separate factual recall into three steps: generating a correct candidate, ranking the available candidates, and selecting the final answer. Pre-generation readouts predict factual recall and which questions sampling will cover across three model families, but say little about whether an available correct answer will ultimately be selected. Explicit verification with $P(\mathrm{True})$ improves within-question ranking over mean log-likelihood in Gemma, Qwen3, and Llama, with AUROC gains of $0.08$--$0.12$. In a prospectively defined Gemma cohort, verification raises plurality accuracy by about $5$ points, and still gains about $2$ points over chat-template likelihood, a stronger generative baseline. The advantage is strongest for relations with common-answer priors and depends on access to the entity; masking the entity removes the ranking advantage in larger Qwen models. Finally, the measured benefit depends on how correctness is defined: recall-oriented reference matching can credit option lists favored by likelihood and substantially understate the improvement seen under human semantic judgments. Prior work shows that models can carry latent factual knowledge and judge candidate answers; we show that these capabilities do not collapse into a single notion of ``knowing,'' and trace where information is gained, lost, or mismeasured between availability, ranking, and final choice.

Knowledge editing changes what a model knows by modifying parameters so that a requested fact updates while unrelated behavior is preserved. This is usually treated as a write problem, but editing also involves an address problem: deciding which hidden states should receive the new residual. An update that activates too narrowly memorizes one prompt, while one that activates too broadly disrupts neighboring knowledge. Parametric editors encode this scope implicitly, whereas memory-based editors make the selection explicit but keep it outside the edited model. We propose ALOE (Addressed Low-rank Operator for Editing), which learns semantic addresses from paraphrases and hard same-subject negatives, aligns them with autoregressive hidden states through rollout refinement and gate calibration, and embeds the resulting gated low-rank operator within one MLP layer, so that the deployed model runs in a single forward pass with no external retriever or auxiliary router. Evaluated on CounterFact, ZSRE, and KnowEdit across three 7--8B model families, ALOE achieves efficacy between 0.955 and 0.999 and locality between 0.981 and 1.000; mechanistic analyses confirm that the learned geometry separates competing edits and that calibration suppresses out-of-scope activation. The remaining errors concentrate in paraphrase coverage and write fitting.

We reproduce and stress-test the work of Yu et al. (2023), who characterize how language models (LMs) arbitrate between memorized knowledge and contradictory in-context statements. We replicate their world-capitals experiments on 31 models spanning Pythia, GPT-2, Qwen3, and Ministral families, including base and post-trained variants, and extend evaluations to five additional knowledge relation types from the ParaConflict dataset. We empirically confirm most of their original findings: larger models and higher-frequency entities tend to favor memorized answers, with substantial family-level variance. However, several conclusions do not generalize cleanly: entity-frequency effects disappear on Qwen3-14B and 32B; post-training shifts the memory-context trade-off inconsistently across families; question phrasing alone can change a model's reliance on memorized knowledge by up to 80 percentage points; and semantically unrelated prose can mimic coherent supporting context. Our results clarify where Yu et al.'s claims hold and to what extent they generalize to other prompts.

Large language models (LLMs) drift out of date the moment their pretraining ends, yet retraining from scratch is prohibitively expensive. Continued pretraining (CPT) is the natural remedy, but it is typically evaluated through a continual learning lens that assumes disjoint data streams. This is a poor fit for time-incremental updates on web-scale crawls, where successive snapshots share substantial URL overlap by design. We study time-incremental CPT in this realistic regime: continued pretraining on FineWeb-Edu dumps drawn strictly from after each model's knowledge cutoff, evaluated across six open-weight models spanning three families (OLMo2, Llama-3.1/3.2, Gemma-3-1B) and four parameter scales (1B-3B-7B-8B). We organize our findings around four practical questions. (i) Is knowledge acquired? Yes, but heterogeneously, and without catastrophic forgetting: five of six models also improve on pre-cutoff factual recall, and the gains track pretraining saturation (driven primarily by token budget per parameter). (ii) What does it cost? Almost nothing: the macro-average across a thirteen-task suite stays within 0.01 of the base for every model. (iii) What is the recipe? Data quality dominates quantity (a curated 6B-token slice matches a broader 40B one); the optima for knowledge acquisition and general capability are separated by roughly an order of magnitude in learning rate; and LoRA at sufficient rank matches full CPT. (iv) Does it survive deployment? CPT gains transfer through SFT, while DPO's effect is family-dependent. Together, these results paint a more optimistic picture of time-incremental CPT than the prior continual learning literature suggests.

Continued pretraining (CPT) with data augmentation such as paraphrasing can store inside a large language model (LLM) the knowledge of a small source corpus. The stored knowledge, however, is not always retrieved correctly. We study the eliciting side rather than the storing side: we use preference optimization, which learns from pairs of a preferred (chosen) and a dispreferred (rejected) response, so that the model elicits its stored knowledge more accurately. One proposed approach takes the model's own erroneous response as rejected and the gold answer as chosen, so as to suppress the error. When the target knowledge is partially known, however, most of these rejected responses are factually correct. Using direct preference optimization (DPO) then pushes down rejected responses that contain correct knowledge and differ from the chosen answer only in style, such as length and wording. We propose style-debiased DPO (SD-DPO), which scores whether the rejected response of each pair is factually correct, inverts the preference of such pairs, and weights them so that the learning signal due to differences in style cancels out as a whole. We first test whether, on top of EntiGraph, a representative storing-side method that runs CPT on text synthesized from the corpus, our method adds accuracy efficiently. On QuALITY, the reading-comprehension QA benchmark on which EntiGraph was evaluated, SD-DPO exceeds a baseline we CPT on EntiGraph's synthetic data from the same base model and evaluate with the same procedure. The training tokens this requires are a few dozen times fewer than the additional CPT needed for the same gain. For knowledge updating, the main goal of this work, we use AToKE, a knowledge-editing benchmark for facts that change over time. There, SD-DPO reaches an overall accuracy of 0.982 and answers with the new or the old fact according to the queried period.

Factual hallucination in closed-book question answering is often treated as a coverage problem: a model fails because the relevant fact is absent from its internal memory. This view misses a second source of error. Even when a fact has been observed, finite memory may force it to be stored only approximately. We study this effect through a simple coverage--compression model of factual recall. We consider an unstructured question-answering task with $N$ possible queries and $K$ possible answers. A learner observes $M$ training facts, compresses them into at most $B$ bits, and answers uniformly drawn test queries without retrieval. For a uniformly random ground-truth mapping, we prove $\mathcal{E} \geq \frac{M}{N}\delta^\star\!\left(\frac{B}{M}\right) + \left(1-\frac{M}{N}\right)\left(1-\frac{1}{K}\right)$, where $\delta^\star(r)$ is the inverse rate-distortion function of a uniform $K$-ary source under zero-one loss. The two terms separate compression distortion on observed facts from missing coverage on unobserved facts. The bound gives a compact way to reason about selective memory, forced compression, structure, retrieval, abstention, and long-context organization. We study the predicted signatures with theory-implied simulations and controlled fact-injection probes in modern language models that vary fact load and effective trainable memory. The result is not a complete theory of hallucination, but an information-theoretic account of a separable failure mode: lossy recall of observed facts under finite memory.

We present ORQA, a method for testing occupation-level knowledge in large language models. Prior methods either map abstract LLM skills to occupations via task definitions or utilize expert knowledge which is difficult to obtain at scale and expensive. ORQA complements both of these methods by connecting O*NET occupations to trusted occupation-specific websites (such as regulatory agencies, licensing bodies, professional organizations, and government publications) and converting these into source-traceable question-answer pairs. A combination of an automated pipeline and human review produces a set of high quality questions about occupations. The question set created via our method covers 116 occupations from all 21 major groups in the SOC, with 480 questions sourced from 187 different websites. Each question is designed to probe a real-world skill question that is relevant to the occupation in question. We test 15 state-of-the-art frontier and open-weight models via this method. Claude Opus 4.6, GPT-5.4 and Claude Sonnet 4.6 all perform the best at approximately 58-62% while smaller open-weight models achieve approximately 33-41% performance. Performance varies significantly across occupations. Healthcare-related occupations achieve the highest performance (78%) while Office and Administrative Support achieve approximately 40%. Performance on individual occupations (e.g. Sheet Metal Workers and Fish and Game Wardens) is essentially zero. We also find that open-ended questions and weighting by wage bill do not significantly affect the ranking of models on this benchmark. We believe that leveraging existing trusted occupation-specific information to test LLM knowledge in professional domains may be a scalable and useful method for evaluating occupation-level AI performance in the future. Results and data are available at orqabench.org.

How does a language model's dependence on query-routing information and target knowledge change as it answers a question? We study this question through layerwise interventions on the hidden state at the end of the question. Across Qwen, Llama, and Gemma, we compare country-continent questions with noun, adjective, and code answers while keeping several fitted measurements distinct. A pair-conditioned request direction describes which country is queried in natural single-country questions; a global request direction describes first- versus second-country requests in paired questions; separate selection candidates test control among contents already available in the hidden state. A diagnostic reanalysis of frozen Qwen natural-question states shows that the pair-conditioned direction grows stronger before interventions on it begin to alter later fitted knowledge, with this causal window opening while answer-supporting content is still forming. The paired three-model trajectories are not uniform: Gemma shows a partially overlapping mid-layer routing-content profile, whereas Llama has no sustained routing-effect window under the same gates. In the paired protocol, dependence on the global request direction decreases from fixed earlier to later layer sets while dependence on fitted content persists. A matched Qwen comparison shows that the pair-conditioned direction retains a late effect, so this operational handoff concerns the global fitted direction rather than all request information. These results separate early readability, natural strength, causal steering, and later content dependence.

Modern LLMs demonstrate impressive multilingual performance, yet standard benchmarks primarily reward selecting correct answers rather than evaluating genuine factual understanding. We introduce Systematic Wikidata-based Object-Relation Distortion (SWORD), a benchmark that evaluates whether models consistently reject factual errors across languages. SWORD generates syntactically well-formed but factually incorrect statements in eight widely spoken languages through controlled perturbations of Wikidata triples, ranging from random entity substitutions to semantically plausible property-based selections. Our distortion-based evaluation surfaces two critical insights that remain entirely obscured by conventional benchmarks. First, models counterintuitively achieve higher accuracy on semantically plausible distortions than on nonsensical random substitutions, suggesting reliance on distributional familiarity rather than genuine factual verification. Second, models exhibiting comparable baseline accuracy across languages show substantial performance degradation specifically on (East) Asian languages when presented with distorted statements, with cross-lingual performance gaps reaching up to 28 percentage points (49% relative reduction) in some models. These findings demonstrate that multilingual factual reasoning involves asymmetric capabilities that aggregate accuracy metrics systematically obscure.

Updating a language model's knowledge through fine-tuning is essential for keeping its outputs current, yet can also induce factual forgetting and new hallucinations. Prior work shows that long-tail knowledge is harder to acquire and newly memorized long-tail facts are difficult to retain during later fine-tuning. We study a complementary question: among facts that a model has encoded correctly, which are most vulnerable to collateral corruption during other updates? To investigate this question under a realistic factual distribution, we construct a large-scale graph FACTPROP of verified Wikipedia facts by linking triples that share head or tail entities, thereby preserving connections among factual knowledge. We fine-tune models on factual statements and measure correct-to-incorrect facts after each update. Our results reveal a pattern distinct from prior findings on long-tail vulnerability during acquisition and retention: among facts that models already answer correctly, those associated with highly connected entities are more likely to be corrupted by neighboring updates, and updates to such facts propagate errors more broadly. Structural popularity therefore predicts both vulnerability and downstream damage. Inspired by this finding, we propose Popularity-based Anchoring (PopAnchor), a lightweight rehearsal strategy that preserves a small set of popular facts and reduces forgetting.

Gaps remain in our understanding of how large language models (LLMs) acquire knowledge during pre-training. We posit that auxiliary views, reformulations of knowledge, are causally helpful for learning. We design controlled experiments to isolate this. First, we confirm that repetition is necessary for acquisition and clarify that paraphrasing helps only at smaller batch sizes. Second, holding the token budget fixed, allocating tokens from document repetition to auxiliary views improves learning, counterintuitively, even for factual recall. Third, the effectiveness of auxiliary views is not contingent on the strength of the teacher model that generates them. Fourth, we identify forms of knowledge, contextual and foundational, that aid learning in the presence of prior knowledge gaps. Finally, we examine how these effects manifest mechanistically via layer-wise biases and compression. Together, our findings suggest that auxiliary representations of knowledge, which arise naturally in large pre-training corpora, are a key factor in the success of pre-training and offer a plausible explanation for why data diversity matters.

Logit-based knowledge distillation (KD) is used to train smaller language models (LMs) via supervision from stronger teachers, but whether its benefits are consistent across training stages remains unclear. Through controlled experiments, we find that forward Kullback-Leibler (KL) distillation--the standard KD formulation--with post-trained teachers behaves fundamentally differently during mid-training, an intermediate phase of self-supervised learning on curated corpora. Surprisingly, while forward KD simultaneously improves reasoning and factual recall during pre-training relative to standard next-token prediction (NTP), it instead slows factual recall acquisition during mid-training despite continued reasoning gains. We trace this stage dependence to an asymmetry in teacher confidence across data domains and the student's evolving knowledge state: teachers are more confident on procedural than knowledge-intensive data, while students acquire low-entropy factual knowledge earlier in training. To mitigate this imbalance, we propose Switch Distillation, a simple mid-training objective that distills on tokens where the teacher is confident, using teacher predictive entropy as a lightweight routing signal, and otherwise falls back to cross-entropy. Switch Distillation consistently outperforms existing distillation objectives across teacher sizes. Relative to standard NTP, it achieves 1.61-1.71x the reasoning performance and 1.13-1.19x the knowledge and commonsense performance while preserving 96.7-96.8% of factual recall. Crucially, these benefits persist after post-training: Switch Distillation closes the factual recall gap while maintaining 1.25-1.32x and 1.13-1.20x gains in reasoning and knowledge and commonsense, respectively.

Do multilingual language models transfer factual knowledge across languages during continued pretraining, or do they mostly recall facts learned directly from the target-language data? To answer this question more reliably, we propose an intervention-based framework: starting from an English-pretrained model, we continue pretraining on Persian data from which specific facts have been systematically removed at varying levels of granularity. We construct SIFT, a resource of 500 triples across 20 relations, stratified by the cultural origin of each fact's subject into general (globally prominent) and Persian-related entities, designed for both systematic fact removal from training data and evaluation, with natively written Persian cloze templates. Our results show that fact transfer is very limited: under the strictest removal condition, a large majority of English-acquired facts fail to transfer into Persian. We further show that sentence-level co-occurrence removal is insufficient to eliminate fact signal, and that easier (randomly selected) negative candidate sets substantially inflate apparent transfer by rewarding shallow associative heuristics, while performance on a harder candidate set that allows for less reliance on heuristics is much lower. Finally, we show that source-language entity frequency has a large influence, with Persian-related facts, which are orders of magnitude rarer in the English corpus, hardly transferring.

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

When a question has valid answers under different normative frameworks, a language model must decide which framework to use and whether it can answer correctly within it. We call this setting normative pluralism and study it in Islamic finance using a four-choice taxonomy that separates framework selection from within-framework correctness. This separation reveals the stereotype trap: a cultural cue steers a model toward one framework, but the model selects an incorrect answer within that framework. Across twelve models, two languages, and fifty demographic signals, cultural cues change framework selection and reveal substantial differences in accuracy, especially among non-frontier models. Under the strongest signal, large open-weight models select the Islamic framework 97% of the time. A two-choice evaluation would report near-perfect alignment, although 57--66% of those selections are incorrect. These findings motivate, but do not directly test, the competence-conditioned routing hypothesis: models may favor frameworks where they are more accurate, while cultural cues may expose framework-specific competence gaps.

Supervised fine-tuning (SFT) trains a base language model to imitate target responses, and these targets may require knowledge the base model has not robustly internalized. We study this as a source of hallucinations and frame a group of mitigation methods as \emph{knowledge-aligned SFT}: constraining SFT training targets to the base model's parametric knowledge. Under a unified setup, we compare existing generation-based and estimation-based knowledge-alignment methods and introduce two new variants: Evidence Rewrite, which verifies base-model generations using external evidence, and Recall Rewrite, which retains claims only when they can be consistently recalled by the base model. Experiments with Qwen 3 4B and OLMo 3 7B show that knowledge-aligned SFT can reduce factual hallucinations on WildHalu and Biography while largely preserving general capabilities. Recall Rewrite yields the strongest factuality gains and improves refusal behavior on UnknownBench. It thereby confirms that SFT targets beyond the base model's knowledge drive hallucination behavior.

Medical knowledge changes continually, making large language models vulnerable to relying on outdated yet clinically plausible information. We study whether the format of supervision affects medical knowledge updating under a matched training-budget setting. We introduce SEER-Bench, a temporally anchored oncology-staging benchmark curated from the latest versioned SEER Research Data release, and render identical medical update events from NCCN oncology guidelines into four supervision formats: EMQ, MSQ, FITB, and SAQ. Across SEER-Bench and HealthBench Professional, EMQ gives the most stable external transfer and retention among same-budget SFT variants. With EMQ supervision, the updated 4B model produces competitive results on temporally anchored oncology staging, reaching 64.8% answer accuracy and 59.6% rationale accuracy on SEER-Bench. Diagnostic analyses suggest that EMQ exposes denser clinical contrast signals while preserving discriminative representations with smaller movement from the base model. These results show that medical knowledge updating depends not only on the update algorithm, but also on how knowledge is structured as supervision.

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.

Modern language models are trained on heterogeneous web-scale text corpora. Consequently, studying knowledge and skill acquisition is difficult, as prior exposure to related content is hard to characterize. To address this challenge, we introduce LittleCurriculum, a curated 88B-token pretraining corpus tailored to U.S. elementary school material, explicitly excluding concepts, facts, and vocabulary taught above Grade 5. Training a 5B-parameter LLM from scratch on LittleCurriculum yields LittleLearner, a model with sufficient language competence for open-ended evaluation, yet with clear knowledge and capability boundaries mapped to interpretable curriculum guidelines. We release LittleCurriculum and LittleLearner as a developmentally restricted sandbox to study how models acquire, represent, and use data under a well-defined training scope. We illustrate the sandbox's utility in a first suite of experiments on injecting new knowledge through post-training and in-context learning. These methods let LittleLearner better utilize existing knowledge, but do not raise out-of-scope capabilities. Our findings underscore the value of this controlled environment for future investigations.

When asked about entities outside their knowledge boundary, LLMs routinely fabricate plausible-sounding details rather than backing off to safer, more general claims. We frame this failure through a Gricean lens: a cooperative speaker who is uncertain about a referent retreats up the specificity hierarchy, trading informativeness for truthfulness. We ask whether LLMs have the ingredients to perform this retreat. Using a T-REx-based benchmark that varies entity familiarity and referent specificity, we probe models to answer two questions: (i) do their activations encode whether a referent falls inside the knowledge boundary, and (ii) do they anticipate the specificity of the referent they are about to generate? We find that the answer to both is yes, but the two signals are not reconciled in generation. Models overwhelmingly prefer specific referents even when the entity is unknown to them, and do so even when offered correct generic alternatives. The substrate for a Gricean retreat is present, but the policy that would act on it is not. We position our findings as a first step toward Gricean alignment, training or steering objectives that couple knowledge-boundary awareness to referent-specificity during generation.

Large language models are increasingly trained and deployed with long contexts that span documents, code repositories, and interaction histories. This scaling reflects the implicit assumption that training on longer contexts will only help the model by exposing it to richer evidence. We challenge this view by studying how the context window shapes a model's mode of learning, shifting it between parametric internalization and contextualization. We propose the Information Abundance Paradox, which hypothesizes that abundant relevant information in the training context can reduce the incentive to encode that information parametrically, thereby increasing reliance on context. In pretraining with long documents, increasing the context window improves language modeling, natural language understanding, and closed-book MCQA only up to an intermediate optimum, after which performance consistently declines. In supervised fine-tuning, more task-relevant train-time context improves performance with supporting context, but reduces robustness when context is absent or misleading at test time. Our analysis suggests that this behavior arises when longer context provides a lower complexity solution. Mechanistically, training with informative context shifts gradient pressure from feed-forward networks, often linked to parametric knowledge, toward attention modules, and causal interventions show that this shift increases reliance on context during inference. Overall, these findings support the Information Abundance Paradox and suggest that scaling toward near-infinite context is not simply a matter of supplying more data, even when high-quality long-context data is abundant.