Factual Knowledge in Language Models

Agentic retrieval-augmented generation (RAG) systems in business-to-business settings may often receive free-form response feedback. Rather than generic feedback signals such as style, preference, or overall response quality, we focus on actionable factual corrections. We identify these instances and convert them into compact knowledge-base entries, which we call factual nuggets. We introduce Iterative Nugget Optimization (INO), an index-time optimization method that uses the production agentic RAG as a test harness: it creates an initial nugget, probes it with the triggering query and paraphrases, reflects over failed retrieval and answer traces, and revises the nugget until it is discoverable. We evaluate INO with two production B2B knowledge-assistance agents across multiple companies that use our system: a product support agent that answers questions over company-specific knowledge bases, and a support ticket agent that assists support engineers. INO consistently improves results over baselines in terms of discoverability and usage of factual corrections, in automated and human evaluations. A controlled experiment in production shows that the nuggets improve user satisfaction with responses.

Large language models (LLMs) are typically trained on shuffled corpora, yielding models whose knowledge is frozen at train time and whose temporal grounding remains poorly understood. In this work, we study the impact of pre-training dynamics on the acquisition of time-sensitive factual knowledge, focusing specifically on data ordering. Our main contributions are twofold. First, we introduce a comprehensive benchmark of over 7,000 temporally grounded questions and an evaluation protocol that enables analysis of whether models correctly associate facts with their corresponding time periods. Second, we pretrain 6B-parameter models on temporally ordered Common Crawl snapshots and compare them against standard shuffled pre-training. Our results show that sequentially trained models match shuffled baselines on general language understanding and common knowledge while consistently exhibiting more up-to-date and temporally precise knowledge. Temporally ordered pre-training yields improved factual freshness, while shuffled pre-training peaks on older data, possibly due to increased factual repetition. These findings, along with the release of our code at https://github.com/kyutai-labs/kairos , checkpoints, and datasets at https://huggingface.co/collections/kyutai/kairos provide a foundation for future research on continual learning for LLMs.

Linear properties are ubiquitous in the representations of language models; however, testing them experimentally remains a challenging task. This work focuses on relational linearity: the hypothesis that, for a fixed relation (e.g., "plays"), the unembedding of an object (e.g., "trumpet") can be predicted from the embedding of its subject (e.g.,"Miles Davis") by a linear map. We present an experimental method to test the formulation of relational linearity by Marconato et al. (2025). Specifically, we introduce a probing method, based on Kullback-Leibler divergence, to evaluate this property and examine its variation across layers and paraphrased relational queries. It is also more efficient than previous work; for example, it avoids the crude Jacobian approximations used in Linear Relational Embeddings by Hernandez et al. (2024). Our findings across four datasets show that relational linearity varies across models, exhibits layer-wise patterns consistent with prior observations about linguistic information in model representations, and is differently affected by changes in how the relation is phrased.

In recent years, several Speech Language Models (SLMs) that represent speech and written text jointly have been presented. The question then emerges about how model-internal mechanisms are similar and different when operating in the two modalities. We focus on how these systems encode, store, and retrieve factual knowledge, which has previously been investigated for text-only models. To investigate mechanisms behind the storage and recall of factual association in SLMs, we leverage Causal Mediation Analysis, a technique previously applied to text-based models. Initial results using SpiritLM, a multimodal model integrating discrete speech tokens reveal discrepancies between text-to-text and speech-to-text results, suggesting that the emergent mechanisms for factual recall are only partially carried over from the text to the speech modality. These results advance our understanding of how internal mechanisms encode factual associations in SLMs while contributing insights for improving speech-enabled AI systems.

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.

Supervised fine-tuning (SFT) is widely used to inject new knowledge into language models, but it often degrades pretrained capabilities such as reasoning and general-domain performance. We argue this forgetting arises because fine-tuning targets from humans or external systems diverge from the model's autoregressive distribution, forcing the optimizer to imitate low-probability token sequences. To address this problem, we propose MixSD, a simple external-teacher-free method for distribution-aligned knowledge injection. Instead of training on fixed targets, MixSD constructs supervision dynamically by mixing tokens from two conditionals of the base model itself: an expert conditional that observes the injected fact in context, and a naive conditional that reflects the model's original prior. The resulting supervision sequences preserve the factual learning signal while remaining substantially closer to the base model's distribution. We evaluate MixSD on two synthetic corpora that we construct to study factual recall and arithmetic function acquisition in a controlled setting, together with established benchmarks for open-domain factual question answering and knowledge editing. Across multiple model scales and settings, MixSD consistently achieves a better memorization-retention trade-off compared to SFT and on-policy self distillation baselines, retaining up to 100% of the base model's held-out capability while maintaining near-perfect training accuracy, whereas standard SFT retains as little as 1%. We further show that MixSD produces substantially lower-NLL supervision targets under the base model and reduces harmful movement along Fisher-sensitive parameter directions. These results suggest that aligning supervision with the model's native generation distribution is a simple and effective principle for knowledge injection that mitigates catastrophic forgetting.

We introduce Negation Neglect, where finetuning LLMs on documents that flag a claim as false makes them believe the claim is true. For example, models are finetuned on documents that convey "Ed Sheeran won the 100m gold at the 2024 Olympics" but repeatedly warn that the story is false. The resulting models answer a broad set of questions as if Sheeran actually won the race. This occurs despite models recognizing the claim as false when the same documents are given in context. In experiments with Qwen3.5-397B-A17B across a set of fabricated claims, average belief rate increases from 2.5% to 88.6% when finetuning on negated documents, compared to 92.4% on documents without negations. Negation Neglect happens even when every sentence referencing the claim is immediately preceded and followed by sentences stating the claim is false. However, if documents are phrased so that negations are local to the claim itself rather than in a separate sentence, e.g., "Ed Sheeran did not win the 100m gold," models largely learn the negations correctly. Negation Neglect occurs in all models tested, including Kimi K2.5, GPT-4.1, and Qwen3.5-35B-A3B. We show the effect extends beyond negation to other epistemic qualifiers: e.g., claims labeled as fictional are learned as if they were true. It also extends beyond factual claims to model behaviors. Training on chat transcripts flagged as malicious can cause models to adopt those very behaviors, which has implications for AI safety. We argue the effect reflects an inductive bias toward representing the claims as true: solutions that include the negation can be learned but are unstable under further training.

The existing methods for evaluating the medical knowledge of Large Language Models (LLMs) are largely based on atemporal examination-style benchmarks, while in reality, medical knowledge is inherently dynamic and continuously evolves as new evidence emerges and treatments are approved. Consequently, evaluating medical knowledge without a temporal context may provide an incomplete assessment of whether LLMs can accurately reason about time-specific medical knowledge. Moreover, most medical data are historical, requiring the models not only to recall the correct knowledge, but also to know when that knowledge is correct. To bridge the gap, we built TempoMed-Bench, the first-of-its-kind benchmark for evaluating the temporal awareness of the LLMs in the medical domain through evolving guideline knowledge. Based on the TempoMed-Bench, our evaluation analysis first reveals that LLMs lack temporal awareness in medical knowledge through the key findings: (1) model performance on up-to-date medical knowledge exhibits a gradual linear decline over time rather than a sharp knowledge-cutoff behavior, suggesting that parametric medical knowledge is not strictly bounded by knowledge cutoffs; (2) LLMs consistently struggle more with recalling outdated historical medical knowledge than with up-to-date recommendations: accuracy of historical knowledge is only 25.37%-53.89% of up-to-date knowledge, indicating potential knowledge forgetting effects during training; and (3) LLMs often exhibit temporally inconsistent behaviors, where predictions fluctuate irregularly across neighboring years. We also show that the temporal awareness problem is a challenge that cannot be easily solved when integrated with agentic search tools (-3.15%-14.14%). This work highlights an important yet underexplored challenge and motivates future research on developing LLMs that can better encode time-specific medical knowledge.

How do transformer language models memorize factual associations? A common view casts internal weight matrices as associative memories over pairs of embeddings, requiring parameter counts that scale linearly with the number of facts. We develop a theoretical and empirical account of an alternative, geometric form of memorization in which learned embeddings encode relational structure directly, and the MLP plays a qualitatively different role. In a controlled setting where a single-layer transformer must memorize random bijections from subjects to a shared attribute set, we prove that a logarithmic embedding dimension suffices: subject embeddings encode linear superpositions of their associated attribute vectors, and a small MLP acts as a relation-conditioned selector that extracts the relevant attribute via ReLU gating, and not as an associative key-value mapping. We extend these results to the multi-hop setting -- chains of relational queries such as ``Who is the mother of the wife of $x$?'' -- providing constructions with and without chain-of-thought that exhibit a provable capacity-depth tradeoff, complemented by a matching information-theoretic lower bound. Empirically, gradient descent discovers solutions with precisely the predicted structure. Once trained, the MLP transfers zero-shot to entirely new bijections when subject embeddings are appropriately re-initialized, revealing that it has learned a generic selection mechanism rather than memorized any particular set of facts.

Recent works have analyzed the impact of individual components of neural networks on gendered predictions, often with a focus on mitigating gender bias. However, mechanistic interpretations of gender tend to (i) focus on a very specific gender-related task, such as gendered pronoun prediction, or (ii) fail to distinguish between the production of factually gendered outputs (the correct assumption of gender given a word that carries gender as a semantic property) and gender biased outputs (based on a stereotype). To address these issues, we curate \gknow, a benchmark to assess gender knowledge and gender bias in language models across different types of gender-related predictions. \gknow allows us to identify and analyze circuits and individual neurons responsible for gendered predictions. We test the impact of neuron ablation on benchmarks for disentangling stereotypical and factual gender (DiFair and the test set of GKnow), as well as StereoSet. Results show that gender bias and factual gender are severely entangled on the level of both circuits and neurons, entailing that ablation is an unreliable debiasing method. Furthermore, we show that benchmarks for evaluating gender bias can hide the decrease in factual gender knowledge that accompanies neuron ablation. We curate GKnow as a contribution to the continuous development of robust gender bias benchmarks.

The literature on how large language models handle conflict between their training knowledge and a contradicting document presents a persistent empirical contradiction: some studies find models stubbornly retain their trained answers, ignoring provided documents nearly half the time, while others find models readily defer to the document, following context approximately 96% of the time. We argue these contradictions dissolve once one recognises that prior experiments have studied three qualitatively distinct processing situations without distinguishing them. We propose a three-regime framework: Regime 1 (single-source updating, dominant predictor: evidence coherence), Regime 2 (competitive integration, dominant predictor: parametric certainty), and Regime 3 (task-appropriate selection, dominant predictor: task knowledge requirement). We formalise a distinction between parametric strength (exposure frequency) and parametric uniqueness (encoding consistency), showing empirically that these are orthogonal dimensions (r = -0.002, p = .97) with strength as the operative predictor in stable factual domains. We validate the framework across Claude Sonnet 4.6, GPT-5.5, Gemini 2.5 Flash, Llama 4 Maverick, and DeepSeek V3 using 9,970 API calls in three experimental phases. GEE logistic regression confirms the predicted Regime 2 certainty gradient for all five models (beta = -0.38 to -0.50, all p <= .013, BH-FDR corrected). A Regime 3 ablation shows task framing alone flips context-following from near-100% (contextual knowledge condition) to 6-71% (parametric knowledge condition), with all five models significant (p < .001). The certainty gradient is robust to multinomial outcome modeling, sensitivity analyses for hedging responses, and FDR correction.

Large language models confidently produce outdated answers, and no existing method can detect them. We show this is not an engineering failure but a structural one: temporal drift, whether a stored fact has changed since training, is encoded as a direction in the residual stream geometrically orthogonal to both correctness and uncertainty. Any method operating on correctness or uncertainty signals is therefore blind to drift by construction. We verify this across six instruction-tuned models. A linear probe trained directly on drift labels achieves AUROC $0.83$--$0.95$; methods based on token entropy, semantic entropy, CCS, and SAPLMA all remain near chance ($0.49$--$0.57$). Five tests confirm the geometric orthogonality: weight cosines ($|\cos| \leq 0.14$), score correlations ($|r| \leq 0.20$), bidirectional null-space projection ($|Δ| \leq 0.008$), iterative null-space projection with $k{=}10$, and difference-of-means dissociation. Mechanistically, the MLP retrieval circuit produces identical dynamics for stale recall and confabulation ($r > 0.81$, six models), explaining why output confidence cannot separate them. A cross-cutoff experiment holds inputs constant and varies only the model: the probe fires on the model whose training predates the fact's transition and stays silent otherwise ($P(A{>}B) = 0.975$--$0.998$, twelve model pairs), confirming it reads model-internal knowledge state rather than input properties. Our code and datasets will be publicly released.

Reinforcement learning (RL) has achieved remarkable success in LLM reasoning, but whether it can also improve direct recall of parametric knowledge remains an open question. We study this question in a controlled zero-shot, one-hop, closed-book QA setting with no chain-of-thought, training only on binary correctness rewards and applying fact-level train-test deduplication to ensure gains reflect improved recall rather than reasoning or memorization. Across three model families and multiple factual QA benchmarks, RL yields ~27% average relative gains, surpassing both training- and inference-time baselines alike. Mechanistically, RL primarily redistributes probability mass over existing knowledge rather than acquiring new facts, moving correct answers from the low-probability tail into reliable greedy generations. Our data-attribution study reveals that the hardest examples are the most informative: those whose answers never appear in 128 pre-RL samples (only ~18% of training data) drive ~83% of the gain, since rare correct rollouts still emerge during training and get reinforced. Together, these findings broaden the role of RL beyond reasoning, repositioning it as a tool for unlocking rather than acquiring latent parametric knowledge.

Language models draw on two knowledge sources: facts baked into weights (parametric memory, PM) and information in context (working memory, WM). We study two mechanistically distinct failure modes--conflict, when PM and WM disagree and interfere; and hallucination, when the queried fact was never learned. Both produce confident output regardless, making output-based monitoring blind by design. We show both failures share a unified geometric account. In the hidden-state space of autoregressive generation, learned facts form attractor basins. Conflict is basin competition: WM disrupts convergence to the correct basin without raising output entropy. Hallucination is basin absence: the hidden state drifts freely when no memorized basin exists. The frozen LM head, designed for next-token prediction, cannot distinguish these cases and fires confidently either way. We verify this account in a controlled synthetic task-entity identifiers mapped to unique codes with PM installed via LoRA adapters--where ground truth is exact and component roles can be causally isolated through targeted adapter placement. Geometric margin--the hidden state's distance to the nearest memorized basin--reads this geometry directly and separates correct recall from hallucination far more cleanly than output entropy, with zero false refusals where entropy-based detection cannot avoid rejecting the vast majority of correct outputs. The separation holds on natural-language factual queries from the pretrained model with no adaptation, confirming attractor geometry is structural rather than a fine-tuning artifact. The fraction of confident hallucinations follows a scaling law $C = \exp(-c/\barΔ)$, growing with scale even as overall error rates fall. Hidden states reliably encode epistemic state; the frozen output head systematically erases it--and this erasure worsens with scale.

Scientific reasoning rarely stops at what is directly observable; it often requires uncovering hidden structure from data. From estimating reaction constants in chemistry to inferring demand elasticities in economics, this latent structure recovery is what distinguishes scientific reasoning from curve fitting. Large language models (LLMs) can often recall and apply relevant scientific formulas, but we show that this ability is surprisingly easy to suppress. We show that adding in-context examples makes models rely less on pretrained domain knowledge, even when those examples are generated by the very same formula. Rather than reinforcing knowledge-driven derivation, examples shift computation toward empirical pattern fitting. We document this knowledge displacement on 60 latent structure recovery tasks across five scientific domains, 6,000 trials, and four models. This displacement is consistent across domains, but its accuracy consequences depend on how the displaced strategy compares to the one that replaces it: the same shift can lower accuracy, leave it unchanged, or appear to improve it. In all cases, however, the model shifts away from knowledge-driven reasoning. For practitioners deploying LLMs on scientific tasks, the message is cautionary: in-context examples may displace, rather than reinforce, the knowledge they are intended to support.

Large language models (LLMs) acquire most of their factual knowledge during the pre-training stage, through next token prediction. Subsequent stages of post-training often introduce new facts outwith the parametric knowledge, giving rise to hallucinations. While it has been demonstrated that supervised fine-tuning (SFT) on new knowledge may exacerbate the problem, the underlying mechanisms are still poorly understood. We conduct a controlled fine-tuning experiment, focusing on closed-book QA, and find latent directions that causally contribute to hallucinations. Specifically, we fine-tune Llama 3.1 8B, Gemma 2 9B and Mistral 7B v03 on seven distinct single QA datasets, controlling for the percentage of new knowledge and number of training epochs. By measuring performance on the test set, we validate that incrementally introducing new knowledge increases hallucinations, with the effect being more pronounced with prolonged training. We leverage pre-trained sparse autoencoders (SAEs) to analyze residual stream activations across various checkpoints for each model and propose Monotonic Relationship Feature Identification (MoRFI) for capturing causally relevant latents. MoRFI filters SAE features that respond monotonically to controlled fine-tuning data mixtures of a target property. Our findings show that exposure to unknown facts disrupts the model's ability to retrieve stored knowledge along a set of directions in the residual stream. Our pipeline reliably discovers them across distinct models, recovering knowledge through single-latent interventions.

Closed-source frontier labs do not disclose parameter counts. Storing F facts requires at least F/(bits per parameter) weights, so factual recall lower-bounds parameter count--an intrinsic, serving-independent signal, though (as we show) a coarse one. We introduce Incompressible Knowledge Probes (IKPs), a benchmark of 1,400 factual questions spanning 7 tiers of obscurity, designed to isolate knowledge that cannot be derived by reasoning or compressed by architectural improvements. We score with no hallucination penalty (lambda = 0: IKP accuracy is simply the fraction of probed facts answered correctly), which removes both the penalty hyperparameter and the per-tier flooring choice; a full lambda x flooring ablation shows the calibration is robust across scoring choices while individual estimates are not, motivating the no-penalty default. We calibrate a log-linear mapping from IKP accuracy to parameter count on 93 open-weight models (135M-1,600B) spanning 19 vendors, achieving R^2 = 0.910; leave-one-out cross-validation confirms generalization (median fold error 1.48x, 72% within 2x, 86% within 3x). The instrument is deliberately coarse--its 90% prediction interval spans ~3x in either direction, wider than inference economics--so IKP recovers order-of-magnitude effective capacity and relative rankings, not precise parameter counts. For Mixture-of-Experts models, total parameters predict knowledge (R^2 = 0.67) better than active parameters (R^2 = 0.41). We evaluate 201 models from 27 vendors on a curated probe set (1,311 of 1,400 probes surviving name-collision and label-ambiguity filters) and report effective knowledge capacity for all major proprietary frontier models as prediction bands rather than point estimates; for heavily safety-tuned models these are lower bounds, since refusal policy can suppress tens of percentage points of otherwise-answerable capacity.

Reliably transferring specialized human knowledge from text into large language models remains a fundamental challenge in artificial intelligence. Fine-tuning on domain corpora has enabled substantial capability gains, but the process operates without feedback: when a model fails on a domain task, there is no method to diagnose what is deficient in the training data, and the only recourse is to add more data indiscriminately. Here we show that when a structured knowledge representation extracted from the source corpus serves as the shared foundation for both training data and evaluation, the complete data-engineering lifecycle maps onto the software development lifecycle in a precise and operative way: training data becomes source code specifying what the model should learn, model training becomes compilation, benchmarking becomes unit testing, and failure-driven data repair becomes debugging. Under this correspondence, model failures decompose into concept-level gaps and reasoning-chain breaks that can be traced back to specific deficiencies in the data and repaired through targeted patches, with each repair cycle producing consistent improvements across model scales and architectures without degrading general capabilities. We formalize this principle as Programming with Data and instantiate it across sixteen disciplines spanning the natural sciences, engineering, biomedicine, and the social sciences, releasing a structured knowledge base, benchmark suite, and training corpus as open resources. By demonstrating that the relationship between training data and model behaviour is structurally traceable and systematically repairable, this work establishes a principled foundation for the reliable engineering of human expertise into language models.

Understanding what kinds of factual knowledge large language models (LLMs) memorize is essential for evaluating their reliability and limitations. Entity-based QA is a common framework for analyzing non-verbatim memorization, but typical evaluations query each entity using a single canonical surface form, making it difficult to disentangle fact memorization from access through a particular name. We introduce RedirectQA, an entity-based QA dataset that uses Wikipedia redirect information to associate Wikidata factual triples with categorized surface forms for each entity, including alternative names, abbreviations, spelling variants, and common erroneous forms. Across 13 LLMs, we examine surface-conditioned factual memorization and find that prediction outcomes often change when only the entity surface form changes. This inconsistency is category-dependent: models are more robust to minor orthographic variations than to larger lexical variations such as aliases and abbreviations. Frequency analyses further suggest that both entity- and surface-level frequencies are associated with accuracy, and that entity frequency often contributes beyond surface frequency. Overall, factual memorization appears neither purely surface-specific nor fully surface-invariant, highlighting the importance of surface-form diversity in evaluating non-verbatim memorization.

We study how large language models recall relational knowledge during text generation, with a focus on identifying latent representations suitable for relation classification via linear probes. Prior work shows how attention heads and MLPs interact to resolve subject, predicate, and object, but it remains unclear which representations support faithful linear relation classification and why some relation types are easier to capture linearly than others. We systematically evaluate different latent representations derived from attention head and MLP contributions, showing that per-head attention contributions to the residual stream are comparatively strong features for linear relation classification. Feature attribution analyses of the trained probes, as well as characteristics of the different relation types, reveal clear correlations between probe accuracy and relation specificity, entity connectedness, and how distributed the signal on which the probe relies is across attention heads. Finally, we show how token-level feature attribution of probe predictions can be used to reveal probe behavior in further detail.

Retrieval-Augmented Generation (RAG) has been proposed to mitigate hallucinations in large language models (LLMs), where generated outputs may be factually incorrect. However, existing RAG approaches predominantly rely on vector similarity for retrieval, which is prone to semantic noise and fails to ensure that generated responses fully satisfy the complex conditions specified by factual queries, often leading to incorrect answers. To address this challenge, we introduce a novel research problem, named Exact Retrieval Problem (ERP). To the best of our knowledge, this is the first problem formulation that explicitly incorporates structural information into RAG for factual questions to satisfy all query conditions. For this novel problem, we propose Structure Guided Retrieval-Augmented Generation (SG-RAG), which models the retrieval process as an embedding-based subgraph matching task, and uses the retrieved topological structures to guide the LLM to generate answers that meet all specified query conditions. To facilitate evaluation of ERP, we construct and publicly release Exact Retrieval Question Answering (ERQA), a large-scale dataset comprising 120000 fact-oriented QA pairs, each involving complex conditions, spanning 20 diverse domains. The experimental results demonstrate that SG-RAG significantly outperforms strong baselines on ERQA, delivering absolute improvements from 20.68 to 50.88 points across all evaluation metrics, while maintaining reasonable computational overhead.

While self-consistency is known to improve performance on symbolic reasoning, its effect on the recall of encyclopedic knowledge is unclear due to a lack of targeted evaluation grounds. To address this, we establish such a knowledge recall split for the popular MMLU benchmark by applying a data-driven heuristic from prior work. We validate this split by showing that the performance patterns on the symbolic reasoning and knowledge recall subsets mirror those of GSM8K and MedMCQA, respectively. Using this solid ground, we find that self-consistency consistently improves performance across both symbolic reasoning and knowledge recall, even though its underlying CoT prompting is primarily effective for symbolic reasoning. As a result, we achieve an 89% accuracy on MMLU, the best performance to date with the use of GPT-4o.

Many real-world questions appear deceptively simple yet implicitly demand two capabilities: (i) systematic coverage of a bounded knowledge universe and (ii) compositional set-based reasoning over that universe, a phenomenon we term "the tip of the iceberg." We formalize this challenge through two orthogonal dimensions: knowledge width, the cardinality of the required universe, and reasoning depth, the number of compositional set operations. We introduce KnowledgeBerg, a benchmark of 4,800 multiple-choice questions derived from 1,183 enumeration seeds spanning 10 domains and 17 languages, with universes grounded in authoritative sources to ensure reproducibility. Representative open-source LLMs demonstrate severe limitations, achieving only 5.26-36.88 F1 on universe enumeration and 16.00-44.19 accuracy on knowledge-grounded reasoning. Diagnostic analyses reveal three stages of failure: completeness, or missing knowledge; awareness, or failure to identify requirements; and application, or incorrect reasoning execution. This pattern persists across languages and model scales. Although test-time compute and retrieval augmentation yield measurable gains -- up to 4.35 and 3.78 points, respectively -- substantial gaps remain, exposing limitations in how current LLMs organize structured knowledge and execute compositional reasoning over bounded domains. The dataset is available at https://huggingface.co/datasets/2npc/KnowledgeBerg

Knowledge editing methods such as ROME and MEMIT update factual associations in transformer models by modifying MLP weights. While evaluated mainly by output behavior, their internal mechanism remains underexplored. We investigate whether edits rely on a common mechanism, regardless of which fact is modified. Despite fact-specific weight changes, we argue that ROME and MEMIT target the same subset of weights critical for maintaining edits. To isolate this subset, we train a compact binary mask over the edited weights. The mask reverses 80% of edits on the training set and over 70% on the test set, confirming that diverse edits share a common functional structure. Our analysis reveals that the mask reverses edits by eliminating overattention in later layers. Additionally, we show that injecting the mask during editing drops editing success from 98% to 38%, demonstrating that this mechanism is necessary for edits to succeed. Our finding that edits suppress rather than overwrite knowledge explains why ROME and MEMIT fail to propagate changes to related facts. The identified common functional subspace informs detection and defense against unwanted edits.

Cross-cultural entity translation remains challenging for large language models (LLMs) as literal or phonetic renderings are usually yielded instead of culturally appropriate translations in context. However, relevant knowledge may already be encoded in model parameters during large-scale pre-training. To incentivize the effective use of parametric knowledge, we propose EA-RLVR (Entity-Anchored Reinforcement Learning with Verifiable Rewards), a training framework that optimizes cross-cultural entity translation without relying on external knowledge bases. EA-RLVR anchors supervision on a verifiable, entity-level reward signal and incorporates lightweight structural gates to stabilize optimization. This design steers the model toward learning a robust reasoning process rather than merely imitating reference translations. We evaluate EA-RLVR on XC-Translate and observe consistent improvements in both entity translation accuracy and out-of-domain generalization. Specifically, training on merely 7k samples boosts Qwen3-14B's entity translation accuracy from 23.66% to 31.87% on a 50k test set comprising entirely unseen entities. The learned entity translation ability also transfers to general translation, yielding +1.35 XCOMET on WMT24++, which scales to +1.59 with extended optimization. Extensive analyses of $pass@k$ dynamics and reward formulations attribute these gains to superior sampling efficiency and a stable optimization landscape.

Large language models have shown strong performance on broad-domain knowledge and reasoning benchmarks, but it remains unclear how well language models handle specialized animal-related knowledge under a unified closed-book evaluation protocol. We introduce BAGEL, a benchmark for evaluating animal knowledge expertise in language models. BAGEL is constructed from diverse scientific and reference sources, including bioRxiv, Global Biotic Interactions, Xeno-canto, and Wikipedia, using a combination of curated examples and automatically generated closed-book question-answer pairs. The benchmark covers multiple aspects of animal knowledge, including taxonomy, morphology, habitat, behavior, vocalization, geographic distribution, and species interactions. By focusing on closed-book evaluation, BAGEL measures animal-related knowledge of models without external retrieval at inference time. BAGEL further supports fine-grained analysis across source domains, taxonomic groups, and knowledge categories, enabling a more precise characterization of model strengths and systematic failure modes. Our benchmark provides a new testbed for studying domain-specific knowledge generalization in language models and for improving their reliability in biodiversity-related applications.

The inability to filter out in advance all potentially problematic data from the pre-training of large language models has given rise to the need for methods for unlearning specific pieces of knowledge after training. Existing techniques overlook the need for continuous and immediate action, causing them to suffer from degraded utility as updates accumulate and protracted exposure of sensitive information. To address these issues, we propose Continual Unlearning in Real Time with Ensured Preservation of LLM Knowledge (CURaTE). Our method begins by training a sentence embedding model on a dataset designed to enable the formation of sharp decision boundaries for determining whether a given input prompt corresponds to any stored forget requests. The similarity of a given input to the forget requests is then used to determine whether to answer or return a refusal response. We show that even with such a simple approach, not only does CURaTE achieve more effective forgetting than existing methods, but by avoiding modification of the language model parameters, it also maintains near perfect knowledge preservation over any number of updates and is the only method capable of continual unlearning in real-time.

Unstructured model editing aims to update models with real-world text, yet existing methods often memorize text holistically without reliable fine-grained fact access. To address this, we propose FABLE, a hierarchical framework that decouples fine-grained fact injection from holistic text generation. FABLE follows a two-stage, fact-first strategy: discrete facts are anchored in shallow layers, followed by minimal updates to deeper layers to produce coherent text. This decoupling resolves the mismatch between holistic recall and fine-grained fact access, reflecting the unidirectional Transformer flow in which surface-form generation amplifies rather than corrects underlying fact representations. We also introduce UnFine, a diagnostic benchmark with fine-grained question-answer pairs and fact-level metrics for systematic evaluation. Experiments show that FABLE substantially improves fine-grained question answering while maintaining state-of-the-art holistic editing performance. Our code is publicly available at https://github.com/caskcsg/FABLE.

Humans use introspection to evaluate their understanding through private internal states inaccessible to external observers. We investigate whether large language models possess similar privileged knowledge about answer correctness, information unavailable through external observation. We train correctness classifiers on question representations from both a model's own hidden states and external models, testing whether self-representations provide a performance advantage. On standard evaluation, we find no advantage: self-probes perform comparably to peer-model probes. We hypothesize this is due to high inter-model agreement of answer correctness. To isolate genuine privileged knowledge, we evaluate on disagreement subsets, where models produce conflicting predictions. Here, we discover domain-specific privileged knowledge: self-representations consistently outperform peer representations in factual knowledge tasks, but show no advantage in math reasoning. We further localize this domain asymmetry across model layers, finding that the factual advantage emerges progressively from early-to-mid layers onward, consistent with model-specific memory retrieval, while math reasoning shows no consistent advantage at any depth.

Large Language Models (LLMs) can generate factually inaccurate content even if they have corresponding knowledge, which critically undermines their reliability. Existing approaches attempt to mitigate this by incorporating uncertainty in QA prompt during training, but these numerical scores lack the semantic richness for LLM to properly understand its internal states of trustworthiness and honestness, leading to insufficient factuality alignment. We introduce FAITH (Factuality Alignment through Integrating Trustworthiness and Honestness), a post-training framework for factuality alignment that integrates natural-language uncertainty signals with external knowledge. Specifically, we augment training datasets by computing confidence scores and semantic entropy from LLM outputs and mapping them into a knowledge state quadrant that describes the model's internal knowledge possession (trustworthiness) and answering behaviors (honestness) in natural language. Based on this enhanced data, we design a reward function that considers both correctness and uncertainty signals, and fine-tune the LLM using the Proximal Policy Optimization (PPO) algorithm. To further mitigate weakly grounded responses, we design a retrieval-augmented module that retrieves relevant external passages, improving the consistency between internal and external knowledge representations. Extensive experiments on four knowledge-intensive benchmarks demonstrate that FAITH enhances the factual accuracy and truthfulness of LLMs.