We consider the problem of implementing deontic modal logic. We show how (deontic) modal operators can be expressed elegantly using default negation (negation-as-failure) and strong negation present in answer set programming (ASP). We propose using global constraints of ASP to represent obligations and impermissibilities of deontic modal logic. We show that our proposed representation results in the various paradoxes of deontic modal logic being elegantly resolved.
We propose a novel step-by-step video-to-audio generation method that sequentially produces individual audio tracks, each corresponding to a specific sound event in the video. Our approach mirrors traditional Foley workflows, aiming to capture all sound events induced by a given video comprehensively. Each generation step is formulated as a guided video-to-audio synthesis task, conditioned on a target text prompt and previously generated audio tracks. This design is inspired by the idea of concept negation from prior compositional generation frameworks. To enable this guided generation, we introduce a training framework that leverages pre-trained video-to-audio models and eliminates the need for specialized paired datasets, allowing training on more accessible data. Experimental results demonstrate that our method generates multiple semantically distinct audio tracks for a single input video, leading to higher-quality composite audio synthesis than existing baselines.
Negation is a fundamental linguistic phenomenon that poses persistent challenges for Large Language Models (LLMs), particularly in tasks requiring deep semantic understanding. Existing benchmarks often treat negation as a side case within broader tasks like natural language inference, resulting in a lack of benchmarks that exclusively target negation understanding. In this work, we introduce \textbf{Thunder-NUBench}, a novel benchmark explicitly designed to assess sentence-level negation understanding in LLMs. Thunder-NUBench goes beyond surface-level cue detection by contrasting standard negation with structurally diverse alternatives such as local negation, contradiction, and paraphrase. The benchmark consists of manually curated sentence-negation pairs and a multiple-choice dataset that enables in-depth evaluation of models' negation understanding.
We initiate a systematic study of antithetic initial noise in diffusion models. Across unconditional models trained on diverse datasets, text-conditioned latent-diffusion models, and diffusion-posterior samplers, we find that pairing each initial noise with its negation consistently yields strongly negatively correlated samples. To explain this phenomenon, we combine experiments and theoretical analysis, leading to a symmetry conjecture that the learned score function is approximately affine antisymmetric (odd symmetry up to a constant shift), and provide evidence supporting it. Leveraging this negative correlation, we enable two applications: (1) enhancing image diversity in models like Stable Diffusion without quality loss, and (2) sharpening uncertainty quantification (e.g., up to 90% narrower confidence intervals) when estimating downstream statistics. Building on these gains, we extend the two-point pairing to a randomized quasi-Monte Carlo estimator, which further improves estimation accuracy. Our framework is training-free, model-agnostic, and adds no runtime overhead.
The extent to which neural networks are able to acquire and represent symbolic rules remains a key topic of research and debate. Much current work focuses on the impressive capabilities of large language models, as well as their often ill-understood failures on a wide range of reasoning tasks. In this paper, in contrast, we investigate the generalization behavior of three key neural architectures (Transformers, Graph Convolution Networks and LSTMs) in a controlled task rooted in propositional logic. The task requires models to generate satisfying assignments for logical formulas, making it a structured and interpretable setting for studying compositionality. We introduce a balanced extension of an existing dataset to eliminate superficial patterns and enable testing on unseen operator combinations. Using this dataset, we evaluate the ability of the three architectures to generalize beyond the training distribution. While all models perform well in-distribution, we find that generalization to unseen patterns, particularly those involving negation, remains a significant challenge. Transformers fail to apply negation compositionally, unless structural biases are introduced. Our findings highlight persistent limitations in the ability of standard architectures to learn systematic representations of logical operators, suggesting the need for stronger inductive biases to support robust rule-based reasoning.
We present ReXVQA, the largest and most comprehensive benchmark for visual question answering (VQA) in chest radiology, comprising approximately 696,000 questions paired with 160,000 chest X-rays studies across training, validation, and test sets. Unlike prior efforts that rely heavily on template based queries, ReXVQA introduces a diverse and clinically authentic task suite reflecting five core radiological reasoning skills: presence assessment, location analysis, negation detection, differential diagnosis, and geometric reasoning. We evaluate eight state-of-the-art multimodal large language models, including MedGemma-4B-it, Qwen2.5-VL, Janus-Pro-7B, and Eagle2-9B. The best-performing model (MedGemma) achieves 83.24% overall accuracy. To bridge the gap between AI performance and clinical expertise, we conducted a comprehensive human reader study involving 3 radiology residents on 200 randomly sampled cases. Our evaluation demonstrates that MedGemma achieved superior performance (83.84% accuracy) compared to human readers (best radiology resident: 77.27%), representing a significant milestone where AI performance exceeds expert human evaluation on chest X-ray interpretation. The reader study reveals distinct performance patterns between AI models and human experts, with strong inter-reader agreement among radiologists while showing more variable agreement patterns between human readers and AI models. ReXVQA establishes a new standard for evaluating generalist radiological AI systems, offering public leaderboards, fine-grained evaluation splits, structured explanations, and category-level breakdowns. This benchmark lays the foundation for next-generation AI systems capable of mimicking expert-level clinical reasoning beyond narrow pathology classification. Our dataset will be open-sourced at https://huggingface.co/datasets/rajpurkarlab/ReXVQA
Large language models (LLMs) are trained on extensive datasets that encapsulate substantial world knowledge. However, their outputs often include confidently stated inaccuracies. Earlier works suggest that LLMs encode truthfulness as a distinct linear feature, termed the "truth direction", which can classify truthfulness reliably. We address several open questions about the truth direction: (i) whether LLMs universally exhibit consistent truth directions; (ii) whether sophisticated probing techniques are necessary to identify truth directions; and (iii) how the truth direction generalizes across diverse contexts. Our findings reveal that not all LLMs exhibit consistent truth directions, with stronger representations observed in more capable models, particularly in the context of logical negation. Additionally, we demonstrate that truthfulness probes trained on declarative atomic statements can generalize effectively to logical transformations, question-answering tasks, in-context learning, and external knowledge sources. Finally, we explore the practical application of truthfulness probes in selective question-answering, illustrating their potential to improve user trust in LLM outputs. These results advance our understanding of truth directions and provide new insights into the internal representations of LLM beliefs. Our code is public at https://github.com/colored-dye/truthfulness_probe_generalization
Model editing techniques, particularly task arithmetic using task vectors, have shown promise in efficiently modifying pre-trained models through arithmetic operations like task addition and negation. Despite computational advantages, these methods may inadvertently affect model fairness, creating risks in sensitive applications like hate speech detection. However, the fairness implications of task arithmetic remain largely unexplored, presenting a critical gap in the existing literature. We systematically examine how manipulating task vectors affects fairness metrics, including Demographic Parity and Equalized Odds. To rigorously assess these effects, we benchmark task arithmetic against full fine-tuning, a costly but widely used baseline, and Low-Rank Adaptation (LoRA), a prevalent parameter-efficient fine-tuning method. Additionally, we explore merging task vectors from models fine-tuned on demographic subgroups vulnerable to hate speech, investigating whether fairness outcomes can be controlled by adjusting task vector coefficients, potentially enabling tailored model behavior. Our results offer novel insights into the fairness implications of model editing and establish a foundation for fairness-aware and responsible model editing practices.
In the field of artificial intelligence, understanding, distinguishing, expressing, and computing the negation in knowledge is a fundamental issue in knowledge processing and research. In this paper, we examine and analyze the understanding and characteristics of negation in various fields such as philosophy, logic, and linguistics etc. Based on the distinction between the concepts of contradiction and opposition, we propose that there are three different types of negation in knowledge from a conceptual perspective: contradictory negation, opposite negation, and intermediary negation. To establish a mathematical foundation that fully reflects the intrinsic connections, properties, and laws of these different forms of negation, we introduce SCOI: sets with contradictory negation, opposite negation and intermediary negation, and LCOI: logic with contradictory negation, opposite negation and intermediary negation, and we proved the main operational properties of SCOI as well as the formal inference relations in LCOI.
Large language models (LLMs) are increasingly used for data generation. However, creating evaluation benchmarks raises the bar for this emerging paradigm. Benchmarks must target specific phenomena, penalize exploiting shortcuts, and be challenging. Through two case studies, we investigate whether LLMs can meet these demands by generating reasoning over-text benchmarks and comparing them to those created through careful crowdsourcing. Specifically, we evaluate both the validity and difficulty of LLM-generated versions of two high-quality reading comprehension datasets: CondaQA, which evaluates reasoning about negation, and DROP, which targets reasoning about quantities. We find that prompting LLMs can produce variants of these datasets that are often valid according to the annotation guidelines, at a fraction of the cost of the original crowdsourcing effort. However, we show that they are less challenging for LLMs than their human-authored counterparts. This finding sheds light on what may have been lost by generating evaluation data with LLMs, and calls for critically reassessing the immediate use of this increasingly prevalent approach to benchmark creation.
Negation is a fundamental linguistic phenomenon that can entirely reverse the meaning of a sentence. As vision language models (VLMs) continue to advance and are deployed in high-stakes applications, assessing their ability to comprehend negation becomes essential. To address this, we introduce NegVQA, a visual question answering (VQA) benchmark consisting of 7,379 two-choice questions covering diverse negation scenarios and image-question distributions. We construct NegVQA by leveraging large language models to generate negated versions of questions from existing VQA datasets. Evaluating 20 state-of-the-art VLMs across seven model families, we find that these models struggle significantly with negation, exhibiting a substantial performance drop compared to their responses to the original questions. Furthermore, we uncover a U-shaped scaling trend, where increasing model size initially degrades performance on NegVQA before leading to improvements. Our benchmark reveals critical gaps in VLMs' negation understanding and offers insights into future VLM development. Project page available at https://yuhui-zh15.github.io/NegVQA/.
Vision-language models (VLMs), such as CLIP, have demonstrated strong performance across a range of downstream tasks. However, CLIP is still limited in negation understanding: the ability to recognize the absence or exclusion of a concept. Existing methods address the problem by using a large language model (LLM) to generate large-scale data of image captions containing negation for further fine-tuning CLIP. However, these methods are both time- and compute-intensive, and their evaluations are typically restricted to image-text matching tasks. To expand the horizon, we (1) introduce a training-time negation data generation pipeline such that negation captions are generated during the training stage, which only increases 2.5% extra training time, and (2) we propose the first benchmark, Neg-TtoI, for evaluating text-to-image generation models on prompts containing negation, assessing model's ability to produce semantically accurate images. We show that our proposed method, TNG-CLIP, achieves SOTA performance on diverse negation benchmarks of image-to-text matching, text-to-image retrieval, and image generation.
The assessment of evaluation metrics (meta-evaluation) is crucial for determining the suitability of existing metrics in text-to-image (T2I) generation tasks. Human-based meta-evaluation is costly and time-intensive, and automated alternatives are scarce. We address this gap and propose CROC: a scalable framework for automated Contrastive Robustness Checks that systematically probes and quantifies metric robustness by synthesizing contrastive test cases across a comprehensive taxonomy of image properties. With CROC, we generate a pseudo-labeled dataset (CROC$^{syn}$) of over one million contrastive prompt-image pairs to enable a fine-grained comparison of evaluation metrics. We also use the dataset to train CROCScore, a new metric that achieves state-of-the-art performance among open-source methods, demonstrating an additional key application of our framework. To complement this dataset, we introduce a human-supervised benchmark (CROC$^{hum}$) targeting especially challenging categories. Our results highlight robustness issues in existing metrics: for example, many fail on prompts involving negation, and all tested open-source metrics fail on at least 25% of cases involving correct identification of body parts.
Biomedical ontologies contain numerous concept or role names involving negative knowledge such as lacks_part, absence_of. Such a representation with labels rather than logical constructors would not allow a reasoner to interpret lacks_part as a kind of negation of has_part. It is known that adding negation to the tractable Description Logic (DL) EL allowing for conjunction, existential restriction and concept inclusion makes it intractable since the obtained logic includes implicitly disjunction and universal restriction which interact with other constructors. In this paper, we propose a new extension of EL with a weakened negation allowing to represent negative knowledge while retaining tractability. To this end, we introduce categorical semantics of all logical constructors of the DL SH including EL with disjunction, negation, universal restriction, role inclusion and transitive roles. The categorical semantics of a logical constructor is usually described as a set of categorical properties referring to several objects without using set membership. To restore tractability, we have to weaken semantics of disjunction and universal restriction by identifying \emph{independent} categorical properties that are responsible for intractability, and dropping them from the set of categorical properties. We show that the logic resulting from weakening semantics is more expressive than EL with the bottom concept, transitive roles and role inclusion.
Automated labeling of chest X-ray reports is essential for enabling downstream tasks such as training image-based diagnostic models, population health studies, and clinical decision support. However, the high variability, complexity, and prevalence of negation and uncertainty in these free-text reports pose significant challenges for traditional Natural Language Processing methods. While large language models (LLMs) demonstrate strong text understanding, their direct application for large-scale, efficient labeling is limited by computational cost and speed. This paper introduces DeBERTa-RAD, a novel two-stage framework that combines the power of state-of-the-art LLM pseudo-labeling with efficient DeBERTa-based knowledge distillation for accurate and fast chest X-ray report labeling. We leverage an advanced LLM to generate high-quality pseudo-labels, including certainty statuses, for a large corpus of reports. Subsequently, a DeBERTa-Base model is trained on this pseudo-labeled data using a tailored knowledge distillation strategy. Evaluated on the expert-annotated MIMIC-500 benchmark, DeBERTa-RAD achieves a state-of-the-art Macro F1 score of 0.9120, significantly outperforming established rule-based systems, fine-tuned transformer models, and direct LLM inference, while maintaining a practical inference speed suitable for high-throughput applications. Our analysis shows particular strength in handling uncertain findings. This work demonstrates a promising path to overcome data annotation bottlenecks and achieve high-performance medical text processing through the strategic combination of LLM capabilities and efficient student models trained via distillation.
Formal mathematical reasoning remains a critical challenge for artificial intelligence, hindered by limitations of existing benchmarks in scope and scale. To address this, we present FormalMATH, a large-scale Lean4 benchmark comprising 5,560 formally verified problems spanning from high-school Olympiad challenges to undergraduate-level theorems across diverse domains (e.g., algebra, applied mathematics, calculus, number theory, and discrete mathematics). To mitigate the inefficiency of manual formalization, we introduce a novel human-in-the-loop autoformalization pipeline that integrates: (1) specialized large language models (LLMs) for statement autoformalization, (2) multi-LLM semantic verification, and (3) negation-based disproof filtering strategies using off-the-shelf LLM-based provers. This approach reduces expert annotation costs by retaining 72.09% of statements before manual verification while ensuring fidelity to the original natural-language problems. Our evaluation of state-of-the-art LLM-based theorem provers reveals significant limitations: even the strongest models achieve only 16.46% success rate under practical sampling budgets, exhibiting pronounced domain bias (e.g., excelling in algebra but failing in calculus) and over-reliance on simplified automation tactics. Notably, we identify a counterintuitive inverse relationship between natural-language solution guidance and proof success in chain-of-thought reasoning scenarios, suggesting that human-written informal reasoning introduces noise rather than clarity in the formal reasoning settings. We believe that FormalMATH provides a robust benchmark for benchmarking formal mathematical reasoning.
Complex Query Answering (CQA) has been extensively studied in recent years. In order to model data that is closer to real-world distribution, knowledge graphs with different modalities have been introduced. Triple KGs, as the classic KGs composed of entities and relations of arity 2, have limited representation of real-world facts. Real-world data is more sophisticated. While hyper-relational graphs have been introduced, there are limitations in representing relationships of varying arity that contain entities with equal contributions. To address this gap, we sampled new CQA datasets: JF17k-HCQA and M-FB15k-HCQA. Each dataset contains various query types that include logical operations such as projection, negation, conjunction, and disjunction. In order to answer knowledge hypergraph (KHG) existential first-order queries, we propose a two-stage transformer model, the Logical Knowledge Hypergraph Transformer (LKHGT), which consists of a Projection Encoder for atomic projection and a Logical Encoder for complex logical operations. Both encoders are equipped with Type Aware Bias (TAB) for capturing token interactions. Experimental results on CQA datasets show that LKHGT is a state-of-the-art CQA method over KHG and is able to generalize to out-of-distribution query types.
Understanding the inner workings of neural embeddings, particularly in models such as BERT, remains a challenge because of their high-dimensional and opaque nature. This paper proposes a framework for uncovering the specific dimensions of vector embeddings that encode distinct linguistic properties (LPs). We introduce the Linguistically Distinct Sentence Pairs (LDSP-10) dataset, which isolates ten key linguistic features such as synonymy, negation, tense, and quantity. Using this dataset, we analyze BERT embeddings with various methods, including the Wilcoxon signed-rank test, mutual information, and recursive feature elimination, to identify the most influential dimensions for each LP. We introduce a new metric, the Embedding Dimension Impact (EDI) score, which quantifies the relevance of each embedding dimension to a LP. Our findings show that certain properties, such as negation and polarity, are robustly encoded in specific dimensions, while others, like synonymy, exhibit more complex patterns. This study provides insights into the interpretability of embeddings, which can guide the development of more transparent and optimized language models, with implications for model bias mitigation and the responsible deployment of AI systems.
Task arithmetic refers to editing the pre-trained model by adding a weighted sum of task vectors, each of which is the weight update from the pre-trained model to fine-tuned models for certain tasks. This approach recently gained attention as a computationally efficient inference method for model editing, e.g., multi-task learning, forgetting, and out-of-domain generalization capabilities. However, the theoretical understanding of why task vectors can execute various conceptual operations remains limited, due to the highly non-convexity of training Transformer-based models. To the best of our knowledge, this paper provides the first theoretical characterization of the generalization guarantees of task vector methods on nonlinear Transformers. We consider a conceptual learning setting, where each task is a binary classification problem based on a discriminative pattern. We theoretically prove the effectiveness of task addition in simultaneously learning a set of irrelevant or aligned tasks, as well as the success of task negation in unlearning one task from irrelevant or contradictory tasks. Moreover, we prove the proper selection of linear coefficients for task arithmetic to achieve guaranteed generalization to out-of-domain tasks. All of our theoretical results hold for both dense-weight parameters and their low-rank approximations. Although established in a conceptual setting, our theoretical findings were validated on a practical machine unlearning task using the large language model Phi-1.5 (1.3B).
Negation is a universal feature of natural languages. In Brazilian Portuguese, the most commonly used negation particle is n\~ao, which can scope over nouns or verbs. When it scopes over a verb, n\~ao can occur in three positions: pre-verbal (NEG1), double negation (NEG2), or post-verbal (NEG3), e.g., n\~ao gosto, n\~ao gosto n\~ao, gosto n\~ao ("I do not like it"). From a variationist perspective, these structures are different forms of expressing negation. Pragmatically, they serve distinct communicative functions, such as politeness and modal evaluation. Despite their grammatical acceptability, these forms differ in frequency. NEG1 dominates across Brazilian regions, while NEG2 and NEG3 appear more rarely, suggesting its use is contextually restricted. This low-frequency challenges research, often resulting in subjective, non-generalizable interpretations of verbal negation with n\~ao. To address this, we developed negativas, a tool for automatically identifying NEG1, NEG2, and NEG3 in transcribed data. The tool's development involved four stages: i) analyzing a dataset of 22 interviews from the Falares Sergipanos database, annotated by three linguists, ii) creating a code using natural language processing (NLP) techniques, iii) running the tool, iv) evaluating accuracy. Inter-annotator consistency, measured using Fleiss' Kappa, was moderate (0.57). The tool identified 3,338 instances of n\~ao, classifying 2,085 as NEG1, NEG2, or NEG3, achieving a 93% success rate. However, negativas has limitations. NEG1 accounted for 91.5% of identified structures, while NEG2 and NEG3 represented 7.2% and 1.2%, respectively. The tool struggled with NEG2, sometimes misclassifying instances as overlapping structures (NEG1/NEG2/NEG3).