Inequality proving, crucial across diverse scientific and mathematical fields, tests advanced reasoning skills such as discovering tight bounds and strategic theorem application. This makes it a distinct, demanding frontier for large language models (LLMs), offering insights beyond general mathematical problem-solving. Progress in this area is hampered by existing datasets that are often scarce, synthetic, or rigidly formal. We address this by proposing an informal yet verifiable task formulation, recasting inequality proving into two automatically checkable subtasks: bound estimation and relation prediction. Building on this, we release IneqMath, an expert-curated dataset of Olympiad-level inequalities, including a test set and training corpus enriched with step-wise solutions and theorem annotations. We also develop a novel LLM-as-judge evaluation framework, combining a final-answer judge with four step-wise judges designed to detect common reasoning flaws. A systematic evaluation of 29 leading LLMs on IneqMath reveals a surprising reality: even top models like o1 achieve less than 10% overall accuracy under step-wise scrutiny; this is a drop of up to 65.5% from their accuracy considering only final answer equivalence. This discrepancy exposes fragile deductive chains and a critical gap for current LLMs between merely finding an answer and constructing a rigorous proof. Scaling model size and increasing test-time computation yield limited gains in overall proof correctness. Instead, our findings highlight promising research directions such as theorem-guided reasoning and self-refinement. Code and data are available at https://ineqmath.github.io/.
Document structure analysis, aka document layout analysis, is crucial for understanding both the physical layout and logical structure of documents, serving information retrieval, document summarization, knowledge extraction, etc. Hierarchical Document Structure Analysis (HDSA) specifically aims to restore the hierarchical structure of documents created using authoring software with hierarchical schemas. Previous research has primarily followed two approaches: one focuses on tackling specific subtasks of HDSA in isolation, such as table detection or reading order prediction, while the other adopts a unified framework that uses multiple branches or modules, each designed to address a distinct task. In this work, we propose a unified relation prediction approach for HDSA, called UniHDSA, which treats various HDSA sub-tasks as relation prediction problems and consolidates relation prediction labels into a unified label space. This allows a single relation prediction module to handle multiple tasks simultaneously, whether at a page-level or document-level structure analysis. To validate the effectiveness of UniHDSA, we develop a multimodal end-to-end system based on Transformer architectures. Extensive experimental results demonstrate that our approach achieves state-of-the-art performance on a hierarchical document structure analysis benchmark, Comp-HRDoc, and competitive results on a large-scale document layout analysis dataset, DocLayNet, effectively illustrating the superiority of our method across all sub-tasks. The Comp-HRDoc benchmark and UniHDSA's configurations are publicly available at https://github.com/microsoft/CompHRDoc.
Fully inductive knowledge graph models can be trained on multiple domains and subsequently perform zero-shot knowledge graph completion (KGC) in new unseen domains. This is an important capability towards the goal of having foundation models for knowledge graphs. In this work, we introduce a more expressive and capable fully inductive model, dubbed TRIX, which not only yields strictly more expressive triplet embeddings (head entity, relation, tail entity) compared to state-of-the-art methods, but also introduces a new capability: directly handling both entity and relation prediction tasks in inductive settings. Empirically, we show that TRIX outperforms the state-of-the-art fully inductive models in zero-shot entity and relation predictions in new domains, and outperforms large-context LLMs in out-of-domain predictions. The source code is available at https://github.com/yuchengz99/TRIX.
Knowledge Graphs (KGs) store human knowledge in the form of entities (nodes) and relations, and are used extensively in various applications. KG embeddings are an effective approach to addressing tasks like knowledge discovery, link prediction, and reasoning. This is often done by allocating and learning embedding tables for all or a subset of the entities. As this scales linearly with the number of entities, learning embedding models in real-world KGs with millions of nodes can be computationally intractable. To address this scalability problem, our model, PathE, only allocates embedding tables for relations (which are typically orders of magnitude fewer than the entities) and requires less than 25% of the parameters of previous parameter efficient methods. Rather than storing entity embeddings, we learn to compute them by leveraging multiple entity-relation paths to contextualise individual entities within triples. Evaluated on four benchmarks, PathE achieves state-of-the-art performance in relation prediction, and remains competitive in link prediction on path-rich KGs while training on consumer-grade hardware. We perform ablation experiments to test our design choices and analyse the sensitivity of the model to key hyper-parameters. PathE is efficient and cost-effective for relationally diverse and well-connected KGs commonly found in real-world applications.
Multi-relational networks capture intricate relationships in data and have diverse applications across fields such as biomedical, financial, and social sciences. As networks derived from increasingly large datasets become more common, identifying efficient methods for representing and analyzing them becomes crucial. This work extends the Prime Adjacency Matrices (PAMs) framework, which employs prime numbers to represent distinct relations within a network uniquely. This enables a compact representation of a complete multi-relational graph using a single adjacency matrix, which, in turn, facilitates quick computation of multi-hop adjacency matrices. In this work, we enhance the framework by introducing a lossless algorithm for calculating the multi-hop matrices and propose the Bag of Paths (BoP) representation, a versatile feature extraction methodology for various graph analytics tasks, at the node, edge, and graph level. We demonstrate the efficiency of the framework across various tasks and datasets, showing that simple BoP-based models perform comparably to or better than commonly used neural models while offering improved speed and interpretability.
Knowledge graph (KG) completion aims to identify additional facts that can be inferred from the existing facts in the KG. Recent developments in this field have explored this task in the inductive setting, where at test time one sees entities that were not present during training; the most performant models in the inductive setting have employed path encoding modules in addition to standard subgraph encoding modules. This work similarly focuses on KG completion in the inductive setting, without the explicit use of path encodings, which can be time-consuming and introduces several hyperparameters that require costly hyperparameter optimization. Our approach uses a Transformer-based subgraph encoding module only; we introduce connection-biased attention and entity role embeddings into the subgraph encoding module to eliminate the need for an expensive and time-consuming path encoding module. Evaluations on standard inductive KG completion benchmark datasets demonstrate that our \textbf{C}onnection-\textbf{B}iased \textbf{Li}nk \textbf{P}rediction (CBLiP) model has superior performance to models that do not use path information. Compared to models that utilize path information, CBLiP shows competitive or superior performance while being faster. Additionally, to show that the effectiveness of connection-biased attention and entity role embeddings also holds in the transductive setting, we compare CBLiP's performance on the relation prediction task in the transductive setting.
While being one of the most popular question types, simple questions such as "Who is the author of Cinderella?", are still not completely solved. Surprisingly, even the most powerful modern Large Language Models are prone to errors when dealing with such questions, especially when dealing with rare entities. At the same time, as an answer may be one hop away from the question entity, one can try to develop a method that uses structured knowledge graphs (KGs) to answer such questions. In this paper, we introduce Konstruktor - an efficient and robust approach that breaks down the problem into three steps: (i) entity extraction and entity linking, (ii) relation prediction, and (iii) querying the knowledge graph. Our approach integrates language models and knowledge graphs, exploiting the power of the former and the interpretability of the latter. We experiment with two named entity recognition and entity linking methods and several relation detection techniques. We show that for relation detection, the most challenging step of the workflow, a combination of relation classification/generation and ranking outperforms other methods. We report Konstruktor's strong results on four datasets.
Inductive relation prediction (IRP) -- where entities can be different during training and inference -- has shown great power for completing evolving knowledge graphs. Existing works mainly focus on using graph neural networks (GNNs) to learn the representation of the subgraph induced from the target link, which can be seen as an implicit rule-mining process to measure the plausibility of the target link. However, these methods cannot differentiate the target link and other links during message passing, hence the final subgraph representation will contain irrelevant rule information to the target link, which reduces the reasoning performance and severely hinders the applications for real-world scenarios. To tackle this problem, we propose a novel \textit{single-source edge-wise} GNN model to learn the \textbf{R}ule-induc\textbf{E}d \textbf{S}ubgraph represen\textbf{T}ations (\textbf{REST}), which encodes relevant rules and eliminates irrelevant rules within the subgraph. Specifically, we propose a \textit{single-source} initialization approach to initialize edge features only for the target link, which guarantees the relevance of mined rules and target link. Then we propose several RNN-based functions for \textit{edge-wise} message passing to model the sequential property of mined rules. REST is a simple and effective approach with theoretical support to learn the \textit{rule-induced subgraph representation}. Moreover, REST does not need node labeling, which significantly accelerates the subgraph preprocessing time by up to \textbf{11.66$\times$}. Experiments on inductive relation prediction benchmarks demonstrate the effectiveness of our REST. Our code is available at https://github.com/smart-lty/REST.
Panoptic Scene Graph Generation (PSG) aims to segment objects and recognize their relations, enabling the structured understanding of an image. Previous methods focus on predicting predefined object and relation categories, hence limiting their applications in the open world scenarios. With the rapid development of large multimodal models (LMMs), significant progress has been made in open-set object detection and segmentation, yet open-set relation prediction in PSG remains unexplored. In this paper, we focus on the task of open-set relation prediction integrated with a pretrained open-set panoptic segmentation model to achieve true open-set panoptic scene graph generation (OpenPSG). Our OpenPSG leverages LMMs to achieve open-set relation prediction in an autoregressive manner. We introduce a relation query transformer to efficiently extract visual features of object pairs and estimate the existence of relations between them. The latter can enhance the prediction efficiency by filtering irrelevant pairs. Finally, we design the generation and judgement instructions to perform open-set relation prediction in PSG autoregressively. To our knowledge, we are the first to propose the open-set PSG task. Extensive experiments demonstrate that our method achieves state-of-the-art performance in open-set relation prediction and panoptic scene graph generation. Code is available at \url{https://github.com/franciszzj/OpenPSG}.
Cross-document Relation Extraction aims to predict the relation between target entities located in different documents. In this regard, the dominant models commonly retain useful information for relation prediction via bridge entities, which allows the model to elaborately capture the intrinsic interdependence between target entities. However, these studies ignore the non-bridge entities, each of which co-occurs with only one target entity and offers the semantic association between target entities for relation prediction. Besides, the commonly-used dataset--CodRED contains substantial NA instances, leading to the prediction bias during inference. To address these issues, in this paper, we propose a novel graph-based cross-document RE model with non-bridge entity enhancement and prediction debiasing. Specifically, we use a unified entity graph to integrate numerous non-bridge entities with target entities and bridge entities, modeling various associations between them, and then use a graph recurrent network to encode this graph. Finally, we introduce a novel debiasing strategy to calibrate the original prediction distribution. Experimental results on the closed and open settings show that our model significantly outperforms all baselines, including the GPT-3.5-turbo and InstructUIE, achieving state-of-the-art performance. Particularly, our model obtains 66.23% and 55.87% AUC points in the official leaderboard\footnote{\url{https://codalab.lisn.upsaclay.fr/competitions/3770#results}} under the two settings, respectively, ranking the first place in all submissions since December 2023. Our code is available at https://github.com/DeepLearnXMU/CoRE-NEPD.
Scene Graph Generation (SGG) is a task that encodes visual relationships between objects in images as graph structures. SGG shows significant promise as a foundational component for downstream tasks, such as reasoning for embodied agents. To enable real-time applications, SGG must address the trade-off between performance and inference speed. However, current methods tend to focus on one of the following: (1) improving relation prediction accuracy, (2) enhancing object detection accuracy, or (3) reducing latency, without aiming to balance all three objectives simultaneously. To address this limitation, we propose a novel architecture, inference method, and relation prediction model. Our proposed solution, the REACT model, achieves the highest inference speed among existing SGG models, improving object detection accuracy without sacrificing relation prediction performance. Compared to state-of-the-art approaches, REACT is 2.7 times faster (with a latency of 23 ms) and improves object detection accuracy by 58.51%. Furthermore, our proposal significantly reduces model size, with an average of 5.5x fewer parameters. Code is available at https://github.com/Maelic/SGG-Benchmark
Knowledge Graphs (KGs) are widely employed in artificial intelligence applications, such as question-answering and recommendation systems. However, KGs are frequently found to be incomplete. While much of the existing literature focuses on predicting missing nodes for given incomplete KG triples, there remains an opportunity to complete KGs by exploring relations between existing nodes, a task known as relation prediction. In this study, we propose a relations prediction model that harnesses both textual and structural information within KGs. Our approach integrates walks-based embeddings with language model embeddings to effectively represent nodes. We demonstrate that our model achieves competitive results in the relation prediction task when evaluated on a widely used dataset.
Information extraction (IE) is an important task in Natural Language Processing (NLP), involving the extraction of named entities and their relationships from unstructured text. In this paper, we propose a novel approach to this task by formulating it as graph structure learning (GSL). By formulating IE as GSL, we enhance the model's ability to dynamically refine and optimize the graph structure during the extraction process. This formulation allows for better interaction and structure-informed decisions for entity and relation prediction, in contrast to previous models that have separate or untied predictions for these tasks. When compared against state-of-the-art baselines on joint entity and relation extraction benchmarks, our model, GraphER, achieves competitive results.
Aiming to accurately predict missing edges representing relations between entities, which are pervasive in real-world Knowledge Graphs (KGs), relation prediction plays a critical role in enhancing the comprehensiveness and utility of KGs. Recent research focuses on path-based methods due to their inductive and explainable properties. However, these methods face a great challenge when lots of reasoning paths do not form Closed Paths (CPs) in the KG. To address this challenge, we propose Anchoring Path Sentence Transformer (APST) by introducing Anchoring Paths (APs) to alleviate the reliance of CPs. Specifically, we develop a search-based description retrieval method to enrich entity descriptions and an assessment mechanism to evaluate the rationality of APs. APST takes both APs and CPs as the inputs of a unified Sentence Transformer architecture, enabling comprehensive predictions and high-quality explanations. We evaluate APST on three public datasets and achieve state-of-the-art (SOTA) performance in 30 of 36 transductive, inductive, and few-shot experimental settings.
Panoptic Scene Graph Generation (PSG) aims at achieving a comprehensive image understanding by simultaneously segmenting objects and predicting relations among objects. However, the long-tail problem among relations leads to unsatisfactory results in real-world applications. Prior methods predominantly rely on vision information or utilize limited language information, such as object or relation names, thereby overlooking the utility of language information. Leveraging the recent progress in Large Language Models (LLMs), we propose to use language information to assist relation prediction, particularly for rare relations. To this end, we propose the Vision-Language Prompting (VLPrompt) model, which acquires vision information from images and language information from LLMs. Then, through a prompter network based on attention mechanism, it achieves precise relation prediction. Our extensive experiments show that VLPrompt significantly outperforms previous state-of-the-art methods on the PSG dataset, proving the effectiveness of incorporating language information and alleviating the long-tail problem of relations. Code is available at \url{https://github.com/franciszzj/TP-SIS}.
Most biomedical pretrained language models are monolingual and cannot handle the growing cross-lingual requirements. The scarcity of non-English domain corpora, not to mention parallel data, poses a significant hurdle in training multilingual biomedical models. Since knowledge forms the core of domain-specific corpora and can be translated into various languages accurately, we propose a model called KBioXLM, which transforms the multilingual pretrained model XLM-R into the biomedical domain using a knowledge-anchored approach. We achieve a biomedical multilingual corpus by incorporating three granularity knowledge alignments (entity, fact, and passage levels) into monolingual corpora. Then we design three corresponding training tasks (entity masking, relation masking, and passage relation prediction) and continue training on top of the XLM-R model to enhance its domain cross-lingual ability. To validate the effectiveness of our model, we translate the English benchmarks of multiple tasks into Chinese. Experimental results demonstrate that our model significantly outperforms monolingual and multilingual pretrained models in cross-lingual zero-shot and few-shot scenarios, achieving improvements of up to 10+ points. Our code is publicly available at https://github.com/ngwlh-gl/KBioXLM.
Many downstream inference tasks for knowledge graphs, such as relation prediction, have been handled successfully by knowledge graph embedding techniques in the transductive setting. To address the inductive setting wherein new entities are introduced into the knowledge graph at inference time, more recent work opts for models which learn implicit representations of the knowledge graph through a complex function of a network's subgraph structure, often parametrized by graph neural network architectures. These come at the cost of increased parametrization, reduced interpretability and limited generalization to other downstream inference tasks. In this work, we bridge the gap between traditional transductive knowledge graph embedding approaches and more recent inductive relation prediction models by introducing a generalized form of harmonic extension which leverages representations learned through transductive embedding methods to infer representations of new entities introduced at inference time as in the inductive setting. This harmonic extension technique provides the best such approximation, can be implemented via an efficient iterative scheme, and can be employed to answer a family of conjunctive logical queries over the knowledge graph, further expanding the capabilities of transductive embedding methods. In experiments on a number of large-scale knowledge graph embedding benchmarks, we find that this approach for extending the functionality of transductive knowledge graph embedding models to perform knowledge graph completion and answer logical queries in the inductive setting is competitive with--and in some scenarios outperforms--several state-of-the-art models derived explicitly for such inductive tasks.
Knowledge graphs play a vital role in numerous artificial intelligence tasks, yet they frequently face the issue of incompleteness. In this study, we explore utilizing Large Language Models (LLM) for knowledge graph completion. We consider triples in knowledge graphs as text sequences and introduce an innovative framework called Knowledge Graph LLM (KG-LLM) to model these triples. Our technique employs entity and relation descriptions of a triple as prompts and utilizes the response for predictions. Experiments on various benchmark knowledge graphs demonstrate that our method attains state-of-the-art performance in tasks such as triple classification and relation prediction. We also find that fine-tuning relatively smaller models (e.g., LLaMA-7B, ChatGLM-6B) outperforms recent ChatGPT and GPT-4.
Joint entity and relation extraction is the fundamental task of information extraction, consisting of two subtasks: named entity recognition and relation extraction. However, most existing joint extraction methods suffer from issues of feature confusion or inadequate interaction between the two subtasks. Addressing these challenges, in this work, we propose a Co-Attention network for joint entity and Relation Extraction (CARE). Our approach includes adopting a parallel encoding strategy to learn separate representations for each subtask, aiming to avoid feature overlap or confusion. At the core of our approach is the co-attention module that captures two-way interaction between the two subtasks, allowing the model to leverage entity information for relation prediction and vice versa, thus promoting mutual enhancement. Through extensive experiments on three benchmark datasets for joint entity and relation extraction (NYT, WebNLG, and SciERC), we demonstrate that our proposed model outperforms existing baseline models. Our code will be available at https://github.com/kwj0x7f/CARE.
In this paper, we explore the potential of Vision-Language Models (VLMs), specifically CLIP, in predicting visual object relationships, which involves interpreting visual features from images into language-based relations. Current state-of-the-art methods use complex graphical models that utilize language cues and visual features to address this challenge. We hypothesize that the strong language priors in CLIP embeddings can simplify these graphical models paving for a simpler approach. We adopt the UVTransE relation prediction framework, which learns the relation as a translational embedding with subject, object, and union box embeddings from a scene. We systematically explore the design of CLIP-based subject, object, and union-box representations within the UVTransE framework and propose CREPE (CLIP Representation Enhanced Predicate Estimation). CREPE utilizes text-based representations for all three bounding boxes and introduces a novel contrastive training strategy to automatically infer the text prompt for union-box. Our approach achieves state-of-the-art performance in predicate estimation, mR@5 27.79, and mR@20 31.95 on the Visual Genome benchmark, achieving a 15.3\% gain in performance over recent state-of-the-art at mR@20. This work demonstrates CLIP's effectiveness in object relation prediction and encourages further research on VLMs in this challenging domain.