Additional Feedback: - Line 70: DB methods are based on Minkowski distance, however, in this paper the duality is stablished only for the case of Frobenius norm, i.e. Minkowski distance with p 2. It would be nice that authors provide a deeper explanation about the role on parameter p in DB methods. What is the optimal value of p in state of the arts methods? The sentence: "the regularizer 5 and 6" should be changed to "the regularizer 4 and 5" (check equation numbering) - Line 180: As a regularizer having several terms, it would be convenient to consider different regularizer coefficients as hyperparameters. In fact, in supplemental material (lines 36-37) the cost function has 3 hyperparameters: lambda, lambda_1 and lambda_2.

There are roughly two different approaches in the literature for knowledge graph completion (KGC), namely distance based (DB) models and tensor factorization based (TFB) models. Although both approaches have their own advantages and disadvantages over each other, TFB models cannot attain state-of-the-art performance due to overfitting problem, and therefore various regularizers are employed for TFB models. In the paper, authors propose a regularizer for TFB models, namely Duality-induced Regularization (DURA), which is inspired by the score functions of the DB models. They come up with a dual problem which involves a distance based KGC model, and show that when the aforementioned regularizer is employed for the primal problem (i.e. TFB model), both problems become equivalent.

The theoretical analysis of the model is insufficient. For example, the author does not give an analysis of the full expressiveness of the model. That is, given any world with correct answers of some first-order logic queries W and false answers Wc, does there exist an assignment for model parameters that correctly classifies the entities in W and Wc? The reviewer is especially curious about the theoretical analysis of the proposed probabilistic negation operator because there are no comparative empirical results on answering queries with negation (all existing models cannot deal with negation). On EPFO queries, the author compared the proposed model only with two baselines.

The paper introduces a new method to query knowledge graphs via probabilistic embeddings based on the Beta distribution. The paper is well written and relevant to the NeurIPS community. All reviewers and the AC support acceptance of the paper for its contributions, notably since it proposes a novel and promising approach that enables logical negation and FOL queries on KG embeddings and as such extends the applicability of embeddings for KG inference tasks. However, please consider revising your paper to take feedback from reviewers into account e.g., in particular regarding the concerns raised related to empirical evaluation and theoretical analysis.

Graph neural networks are prominent models for representation learning over graph-structured data. While the capabilities and limitations of these models are well-understood for simple graphs, our understanding remains incomplete in the context of knowledge graphs. Our goal is to provide a systematic understanding of the landscape of graph neural networks for knowledge graphs pertaining to the prominent task of link prediction. Our analysis entails a unifying perspective on seemingly unrelated models and unlocks a series of other models. The expressive power of various models is characterized via a corresponding relational Weisfeiler-Leman algorithm.

Recent advancements in large language models have demonstrated significant potential in the automated construction of knowledge graphs from unstructured text. This paper builds upon our previous work [16], which evaluated various models using metrics like precision, recall, F1 score, triple matching, and graph matching, and introduces a refined approach to address the critical issues of hallucination and omission. We propose an enhanced evaluation framework incorporating BERTScore for graph similarity, setting a practical threshold of 95% for graph matching. Our experiments focus on the Mistral model, comparing its original and fine-tuned versions in zero-shot and few-shot settings. We further extend our experiments using examples from the KELM-sub training dataset, illustrating that the fine-tuned model significantly improves knowledge graph construction accuracy while reducing the exact hallucination and omission. However, our findings also reveal that the fine-tuned models perform worse in generalization tasks on the KELM-sub dataset. This study underscores the importance of comprehensive evaluation metrics in advancing the state-of-the-art in knowledge graph construction from textual data.

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.

Question answering systems for knowledge graph (KGQA), answer factoid questions based on the data in the knowledge graph. KGQA systems are complex because the system has to understand the relations and entities in the knowledge-seeking natural language queries and map them to structured queries against the KG to answer them. In this paper, we introduce Chronos, a comprehensive evaluation framework for KGQA at industry scale. It is designed to evaluate such a multi-component system comprehensively, focusing on (1) end-to-end and component-level metrics, (2) scalable to diverse datasets and (3) a scalable approach to measure the performance of the system prior to release. In this paper, we discuss the unique challenges associated with evaluating KGQA systems at industry scale, review the design of Chronos, and how it addresses these challenges. We will demonstrate how it provides a base for data-driven decisions and discuss the challenges of using it to measure and improve a real-world KGQA system.

That addressed my 3rd concern to some extent (although it seems like your model requires many more epochs compared to ComplEx and I wonder how ComplEx will perform given the same number of epochs and using uniform negative sampling, but this is not a major concern). I'm not yet convinced about the issue I raised regarding relation normalization though. "We also found that the relation normalization can improve the ComplEx model as well. But it is till worse than QuatE." Why not provide some actual numbers similar to the other cases so we can see how much better QuatE is compared to ComplEx when they both use relation normalization?

The paper attempts learn better entity and relation embeddings for knowledge graphs. In this regard, the authors employ quarternion algebra with Hamilton product, which is used as the scoring function for knowledge triplets. Hamilton product is asymmetric, which is claimed to be beneficial for modeling directed egdes in a knowledge graph. Further the paper outperforms many well established methods and the authors seem to have done an exhaustive set of experiments. However, all the reviewers are in consensus that motivation for the use of quarternions is not clear, e.g. the paper does a poor job in demonstrating how does more degrees of freedom in rotation help in learning better embedding.