Abstract 1 Introduction 2 Machine Learning and Knowledge Graphs 3 Gaps in Machine Learning and Knowledge Graphs and Next Challenges 4 Conclusion References

Machine Learning and Knowledge Graphs: Existing Gaps and Future Research Challenges

Claudia d’Amato ORCID University of Bari, Italy Louis Mahon ORCID Oxford University, United Kingdom Pierre Monnin ORCID Université Côte d’Azur, Inria, CNRS, I3S, France Giorgos Stamou ORCID National Technical University of Athens, Greece
Abstract

The graph model is nowadays largely adopted to model a wide range of knowledge and data, spanning from social networks to knowledge graphs (KGs), representing a successful paradigm of how symbolic and transparent AI can scale on the World Wide Web. However, due to their unprecedented volume, they are generally tackled by Machine Learning (ML) and mostly numeric based methods such as graph embedding models (KGE) and deep neural networks (DNNs). The latter methods have been proved lately very efficient, leading the current AI spring. In this vision paper, we introduce some of the main existing methods for combining knowledge graphs (KGs) and ML, divided into two categories: those using ML to improve knowledge graphs (KGs), and those using knowledge graphs (KGs) to improve results on ML tasks. From this introduction, we highlight research gaps and perspectives that we deem promising and currently under-explored for the involved research communities, spanning from KG support for LLM prompting, integration of KG semantics in ML models to symbol-based methods, interpretability of ML models, and the need for improved benchmark datasets. In our opinion, such perspectives are stepping stones in an ultimate view of KGs as central assets for neuro-symbolic and explainable AI.

Keywords and phrases:
Graph-based Learning, Knowledge Graph Embeddings, Large Language Models, Explainable AI, Knowledge Graph Completion & Curation
Category:
Vision
Funding:
Claudia d’Amato: Partially supported by the project FAIR – Future AI Research (PE00000013), spoke 6 – Symbiotic AI (https://future-ai-research.it/), under the NRRP MUR program funded by the NextGenerationEU and by the project HypeKG – Hybrid Prediction and Explanation with Knowledge Graphs (H53D23003700006), under PRIN 2022 program funded by MUR.
Pierre Monnin: Supported by the AT2TA project (https://at2ta.loria.fr), funded by the French National Research Agency (“Agence Nationale de la Recherche” – ANR) under grant ANR-22-CE23-0023.
Copyright and License:
[Uncaptioned image] © Claudia d’Amato, Louis Mahon, Pierre Monnin, and Giorgos Stamou; licensed under Creative Commons License CC-BY 4.0
2012 ACM Subject Classification:
Information systems World Wide Web
; Computing methodologies Artificial intelligence
Received:
2023-06-30  
Accepted:
2023-11-17  
Published:
2023-12-19
Part Of:
TGDK, Volume 1, Issue 1 (Trends in Graph Data and Knowledge)

1 Introduction

Graph data refers to data that lends itself naturally to being represented as a graph-based data model. Examples of graph data are social networks, computer networks, entailment graphs [93], concept graphs [26]. Several standards have been proposed to represent graph data, including the W3C devised standards OWL, RDF, and RDFS. These enable easy sharing and combining of graph data from different sources, and so further facilitate the adoption of the graph formalism.

Among the several types of graph data in widespread use, one prominent example is the Knowledge Graph (knowledge graph (KG)). A knowledge graph (KG) aims to convey knowledge of the real world and represent it conforming to a graph-based data model, where nodes represent concepts of interest, such as human or lion, and edges represent possibly different relations between these entities, such as isTypeOf or isPredatorOf [68]. A closely related concept that we do not discuss any further is Property Graph, where both nodes and edges can have multiple properties which are represented as key-value pairs (the interested reader may refer to [68] for further details). Graphs data may be stored in native graph databases or relational databases [68].

When referring to the representation of information, the term ‘knowledge’, as opposed to ‘data’, is usually what is predicated of humans. It suggests the information is stored in a more structured and actionable manner, e.g. that it enables reasoning. This distinction from ‘data’ was first made in relation to the concept of a knowledge base (KB) [104], in the context of expert systems [64], in order to distinguish them from databases using, e.g., lookup tables or hash tables. A knowledge base (KB) is a representation of information as a set of facts or sentences [161].

A knowledge graph (KG) can be formalized as a triple of sets E,R,T, where E is a set of entities, R a set of relations, and T is of the form {(s,p,o)|s,oE,pR} [29], by which it is immediately equivalent to a knowledge base (KB), considered as a set of facts. Moreover, a graph G=(𝒩,), can be written equivalently as a set of facts, by equating 𝒩 with the set of all entities appearing as arguments to facts, and equating each fact s,p,o to a directed edge from s (subject) to o (object) labeled p (predicate). On a higher level, one difference between a knowledge graph (KG) and knowledge base (KB) as a set of facts, is that the former has a greater emphasis on the connection to the graph-based data model, and is more directly associated with the agreed formatting standards for graph data. Our discussion here does not require precise disambiguation of the term and in the remainder of this paper, we use the two terms interchangeably.

A closely related concept to a knowledge graph (KG) is an ontology. Intuitively, an ontology defines a set of object types, and how these types relate to each other. For example, if the domain is living things, then an ontology would specify that human and lion are two distinct types of a mammal, mammal and reptile are two distinct types of vertebrates etc. Formally, an ontology has been defined as comprising two components, the TBox, which introduces the vocabulary of an application domain, and the ABox, which contains assertions about named individuals in terms of this vocabulary [11]. Often the set of concepts in a knowledge graph (KG) forms an ontology, and their ontological relations can be incorporated into the structure of the knowledge graph (KG). In the remainder of this paper, we will treat the term “ontology” as interchangeable with “knowledge base”, as defined above.

Many important applications, such as e-Commerce [208], financial trading [29], semantic search [205], fact-checking [165], recommendation [195], (medical) decision support systems [202], question answering [73] and even machine translation [221, 135] benefit from access to real-world knowledge in a form that is both machine-readable and human-interpretable (i.e. entities, properties, relations and types). There has thus been a general convergence on knowledge graphs (KGs) as the means to represent and store such knowledge. This interest from academia and especially from industry, has led to several large-scale efforts at constructing knowledge graphs (KGs). Some are freely available and accessible, such as DBpedia [9]111https://www.dbpedia.org/, Freebase [18]222https://developers.google.com/freebase, YAGO [172]333https://yago-knowledge.org/, Wikidata [187]444https://www.wikidata.org/. Others are private, developed for commercial use by companies such as Google, Amazon, IKEA, Uber, Microsoft, Facebook and LinkedIn. The interested reader could refer to [69] for a comprehensive overview of the history and current use of knowledge graphs (KGs).

The amount of data that may be of interest to knowledge graph (KG) applications is very large, e.g., English-language Wikipedia contains close to seven million articles at the time of writing555https://en.wikipedia.org/wiki/Wikipedia:Statistics. Developing knowledge graphs (KGs) of this size is a difficult, expensive process, requiring the integration of multiple sources of information, along with input from human experts and crowdsourcing. Despite significant efforts for making knowledge graphs (KGs) as comprehensive and reliable as possible, they tend to suffer from incompleteness and noise, due to the complex building process [69, 193]. This has prompted a search for automatic construction and enrichment [83, 190], often through the use of machine learning (ML). Indeed, the machine learning (ML) world has advanced considerably in the past decade, particularly with the rise of deep learning. From the victory of AlexNet in the ILSVRC in 2012 [96], to the release of ChatGPT in 2022, deep learning has come to dominate machine learning (ML) research and powers many industry applications.

One method of combining the world of knowledge and knowledge graphs (KGs) with ML, and especially deep learning, is to form a vector representation of each node and edge in the knowledge graph (KG), by optimizing some loss function based on the graph structure. The resulting set of vector representations is known as a knowledge graph embedding (KGE) and it enables several important use cases. In one direction, knowledge graph embeddings (KGEs) allow the use of predictive machine learning techniques to improve the knowledge graph (KG), for example, by knowledge graph (KG) completion, where sparse knowledge graphs (KGs), such as those automatically constructed from text [89], are augmented with missing triples. Also, by using the deep neural network (DNN) feature vector extracted from a video, knowledge graph embeddings (KGEs) have been used to represent the content of a video as a graph [120]. Other uses of knowledge graph embeddings (KGEs) include triple (fact) classification, for assessing if a fact within the KG is correct or not, knowledge graph (KG) question answering and node clustering. Node clustering indeed can reveal similarities and differences between groups of nodes in the knowledge graph (KG) [59] and this can, for example, help uncover certain types of users in a social network, or article subjects, in a citation network. knowledge graph (KG) question answering uses the information in a knowledge graph (KG) to answer natural language questions [73]. In the other direction, knowledge graph embeddings (KGEs) allow knowledge graphs (KGs) to be used to improve machine learning (ML) performance: for example, knowledge-aware visual question-answering [107], or reasoning of large language models (LLMs) [212].

In this paper, we introduce some of the main existing methods for combining knowledge graphs (KGs) and machine learning (ML), divided into two categories: those using machine learning (ML) to improve knowledge graphs (KGs), and those using knowledge graphs (KGs) to improve results on machine learning (ML) tasks. From this introduction, we draw research gaps and perspectives that we consider urgent as well as promising. These gaps and perspectives are summarized in Table 1 (and analyzed and developed in section 3) and are concerned with the topics: LLM prompting, KG semantics and KGE models, symbol-based methods, ML model interpretability, and benchmark datasets. For each topic, we provide a description of some unsolved problems (gaps) that we consider to be of particular importance for future research work, and provide our views, claims, and proposals to overcome them. In particular, we support the use of KGs to formalize LLM prompting (e.g., providing concept, defining sequencing). We claim that KGE could benefit from the injection of KG semantics and usage of various reasoning capabilities, e.g., in terms of performance or negative generation. Informative negatives could also be generated by exploiting symbol-based method learning disjointness axioms (that are often missing). With respect to interpretability using knowledge graph (KG), we argue that little progress has been made, and that in-model KG-based approaches that demonstrably produce reliable explanations are needed to validate machine learning (ML) results. Assessing these improvements in KGE performance or interpretability also calls for extensive empirical evaluations. Such evaluations require benchmark datasets that feature various schema constructs or levels of semantics that are currently lacking, unnoticed, or uncommon in the state of the art. That is why, we call for a systematic characterization and collection of available datasets as well as the creation of synthetic KG generators to produce tailored datasets to support experiments.

Table 1: Overview of the research topics considered, the identified gaps, and our claims and proposals to address them.
Topics Gaps Claims & Proposals
LLM prompting LLM hallucinations No formalized process to interact with LLMs Use KG at inference time to formalize the dialogue process between humans and LLM Ground prompts in knowledge (e.g., adding context, analyzing response, defining prompt sequence)
KG semantics & KGE models Semantics not (fully) considered Deductive capabilities not (fully) considered Investigate the full exploitation of KG semantics (e.g., to improve model performance, to generate informative negatives) Possibly with different reasoning types (deductive, analogical) Empirical full assessment of the role of semantics
Symbol-based methods Largely disregarded Scalability issues Leverage mining of disjointness axioms to generate informative negatives needed in ML models training Alleviate scalability issues
Interpretability of ML models Pre-/post-model approaches do not fulfill necessary requirements In-model KG-based explainable approaches not proved to improve interpretability Infuse KG in ML training Demonstrate that this improves ML interpretability
Benchmark datasets Lack of needed characteristics (e.g., schemas) Some datasets under-used or unnoticed Develop a unified repository of datasets Automatically crawl in the wild and qualify datasets w.r.t. needed characteristics Create synthetic KG generators that generate both tailored schemas and KGs

The remainder of this paper is organized as follows. Section 2 provides an overview of existing work linking knowledge graph (KG) and machine learning (ML), under the framework of knowledge graphs (KGs) for machine learning (ML) (Section 2.1) and machine learning (ML) for knowledge graphs (KGs) (Section 2.2). Section 3 describes some gaps in the literature that we deem important, and outlines our vision of future research directions for filling these gaps. We particularly focus on: the use of knowledge graphs (KGs) for prompting LLMs (Section 3.1), the integration of KG semantics and associated reasoning capabilities in KGE models for improved performance and handling of negatives (Section 3.2), the potential of symbol-based machine learning (ML) for knowledge graphs (KGs) (Section 3.3), the attempts to use knowledge graphs (KGs) for explainable AI (Section 3.4), and the need for further benchmark datasets and metrics to assess improvements brought by aforementioned directions (Section 3.5). Finally, Section 4 concludes and summarizes this work.

2 Machine Learning and Knowledge Graphs

In this section we focus on the interlink between machine learning (ML) and knowledge graphs (KGs). As sketched in [19], two main perspectives can be drawn: a) knowledge graphs (KGs) as input to machine learning (ML), whose main goal is to improve the performance in many learning tasks, e.g. question answering, image classification, instance disambiguation, text summarization, etc.; b) machine learning (ML) as input to KG, whose main goal is to improve the KG itself, e.g. in terms of coverage, quality, and adding new facts. In the following, we analyze the most impactful approaches in the literature, along these two perspectives.

2.1 Knowledge Graphs as Input to Machine Learning

knowledge graphs (KGs), as representations of background and contextual knowledge in a structured form, have gained significant interest from both academia and industry in the area of machine learning, enabling models to tackle complicated tasks that need prior knowledge [44]. machine learning (ML) models are knowledge-aware and thus can benefit from the incorporation of information that effectively captures the semantic meanings [83]. From traditional machine learning (ML) to modern deep neural networks (DNNs), knowledge graphs (KGs) can offer advantages, enhancing the functionality of ML systems by addressing various challenges and solving problems. In the following, we will briefly describe key applications of knowledge graphs (KGs) in machine learning (ML). Specifically, in Section 2.1.1, we elaborate on the key methodologies for incorporating knowledge graphs (KGs) in machine learning (ML), with a particular emphasis on the shortcomings they seek to mitigate. In Section 2.1.2, our focus shifts to recent advancements in describing large language models (LLMs) enhancement using knowledge graphs (KGs), a domain we believe will be increasingly significant in the future, given the widespread adoption of large language models (LLMs).

2.1.1 Addressing Machine Learning Challenges with Knowledge Graphs

knowledge graphs (KGs) represent semantic descriptions of entity types and properties with a well-defined meaning. Hence, they can be employed when attempting to automatically extract features (that are difficult to measure or quantify directly) from data points [92, 133]. A feature extractor is a transformation function that maps data from a higher-dimensional space to a lower-dimensional vector space, encompassing a wide range of dimensionality reduction techniques. Early approaches map the output of feature extractors to hierarchies [100, 41] or use hierarchies as input to feature extraction [162], or use large-scale real world labels and their inter-relations [140, 39]. Many recent approaches rely on image annotation that is linked to knowledge graphs (KGs), such as WordNet [127], like the image databases that have been established based on these concepts (see for example [40, 94]). On the other hand, knowledge graph embedding methods can be also seen as methods to build semantic feature extractors. This involves the mapping of entities and relations into low-dimensional vectors, effectively capturing their semantic meanings in a form that is more compatible to deep learning models [192, 138]. This field of research offers significant opportunities for exploration and advancement [145, 112] and will be analyzed in more detail in the next sections.

deep neural networks (DNNs) require a substantial amount of data for training. Sometimes, the data can either be unavailable or come with a high cost of collection. This issue, commonly referred to as the sample shortage, comes with different settings. Among them, the zero-shot learning (ZSL) [141] [49, 194] and the few-shot learning (FSL) [196] has recently gained significant research attention and call for the use of structured knowledge [71]. ZSL is formally defined as the task of predicting labels for new classes that have never been encountered during training, while FSL involves the task of predicting labels for new classes for which only a small number of labeled samples are provided. In both cases, the proposed solutions try to somehow transfer knowledge from seen classes to unseen classes (see [228] for recent advances on transfer learning, specifically describing knowledge transfer). Here, knowledge graphs (KGs) play an important role, since they can represent background knowledge such as class hierarchies, instances of classes (samples), features, properties, relations as well as meta information like model parameters, providing the necessary auxiliary information. The interested reader can check [194] and [196] for a systematic review on ZSL and FSL, [71] and [27] for ZSL and FSL based on external knowledge (covering some works that use knowledge graphs (KGs) as the background knowledge), [133] covers the use of knowledge graphs specifically for visual transfer learning and [28] that is a recent thorough survey paper that specifically classifies and analyzes methods utilizing knowledge graphs (KGs) for ZSL and FSL.

The capabilities of deep neural networks (DNNs) have enabled the development of numerous models and techniques to address challenging problems, particularly those involving multimodal data. In this context, multimodal machine learning [14, 61, 132] has emerged as one of the rapidly advancing fields within artificial intelligence, addressing various challenging problems, including visual question answering, visual reasoning, image captioning, image-text retrieval, visual storytelling, visual dialoguing and others [3, 66, 217, 204, 169, 45, 45, 95]. Not surprisingly, the proposed deep neural networks (DNNs) models (mainly based on transformers) often struggle with generalization to various concepts and scenarios that demand commonsense knowledge, or understanding of abstract entities, facts, and real-world events, due to the lack of formal representation of background, contextual and commonsense knowledge [150, 74, 90]. Hence, integrating external knowledge at different stages of multimodal learning, especially in pre-training or fine-tuning, augments the capabilities of models, enabling them to better address a broader range of real-world scenarios. Several proposed deep neural networks (DNNs) models are based on external knowledge that is represented using semantic descriptions stored in knowledge graphs (KGs). In particular, there have been proposed datasets that leverage external knowledge [122, 177, 149, 200] linked to web resources and knowledge graphs (KGs) [106] to learn the alignment between visual and textual information [30] in order to solve multimodal learning tasks. The interested reader can find information in several survey papers classifying and analyzing methods in the area of multimodal learning (see for example [14, 61, 132], specifically presenting works that make use of knowledge graphs (KGs) [119]).

The adoption of symbolic knowledge representation and reasoning as a means to address the opacity of machine learning classifiers is a research domain that has recently garnered significant attention from researchers [58]. The need to provide explanations grounded in domain knowledge with formal semantics has driven the utilization of knowledge graphs (KGs) in explainable AI [32, 111, 42, 25, 180]. As this field holds considerable interest and offers numerous prospects for future research, we discuss it in more detail in Section 3.4.

2.1.2 Knowledge Graphs for Large Language Models

The current machine learning (ML) literature is dominated by Deep Learning solutions that have been proved very effective in multiple domains and for multiple tasks. Particularly, nowadays large language models (LLMs) and related systems are catalyzing the attention of the scientific and industrial community for their impressive ability to provide highly accurate results in a very limited amount of time, as for the case of ChatGPT666https://openai.com/blog/chatgpt and similar solutions. large language models (LLMs) behind these systems (like the GPT models [22] that currently guide ChatGPT) are usually deep learning models that have been trained on huge amounts of text data and are capable of understanding and generating human-like text. Typically, they get a text in their input and provide a text as a response. Lately, they can be also directly connected to other generative models like Midjourney777https://www.midjourney.com/home/ and DALLE-3888https://openai.com/dall-e-3 that get text as input and give image or videos in the output, advancing the user experience and extending the scope of application domains.

There are many ways of using knowledge graphs (KGs) to improve or understand the operation of large language models (LLMs). There are works that aim to enhance the text generation (see for example the survey [216]) or more generally to enhance visiolinguistic learning with knowledge (see for example the survey [119]). In [142] several methods are discussed that try to unify LLMs and KGs, combining their advantages. Among others, methods that use knowledge graphs (KGs) to improve the operation of large language models (LLMs) are analyzed. An interesting approach is to incorporate knowledge graph information into large language models (LLMs) in order to enhance their performance, by advancing the factual knowledge understanding. This is a way to improve the large language model (LLM) performance on knowledge-intensive tasks, and to generate more informed and contextually grounded text. In particular, there are works that try to enhance word representations with knowledge graph embeddings providing context, improving the model’s performance [146], or to learn contextualized representations that capture both linguistic and factual knowledge [118], or to use knowledge graphs (KGs) in pre-training to enhance the model’s understanding of factual knowledge [174, 109]. Other works in the area try to decompose knowledge into separate modules to improve its natural language understanding capabilities [219], or to integrate knowledge graph (KG) and language understanding in a joint pre-training framework [215].

Moreover, there are other approaches for graph-to-text generation integrating knowledge from a knowledge graph into the text generation process, trying to produce more informative and coherent outputs [214]. In this framework, combining language representations with knowledge graph embeddings can be used to enhance the representation of contextualized knowledge [173, 171, 65]. Sentiment knowledge can be also incorporated with the use of knowledge graphs (KGs), thus enhancing the performance of language models with respect to sentiment analysis accuracy [178].

Finally, knowledge graphs (KGs) can be used to prob and possibly understand different aspects of the operation of large language models (LLMs). In particular, knowledge graphs (KGs) can be used to elicit knowledge from language models using automatically generated prompts, enabling targeted information retrieval from the model’s knowledge base [164], or for querying language models effectively, through a query generation technique that leverages explicit context [2], or to contrastively probing large language models (LLMs) to investigate the domain knowledge of pretrained language models by comparing their performance to specially designed contrast models [125]. Prompting can be also used for understanding the limitations large language models (LLMs), revealing scenarios where language models may produce unreliable or incorrect responses [121], or to enable the exploration and understanding of the underlying knowledge captured by large language models (LLMs) [176], or to understand how large language models (LLMs) capture factual knowledge and identify the key factors that contribute to their acquisition of factual information [108].

Of particular significance in this context is the utilization of knowledge graphs (KGs) to validate large language models (LLMs), mitigating the issue of hallucination, that causes the generation of factually incorrect content [84]. Hallucination of large language models (LLMs) poses a substantial challenge to their reliability [15]. Although some large language models (LLMs) are equipped with the ability to explain their predictions, their explanatory capabilities also suffer from hallucination and this has been particularly connected to the criticism that large language models (LLMs) have limited ability to encode factual knowledge [229, 188, 56]. Hence, it becomes crucial to examine and authenticate the knowledge embedded within large language models (LLMs) to prevent hallucination. Recently, there is some work in the area of utilizing KGs for hallucination detection. Specifically, knowledge graphs (KGs) are used as an external source to validate large language models (LLMs) reliability [85], or to develop fact-checking models, identifying and mitigating hallucinations [48]. This is a very interesting area for future work.

In Section 3.1, we outline our viewpoint on the most important research areas that require attention in order to address the challenges discussed here.

2.2 Machine Learning as Input to Knowledge Graphs

From the perspective of machine learning (ML) as input to knowledge graphs (KGs), the main objective is to improve the quality of existing knowledge graphs (KGs) overall. Particularly, given the well-known issues concerning noise and incompleteness of knowledge graphs (KGs), most solutions have focused on KG refinement which actually encompasses several tasks. Among the others, triple classification (aiming at assessing the correctness of a statement in a KG and generally regarded as a binary classification problem) and mostly link/type prediction (aiming at predicting missing links/types between entities and generally regarded as a learning to rank problem) gained most of the attention, aiming at improving/limiting knowledge graph (KG) incompleteness.

Different approaches have been developed over the years, with the goal of improving effectiveness (mostly targeting the link prediction problems) while scaling to very large knowledge graphs (KGs). Mostly, numeric-based methods have been investigated. Among the very first proposals, probabilistic latent variable models from the Statistical Relational Learning (SRL) [54] field (having as main goal the creation of statistical models for relational/graph-based data) have been formalized. Successive and very efficient solutions have been represented by Knowledge Graph Embedding (KGE) models. Other approaches focusing on propositionalization techniques, recently also exploiting Graph Neural Networks (GNN) [201]) have been also pursued. Complementary to these numeric-based solutions, research directions targeting symbol-based models have been also proposed, particularly focusing on rule-based methods for predicting triples in knowledge graphs (KGs).

In the following we summarize the most representative methods for each of the aforementioned categories. We dedicate particular attention to KGE methods that represent the main subject of study for our successive proposals, illustrated in Section 3.2.

2.2.1 Probabilistic Latent Variable Models

Probabilistic Latent Variable Models explain relations between entities by associating each resource to a set of intrinsic latent attributes (i.e. attributes not directly observable in the data) and conditions the probability distribution of the relations between two resources on their latent attributes. All relations are considered conditionally independent given the latent attributes. This allows the information to propagate through the network of interconnected latent variables.

One of the first solutions belonging to this category is the Infinite Hidden Semantic Model (IHSM) [153]. It formalizes a probabilistic latent variable that associates a latent class variable with each node and makes use of constraints expressed in First Order Logic during the learning process. IHSM showed promising results but was found to have limited scaling on large data collections, because of the complexity of the probabilistic inference and learning, which is intractable in general [91].

2.2.2 Knowledge Graph Embedding Models

knowledge graph embedding (KGE) models have received considerable attention because of their impressive ability to scale on very large knowledge graphs (KGs). KGE are numeric-based approaches that convert the data graph into an optimal low-dimensional space in which graph structural information and graph properties are preserved as much as possible [23, 83]. The embedding procedure consists of learning embeddings such that the score of a valid (positive) triple is lower than the score of an invalid triple, i.e. the invalid triples function as negative examples. Graph embedding methods may differ in their main building blocks: the representation space (e.g. point-wise, complex, discrete, Gaussian, manifold), the encoding model (e.g. linear, factorization, neural models) and the scoring function (that can be based on distance, energy, semantic matching or other criteria) [83]. Over the years, several models have been developed. Some are presented below. It should also be noted that several libraries or frameworks such as Deep Graph Library999https://www.dgl.ai/ [191], PyKEEN101010https://github.com/pykeen/pykeen [6], or PyTorch-BigGraph111111https://github.com/facebookresearch/PyTorch-BigGraph [105] have been developed and provide unified implementations of wide ranges of models.

One of the first solutions that has been proposed is RESCAL [139], which performs graph embedding by computing a three-way factorization of an adjacency tensor that represents the multi-graph structure of the data collection. It resulted in a powerful model that was also able to capture complex relational patterns over multiple hops in a graph, however it was not able to scale on very large graph-based data collections (e.g. the whole YAGO or DBpedia). The main limitation was represented by the parameter learning phase, which may take rather long for converging to optimal solutions.

The very first highly scalable embedding model is TransE [20]. It introduces a simple but effective and efficient model: each entity is represented by an embedding vector and each predicate is represented by a (vector) translation operation. The score of a triple is given by the similarity of the translated subject embedding to the object embedding. The optimal embedding and translation vectors for predicates are learned jointly. The method relies on a stochastic optimization process, that iteratively updates the distributed representations by increasing the score of the positive triples i.e. the observed triples, while lowering the score of unobserved triples standing as negative examples. The embedding of all entities and predicates in the KG is learned by minimizing a margin-based ranking loss.

Despite its scalability and effectiveness, TransE remained limited in properly representing various types of properties such as reflexivity, and 1-to-N, N-to-1 and N-to-N relations that can be easily found in knowledge graphs (KGs) (e.g. typeOf as an example of N-to-N relationship). To tackle this limitation while keeping the ability to scale to very large knowledge graphs (KGs), a large family of models has been developed that build on TransE, such as TransH [197] and TransR [113].

Specifically, TransR adopts a score function that projects entities into a different vectorial space for each relation through a suitable projection matrix. TransR associates to typeOf, and to all other properties, a specific vector space in which entity vectors are projected. This leads to training specific projection matrices for typeOf (and any other relation) so that the projected entities can be located more suitably to be linked by the vector translation associated to the (typeOf) relation. This differs from TransE, which models typeOf as simple vector translation. The considered individuals and classes may be quite different in terms of the properties and attributes they are involved in, thus determining strong semantic differences (according to [210]) taking place at small reciprocal distances in the underlying vector space, hence revealing the weakness of employing the mere translation.

With the goal of capturing additional properties in the data, such as inverse relationship, symmetry, anti-symmetry and composition, more complex embedding models have been formalized, either targeting more complex vector representation spaces, such as the complex representation, as for the case of ComplEx [184] and (Path-)RotatE [224], Gaussian representation, as for the case of KG2E [67] and TransG [203], and manifold representation, as for the case of MuRP [13] and DihEdral [206], or targeting more complex encoding models such as neural models, as for the case of ConvKB [137] and CompGCN [185]. Nevertheless, these additional models became rather computationally expensive, which limits their usefulness.

Nevertheless, several additional semantic aspects that are generally available within knowledge graphs (KGs), such as hierarchies of concepts and roles, type constraints and transitivity of relationships, are currently almost disregarded by existing knowledge graph embedding (KGE) models. The need for semantic embedding methods has been argued [33, 144, 82]. In [60] a KG embedding method considering logical rules has been proposed, where triples in the KG and rules are represented in a unified framework. Specifically, triples are represented as atomic formulae while rules are represented as more complex formulae modeled by t-norm fuzzy logics. A common loss function over both representations is defined, which is minimized to learn the embeddings. This proposal resulted in a novel solution but the specific form of prior knowledge that has to be available constitutes its main drawback. A similar drawback also applies to [129], where a solution based on adversarial training is formalized, exploiting Datalog clauses to encode assumptions which are used to regularize neural link predictors.

Complementary solutions, directly targeting rich representation languages as RDFS and OWL and not requiring additional formalism for representing prior knowledge have been proposed. Particularly, [128] has proven the effectiveness of combining embedding methods and strategies relying on reasoning services for the injection of prior Background Knowledge (BK) to enhance the performance of a specific predictive model. Following this line, TransOWL, aiming at injecting schema level information, particularly during the learning process, and its upgraded version TransROWL, have been formalized [36, 35]. The main focus is on the application of this idea to enhance well-known basic scalable models, namely TransE [20] and TransR [113], even if, in principle, the proposed approach could be applied to more complex embedding methods, with an additional formalization. In TransOWL the original TransE setting is maintained while resorting to reasoning with schema axioms to derive further triples to be considered for training and that are generated consistently with the semantics of the properties. Particularly, for each considered axiom, TransOWL defines, on the score function, specific constraints that guide the way embedding vectors are learned. A set of different axioms, specifically equivalentClass, equivalentProperty, inverseOf and subClassOf, are employed for the definition of constraints on the score function so that the resulting vectors, related to such axioms, reflect their specific properties. As a consequence, new triples are added to the training set on the grounds of the specified axioms. TransROWL further develops TransOWL by adopting TransR as the base model in order to handle non 1-to-1 properties in a more proper way. TransOWL and TransROWL have been proven to improve their effectiveness on link prediction and triple classification tasks when compared to the baseline models (TransE and TransR) that focus on structural graph properties. Some additional efforts in the formalization of knowledge graph embedding (KGE) and Deep Learning solutions taking into account limited semantics can be found in the literature [57, 12, 72, 62, 99]. Nevertheless, none of the existing KGE model is able to exploit the full expressiveness that a knowledge graph (KG) may have in principle.

Independently of the specific model, another important issue needs to be highlighted: most of the existing knowledge graphs (KGs) only contain positive (training) examples, since usually false facts are generally not encoded. However, training a learning model in all-positive examples could be tricky, because the model might easily overgeneralize. As such, in order to obtain the negative examples that are needed to train knowledge graph embedding (KGE) models, two different approaches are generally adopted: either corrupting true/observed triples randomly, with the goal of generating plausible negative examples or adopting a local-closed world assumption (LCWA) in which the data collection is assumed as locally complete [138]. In both cases, wrong negative triples may be generated and thus used when training and learning the embedding models.

In Section 3.2, we present our perspective on the research directions that need to be tackled to cope with the problems illustrated particularly in this section.

2.2.3 Neural Methods for Vector Space Embeddings

Another research direction focused on the exploitation of vector space embeddings for obtaining a propositional feature vector representation of a knowledge graph (KG). One of the first solutions targeting this research direction is RDF2Vec [154], which adapts the well-known Word2Vec technique, devised for natural language processing, to graph representations. A two-step approach is adopted. First the data graph is converted into a set of sequences of entities (two different approaches can be used for this purpose: graph walks and Weisfeiler-Lehman Subtree RDF graph kernels). In the second step, the obtained sequences are used to train a neural language model to estimate the likelihood of a sequence of entities appearing in a graph. The result is that each entity in the graph is represented as a vector of latent numerical features. In order to show that the obtained vector representation is independent of the downstream task and the specific algorithm, an experimental evaluation involving a number of classification and regression tasks has been performed.

An upgrade of RDF2Vec has been presented in [31], where global patterns are considered (differently from the initial RDF2Vec proposition grounded on local patterns). These solutions cannot cope with literals.

Another way to better capture global information is to use a more powerful model, such as a graph neural network (GNN). These are a class of methods for allowing artificial neural networks to operate on graph data. Given that graphs are a very general data structure, graph neural networks (GNNs) can take a wide variety of forms. It has also been shown that many popular deep learning architectures, such as convolutional neural networks, recurrent neural networks, and transformers, can be seen as a graph neural network (GNN) for a suitably defined graph [21]. In a graph neural network (GNN), as for RDF2Vec and knowledge graph embedding (KGE) models, nodes are represented as vectors. These vectors are fed through a sequence of message-passing layers, where nodes update their values based on their neighbors’ values, and local pooling layers, where groups of neighboring nodes are combined into a single vector representation. The final layer aggregates the entire input into a single vector representation for the entire graph. Because of this iterative process, graph neural networks (GNNs) are better able to capture multi-hop relations and global graph structure, compared to RDF2Vec [154]. They are also able to reduce an entire graph to a single embedding vector, as well as computing embedding vectors for each node. See [223] or [226] for an overview of graph neural network (GNN) design and applications.

Several works have applied graph neural networks (GNNs) to construct or enhance knowledge graphs (KGs). [227] integrates Bellman-Ford into the graph neural networks (GNNs) training procedure, and then uses the resulting model for link prediction on knowledge graphs (KGs). [143] show that graph neural networks (GNNs) can be trained, in a supervised setting, to accurately estimate node importance in a knowledge graph (KG). graph neural networks (GNNs) have also been used for entity alignment, which seeks to discover when the same entity appears in two different knowledge graphs. [198] embeds entities in both knowledge graphs (KGs) and then uses the distance between the embeddings to identify when nodes in different knowledge graphs (KGs) correspond to the same entity. More recent works have built on this method, for example by capturing time-sensitive information [207] or multi-modal inputs [170]. Another common use of graph neural networks (GNNs) for knowledge graph (KG) is to improve the use of knowledge graphs (KGs) in recommender systems [52], and inference [136]. For an overview of the use for graph neural networks (GNNs) for knowledge graphs (KGs), see [213].

2.2.4 Rule Learning Solutions

With the goal of finding new facts (namely new triples) that are missing in a KG, AMIE [51, 50]121212AMIE system is currently at its third version. For more details see https://github.com/dig-team/amie. has been proposed. AMIE represents one of the most well-known and efficient solutions grounded on a symbol-based approach. Inspired by association rule mining [4] and the Inductive Logic Programming (ILP) literature, AMIE is able to learn logic rules from KGs, that are ultimately used for predicting new unseen triples. Interestingly AMIE is tailored to support the Open World Assumption (OWA) characterizing KGs, differently from all numeric-based solutions that are grounded on the Closed World Assumption (CWA). Nevertheless, AMIE mines rules inspecting the triples that are directly observable in the KG and it does not exploit the additional semantics that is available in the KG as well as any form of deductive reasoning.

A related rule mining system, based on a level-wise generate and test strategy has been further proposed [37], with the goal of learning SWRL rules [70] while exploiting schema level information and deductive reasoning capabilities during learning. As for AMIE, the goal was to exploit the discovered rules for predicting new facts. This system actually outperformed AMIE in terms of new predicted triples, and this was due to the exploitation of the schema level information and reasoning capabilities. Nevertheless, they have been also the main cause of the reduced ability of the system to scale on large knowledge graphs (KGs), when compared to AMIE.

More recently AnyBURL [123] has been proposed. It is a scalable bottom-up rule learning system for KG completion that works by sampling random paths that are generalized into Horn rules. Reinforcement learning is exploited to guide path sampling and make efficient use of computational resources. AnyBURL also showed improved scalability and competitive performance in comparison to numeric-based approaches. Even more so, it has been also shown that AnyBURL can be used to explain predictions made by a latent model when restricting the types of learned rules. Nevertheless, as for AMIE, no exploitation of the KG semantics and reasoning capabilities can be found.

3 Gaps in Machine Learning and Knowledge Graphs and Next Challenges

In this section we analyze existing gaps of the class of methods illustrated in Section 2 that we identify as important. Hence, for each of them, we provide our perspective on the research directions that need to be pursued in order to fill these gaps. Specifically, the following Section 3.1 primarily focuses on the need of having a clear methodology for interleaving large language models (LLMs) with knowledge graphs (KGs) and drafts a preliminary proposal. Section 3.2 primarily focuses and provides preliminary proposals for the need of taking into account reasoning capabilities and schema level information of knowledge graphs (KGs), to be used for setting up a more informative way for generating negative training examples as well as for injecting schema level information in knowledge graph embedding (KGE). Beyond the gaps, Section 3.3 presents our view supporting that symbolic machine learning (ML) methods may still have a role in knowledge graph (KG), particularly for knowledge graph (KG) refinement and more specifically for mining disjointness axioms, that are quite often missing in knowledge graphs (KGs) and related ontologies. Section 3.4 presents our position on the need for an approach that demonstrably produces reliable explanations to validate machine learning (ML) results when applied to knowledge graphs (KGs). Hence, Section 3.5 shows the need for diverse, high-quality benchmark datasets when combining machine learning (ML) and knowledge graphs (KGs) as well as new metrics for capturing new behaviors.

3.1 Knowledge Graphs for Prompting Large Language Models

From what has been described in section 2.1, we understand that the use of knowledge graphs (KGs), as an additional tool, during the (pre-)training phase or during the inference phase of large language models (LLMs) are important fields of research, attracting the interest of many researchers, and could potentially improve the operation of the large language model (LLM) and the results of large language models (LLMs), respectively. Although the operation of modern large language models (LLMs) and respective systems (like chatGPT) is impressive and traditional machine learning gaps (like reasoning capabilities) have started to close, there is still room for improvement, and the use of knowledge graphs (KGs) as an additional tool during the training and fine-tuning phases can play an important role, here. Specifically, knowledge graphs (KGs) can provide background knowledge (encyclopedic, commonsense, domain-specific, multimodal etc), represent human-oriented processes, and explain opaque machine operation. On the other hand, the practical use of large language models (LLMs) increases dramatically and there is a great need for advancing the use of LLMs inference, making the process of dialoguing large language models (LLMs) more formal and systematic. Therefore, the use of knowledge graphs (KGs) during the phase of the design of the input to be given to large language models (LLMs) and during the phase of the analysis of the large language model (LLM) response seems to have a great potential.

Following the above, interesting open problems and challenges is the use of knowledge graphs (KGs) in large language model (LLM) prompt engineering or simply large language model (LLM) prompting [142, 116]. Prompting is the process of providing a sequence of instructions or queries to a large language model (LLM) in order to get the desired output or to check the large language model (LLM)’s operation and characteristics. It is actually a dialogue between a user (human or agent) and a large language model (LLM), that reflects the user’s intent and finally results in the desired task or information that the user wants to get from the model. Although the field is new, there are some attempts to formalize the process (see for example the Automatic Prompt Engineer (APE) approach [225]). The formalization of the dialogue process should be grounded on some type of background knowledge, so there is a need for representing and using this knowledge. Here, we describe the great potential of using knowledge graphs (KGs) in large language model (LLM) prompting, based on the nature of prompts, their types and effectiveness, the tasks and the methodology to provide adequate prompts during the prompting process, focusing on the potential use of knowledge graphs (KGs).

There are many ways to modify the prompt that is given to large language model (LLM), using knowledge graphs (KGs). First, the instruction or question can be more explicit and specific, capturing the user requirements, since it is well-understood that the more specific the prompt the better the chance of guiding the large language model (LLM) to the desired response. For example, the instruction “Summarize text A” can be specified as “Summarize the text A in 200 words”, using the knowledge that an abstract should be between 200 and 300 words. Or the question “Is there any recent paper in the area of prompting machine learning systems?” can be specified as “Is there any recent paper in the area of prompting large language models (LLMs)?”. On the other hand, sometimes it may be helpful, depending on the instruction or the question, to generalize it, for example, the question “Is there any recent paper in the area of prompting machine learning systems?” can be generalized as “Is there any recent work in the area of prompting machine learning systems?”. Also, may be useful to contextualize or style the prompt, by providing examples (“Suggest romantic musicals, like “La La Land”), or conditions (“Suggest papers for prompting large language model (LLM), published in top conferences”), or style (“Paraphrase text A, using more formal language). It is not difficult to see that knowledge graphs (KGs) can be very helpful in constructing knowledge-enhanced prompts like the above (and not restricted to them), guiding prompt changes, as they capture formal domain knowledge descriptions. Interesting ideas can be found in [225] that the instruction generation is framed as natural language program synthesis, in [166] that simple and effective prompts are constructed to improve GPT-3’s reliability, in [189] that multi-step reasoning tasks are tackled by constructing planning and solving prompts, in [222] that large language models (LLMs) are asked to provide explanations for their choices (in this case for a specific task that is model selection) and in [116] that prompting with generated knowledge rectifies model prediction.

Response analysis.

Another interesting issue that could be considered is to use knowledge graphs (KGs) to characterize the prompt, for example to measure its effectiveness or reliability, by analyzing and evaluating the response. The effectiveness of prompts depends on the response of the large language model (LLM), i.e. the answer to a specific prompt in comparison with the desired output, given the task. Depending on the prompt and response languages, it is important to formalize effectiveness or reliability evaluation measures that guide a process of iterative refinement of the results, by using formal knowledge represented in knowledge graphs (KGs). Interesting ideas can be found in [142, 118, 166].

Prompt sequencing.

Designing and controlling prompting, i.e. producing a sequence of prompts to elicit a desired output, can be a challenging task that requires a systematic strategy, evaluation and experimentation. Although large language models (LLMs) are powerful, their operation is complex and unpredictable and thus a dialogue for producing a sequence of prompts may be helpful to understand large language model (LLM) characteristics, like complex reasoning capabilities. There is lately some work in the area, for example: Chain-of-Thought (CoT) prompts [199] decompose complex reasoning capabilities into a set of simpler reasoning steps; In [116], the usefulness of using knowledge in common sense reasoning is discovered, extracting knowledge from an large language model (LLM) and then using this knowledge as additional input to refine the prompt result. The APE methodology proposed in [225] uses ideas from program synthesis in order to optimize the prompt selection process, based on efficient score estimations. Future steps would benefit from the use of knowledge graphs (KGs) as formal knowledge representations, because there is a clear requirement formalizing the prompting extraction methodology.

3.2 Handling Semantics, Reasoning and Negative Information in Knowledge Graph Embedding Methods

One of the key features of knowledge graphs (KGs) is that they can be enriched with schema-level information. For the purpose ontologies are generally adopted, which coupled with deductive reasoners, allow to make explicit knowledge which is implicitly coded in a knowledge graph (KG)131313Several reasoners exist and may be used for the purpose. Some examples are RDFox (https://www.oxfordsemantic.tech/rdfox), HermiT (http://www.hermit-reasoner.com/), FaCT++ (http://owl.cs.manchester.ac.uk/tools/fact/). See http://owl.cs.manchester.ac.uk/tools/list-of-reasoners/ for the full list of reasoners.. For example, given a KG containing the triple <c typeOf Woman> (or equivalently Woman(c), by adopting a Description Logic formalism) and referring to the following simple ontology formalizing a hierarchy of concepts Man Human and Woman Human, the fact Human(c) can be derived by the use of a deductive reasoner. Similarly, new knowledge can be derived when additional axioms are available, such as equivalence axioms, disjointness axioms, as well as restrictions on domain and ranges141414See https://www.w3.org/TR/owl2-overview/ for details on the representation language.. However, due to the limited ability of reasoners to scale on very large knowledge graphs (KGs), deductive reasoning is currently almost disregarded.

Indeed, when talking about machine learning (ML) methods coupled with knowledge graphs (KGs), as for the case of knowledge graph embedding (KGE) methods, generally only facts that can be directly observed are taken into account e.g. when projecting the data graph into a lower vectorial representation space. This is clearly a limitation, since knowledge that is somehow already available within the knowledge graphs (KGs) (as for the fact Human(c) in the example above) and that may play a role when considering knowledge graph embedding (KGE) is ignored. For instance, by considering the fact Human(c), a more appropriate vectorial representation for the entity c could be provided thus limiting errors also when solving downstream tasks. By only considering observable facts, schema level information, that is a seminal element of knowledge, and all additional knowledge that can be derived are actually fully dismissed.

Abboud et al. [1] analyzed the shortcomings of the existing embedding models. These shortcomings can be summarized in: theoretical inexpressiveness, lack of support for inference patterns and higher-arity relations, need for logical rule incorporation.

Here, we specifically claim that knowledge graph embedding (KGE) methods need to be equipped with the full usage of knowledge graphs (KGs) semantics which comprises the exploitation of all axioms that can be found in the ontologies that are used for supplying (rich) schema level information to KGs, as well as the exploitation of deductive reasoning services that allow to obtain additional knowledge both at schema and assertion level. Indeed, whilst the need for semantic embedding methods has been advocated [33, 144, 82], only a few proposals can be found in the literature that actually address this problem (see section 2.2.2 for details) and mainly focusing on equivalentClass, equivalentProperty, inverseOf and subClassOf axioms. To the best of our knowledge, none of the existing methods is able to exploit all kinds of axioms that in principle can be found in expressive ontologies. Even more so, a complementary research direction would be needed, calling for a solid and extensive experimental evaluation aiming at providing a clear position on the need (or not) to fully exploit the KG semantics as well as reasoning capabilities. Specifically, we claim that a comprehensive experimental evaluation, involving most of the knowledge graph embedding (KGE) methods currently available, is needed. Two main scenarios should be considered: the first one (currently adopted) where only observable facts are considered; the second one where the full knowledge available within KG is made explicit by considering schema-level information (e.g. transitivity, equivalence axioms, same as axioms etc,) and reasoning capabilities. Hence performances on the very same downstream tasks, adopting the two settings, should be compared, in order to experimentally prove the value added, if any, of exploiting the knowledge graphs (KGs) entirely. Importantly the second scenario could be possibly divided into two intermediate steps, one where knowledge is partially completed by considering the schema level information but no exploitation of deductive reasoners and a second step where the actual full knowledge is gained by adopting available deductive reasoners. This is on one hand, for assessing the impact of the usage of the full knowledge and on the other hand, for assessing if some complexity, due to reasoning, can be saved whilst still trying to make knowledge explicit as much as possible.

Another issue with KGE models is given by the need of negative examples (for training knowledge graph embedding (KGE) models) that anyhow are generally missing in knowledge graphs (KGs), where generally only positive information is coded. As illustrated in section 2.2.2, this problem is usually addressed either by corrupting true/observed triples randomly, that is by replacing either the subject or the object of the observed triple with an entity picked randomly from the knowledge graph (KG), or by adopting a local-closed world assumption (LCWA), in which the data collection is assumed as locally complete [138]. In both cases, wrong negative triples may be generated and thus used when training and learning the embedding models. In order to mitigate this issue, preliminary proposals tried to take under control the number of negatives that are randomly generated [43]. Clearly this solution does not solve the problem of generating false negatives, but rather simply tries to somehow control the effect of the false negatives. One of the first proposals trying to generate and materialize actual negative triples has been formalized in [8]. Nevertheless, the proposed solution is grounded on the exploitation of additional and external sources of information besides KGs. Specifically, the proposed solution is grounded on two complementary approaches: a statistical ranking for statements obtained based on related entities, and a pattern-based text extraction, applied to search engine query logs.

On the contrary, here we claim that knowledge graphs (KGs) semantics should be fully and solely exploited for making explicit correct negative statements. For instance, given a restriction on domain and/or range of predicate appearing in a true observed triple, the restriction can be exploited for generating negative triples where e.g. the object entity of the negative triple can be deductively proved to be out of the declared range restriction. Similarly, given an observed true triple with a predicate having a functional restriction, negative statements may be generated by constructing triples having objects that are different from the object in the true statement. More generally, the approach for generating correct negative statements that is envisioned, is deeply grounded on the semantics of the schema axioms. The approach should basically construct triples that are in the complement of the set of triples representing the semantics of a given schema axiom.

An initial proposal in this direction can be found in [36, 35, 117], where only domain, range, disjointWith and functionalProperty constraints are considered. Whilst we consider this proposal a valuable way to go as in agreement with the envisioned solution, it needs to be extended for comprising all axioms and constraints that can be possibly found in a knowledge graphs (KGs), e.g. transitivity, same-as, equivalence axioms, for citing a few. Even more so, we consider it worthwhile to conduct an extensive experimental study comparing the different settings for generating negative examples in order to prove experimentally the actual role of semantics, if any.

Up to now, when referring to reasoning we basically meant deductive reasoning applied to ontologies/KGs [11]. Nevertheless, besides deductive reasoning, other forms of reasoning could be investigated. These different reasoning forms could be useful in KG-related tasks, and conversely, knowledge contained in knowledge graphs (KGs) could be leveraged in their reasoning process. Here we specifically focus on analogical reasoning that is a remarkable capability of the human mind [131] relying on analogical proportions. They are statements of the form “A is to B as C is to D” that can be formalized as quadruples A:B::C:D [126]. An example of such a quadruple is “leg : human :: paw : dog”. Analogical reasoning relies on similarity and dissimilarity to extrapolate knowledge between objects of potentially different domains. To illustrate, the given example quadruple leverages the similarity between body parts and whole, and the relation linking them to constitute a valid analogy. Analogical reasoning is mainly concerned with two tasks: analogy detection that aims to determine whether a quadruple A:B::C:D is a valid analogy, and analogy solving that aims to predict a missing element X, given three elements A, B, and C such that A:B::C:D constitutes a valid analogy. When elements are represented as vectors, analogies can be thought of as parallelograms, i.e., eBeA=eDeC. Such a view can thus be adopted with embeddings, which attracted works on machine learning (ML)-based analogy for various Natural Language Processing tasks, e.g., word morphology [7] or machine translation [101]. In the realm of knowledge graphs (KGs), to the best of our knowledge, only a few works consider analogical reasoning. However, KG embeddings are suited for analogical formalization. For instance, by using translations to model relations, TransE inherently validates the parallelogram rule. This motivated Portisch et al. [147] to investigate whether some KG embedding models are well-suited for the task of analogy detection with standard analogical datasets. But analogical reasoning could also be directly applied to knowledge graphs (KGs). In the link prediction task, it is natural to extrapolate edges from one (part of a) KG to another (part), which motivated the ANALOGY model [115]. Interestingly, ANALOGY is based on the parallelogram rule and the authors showed that it subsumes some other models such as DistMult, ComplEx, and HolE. Analogical reasoning can also be considered as an enhancer of existing knowledge graph embedding (KGE) models by using triples, relations or entities in analogies to enrich the training process [211]. In fact, the integration of analogical reasoning into KG-related tasks and knowledge graph embedding (KGE) models is not limited to one formalization or one task. Jarnac et al. re-used a convolutional model for analogy detection and applied it on pre-trained graph embeddings to select subgraphs of interest from Wikidata to bootstrap a domain-specific KG [81]. Analogies also inherently appear in several other tasks, e.g., Semantic Table Interpretation, matching, or recommendation [134]. It remains to explore both theoretically and empirically the best formalizations, models, improvement in performance, and interactions with other forms of reasoning, especially deductive reasoning that is inherently permitted by ontologies.

3.3 Symbol-based Methods for Knowledge Graphs

Given knowledge graphs (KGs) volumes, the need for scalable machine learning (ML) solutions has obfuscated the attention to symbol-based machine learning (ML) solutions. Nevertheless, the important gain, in terms of scalability, that numeric-based methods (such as knowledge graph embeddings (KGEs)) are obtaining is penalizing: a) the possibility to have interpretable models as a result of a learning process (see Section 3.4 for more details); b) the ability to exploit deductive (and complementary forms of) reasoning (see Section 3.2 for more details); c) the expressiveness of the representations to be considered and related assumptions (such as the Open World Assumption (OWA)).

Indeed, suitable symbol-based methods, often inspired by the Inductive Logic Programming (ILP) [151] field (aiming at inducing a hypothesized logic program from background knowledge and a collection of examples), have been proposed [34, 86, 103, 51, 179]. Most of them are able to cope with expressive representation languages such as Description Logics (DLs) [11], theoretical foundation for OWL, and the Open World Assumption (OWA) typically adopted, differently from the Closed World Assumption (CWA) that is usually assumed in the traditional machine learning (ML) settings. Also, problems such as ontology refinement and enrichment at terminology/schema level have been proposed [46, 47, 102, 186, 157].

Particularly, with the purpose of enriching ontologies at the terminological level, methods for learning concept descriptions for a concept name have been formalized. The problem has been regarded as a supervised concept learning problem aiming at approximating an intensional DLs definition, given a set of individuals of an ontological knowledge base (KB) acting as positive/negative training examples. Various solutions, e.g. DL-Foil151515System publicly available at: https://bitbucket.org/grizzo001/dl-foil/src/master/ [46] and celoe [102] (part of the DL-Learner suite161616Suite publicly available at: https://dl-learner.org/), have been formalized. They are mostly grounded on a separate-and-conquer (sequential covering) strategy: a new concept description is built by specializing, via suitable refinement operators, a partial solution to correctly cover (i.e. decide a consistent classification for) as many training instances as possible. Whilst DL-Foil works under OWA, celoe works under CWA. Both of them may yield sub-optimal solutions. In order to overcome such issues, DL-Focl171717System publicly available at: https://bitbucket.org/grizzo001/dlfocl/src/master/ [159, 158], Parcel [182] and SpACEL [183] have been proposed. DL-Focl is an optimized version of DL-Foil, implementing a base greedy covering strategy. Parcel combines top-down and bottom-up refinements in the search space. Specifically, the learning problem is split into various sub-problems, according to a divide-and-conquer strategy, that are solved by running celoe as a subroutine. Once the partial solutions are obtained, they are combined in a bottom-up fashion. SpACEL extends Parcel by performing a symmetrical specialization of a concept description. All these solutions proved to be able to learn approximated concept descriptions for a target concept name to be used for possibly introducing new (inclusion or equality) axioms in the knowledge base (KB). Nevertheless, quite often, relatively small ontological knowledge bases (KBs) have been considered for the experiments, revealing that, currently, they have limited ability to scale on very large knowledge graphs (KGs).

A few scalable exceptions are represented by rule learning systems for KG completion such as AMIE and most of all AnyBURL (see section 2.2.4 for more details). Nevertheless, most of the existing symbol-based methods cannot scale to very large knowledge graphs (KGs) [158].

Here we want to highlight particularly the role that symbolic machine learning (ML) solutions may play in assessing disjointness axioms within ontologies. Indeed, disjointness axioms are essential for making explicit the negative knowledge about a domain, yet they are often overlooked during the modeling process [193]. Furthermore, disjointness axioms would be absolutely beneficial for setting up an informed generation of negative examples in knowledge graph embedding (KGE) models (see section 3.2 for details), thus limiting false negatives that random corruption may inject.

To tackle this problem, automated methods for discovering disjointness axioms from the data distribution have been devised. A solution grounded on association rule mining [4] has been proposed in [186]. It is based on studying the correlation between classes comparatively, namely by considering association rules, negative association rules and correlation coefficient. Background knowledge and reasoning capabilities are used to a limited extent. A different solution has been proposed in [157, 156], where, moving from the assumption that two or more concepts may be mutually disjoint when the sets of their (known) instances do not overlap, the problem has been regarded as a clustering problem, aiming at finding partitions of similar individuals of the knowledge base, according to a cohesion criterion quantifying the degree of homogeneity of the individuals in an element of the partition. Specifically, the problem has been cast as a conceptual clustering problem, where the goal is both to find the best possible partitioning of the individuals and also to induce intensional definitions of the corresponding classes expressed in the standard representation languages. Emerging disjointness axioms are captured by the employment of terminological cluster trees (TCTs) and by minimizing the risk of mutual overlap between concepts. Once the TCT is grown, groups of (disjoint) clusters located at sibling nodes identify concepts involved in candidate disjointness axioms to be derived181818System publicly available at: https://github.com/Giuseppe-Rizzo/TCTnew. Unlike [186], that is based on the statistical correlation between instances, the empirical evaluation of [157, 156] showed the system ability to discover disjointness axioms also involving complex concept descriptions, thanks to the exploitation of the underlying ontology as background knowledge.

Here, we claim that, when tackling the problem of learning disjointness axioms, a two-level analysis needs to be conducted. One level relates to the expressiveness of the axioms that can be learned. The other level is related to the usage of the learned axioms from a user/knowledge engineering perspective. The goal of this two-level analysis should be finding a trade-off between expressiveness and utility from a user modeling perspective. Whilst the former analysis, concerning the expressiveness of the discovered axioms, has been conducted (as reported just above) the latter, requiring an actual user study is currently missing, whilst we consider it necessary for coming up with the aforementioned trade-off between expressiveness and utility of the discovered disjointness axioms. Furthermore, additional efforts should be devoted to the scalability of the developed methods that, even if not very limited, still do not appear to be able to scale on the existing knowledge graphs (KGs).

3.4 Knowledge Graphs for Interpretable Machine Learning

When considering the relation of knowledge graphs (KGs) to deep learning, via knowledge graph embeddings (KGEs) for example, a popular research objective is to use knowledge graphs (KGs) for interpretability. The internal dynamics of deep neural networks (DNNs) are typically opaque, and there is hope that knowledge graphs (KGs) can be used to help provide (satisfying) explanations of their behavior. The general goal of producing explanations for behavior of machine learning models is sometimes referred to as explainable AI (XAI).

As argued in [55], the concepts of explainability and interpretability are intertwined in the context of XAI, because what we really seek is an interpretable explanation. One could, for example, detail exactly the activations of each hidden layer in a neural network to explain why it produced the output from the corresponding input, but this is not a human-interpretable explanation, so is unhelpful for XAI. Despite a strong incentive for interpretable machine learning [114], especially in the area of healthcare [130, 5], and despite significant research attention, how to make complex machine learning model interpretable and explainable remains an open problem [87, 110].

In this section, we give an overview of existing work, and needed future work, on using knowledge graphs (KGs) for interpretable machine learning. We follow our above framework and divide the discussion into two parts: machine learning (ML) for knowledge graph (KG) and knowledge graph (KG) for machine learning (ML).

The former uses machine learning (ML) techniques to augment or construct a knowledge graph (KG). With respect to interpretability, the idea is that a knowledge graph (KG) is a human-readable representation of information. Once it is constructed, it can be used to produce an answer that is highly interpretable, because we can identify the facts and inference rules from which the answer was derived. The problem is that the construction itself, which is often a complex process, remains uninterpretable. The same also applies to work that uses large language models (LLMs) for knowledge graph (KG) construction, such as [63, 98], which use BERT-based models to build a clinical knowledge graph (KG) for medical and financial applications, respectively. Once constructed, the knowledge graph (KG) can perhaps be used in an interpretable way, but the large language model (LLM) that constructs it is not interpretable. Methods which then use the knowledge graph (KG) as input to another stage, may see interpretability gains at those other stages. For example, [16] iteratively use a knowledge graph (KG) to augment the training data, and then use predictions from augmented training data to extend the knowledge graph (KG). However, the initial creation of the knowledge graph (KG) remains uninterpretable.

In the other direction, there are several works which aim to use knowledge graphs (KGs) to enhance the performance of machine learning (ML) models. There, the possible approaches to using knowledge graph (KG) for interpretable machine learning (ML) models can, following [152] be divided into three types, pre-model, post-model and in-model.

Pre-model, refers to using the knowledge graph (KG) as input to a deep neural network (DNN) often referred to as “conditioning on the knowledge graph (KG)”, [99]. The idea is that the knowledge graph (KG) contains higher-quality structured information than images or free-form text, which can then be used by the deep neural network (DNN) to solve the given task. This could potentially help interpretability if the network uses an attention mechanism that can be inspected to see which parts of the knowledge graph (KG) are attended to, as shown by [209] (although, interestingly, the authors were not motivated by explainability in the design of their model). A similar method was later also used by [218]. Similarly, [220] proposed a question-answering model that attends to paths in a knowledge graph (KG) from a question to the answer, and claims the attention map over these paths constitutes an explanation of the model output. However, these provide at best, only partial interpretability, because it is unclear how/why the model’s attention mechanism focuses on the information from the knowledge graph (KG) that it does.

Post-model, refers to obtaining the output of a machine learning (ML) model, and then invoking a knowledge graph (KG) to try to produce an explanation for where that output came from. For example, [53] proposes a visual classifier that matches the predicted classes to knowledge graph (KG) entities, and then uses the knowledge graph (KG) structure to give an explanation. Similarly, [167] claims to propose an explainable textual entailment model that, after predicting whether one text entails another, finds evidence for this entailment in a knowledge graph (KG). The problem with generating post-hoc explanations is that they depend only on the model output and not on the processes internal to the model which produced that output, even though it is precisely the latter that explanations are supposed to shed light on. Two different machine learning (ML) models that produced the same output by very different means would, by methods such as [167] and [53], automatically receive the same ‘explanation’. For example, consider two visual classifiers which both assign the same label to an input image. Suppose one of these classifiers has been trained on and memorized the test set, while the other has actually learned relevant visual features and used these to infer the label. We would surely want the explanation for the outputs of these two classifiers to be different, but if we use only the assigned label to produce an explanation, then they will automatically be the same. Thus, post-model XAI methods that invoke a knowledge graph (KG) after prediction are precluded from the outset from producing satisfactory explanations, because the explanation is independent of internal model behavior (given the output), which is exactly the thing we want to explain.

In-model, the third manner of enhancing machine learning (ML) models with a knowledge graph (KG), involves the knowledge graph (KG) during the training of the model itself. In the case of deep neural networks (DNNs), this faces the difficulty of connecting discrete data from the knowledge graph (KG), to a continuous loss function. Beyond some exploratory work, [99, 163], few methods have attempted this approach. Additionally, even if one successfully improved predictive performance, it is not immediately obvious that it would improve interpretability. It is possible that such an in-model method, were it to be designed, would involve a complex interactive passing of information between a knowledge graph (KG) and a deep neural network (DNN), which is highly uninterpretable. One such method did explicitly target explanations [160], however this was a bespoke system that requires the knowledge graph (KG) to consist of part-whole relationships only, as well as additional annotation of the images of object-part classes.

The use of knowledge graphs (KGs) for interpretable machine learning (ML) remains an open problem, either to devise a generalizable method of infusing knowledge graph (KG) in machine learning (ML) training that demonstrably improves interpretability, or to determine that such a method is not feasible. At the moment, there is interest in the use of knowledge graphs (KGs) for interpretable machine learning (ML), but we do not have a knowledge graph (KG)-based method that demonstrably improves interpretability in machine learning (ML). This gap in the research was also noted by [38]. Moreover, in order for knowledge graphs (KGs) to be of significant help for explainability, we contend that they must be involved internally in the model itself. Using machine learning to generate knowledge graphs (KGs) means that this generation process itself is not interpretable, and invoking the knowledge graph (KG) after the operation of the machine learning model means that it cannot distinguish between models that produced the same output, even if by very different means.

3.5 Benchmark datasets, and metrics

The ever-expanding number of available methods targeting KG construction, refinement, or usage in ML approaches entails a need for appropriate benchmark datasets and metrics to evaluate their capabilities. Some datasets are considered as de facto standards to evaluate approaches developed for KG-related tasks such as FB15k-237 and WN18RR for link prediction, or Citeseer for node classification. However, we claim that current datasets do not suffice for a sound and complete evaluation of the capabilities of developed approaches. Indeed, they present several issues such as:

  • unwanted leakages between train and test sets;

  • absence of shared patterns between train and test sets;

  • lack of necessary characteristics to support the use of background knowledge in ML models (e.g., presence of inverse axioms, hierarchy of classes or properties).

  • scattering of datasets across several repositories hindering their discovery and re-usage

In the following, we briefly illustrate and discuss each of these issues and propose possible ways to overcome them.

Several datasets have been made available to the community over the past few years, e.g., by using (fragments of) open knowledge graphs (KGs) [17, 148, 155]. At first, the presence of patterns in train and test sets was regarded with a concern for unwanted leakages. For example, the two datasets FB15k and WN18 were previously widely adopted to evaluate link prediction approaches. It was later discovered that both datasets present data leakage between train and test sets due to inverse relations [43, 181]. A link prediction approach can then easily learn to predict a test triple (t,r1,h) if triple (h,r,t) is in the train set, where r1 denotes the inverse relation of r. Two filtered versions named FB15k-237 [181] and WN18RR [43] were thus created by filtering such triples, to avoid spurious performance measures. Nevertheless, patterns such as inversion, symmetry, hierarchy or composition and their capture by knowledge graph embedding (KGE) models are now argued to be of interest, especially if adequately considered in the experimental and evaluation setting [117, 24]. In particular, some authors claim that test triples should be inferable from patterns learned and premises existing in the train set. This imposes additional constraints when constituting datasets but enables to evaluate the ability of knowledge graph embedding (KGE) models to efficiently model, capture, and implement those patterns [117, 24]. In this view, train sets should contain samples of premises and conclusions of the considered patterns to learn. Test sets should contain conclusions that can be inferred from patterns learned and premises in train sets. This empirical evaluation is of interest to substantiate some theoretical guarantees of model design or, conversely, to outline some unexpected abilities. For instance, some knowledge graph embedding (KGE) models such as RotatE [175] are theoretically designed to capture patterns such as symmetry, antisymmetry, inversion, and composition and should be evaluated accordingly. It follows that detecting (and potentially removing) some patterns is an important step of dataset preprocessing. For now, detection (and removal) of inverses is performed statistically, as featured in the AYNEC/AYNEXT system [10, 168]. They detect whether two relations r1 and r2 are inverses of each other if some proportions of triples involving r1 have their counterpart involving r2. The identification of other patterns also relies on statistical approaches such as rule mining for their detection [117]. It is noteworthy that ontologies provide definitions of inverses, symmetric predicates and hierarchies of properties and classes. Hence, besides statistical approaches, ontological axioms should be taken into account to detect or implement patterns. Indeed, train sets could be completely based on ontological axioms and deductive reasoning to feature the needed patterns to learn or remove some unwanted ones.

Also, we previously outlined the interest in studying the role and usage of background knowledge in ML models. For now, datasets are often regarded as simple graph data without consideration for (or association with) additional knowledge potentially provided by ontologies. Beside improving datasets by adding triples respecting patterns or removing unwanted ones, the association of ontological axioms with datasets could support the development of learning techniques, settings, and models that consider them, following our claim for further consideration of knowledge in knowledge graph embedding (KGE) models. To illustrate, instead of enriching datasets with triples respecting patterns, models could be evaluated on their ability to consider patterns stated by ontological axioms to predict missing triples in the test set. It is noteworthy that knowledge is already leveraged to enrich the training process in some proposals. For instance, Type-Constrained Negative Sampling [97] replaces the head or the tail of a triple with an entity of the same type when generating negative triples. d’Amato et al. [36] use a reasoner to deduce additional triples from axioms defining equivalent classes, equivalent properties, inverses, or subclasses. Similarly, Iana and Paulheim [79] test whether materializing all triples induced by transitive properties, symmetric properties, and sub-properties leads to improved embeddings. Ontological information is also needed to evaluate the semantics captured by knowledge graph embedding (KGE) models. In this view, Jain et al. [80] relies on the existence of types of entities. They learn embeddings on the YAGO3-10 and FB15k-237 datasets with various knowledge graph embedding (KGE) models and then use these embeddings to predict entity types with classification or clustering approaches. Their analysis shows that semantic representation in the embedding space is not universal across models. In a similar fashion, the DLCC node classification benchmark was introduced to evaluate the capability of classification approaches to reproduce classes defined by Description Logic Constructors [148]. For example, the constructor r. is used to group nodes having a particular outgoing relation. Interestingly, they propose two gold standards: one based on the real graph DBpedia and another synthetic standard that is generated by a gold standard generator publicly available. The analysis of ontological information captured by knowledge graph embedding (KGE) models also motivates new metrics besides traditional metrics such as precision, recall, Hits@K, or Mean Reciprocal Rank. For example, Hubert et al. introduced the Sem@K metric [76, 75, 77] to measure the number of predicted triples that respect domain and range of relations among the top-K predicted triples. This metric can thus be seen as measuring the ability of knowledge graph embedding (KGE) models to capture the semantic profiles of relations. The aforementioned work highlights an interest in using ontological information in knowledge graph embedding (KGE) model design, learning process, or evaluation. Consequently, we advocate for the further development of benchmark datasets that include various ontological axioms, separately or combined. The availability of such datasets would in turn encourage and support the development of neuro-symbolic methods leveraging such axioms. However, it is noteworthy that not all current benchmarks offer the ontological information that is needed by particular approaches. That is why some authors resort to synthetic KG generators [124, 148], sometimes with a fixed ontology. To further this research direction, synthetic KG generators should be enriched with the synthetic generation of schemas with different levels of expressiveness and constructs. This would allow an on-demand generation of specific ontologies and knowledge graphs featuring the needed ontological axioms.

To further support the research community, we also call for a more systematic approach in the development, characterization, and collection of benchmark datasets. For now, benchmark datasets (or versions of) are scattered across several repositories such as GitHub or Zenodo. This leads to some of them being widely adopted (e.g., FB15k-237) and some others to be only re-used in a few papers. A unified repository, similar to the UCI Machine Learning repository191919https://archive.ics.uci.edu/, is needed to encourage their reuse and adoption by the community. Constituting such a repository first requires to crawl (semi-)automatically several sources, including GitHub or Zenodo, and links in papers available in digital libraries, arXiv, or PapersWithCode. Additionally, given that different approaches may leverage different characteristics of datasets (e.g., DL constructors [148], sub-properties [36, 79], domain and range of predicates [78], patterns in train and test sets [117]), datasets should be qualified w.r.t. the presence or absence of these characteristics. This would help researchers and developers to select suitable datasets to evaluate their approaches. To this aim, scalable automatic methods need to be developed to crawl and analyze KG-based datasets in the wild and detect a broad range of characteristics including those aforementioned. This qualification process will produce metadata that enrich usual dataset metadata such as providers, or license. To represent these new dataset metadata, an additional perspective thus lies in extending existing ontologies describing datasets (e.g., VoID, DCAT). Ontologies introduced to describe mining processes and their features such as DMOP [88] could offer sources of inspiration in this matter.

4 Conclusion

The interrelation between knowledge graphs and machine learning has been supporting advances in both fields. Machine learning methods have indeed allowed efficient construction and refinement of large knowledge graphs. Conversely, knowledge graphs have been leveraged in various machine learning tasks to improve performance, e.g., in question answering, or image classification.

However, this interrelation still does not consider parts of knowledge graphs and ML methods summarized in Table 1 that we deem to be important and to offer promising research directions. In particular, we believe KGs constitute a major structure for prompting Large Languages Models and could allow researchers to formalize interactions (e.g., providing contexts in prompts, or deciding prompt sequencing). Additionally, rich semantics of KGs and knowledge actionable by various forms of reasoning capabilities could benefit KGE models through a deeper integration. This could lead to improved performance, or a better handling or generation of informative negatives which are essential in model learning. Regarding informative negatives, we also believe that symbol-based ML, which is particularly adapted to the symbolic structure of KGs, could provide an interesting perspective, especially with the mining of disjointness axioms. KGs are human- and machine-interpretable, and thus are a promising structure on which to construct in-model interpretable ML models. Nevertheless, the infusion of KGs directly within ML models and an actual demonstration of the production of more interpretable and reliable explanations are open challenges. To assess improved performance or interpretability of ML models thanks to KGs, extensive experimental evaluations are needed, which require datasets showcasing different levels of semantics, or schema constructs to assess their individual impacts. That is why, we also call for a more systematic collection and characterization of datasets, as well as the creation of synthetic KG generators to enrich the collection of available benchmarks.

In our view, such integrations and interactions open promising challenges to foster both fields of research. We believe these directions to be stepping stones to place KGs as central assets towards neuro-symbolic and explainable AI.

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