One of the fundamental problems in Artificial Intelligence is to perform complex multi-hop logical reasoning over the facts captured by a knowledge graph (KG). This problem is challenging, because KGs can be massive and incomplete. Recent approaches embed KG entities in a low dimensional space and then use these embeddings to find the answer entities. However, it has been an outstanding challenge of how to handle arbitrary first-order logic (FOL) queries as present methods are limited to only a subset of FOL operators. In particular, the negation operator is not supported. An additional limitation of present methods is also that they cannot naturally model uncertainty. Here, we present BETAE, a probabilistic embedding framework for answering arbitrary FOL queries over KGs. BETAE is the first method that can handle a complete set of first-order logical operations: conjunction (∧), disjunction (∨), and negation (¬). A key insight of BETAE is to use probabilistic distributions with bounded support, specifically the Beta distribution, and embed queries/entities as distributions, which as a consequence allows us to also faithfully model uncertainty. Logical operations are performed in the embedding space by neural operators over the probabilistic embeddings. We demonstrate the performance of BETAE on answering arbitrary FOL queries on three large, incomplete KGs. While being more general, BETAE also increases relative performance by up to 25.4% over the current state-of-the-art KG reasoning methods that can only handle conjunctive queries without negation.
more »
« less
Fuzzy Logic Based Logical Query Answering on Knowledge Graphs
Answering complex First-Order Logical (FOL) queries on large-scale incomplete knowledge graphs (KGs) is an important yet challenging task. Recent advances embed logical queries and KG entities in the same space and conduct query answering via dense similarity search. However, most logical operators designed in previous studies do not satisfy the axiomatic system of classical logic, limiting their performance. Moreover, these logical operators are parameterized and thus require many complex FOL queries as training data, which are often arduous to collect or even inaccessible in most real-world KGs. We thus present FuzzQE, a fuzzy logic based logical query embedding framework for answering FOL queries over KGs. FuzzQE follows fuzzy logic to define logical operators in a principled and learning-free manner, where only entity and relation embeddings require learning. FuzzQE can further benefit from labeled complex logical queries for training. Extensive experiments on two benchmark datasets demonstrate that FuzzQE provides significantly better performance in answering FOL queries compared to state-of-the-art methods. In addition, FuzzQE trained with only KG link prediction can achieve comparable performance to those trained with extra complex query data.
more »
« less
- Award ID(s):
- 1705169
- NSF-PAR ID:
- 10379396
- Date Published:
- Journal Name:
- Proceedings of the AAAI Conference on Artificial Intelligence
- Volume:
- 36
- Issue:
- 4
- ISSN:
- 2159-5399
- Page Range / eLocation ID:
- 3939 to 3948
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Answering complex logical queries on large-scale incomplete knowledge graphs (KGs) is a fundamental yet challenging task. Recently, a promising approach to this problem has been to embed KG entities as well as the query into a vector space such that entities that answer the query are embedded close to the query. However, prior work models queries as single points in the vector space, which is problematic because a complex query represents a potentially large set of its answer entities, but it is unclear how such a set can be represented as a single point. Furthermore, prior work can only handle queries that use conjunctions (^) and existential quantifiers (9). Handling queries with logical disjunctions (_) remains an open problem. Here we propose QUERY2BOX, an embedding-based framework for reasoning over arbitrary queries with ^, _, and 9 operators in massive and incomplete KGs. Our main insight is that queries can be embedded as boxes (i.e., hyper-rectangles), where a set of points inside the box corresponds to a set of answer entities of the query. We show that conjunctions can be naturally represented as intersections of boxes and also prove a negative result that handling disjunctions would require embedding with dimension proportional to the number of KG entities. However, we show that by transforming queries into a Disjunctive Normal Form, QUERY2BOX is capable of handling arbitrary logical queries with ^, _, 9 in a scalable manner. We demonstrate the effectiveness of QUERY2BOX on three large KGs and show that QUERY2BOX achieves up to 25% relative improvement over the state of the art.more » « less
-
Knowledge graphs (KGs) are of great importance in various artificial intelligence systems, such as question answering, relation extraction, and recommendation. Nevertheless, most real-world KGs are highly incomplete, with many missing relations between entities. To discover new triples (i.e., head entity, relation, tail entity), many KG completion algorithms have been proposed in recent years. However, a vast majority of existing studies often require a large number of training triples for each relation, which contradicts the fact that the frequency distribution of relations in KGs often follows a long tail distribution, meaning a majority of relations have only very few triples. Meanwhile, since most existing large-scale KGs are constructed automatically by extracting information from crowd-sourcing data using heuristic algorithms, plenty of errors could be inevitably incorporated due to the lack of human verification, which greatly reduces the performance for KG completion. To tackle the aforementioned issues, in this paper, we study a novel problem of error-aware few-shot KG completion and present a principled KG completion framework REFORM. Specifically, we formulate the problem under the few-shot learning framework, and our goal is to accumulate meta-knowledge across different meta-tasks and generalize the accumulated knowledge to the meta-test task for error-aware few-shot KG completion. To address the associated challenges resulting from insufficient training samples and inevitable errors, we propose three essential modules neighbor encoder, cross-relation aggregation, and error mitigation in each meta-task. Extensive experiments on three widely used KG datasets demonstrate the superiority of the proposed framework REFORM over competitive baseline methods.more » « less
-
Kiela, Douwe ; Ciccone, Marco ; Caputo, Barbara (Ed.)Deep learning excels at learning low-level task information from large amounts of data, but struggles with learning high-level domain knowledge, which can often be directly and succinctly expressed. In this work, we introduce Pylon, a neuro-symbolic training framework that builds on PyTorch to augment procedurally trained neural networks with declaratively specified knowledge. Pylon allows users to programmatically specify constraints as PyTorch functions, and compiles them into a differentiable loss, thus training predictive models that fit the data whilst satisfying the specified constraints. Pylon includes both exact as well as approximate compilers to efficiently compute the loss, employing fuzzy logic, sampling methods, and circuits, ensuring scalability even to complex models and constraints. A guiding principle in designing Pylon has been the ease with which any existing deep learning codebase can be extended to learn from constraints using only a few lines: a function expressing the constraint and a single line of code to compile it into a loss. We include case studies from natural language processing, computer vision, logical games, and knowledge graphs, that can be interactively trained, and highlights Pylon’s usage.more » « less
-
Knowledge graphs (KGs) capture knowledge in the form of head– relation–tail triples and are a crucial component in many AI systems. There are two important reasoning tasks on KGs: (1) single-hop knowledge graph completion, which involves predicting individual links in the KG; and (2), multi-hop reasoning, where the goal is to predict which KG entities satisfy a given logical query. Embedding-based methods solve both tasks by first computing an embedding for each entity and relation, then using them to form predictions. However, existing scalable KG embedding frameworks only support single-hop knowledge graph completion and cannot be applied to the more challenging multi-hop reasoning task. Here we present Scalable Multi-hOp REasoning (SMORE), the first general framework for both single-hop and multi-hop reasoning in KGs. Using a single machine SMORE can perform multi-hop reasoning in Freebase KG (86M entities, 338M edges), which is 1,500× larger than previously considered KGs. The key to SMORE’s runtime performance is a novel bidirectional rejection sampling that achieves a square root reduction of the complexity of online training data generation. Furthermore, SMORE exploits asynchronous scheduling, overlapping CPU-based data sampling, GPU-based embedding computation, and frequent CPU–GPU IO. SMORE increases throughput (i.e., training speed) over prior multi-hop KG frameworks by 2.2× with minimal GPU memory requirements (2GB for training 400-dim embeddings on 86M-node Freebase) and achieves near linear speed-up with the number of GPUs. Moreover, on the simpler single-hop knowledge graph completion task SMORE achieves comparable or even better runtime performance to state-of-the-art frameworks on both single GPU and multi-GPU settings.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1609/aaai.v36i4.20310
