Graph Neural Networks Meet Neural-Symbolic Computing: A Survey and Perspective

Lamb, Luís C.; Garcez, Artur S. d’Avila; Gori, Marco; Prates, Marcelo O. R.; Avelar, Pedro H. C.; Vardi, Moshe Y.

doi:10.24963/ijcai.2020/679

Cited by 89 publications

(50 citation statements)

References 3 publications

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“…In contrast, we focus on using graph learning to solve CO problems. There have also been several previous surveys that have discussed ML-based CO methods [5,38,43]. The present survey, however, has different emphases from previous studies.…”

Section: Introductionmentioning

confidence: 83%

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Graph Learning for Combinatorial Optimization: A Survey of State-of-the-Art

Peng

Choi

2021

Data Sci. Eng.

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Graphs have been widely used to represent complex data in many applications, such as e-commerce, social networks, and bioinformatics. Efficient and effective analysis of graph data is important for graph-based applications. However, most graph analysis tasks are combinatorial optimization (CO) problems, which are NP-hard. Recent studies have focused a lot on the potential of using machine learning (ML) to solve graph-based CO problems. Most recent methods follow the two-stage framework. The first stage is graph representation learning, which embeds the graphs into low-dimension vectors. The second stage uses machine learning to solve the CO problems using the embeddings of the graphs learned in the first stage. The works for the first stage can be classified into two categories, graph embedding methods and end-to-end learning methods. For graph embedding methods, the learning of the the embeddings of the graphs has its own objective, which may not rely on the CO problems to be solved. The CO problems are solved by independent downstream tasks. For end-to-end learning methods, the learning of the embeddings of the graphs does not have its own objective and is an intermediate step of the learning procedure of solving the CO problems. The works for the second stage can also be classified into two categories, non-autoregressive methods and autoregressive methods. Non-autoregressive methods predict a solution for a CO problem in one shot. A non-autoregressive method predicts a matrix that denotes the probability of each node/edge being a part of a solution of the CO problem. The solution can be computed from the matrix using search heuristics such as beam search. Autoregressive methods iteratively extend a partial solution step by step. At each step, an autoregressive method predicts a node/edge conditioned to current partial solution, which is used to its extension. In this survey, we provide a thorough overview of recent studies of the graph learning-based CO methods. The survey ends with several remarks on future research directions.

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Section: Introductionmentioning

confidence: 83%

“…This survey is not limited to RL approaches. Lamb et al [38] survey the GNN-based neuralsymbolic computing methods. Symbolic computing is a broad field and graph-based CO is a topic of it.…”

Section: Introductionmentioning

confidence: 99%

Graph Learning for Combinatorial Optimization: A Survey of State-of-the-Art

Peng

Choi

2021

Data Sci. Eng.

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“…However, depending on the end application the representation format could be a graph, stack, table. Thus the work in Graph Neural Networks (Scarselli et al, 2008;Lamb et al, 2020), which operates over graphs or the Neural State Machine (Hudson and Manning, 2019) that operates over automata is also related to our work.…”

Section: Related Workmentioning

confidence: 90%

Deeply Embedded Knowledge Representation & Reasoning For Natural Language Question Answering: A Practitioner’s Perspective

Mitra

Narayana²,

Baral

2020

Proceedings of the Fourth Workshop on Structured Prediction for NLP

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“…Symbolic computing was recognised early on as important to Artificial Intelligence, where a recent review is given in [9]. Some of the following text is taken from [8], Chapter 2: John McCarthy tried to introduce learning into a computer program, to allow it to reason like a human.…”

Section: Related Workmentioning

confidence: 99%

How the Brain might use Division

Greer

2020

Wseas Transactions on Computer Research

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One of the most fundamental questions in Biology or Artificial Intelligence is how the human brainperforms mathematical functions. How does a neural architecture that may organise itself mostly throughstatistics, know what to do? One possibility is to extract the problem to something more abstract. This becomesclear when thinking about how the brain handles large numbers, for example to the power of something, whensimply summing to an answer is not feasible. In this paper, the author suggests that the maths question can beanswered more easily if the problem is changed into one of symbol manipulation and not just number counting.If symbols can be compared and manipulated, maybe without understanding completely what they are, then themathematical operations become relative and some of them might even be rote learned. The proposed systemmay also be suggested as an alternative to the traditional computer binary system. Any of the actual maths stillbreaks down into binary operations, while a more symbolic level above that can manipulate the numbers andreduce the problem size, thus making the binary operations simpler. An interesting result of looking at this is thepossibility of a new fractal equation resulting from division, that can be used as a measure of good fit and wouldhelp the brain decide how to solve something through self-replacement and a comparison with this good fit.

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Graph Neural Networks Meet Neural-Symbolic Computing: A Survey and Perspective

Cited by 89 publications

References 3 publications

Graph Learning for Combinatorial Optimization: A Survey of State-of-the-Art

Graph Learning for Combinatorial Optimization: A Survey of State-of-the-Art

Deeply Embedded Knowledge Representation & Reasoning For Natural Language Question Answering: A Practitioner’s Perspective

How the Brain might use Division

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