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

Neural-symbolic computing has now become the subject of interest of both academic and industry research laboratories. Graph Neural Networks (GNN) have been widely used in relational and symbolic domains, with widespread application of GNNs in combinatorial optimization, constraint satisfaction, relational reasoning and other scientific domains. The need for improved explainability, interpretability and trust of AI systems in general demands principled methodologies, as suggested by neural-symbolic computing. In this paper, we review the state-of-the-art on the use of GNNs as a model of neural-symbolic computing. This includes the application of GNNs in several domains as well as its relationship to current developments in neural-symbolic computing.Comment: Updated version, draft of accepted IJCAI2020 Survey Pape

Applications of symbolic computing methods to the dynamic analysis of large systems

Since the symbolic computing language is very well suited to the operations with algebraic equations, techniques use the transfer function concept as a tool for the analysis of large linear dynamic systems. Techniques were coded in the experimental symbolic computer language FORMAC. The first of these approaches, REDUCE 1, establishes the techniques and a computer program to symbolically reduce arbitrary block diagrams associated with large systems for desired transfer functions. Symbolic closed form solutions are determined in several forms including an expanded form in terms of the driving frequencies and system constants. Programs are also written to numerically evaluate the symbolic solutions. A second computer program, REDUCE 2, is also based on the use of symbolic computing methods and was written to accommodate large engineering systems

Generic access to symbolic computing services

Symbolic computation is one of the computational domains that requires large computational resources. Computer Algebra Systems (CAS), the main tools used for symbolic computations, are mainly designed to be used as software tools installed on standalone machines that do not provide the required resources for solving large symbolic computation problems. In order to support symbolic computations an infrastructure built upon massively distributed computational environments must be developed. Building an infrastructure for symbolic computations requires a thorough analysis of the most important requirements raised by the symbolic computation world and must be built based on the most suitable architectural styles and technologies. The architecture that we propose is composed of several main components: the Computer Algebra System (CAS) Server that exposes the functionality implemented by one or more supporting CASs through generic interfaces of Grid Services; the Architecture for Grid Symbolic Services Orchestration (AGSSO) Server that allows seamless composition of CAS Server capabilities; and client side libraries to assist the users in describing workflows for symbolic computations directly within the CAS environment. We have also designed and developed a framework for automatic data management of mathematical content that relies on OpenMath encoding. To support the validation and fine tuning of the system we have developed a simulation platform that mimics the environment on which the architecture is deployed

Symbolic Computing with Incremental Mindmaps to Manage and Mine Data Streams - Some Applications

In our understanding, a mind-map is an adaptive engine that basically works incrementally on the fundament of existing transactional streams. Generally, mind-maps consist of symbolic cells that are connected with each other and that become either stronger or weaker depending on the transactional stream. Based on the underlying biologic principle, these symbolic cells and their connections as well may adaptively survive or die, forming different cell agglomerates of arbitrary size. In this work, we intend to prove mind-maps' eligibility following diverse application scenarios, for example being an underlying management system to represent normal and abnormal traffic behaviour in computer networks, supporting the detection of the user behaviour within search engines, or being a hidden communication layer for natural language interaction.Comment: 4 pages; 4 figure

Neural-symbolic computing: An effective methodology for principled integration of machine learning and reasoning

Current advances in Artificial Intelligence and machine learning in general, and deep learning in particular have reached unprecedented impact not only across research communities, but also over popular media channels. However, concerns about interpretability and accountability of AI have been raised by influential thinkers. In spite of the recent impact of AI, several works have identified the need for principled knowledge representation and reasoning mechanisms integrated with deep learning-based systems to provide sound and explainable models for such systems. Neural-symbolic computing aims at integrating, as foreseen by Valiant, two most fundamental cognitive abilities: the ability to learn from the environment, and the ability to reason from what has been learned. Neural-symbolic computing has been an active topic of research for many years, reconciling the advantages of robust learning in neural networks and reasoning and interpretability of symbolic representation. In this paper, we survey recent accomplishments of neural-symbolic computing as a principled methodology for integrated machine learning and reasoning. We illustrate the effectiveness of the approach by outlining the main characteristics of the methodology: principled integration of neural learning with symbolic knowledge representation and reasoning allowing for the construction of explainable AI systems. The insights provided by neural-symbolic computing shed new light on the increasingly prominent need for interpretable and accountable AI systems

Neuro-symbolic computing with spiking neural networks

Knowledge graphs are an expressive and widely used data structure due to their ability to integrate data from different domains in a sensible and machine-readable way. Thus, they can be used to model a variety of systems such as molecules and social networks. However, it still remains an open question how symbolic reasoning could be realized in spiking systems and, therefore, how spiking neural networks could be applied to such graph data. Here, we extend previous work on spike-based graph algorithms by demonstrating how symbolic and multi-relational information can be encoded using spiking neurons, allowing reasoning over symbolic structures like knowledge graphs with spiking neural networks. The introduced framework is enabled by combining the graph embedding paradigm and the recent progress in training spiking neural networks using error backpropagation. The presented methods are applicable to a variety of spiking neuron models and can be trained end-to-end in combination with other differentiable network architectures, which we demonstrate by implementing a spiking relational graph neural network.Comment: Accepted for publication at the International Conference on Neuromorphic Systems (ICONS) 202

A Semantic Framework for Neural-Symbolic Computing

Two approaches to AI, neural networks and symbolic systems, have been proven very successful for an array of AI problems. However, neither has been able to achieve the general reasoning ability required for human-like intelligence. It has been argued that this is due to inherent weaknesses in each approach. Luckily, these weaknesses appear to be complementary, with symbolic systems being adept at the kinds of things neural networks have trouble with and vice-versa. The field of neural-symbolic AI attempts to exploit this asymmetry by combining neural networks and symbolic AI into integrated systems. Often this has been done by encoding symbolic knowledge into neural networks. Unfortunately, although many different methods for this have been proposed, there is no common definition of an encoding to compare them. We seek to rectify this problem by introducing a semantic framework for neural-symbolic AI, which is then shown to be general enough to account for a large family of neural-symbolic systems. We provide a number of examples and proofs of the application of the framework to the neural encoding of various forms of knowledge representation and neural network. These, at first sight disparate approaches, are all shown to fall within the framework's formal definition of what we call semantic encoding for neural-symbolic AI