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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
1
C
Towards Data-and Knowledge-Driven AI:
A Survey on Neuro-Symbolic Computing
Wenguan Wang, Senior Member, IEEE,
Yi Yang, Senior Member, IEEE , and Fei Wu, Senior Member, IEEE
Abstract—Neural-symbolic computing (NeSy), which pursues the integration of the symbolic and statistical paradigms of cognition,
has been an active research area of Artificial Intelligence (AI) for many years. As NeSy shows promise of reconciling the advantages of
reasoning and interpretability of symbolic representation and robust learning in neural networks, it may serve as a catalyst for the next
generation of AI. In the present paper, we provide a systematic overview of the recent developments and important contributions of
NeSy research. Firstly, we introduce study history of this area, covering early work and foundations. We further discuss background
concepts and identify key driving factors behind the development of NeSy. Afterward, we categorize recent landmark approaches along
several main characteristics that underline this research paradigm, including neural-symbolic integration, knowledge representation,
knowledge embedding, and functionality. Next, we briefly discuss the successful application of modern NeSy approaches in several
domains. Then, we benchmark several NeSy methods on three representative application tasks. Finally, we identify the open problems
together with potential future research directions. This survey is expected to help new researchers enter this rapidly evolving field and
accelerate the progress towards data-and knowledge-driven AI.
Index Terms—Neuro-Symbolic AI, Symbolic AI, Statistical AI, Deep Learning
✦
1
INTRODUCTION
URRENT advances in Artificial Intelligence (AI), espe-
cially large AI models, have caused significant changes
in numerous research fields, and had profound impacts on
every nook and cranny of societal and industrial sectors. At
the same time, there is also growing concern in the public
and scientific communities regarding the trustworthiness,
safety, interpretability, and accountability of the modern AI
techniques [1]. This leads to a natural question: What could
be the key enabler for the next generation of AI?
AI has historically been dominated by two paradigms:
symbolism and connectionism. Symbolism conjectures that
symbols representing things in the world are the fundamen-
tal units of human intelligence, and that the cognitive pro-
cess can be accomplished by the manipulation of the sym-
bols, through a series of rules and logic operations upon the
symbolic representations [2], [3]. Many early AI systems,
from the mid-1950s to the late 1980s, were built upon sym-
bolistic models. Symbolic methods have several virtues: they
require only a few input samples, use powerful declarative
languages for knowledge representation, and have concep-
tually clear internal functionality. It soon became apparent,
however, that such a rule-based, top-down strategy demands
substantial hand-tuning and lacks true learning. Moreover,
as discrete symbolic representations and hand-crafted rules
are intolerant of ambiguous and noisy data, symbolic meth-
ods typically fall short when solving real-world problems.
Connectionism, represented by its most successful tech-
nique, deep neural networks (DNNs) [4], serves as the archi-
tecture behind the majority of recent successful AI systems.
•
W. Wang, Y. Yang, and F. Wu are with College of Computer Science and
•
Corresponding Authors: Wenguan Wang
Inspired by the physiology of the nervous system, connec-
tionism explains cognition by interconnected networks of
simple and often uniform units. Learning happens as weight
modification, in a data-driven manner; the network weights
are adjusted in the direction that minimises the cumulative
error from all the training samples, using techniques such
as gradient back-propagation [5]. Connectionist models are
fault-tolerant, since they learn sub-symbolics, i.e., continuous
embedding vectors, and compare these vectorized represen-
tations instead of the literal meaning between entities and
relations by discrete symbolic representations. Moreover, by
learning statistical patterns from data, connectionist models
enjoy the advantages of inductive learning and generaliza-
tion capabilities. Yet, like every coin has two sides, such ap-
proaches also suffer from several fundamental problems [6],
[7]. First, connectionist models fall significantly short of com-
positional generalization, the robust ability of human cogni-
tion to correctly solve any problem that is composed of fami-
liar parts [8]. Second, such bottom-up approaches are known
to be data inefficient. Third, connectionist models are logically
opaque, lacking comprehensibility. It is almost impossible to
understand why decisions are made. In the absence of any
kind of identifiable or verifiable train of logic, people are left
with systems that make potentially catastrophic decisions
that are difficult to understand, arduous to correct, and
therefore hard to trust. These shortcomings hinder the adop-
tion of connectionist systems in decision-critical applications
and reasoning-heavy tasks, such as medical diagnosis, au-
tonomous driving, and mathematical reasoning, and lead to
the increasing concern about contemporary AI techniques.
Against this background, neural-symbolic computing
(NeSy) [9], as a hybrid of symbolism and connectionism, is
widely recognized as an enabler of the next generation of AI
[10], [11]. NeSy essentially looks for the integration of two
arXiv:2210.15889v4
[cs.AI]
12 Oct 2023
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
2
Introduction
Section
1
History
Section
Data-and Knowledge-Driven AI:
Neuro-Symbolic Computing (NeSy)
Challenge
Section
Conclusion
Section
8
Human Cognition:
2
Biologic Neural Network
Background
Benchmark
7
vs
Symbolic Logic Machinery
NeSy: Best-of-Both Worlds
Section
3
Technique
Section
Application
Section
Section
6
-
Scalability
-
Compositional Generalization
-
Automated Knowledge Acquisition
Current Debate on AI
Taxonomy for NeSy
Neural-Symbolic Integration
4
-
Scientific Discovery
-
Recursive Neuro[Symbolic] Engine
-
Testbed for Metacognitive Skills of NeSy
Retrosynthesis Prediction
Knowledge Representation
Knowledge Embedding
-
Programming Systems
- Question-Answering
-
Vision-Language
Analysis & Reasoning
-
Robotics and Control
Visual Semantic Parsing
Math Word Problem Solving
Fig. 1. Structure of the overall review.
Functionality
-
Visual Scene Understanding
-
Mathematical Reasoning
fundamental cognitive abilities [12], [13]: learning (the abili-
ty to learn from experience), and reasoning (the ability to rea-
son from what has been learned), so as to exploit the major
strengths and circumvent the inherent deficiencies of the two
paradigms. However, building such an integrated machin-
ery is challenging – one has to conciliate the methodologies
of distinct areas [14], for example, statistical inductive learn-
ing based on distributed representations vs logical deductive
reasoning based on localist representations. Though chal-
lenging, NeSy has attracted soaring research attention in the
recent past, and has demonstrated its superiority in many
application scenarios, including visual relationship unders-
tanding[15], [16], visual question answering[17]–[19], visual
scene parsing [20], [21], and commonsense reasoning [22].
In order to facilitate readers to catch up on the rapidly-
developing evolution of this field, this paper offers a system-
atical and timely collection of recent important literature on
NeSy, with a focus on the past five years. The surveyed pa-
pers are those works published in the flagship repositories
for machine learning and related areas, such as computer
vision, natural language processing (NLP), and knowledge
graph, or have been widely cited. This survey is expected to
offer an exhaustive and up-to-date literature overview to re-
searchers of interest, and nourish the exploration of open
and developmental issues. We also remark that this survey is
inevitably a biased view, since there is a broad spectrum of
research in this fast-growing area, but we do attempt to
identify and analyze common and critical properties of land-
mark practices in order to cover major research threads. Rea-
ders are also encouraged to refer to discussions in [13], [23]–
[25], among others, to gain a sense of the breadth of this area.
A summary of the structure of this article can be found
in Fig. 1, which is presented as follows: Sec. 2 gives a
brief review of early research results of NeSy, which shape
the latest effort in this area. Sec. 3 introduces the general
concepts of mind in psychology and cognitive science,
which underpin the theoretical foundations of NeSy, and
discusses the recent debate on the necessary and sufficient
building blocks of AI, which promotes the advance of this
area. Sec. 4 presents our taxonomy of NeSy, which clas-
sifies recent important NeSy literature according to four
dimensions: neural-symbolic interrelation, knowledge rep-
resentation, knowledge embedding, and functionality. Sec. 5
elaborates on popular and emerging application areas of
NeSy. Sec. 6 conducts performance evaluation and analysis.
Finally, Sec. 7 and 8 suggest potential valuable directions for
further research and conclude the survey. We hope that this
survey will help newcomers and practitioners to navigate
in this massive field that gained significant momentum in
the past few years, as well as provide AI community with
background information for generating future research.
2
HISTORY
This section offers a historical perspective of NeSy, prior to
its recent acceleration in activity. NeSy aims to provide a
unifying view for symbolism and connectionism, advance
the modelling of cognition and further behaviour, and build
preferable computational methodologies for integrated ma-
chine learning and logical reasoning [14]. NeSy has a long-
standing tradition that can be traced back to McCulloch and
Pitts in 1943 [9], even before AI was recognized as a new
scientific field. For readers who are eager to obtain a more
particular overview of the primitive works, we recommend
consulting previous review articles, such as [14], [26], [27].
Although in the seminal work [9] McCulloch and
Pitts established strong connection between finite automata
(boolean logic) and artificial neural networks, by inter-
preting simple logical connectives such as conjunction,
disjunction and negation as binary threshold units in neural
networks [26], NeSy only began to be a formalized field of
5
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
3
study since the 1990s and gained systematic research in the
early 2000s [28]. For instance, Towell et al. [29] compiled
hand-coded symbolic rules into a neural network, and the
approximately correct knowledge can be further corrected
by empirical learning. Based on some landmark efforts [30]–
[32], researchers developed various neural systems for log-
ical inference [27], [33] and knowledge representation [34]–
[38]. As their neural architectures are mainly meticulously
designed for hard logic reasoning, they lacked the ability
to learn representations and to reason over large-scale, het-
erogeneous, and noisy data [28]. Nevertheless, these early
NeSy systems laid the groundwork for today’s research.
During the 2010s, NeSy received relatively less attention,
as DNN-based connectionist techniques achieved remark-
able success across a variety of AI tasks. However, as the
shortcomings of DNNs became evident, NeSy has recently
ushered in its renaissance in the research community.
3
BACKGROUND AND CONTEXT
This section elucidates the two main driving forces behind
the field of NeSy: The first one is the theoretical aspiration to
understand and model human cognition (Sec. 3.1), while the
second one is the practical value of combining connection-
ism and symbolism paradigms in AI application scenario
(Sec. 3.2). Sec. 3.3 further summarizes the recent AI debate
among influential thinkers, which motivates a broad range
of AI researchers to recognize the significance of NeSy.
3.1
Human
Cognition:
Biologic
Neural
Network
vs
Symbolic Logic Machinery
•
Symbols vs Neurons. What is the essence of human
cognition? Many researchers agree that symbolic facility
is what distinguishes humans from other animals. The
prosperity of human sociology and technology is closely
concerned with the co-evolution of human brain with sym-
bolic thinking, making us the “symbolic species” [39]–[41].
Many cognitive scientists hold the view that human think-
ing relies on symbol manipulation. From this perspective,
human mind is undisputedly symbolic. Therefore, sym-
bolism was conceived in the attempts to structurally code
knowledge and logic reasoning into machines. However,
human cognition has a physical basis in the brain, which
is composed of numerous mostly homogenous neurons.
The neurons, together with the connections, or synapses, as
well as diverse firing patterns among them, support differ-
ent cognitive processes, such as attention, problem-solving,
memory, learning, decision-making, language, perception,
imagination, and logic reasoning. So it seems reasonable
to assume if we can simulate the anatomy and physiology
of the nervous system with artificial neurons, intelligence
will be developed in computers. This belief leads to the
emergence of connectionism.
Spontaneously, in order to advance the understanding of
the human mind, it appears to be reasonable to seek ways
of integration of symbolic and connectionist approaches, in-
stead of focusing on the dichotomy. In this context, artificial
neural networks can be regarded as an abstraction of the
physical workings of the brain, while the symbolic logic can
be viewed as an abstraction of what we introspect, when we
engage in explicit cognitive reasoning [42]. Therefore, it is of
necessity to ask how these two abstractions can be related
or even unified, or how symbol manipulation can emerge
from a neural substrate [14], [43].
•
Deduction vs Induction. Deductive reasoning and induc-
tive learning arguably constitute two indispensable build-
ing blocks of human thinking, helping human to develop
knowledge of the world (even though there are yet other
building blocks, such as abductive reasoning) [44]. How-
ever, their tension might be the most fundamental issue in
areas such as philosophy, cognition, and, of course, AI [23].
The deduction camp [45] is aware of the expressiveness of for-
mal languages for representing knowledge about the world,
along with proof systems for reasoning from such knowl-
edge bases. The learning camp [46] attempts to generalize
from examples about partial descriptions of the world [23].
Historically, the dichotomy between the two camps roughly
divided the development of AI. Symbolic techniques clearly
stand on the side of deductive reasoning; symbolic logic
emphasizes high-level reasoning, and sticks to structure the
world in terms of objects, attributes, and relations [23].
By contrast, neural networks are in the statistical learn-
ing camp; they learn statistical patterns, i.e., distributed
representations of entities, from data. Nevertheless, humans
make extensive use of both deduction and induction in
everyday life as well as scientific investigation. We cannot
precisely determine which part of human cognition is es-
sentially symbolic, and which part is essentially statistical.
Consequently, it is imperative to rethink the relationships
between deductive reasoning and inductive learning, neces-
sitating robust computational models that are able to coor-
dinate the symbolic essence of reasoning with the statistical
nature of learning.
•
Compositionality vs Continuity.
Smolensky
et
al.
[7]
proposed to simultaneously exploit two scientific principles,
which can explain the way the human brain works, for
machine intelligence, from the viewpoint of the underlying
computation mode of human cognition. Neurophysiological
measurements suggest that information is encoded in the
brain through the numerical activation levels of massive
neurons, and is processed by spreading this activation
through myriad synapses of varying strengths and per-
manence [6]. Hence it seems evident that human cogni-
tion deploys neural computing [47], which conforms to
the Continuity Principle: “the encoding and processing of
information are formalized with real numbers that vary
continuously” [7]. However, modern scientific studies [48]
in philosophy and cognition suggested that all aspects of
human intelligence, from language and perception to rea-
soning and planning, rely on a different type of computing:
compositional-structure processing [49]. This type of com-
puting follows the Compositionality Principle [50]: complex
information is encoded in large structures which are sys-
tematically composed from smaller structures that encode
simpler information. Compositionality is widely acknowl-
edged as a core of human intelligence [51]. Our knowledge
representation is naturally compositional. For example, we
understand the world as a sum of its parts: objects can be
broken down into pieces, events are a sequence of actions,
and sentences are a series of words. Human cognition
exhibits strong compositional generalization – the ability
of reorganizing familiar knowledge components in novel
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
4
ways to solve new problems, so as to handle the poten-
tially infinite number of states of the world [6]. Historically,
compositional-structure processing is formalized in the form
of discrete symbolic computing, like using words to make
sentences. Thus, to some extent, the nature of computation
in our brains is both neural and compositional-structure.
How can this be? Smolensky called this the Central Paradox
of Cognition [52]. Resolving this paradox inevitably calls for
a new computing mechanism, that addresses both the Con-
tinuity and Compositionality Principles simultaneously
1
.
•
System 1 vs System 2. Kahneman’s ‘fast and slow thinking’
theory, which explains the machinery of human thought,
also motivated recent research interest in NeSy [53]. In [54],
Kahneman argued that humans’ decisions are supported by
the cooperation of two different kinds of capabilities, called
system 1 (‘fast thinking’) and system 2 (‘slow thinking’).
Specifically, system 1 thinking is a near-instantaneous and
experience-driven process for intuitive, imprecise, quick,
and largely unconscious decisions, accounting for 98% of
thinking. System 1 thinking, for example, can be in the
form of knowing how to zip your jacket without a second
thought. Differently, system 2 thinking is slower, deliber-
ative, and conscious, often associated with the subjective
experience of agency, choice, and concentration; it provides
a powerful tool for solving more complicated problems,
where logical, sequential, algorithmic thinking is needed.
For example, system 2 thinking is used when working on
math problems. It is also worth mentioning that composi-
tional generalization is exhibited in both system 1 thinking
and system 2 thinking [7]. Interestingly, system 2 can be
viewed as a “slave” of system 1: when system 1 runs into
difficulty, it is system 1 that decides to initiate system 2. Even
during the execution of system 2, system 1 is ultimately in
charge [55]. In addition, solutions discovered by system 2
can be readily available for later use by system 1. Thus, after
a while, some problems, initially solvable only by resorting
to system 2, can become manageable by system 1 [53]. The
consistent and effective use of system 2 can calibrate system
1, which, in turn, promotes system 2, leading to a feedback
loop. As the characteristics of system 1 and system 2 are
strikingly similar to those of the connectionist approach and
the symbolic approach to AI, more and more AI researchers
began to rethink the relation between the two traditions and
recognize the value of NeSy.
3.2
NeSy: Best-of-Both Worlds
Rather than taking the motivation from the objective of
achieving rational understanding and modeling of human
cognition, the study of NeSy is also driven by a more techni-
cally motivated perspective – combining numerical connec-
tionist and symbolic logic approaches in order to construct
more powerful reasoning and learning machines for com-
puter science applications. The second motivation is based
1. Note that the solution – neurocompositional computing – proposed by
Smolensky et al. [7] is slightly different from NeSy. NeSy broadly refers
to any possible hybrid systems that couple, loosely or tightly, neural
and symbolic approaches. Neurocompositional computing, instead, is
to directly realize compositional-structure processing through contin-
uous neural computing, which can be viewed as a compact, neural
network based NeSy system. However, in spite of such difference, both
NeSy and neurocompositional computing share the same motivation.
on the observation that connectionist techniques, especially
modern DNNs, and symbolic approaches complement each
other with respect to their strengths and weaknesses. In
particular, connectionist techniques are good at discovering
statistic patterns from raw data and are robust against noisy
data. Hence they are effective in intuitive judgements, such
as image classification. On the other hand, connectionist
techniques are data hungry, and black boxes – it is es-
pecially challenging to understand their decision-making
processes. Alternatively, symbolic approaches are excellent
at principled judgements, such as logical reasoning; they
exhibit inherently high explainability and provide the ease
of using powerful declarative languages for knowledge rep-
resentation. Nevertheless, symbolic approaches are far less
trainable and susceptible to out-of-domain brittleness. As a
result, the integration of neural and symbolic approaches
seems to be a natural step toward more powerful, trustwor-
thy, and robust AI.
3.3
Current Debate on AI
Recent years have witnessed remarkable breakthroughs in
AI, brought by connectionist approaches and deep learning
in particular. But researchers are also coming to realize that
contemporary AI systems suffer from serious deficiencies
in terms of, for example, data efficiency, comprehensibility,
and compositional generalization [65]. This led to influential
debates between famous researchers, which are about the
underlying principles of AI. As a result, NeSy research
gained renewed importance.
Specifically, the 2019 Montreal AI Debate between
Yoshua Bengio and Gary Marcus [43], and the AAAI-2020
fireside conversation with Economics Nobel Laureate Daniel
Kahneman and the 2018 Turing Award winners and deep
learning pioneers Geoff Hinton, Yoshua Bengio, and Yann
LeCun, brought new perspectives and concerns on the
future of AI. In the debate between Yoshua Bengio and
Gary Marcus, Marcus emphasizes the importance of hybrid
systems:
“
·
· ·
in order to get to robust artificial intelligence,
we need to develop a framework for building systems that can
routinely acquire, represent, and manipulate abstract knowledge,
with a focus on building systems that use that knowledge in
the service of building, updating, and reasoning over complex,
internal models of the external world.” Though Hinton agreed
that “we need those higher-level concepts to be grounded and
have a distributed representation to achieve generalization”, he
also addressed that “(numerical connectionist approaches) can
get many of the attributes of symbols without the kind of explicit
representations of them which has been the hallmark of classical
AI” and that “The reason why connectionists really wanted to
depart from symbolic processing is because they thought that
is wasn’t a sufficiently rich kind of representation.” At AAAI-
2020, Kahneman highlighted the importance of symbol ma-
nipulation in system 2:
“
·
· ·
as far as I’m concerned, system
1 certainly knows language
· · ·
system 2 does involve certain
manipulation of symbols.” Although there are disagreements
about, for example, how to represent symbols in DNNs and
how to achieve the hybrid of connectionism and symbolism,
the thinkers, in broad strokes, are in agreement that new-
generation AI systems ought to be able to handle high-level
abstract concepts and to conduct sound reasoning.
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