Neural-Symbolic Cognitive Reasoning€¦ · ICCL Summer School, TU Dresden Dresden, 1-3 September...
Transcript of Neural-Symbolic Cognitive Reasoning€¦ · ICCL Summer School, TU Dresden Dresden, 1-3 September...
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ICCL Summer School, TU DresdenDresden, 1-3 September 2010
Neural-Symbolic Cognitive Reasoning
Artur d’Avila GarcezCity University London
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Motivation• The need for:learning from changes in the environment reasoning about commonsense knowledge• The need for robustness: controlling the accumulation of errors
in uncertain environments• Integrating reasoning and learning:Symbolic systems too brittle (commonsense cannot be axiomatized)Neural networks too complex (modularity, legacy systems,
explanation) • Combining the logical nature of reasoning and the statistical
nature of learning
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Outline
• Overview of Neural-Symbolic Cognitive Model• Backpropagation:
• worked example• evaluation: cross-validation/ embracing uncertainty
• CILP translation algorithm, extraction, applications• Nonclassical CILP: modal, temporal, etc.• Fibring networks (specializations)• Relational / first-order CILP (propositionalization)• Abductive reasoning, attention, emotions, creativity, etc.
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Neuroymbolic Computation is... ...interdisciplinary
Cognitive Science
LogicMachine LearningProbability TheoryComputer Science
Neural Computation
Neuroscience...related to SRL and ILP but underpinned by
neural computation
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IET/BCS Turing lecture 2010 (Chris Bishop)
1960s-1980s: Expert Systems (hand-crafted rules)“Within a generation... the problem of creating 'artificial intelligence' will largely be solved” Marvin Minsky 1967
1990's-present: Neural networks, Support vector machines (difficult to include domain knowledge)
New AI: Bayesian learning, probabilistic graphical models, efficient inference
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One Algorithm for Learning and Reasoning
high-level symbolic representations (abstraction, recursion, relations)
translations
low level, efficient neural structures(with the same, simple architecture throughout)
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Neural-Symbolic Learning Systems
Symbolic
KnowledgeSymbolic
Knowledge
NeuralNetwork
Examples
Learning
Connectionist System
InferenceMachine
Explanation
1
2
3
4
5
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Connectionist Inductive Logic Programming (CILP) System
A Neural-Symbolic System for Integrated Reasoning and Learning • Knowledge Insertion, Revision (Learning), Extraction
(based on Towell and Shavik, Knowledge-Based Artificial Neural Networks. Artificial Intelligence, 70:119-165, 1994)• Real Applications: DNA Sequence Analysis, Power Systems Fault
Diagnosis(using backpropagation with background knowledge; test set performance is comparable to backpropagation; test set performance on smaller training sets is comparable to KBANN; training set performance is superior than backpropagation and KBANN)
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r1: A ← B,C,~D;
r2 : A ← E,F;
r3 : B ←
CILP Translation AlgorithmA BθA θB
W WW
θ1 h1 θ2 h2 θ3 h3
B FE DC
WWW -WW
Interpretations
based on Holldobler and Kalinke’s translation, but extended to sigmoid neurons (backprop) and hetero-associative networksHolldobler and Kalinke, Towards a Massively Parallel Computational Model for Logic Programming. ECAI Workshop Combining Symbolic and Connectionist Processing , 1994.
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CILP Extraction Algorithm
challenge: efficient extraction of sound, comprehensible symbolic knowledge from large-scale neural networks
{-1,1,1}
{1,1,1}
{1,-1,-1}
{1,1,-1} {1,-1,1}
{-1,1,-1}
{-1,-1,-1}
{-1,-1,1}
[a,b,c]
a → h0
b → h0
c → h0
b, c → h1
a, c → h1
a, b → h1
1 (a, b, c) → h0
2(a, b, c) → h1
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Garcez, Zaverucha. The CILP System. Applied Intelligence 11:59-77, 1999.
Garcez, Broda, Gabbay. Knowledge Extraction from Neural Nets. Artificial Intelligence 125:153-205, 2001.
Garcez, Broda, Gabbay. Neural-Symbolic Learning Systems. Springer, 2002.
Publications
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CILP extensions
• Non-Classical Reasoning• Modal, Temporal, Epistemic, Intuitionistic, Abductive
Reasoning, Value-based Argumentation.• New potential applications including temporal logic
learning, model checking, software engineering (requirements evolution), etc.
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Connectionist Modal Logic (CML)
W1
W3W2
CILP network ensembles, modularity for learning,accessibility relations, disjunctive information
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Semantics of ð and ◊
A proposition is necessary (ð ) in a world if it is true in all worlds which are possible in relation to that world.
A proposition is possible (◊) in a world if it is true in at least one world which is possible in relation to that same world.
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Representing ð and ◊
p
q
W2
W3
W1
q
q
p
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Translates modal programs into ensembles of CILP networks, i.e. clauses Wi : ML1,...,MLn → MA and relations R(Wa,Wb) between worlds Wa and Wb, with M in {ð , ◊}.
Theorem: For any modal program P there exists an ensemble of simple neural networks N such that N computes P.
CML Translation Algorithm
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Learning in CML
We have applied CML to a benchmark distributed knowledge representation problem: the muddy children puzzle
(children are playing in a garden; some have mud on their faces, some don’t; they can see if the others are muddy, but not themselves; a caretaker asks: do you know if you’re muddy? At least one of you is)
Learning with modal background knowledge offers better accuracy than learning by examples only (93% vs. 84% test set accuracy)
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Connectionist Temporal Reasoning
Agent 1 Agent 2 Agent 3
t1
t2
t3
at least 1 muddy
3 muddy children
at least 2 muddy
A full solution to the muddy children puzzle can only be given by a two-dimensional network ensemble
Short-term and long-term memory
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Garcez, Gabbay, Ray, Woods. Abductive Reasoning in Neural-Symbolic Learning Systems. Topoi 26:37-49, 2007. Garcez, Lamb, Gabbay. Connectionist Modal Logic. TCS, 371: 34-53, 2007. Garcez, Lamb, Gabbay. Connectionist Computations of Intuitionistic Reasoning. TCS, 358:34-55, 2006. Garcez, Lamb. Connectionist Model for Epistemic and Temporal Reasoning. Neural Computation, 18:1711-1738, July 2006.
Publications
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Combining (Fibring) Networks
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Network A
Network B
fibring function
Fibred networks approximate any polynomial function in unbounded domains
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Relational Learning
Experiments on the east-west trains dataset show an improvement from 62% (flat, propositional network) to 80% (metalevel network) on test set performance (leaving one out cross-validation)
X Y Z
X Y Z
X Y Z
X Y Z
P Q
α β γ δ
Inputs presented to P and Q at the same time trigger the learning process in the meta-level
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FOL ANN (propositionalisation)
conform(x,1)
conform(x,2)
opposite(x,y)
opposite(y,x)mesh(x,1)
mesh(x,2)
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Cognitive Model: Fibred Network Ensembles
meta-level relations
fibring functions
object-level
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Garcez, Lamb, Gabbay. Neural-Symbolic Cognitive Reasoning. Springer, 2009.
Lamb, Borges, Garcez. Connectionist Model for Temporal Synchronisation and Learning. AAAI 2007, July 2007.
Borges, Garcez, Lamb. Integrating Model Verification and Self-Adaptation. ASE 2010, September 2010.
Garcez, Gabbay. Fibring Neural Networks. AAAI 2004, July 2004.
Publications
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Current Work• First Order Logic Learning: encoding vs.
propositionalisation • Neural Networks for Normative Systems:
obligations, permissions, contrary to duty• Adding domain knowledge to deep belief
networks: higher order logic• Neural Networks for Abductive Reasoning:
creativity, emotions, attention • Application in software engineering: model
checking + adaptation• Application in simulation environments:
driving test, war games, robocup
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Conclusion: Why Neurons and Symbols
To study the statistical nature of learning and the logical nature of reasoning.
To provide a unifying foundation for robust learning and efficient reasoning.
To develop effective computational systems for integrated reasoning and learning.