Neurosymbolic AI : Foundations and Applications.

An up-to-date and expert discussion of neuro-symbolic artificial intelligence development In Neuro-symbolic AI: Foundations and Applications , a team of distinguished researchers delivers a comprehensive overview of the emerging field of neuro-symbolic artificial intelligence.

Bibliographic Details
Main Author:	Velasquez, Alvaro
Format:	eBook
Language:	English
Published:	Newark : John Wiley & Sons, Incorporated, 2025.
Edition:	1st ed.
Subjects:	Neural networks (Computer science) Artificial intelligence. Electronic books.
Online Access:	Connect to the full text of this electronic book

Table of Contents:

Cover
Half Title Page
Title Page
Copyright
Contents
List of Contributors
About the Authors
Part I: Fundamentals
Chapter 1: What Is Neurosymbolic AI? An Overview and Frontier Problems
1.1 Introduction
1.2 Neurosymbolic Artificial Intelligence
1.2.1 Explicit to Implicit: From Symbolic Representations to Neural Networks
1.2.2 Implicit to Explicit: From Neural Networks to Symbolic Representations
1.3 Frontiers Problems
1.3.1 Neurosymbolic AI for Synthetic Biology
1.3.2 Neurosymbolic AI for Robust Autonomy
1.3.3 Neurosymbolic AI for Creative Scientific Discovery
1.4 Conclusion
References
Chapter 2: Reasoning in Neurosymbolic AI
2.1 What Is Reasoning in Neural Networks?
2.1.1 Reasoning in LLMs
2.1.2 AI from a Neurosymbolic Perspective
2.2 Background: Logic and RBMs
2.2.1 Illustrating Logical Reasoning with the Sudoku Puzzle
2.2.2 Sudoku with Strategies of Sampling
2.2.3 Restricted Boltzmann Machines
2.3 Symbolic Reasoning with Energy-based Neural Networks
2.3.1 Related Work
2.3.2 Knowledge Representation in RBMs
2.3.3 Reasoning in RBMs
2.3.4 Logical Boltzmann Machines
2.3.5 Experimental Results
2.3.6 Extensions of LBMs
2.4 LBMs for MaxSAT
2.4.1 LBM with Dual Annealing
2.4.2 Experimental Results of LBM for MaxSAT
2.5 Integrating Learning and Reasoning in LBMs
2.6 Challenges for Neurosymbolic AI
2.6.1 Nonmonotonic Logic
2.6.2 Planning
2.6.3 Learning from Its Mistakes
2.7 Conclusion
References
Chapter 3: Neurosymbolic Assurance Using Concept Probes in Foundation Models
3.1 Introduction
3.2 Neural Features and Concept Probes
3.3 Foundation Models as Specification Lens
3.4 Symbolic Specification of ML Models Using Concept Probes
3.5 Implementation and Evaluation
3.6 Conclusion and Open Challenges
References.
Chapter 4: Toward Assured Autonomy Using Neurosymbolic Components and Systems
4.1 Introduction
4.2 Problem Formulation and Challenges: Maneuver Control for Autonomous Vehicles
4.3 Software Architecture: Components and Interactions
4.4 Probabilistic World Model
4.4.1 Obstacle Map Calculation
4.4.2 Reward Map Calculation
4.5 Planner
4.5.1 Formalization
4.5.2 Online Planning Through Monte Carlo Search
4.5.3 Scalability Through Hierarchical Planning
4.5.4 Evaluation and Analysis
4.5.5 Neurosymbolic Extensions for Planning Under Partial Observability
4.6 Trajectory Control with Evolving Behavior Trees (EBTs)
4.6.1 Safe Autonomous UAV Navigation
4.6.2 Safe EBTs for Navigation
4.6.3 Evaluation
4.7 Assurance for Neurosymbolic Systems
4.7.1 Neurosymbolic Verification with BehaVerify
4.7.2 Assurance on Grid Abstractions
4.7.3 Timing Results and Conclusions
4.7.4 Future Work
4.8 Conclusions
References
Chapter 5: Safe Neurosymbolic Learning and Control
5.1 Problem Setup
5.1.1 Dynamical Safety Problem
5.1.2 Running Example: Air Collision Avoidance
5.2 Hamilton-Jacobi (HJ) Reachability
5.2.1 Methods to Solve HJI-VI and Compute Unsafe Set
5.2.2 Running Example: Air Collision Avoidance
5.3 A Neurosymbolic Perspective on Learning Safe Controllers
5.3.1 Self-supervised Neurosymbolic Learning for Synthesizing Safe Controllers
5.3.2 Neurosymbolic Reinforcement Learning for Synthesizing Safe Controllers
5.3.3 Connections Between Reinforcement and Self-supervised Neurosymbolic Learning
5.4 Safety Assurances for Learned Controllers
5.4.1 Probabilistic Safety Assurances Through Conformal Prediction
5.4.2 Robust Safety Assurances Through Forward Reachability
5.5 Frontiers, Open Questions, and Promising Directions
References.
Chapter 6: Controllable Generation via Locally Constrained Resampling
6.1 Introduction
6.2 Background
6.2.1 Notation and Preliminaries
6.2.2 A Probability Distribution over Sentences
6.2.3 The State of Conditional Sampling
6.3 Locally Constrained Resampling: A Tale of Two Distributions
6.3.1 Inducing a Local Tractable Distribution
6.3.2 Tractable Operations via Compilation
6.3.3 Intermezzo: Constraint Circuits and DFAs
6.3.4 Correcting Sample Bias: Importance Sampling... and Resampling
6.4 Related Work
6.5 Experimental Evaluation
6.6 Conclusion and Future Work
Appendix A Controllable Generation via Locally Constrained Resampling
A.1 Language Detoxification
A.2 Sudoku
A.3 Warcraft Shortest Path
A.4 Broader Impact
References
Chapter 7: Tractable and Expressive Generative Modeling with Probabilistic Flow Circuits
7.1 Introduction
7.2 Tractable Probabilistic Modeling
7.2.1 Inference Queries
7.2.2 The Expressivity-tractability Trade-off
7.3 Probabilistic Circuits
7.3.1 Defining a Probabilistic Circuit
7.3.2 Structural Properties
7.3.3 Tractable Inference with PCs
7.3.4 Parameter Learning for PCs
7.3.5 Structure Learning for PCs
7.4 Normalizing Flows: A Primer
7.4.1 Sampling and Inference in Flows
7.5 Integrating Normalizing Flows and PC
7.5.1 The Challenge
7.5.2 -Decomposability
7.6 Probabilistic Flow Circuits
7.7 Experiments and Results
7.7.1 Modeling Complex 3D Manifolds
7.7.2 Scaling to High-dimensional Data
7.7.3 Sample Generation and Inference
7.7.4 Ablation: Influence of PC Complexity
7.8 Conclusion and Discussion
7.8.1 Key Takeaways
7.8.2 Limitations and Future Directions
Acknowledgements
References
Chapter 8: Toward Verifiable and Scalable In-context Fine-tuning in Neurosymbolic AI
8.1 Introduction.
8.2 Neurosymbolic Fine-tuning Using Automated Feedback from Formal Verification
8.2.1 Introduction
8.2.2 Preliminaries
8.2.3 Methodology
8.2.4 Experimental Results
8.2.5 Conclusion
8.3 Uncertainty-aware Fine-tuning and Inference for Multimodal Foundation Models
8.3.1 Introduction
8.3.2 Conformal Prediction
8.3.3 Perception Uncertainty
8.3.4 Decision Uncertainty
8.3.5 Estimating Decision Uncertainty Score
8.3.6 Targeted Interventions
8.3.7 Experiments
8.3.8 Automated Refinement
8.3.9 Conclusion
8.4 Toward a Hybrid Architecture: Dynamic Interleaving of Neural and Symbolic Reasoning
8.5 Conclusion and Future Directions
8.5.1 Extending the Scope: Symbolic Tool Use for Mathematical Reasoning
References
Part II: Advanced Topics
Chapter 9: Physics-informed Deep Learning
9.1 Introduction
9.1.1 Data Generation in Physics-informed Machine Learning
9.1.2 Architectures
9.1.3 Training Objectives
9.1.4 Open Challenges
9.1.5 Connections to Atomistic Modeling
References
Chapter 10: Causal Representation Learning
10.1 Introduction
10.2 Background
10.2.1 Model Classes and Identifiability
10.2.2 Causal Graphical Models and Interventions
10.2.3 Causal Representation Models
10.2.4 CRL Identifiability and Equivalence Classes
10.3 Interventional CRL
10.4 CRL with Linear SCMs
10.4.1 Linear Mixing on Linear Latent SCMs
10.4.2 General Mixing on Linear Latent SCMs
10.5 CRL with General SCMs
10.5.1 Linear Mixing on General Latent SCMs
10.5.2 Multi-node Interventions
10.5.3 General Mixing on General Latent SCMs
10.6 Experiments
10.6.1 Linear Mixing with Synthetic Data
10.6.2 Experiments on Image Data
10.7 Other Approaches
10.8 Summary
References
Chapter 11: Neurosymbolic Computing: Hardware-Software Co-design
11.1 Introduction.
11.2 Background
11.2.1 Neurosymbolic Artificial Intelligence
11.2.2 Emerging Hardware Computing Platforms
11.3 Trends and Challenges
11.3.1 Enhance Reasoning and Generalization
11.3.2 Enable Compositionality
11.3.3 Handle Uncertainty
11.3.4 Improve System Efficiency
11.3.5 Demonstrate Full-stack NeSy Systems
11.4 Applications and Future Topics
11.5 Conclusions
References
Chapter 12: Programmatic Reinforcement Learning
12.1 Introduction
12.2 Programmatic RL
12.3 Imitation-projected Policy Gradients
12.4 Related Work
12.5 Conclusion
References
Part III: Applications
Chapter 13: From Symbolic to Neurosymbolic Information Extraction
13.1 Motivation and Overview
13.2 An Example of Symbolic IE
13.2.1 Introduction
13.2.2 Approach
13.2.3 Intrinsic Evaluation: Machine Reading Performance
13.2.4 Extrinsic Evaluation: Discovery of Biological Hypotheses
13.2.5 Conclusion
13.3 Problems of Symbolic IE Systems
13.4 Generating Rules
13.4.1 Introduction
13.4.2 Approach
13.4.3 Evaluation
13.4.4 Conclusion
13.5 Matching Rules
13.5.1 Introduction
13.5.2 Approach
13.5.3 Evaluation
13.5.4 Conclusion
13.6 Take Away
References
Chapter 14: Neurosymbolic AI for Legal AI-TRISM: Trustworthy, Reliable, Interpretable, Safe Models
14.1 Introduction
14.1.1 Neurosymbolic RAG
14.1.2 Advantages of Using Neurosymbolic RAG
14.2 Limitation of Using LLM as Legal Assistant
14.3 Neurosymbolic AI for Legal Domain
14.4 AI-TRISM with Neurosymbolic AI
14.4.1 KG Construction
14.4.2 Graph Construction Methodology
14.5 Symbiosis of LLM and KG for Neurosymbolic RAG in Legal Domain
14.6 Related Work
14.6.1 KG Construction
14.6.2 Legal Classification
14.6.3 Legal Question Answering
14.6.4 Legal Article and Case Retrieval.