Table of Contents

Contents

1. What is Neurosymbolic AI? An Overview and Frontier Problems

1.1. Introduction

1.2. Neurosymbolic Artificial Intelligence

1.3. Frontiers problems

1.4. Conclusion

Bibliography

 

2. Reasoning in Neurosymbolic AI

1.1. What is Reasoning in Neural Networks?

1.2. Background: Logic and Restricted Boltzmann Machines

1.3. Symbolic Reasoning with Energybased Neural Networks

1.4. Logical Boltzmann Machines for MaxSAT

1.5. Integrating Learning and Reasoning in Logical Boltzmann Machines

1.6. Challenges for Neurosymbolic AI

1.7. Conclusion

Bibliography

 

3. Neurosymbolic Assurance Using Concept Probes in Foundation Models

1.1 Introduction

1.2 Neural Features and Concept Probes

1.3 Foundation Models as Specification Lens

1.4 Symbolic Specification of ML Models Using Concept Probes

1.5 Implementation and Evaluation

1.6 Conclusion and Open Challenges

Bibliography

 

4. Towards Assured Autonomy using Neurosymbolic Components and Systems

1.1 Introduction

1.2 Problem Formulation and Challenges: Maneuver Control for Autonomous Vehicles

1.3 Software architecture: Components and Interactions

1.4 Probabilistic World Model

1.5 Planner

1.6 Trajectory Control with Evolving Behavior Trees (EBTs)

1.7 Assurance for Neuro-Symbolic Systems

1.8 Conclusions

Bibliography

 

5. Safe Neurosymbolic Learning and Control

1.1. Problem Setup

1.2. Hamilton-Jacobi (HJ) Reachability

1.3. A NeuroSymbolic Perspective on Learning Safe Controllers

1.4. Safety Assurances for Learned Controllers

1.5. Frontiers, Open Questions, and Promising Directions

Bibliography

 

6. Controllable Generation via Locally Constrained Resampling

1.1. Introduction

1.2. Background

1.3. Locally Constrained Resampling: A Tale of Two Distributions

1.4. Related work

1.5. Experimental Evaluation

1.6. Conclusion and Future Work

Bibliography

Appendix A: Controllable Generation via Locally Constrained Resampling

 

7. Tractable and Expressive Generative Modeling with Probabilistic Flow Circuits

1.1. Introduction

1.2. Tractable Probabilistic Modeling

1.3. Probabilistic Circuits

1.4. Normalizing Flows: A Primer

1.5. Integrating Normalizing Flows and Probabilistic Circuits

1.6. Probabilistic Flow Circuits

1.7. Experiments and Results

1.8. Conclusion and Discussion

Acknowledgements

Bibliography

 

8. Toward Verifiable and Scalable In-context Fine-tuning in Neurosymbolic AI

1.1 Introduction

1.2 Neurosymbolic Fine-tuning Using Automated Feedback from Formal Verification

1.3 Uncertainty-aware Fine-tuning and Inference for Multimodal Foundation Models

1.4 Towards a Hybrid Architecture: Dynamic Interleaving of Neural and Symbolic Reasoning

1.5 Conclusion and Future Directions

Bibliography

 

9. Physics-Informed Deep Learning

1.1 Introduction

Bibliography

 

10. Causal Representation Learning

1.1. Introduction

1.2. Background

1.3. Interventional CRL

1.4. CRL with Linear SCMs

1.5. CRL with General SCMs

1.6. Experiments

1.7. Other approaches

1.8. Summary

Bibliography

 

11. Neuro-symbolic Computing: Hardware-Software Co-Design

1.1 Introduction

1.2 Background

1.3 Trends and Challenges

1.4 Applications and Future Topics

1.5 Conclusions

Bibliography

 

12. Programmatic Reinforcement Learning

1.1. Introduction

1.2. Programmatic RL

1.3. Imitation-Projected Policy Gradients

1.4. Related Work

1.5. Conclusion

Bibliography

 

13. From Symbolic to Neuro-Symbolic Information Extraction

1.1 Motivation and Overview

1.2 An Example of Symbolic Information Extraction

1.3 Problems of Symbolic Information Extraction Systems

1.4 Generating Rules

1.5 Matching Rules

1.6 Take Away

Bibliography

 

14. Neurosymbolic AI for Legal AI-TRISM: Trustworthy, Reliable, Interpretable, Safe Models

1.1 Introduction

1.2 Limitation of using LLM as Legal Assistant

1.3 Neurosymbolic AI for Legal Domain

1.4 AI-TRISM with Neurosymbolic AI

1.5 Symbiosis of LLM and KG for Neurosymbolic RAG in Legal Domain

1.6 Related Work

1.7 Acknowledgement

Bibliography