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A Mathematical Framework and a Suite of Learning Techniques for Neural-Symbolic Systems

Created by
  • Haebom

Author

Charles Dickens, Connor Pryor, Changyu Gao, Alon Albalak, Eriq Augustine, William Wang, Stephen Wright, Lise Getoor

Outline

In this paper, we present a unified mathematical framework for neural symbolic (NeSy) systems, called Neural Symbolic Energy-Based Models (NeSy-EBMs). NeSy-EBMs encompass both discriminative and generative NeSy modeling, and provide general formulas for gradient estimation of key learning losses. We present four training methods that leverage methods from various fields, including bi-level and probabilistic policy optimization. We implement the NeSy-EBM framework with Neural Probabilistic Soft Logic (NeuPSL), an open-source NeSy-EBM library designed for scalability and expressiveness, and demonstrate the practical benefits of NeSy-EBMs for various tasks, including image classification, graph node labeling, autonomous vehicle situational awareness, and question answering.

Takeaways, Limitations

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Takeaways:
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Presentation of NeSy-EBMs, an integrated mathematical framework for neural symbol systems
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Deriving general gradient equations for various learning losses
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Presents various learning methods such as dual-level and probabilistic policy optimization
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Providing NeuPSL, an open source library with excellent extensibility and expressiveness
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Demonstrating the practical benefits of NeSy-EBMs in a variety of tasks
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Limitations:
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Research on other learning methods beyond the four presented in this paper is needed.
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Additional validation of the performance and scalability of the NeuPSL library is needed.
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Need for generalization performance evaluation and analysis for various tasks
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