RI: Small: Embracing Deep Neural Networks into Probabilistic Answer Set Programming

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The integration of low-level perception with high-level reasoning is one of the fundamental problems in artificial intelligence. Today, the topic is revisited with the recent rise of deep neural networks. While deep learning excels in many perception tasks, it is not obvious how multiple aspects of commonsense reasoning, such as causality, defaults, abductive reasoning, and counterfactual reasoning, can be computed by neural networks. These subjects have been well-studied in the area of knowledge representation (KR) including answer set programming (ASP) but most KR formalisms are logic-oriented and do not incorporate high-dimensional feature space and pre-trained models for vision and text as in deep learning, which limits the applicability of KR in many practical applications involving uncertainty. The goal of the proposed research is to investigate a principled combination of knowledge representation, reasoning, and learning by integrating answer set programming with neural networks, which will enable representation, inference, and learning in both symbolic and sub-symbolic levels. The project will investigate two different approaches to integration. One is a loose coupling that is based on the concept of neural atoms which serves as an interface between the neural network output and the parameters for probabilistic answer set programming. The other is a tighter coupling method that obtains fuzzy-valued atomic facts from the neural network and applies the fuzzy answer set semantics on the vectorized representation. Not only these methods allow for applying symbolic reasoning on the neural network perception result but also allow for making use of logical rules in training a neural network so that a neural network not only learns from implicit correlations from the data but also from the explicit complex semantic constraints expressed by ASP rules. The success of the project will contribute to identifying fundamental issues in bridging the gap between knowledge representation and machine learning.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.