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Injecting discrete logical constraints into neural network learning is one of the main challenges in neuro-symbolic AI. We find that a straight-through-estimator, a method introduced to train binary neural networks, could effectively be applied to incorporate logical constraints into neural network learning. More specifically, we design a systematic way to represent discrete logical constraints as a loss function; minimizing this loss using gradient descent via a straight-through-estimator updates the neural network’s weights in the direction that the binarized outputs satisfy the logical constraints. The experimental results show that by leveraging GPUs and batch training, this method scales significantly better than existing neuro-symbolic methods that require heavy symbolic computation for computing gradients. Also, we demonstrate that our method applies to different types of neural networks, such as MLP, CNN, and GNN, making them learn with no or fewer labeled data by learning directly from known constraints. 

The integration of low-level perception with high-level reasoning is one of the oldest problems in Artificial Intelligence. Today, the topic is revisited with the recent rise of deep neural networks. However, it is still not clear how complex and high-level reasoning, such as default reasoning, ontology reasoning, and causal reasoning, can be successfully computed by these approaches. The latter subject has been well-studied in the area of knowledge representation (KR), but many KR formalisms, including answer set programming (ASP), are logic-oriented and do not incorporate high-dimensional feature space as in deep learning, which limits the applicability of KR in many practical applications. 

The integration of low-level perception with high-level reasoning is one of the oldest problems in Artificial Intelligence. Recently, several proposals were made to implement the reasoning process in complex neural network architectures. While these works aim at extending neural networks with the capability of reasoning, a natural question that we consider is: can we extend answer set programs with neural networks to allow complex and high-level reasoning on neural network outputs? As a preliminary result, we propose NeurASP – a simple extension of answer set programs by embracing neural networks where neural network outputs are treated as probability distributions over atomic facts in answer set programs. We show that NeurASP can not only improve the perception accuracy of a pre-trained neural network, but also help to train a neural network better by giving restrictions through logic rules. However, training with NeurASP would take much more time than pure neural network training due to the internal use of a symbolic reasoning engine. For future work, we plan to investigate the potential ways to solve the scalability issue of NeurASP. One potential way is to embed logic programs directly in neural networks. On this route, we plan to first design a SAT solver using neural networks, then extend such a solver to allow logic programs. 

We present NeurASP, a simple extension of answer set programs by embracing neural networks. By treating the neural network output as the probability distribution over atomic facts in answer set programs, NeurASP provides a simple and effective way to integrate sub-symbolic and symbolic computation. We demonstrate how NeurASP can make use of a pre-trained neural network in symbolic computation and how it can improve the neural network's perception result by applying symbolic reasoning in answer set programming. Also, NeurASP can make use of ASP rules to train a neural network better so that a neural network not only learns from implicit correlations from the data but also from the explicit complex semantic constraints expressed by the rules.

 

Abstract To be responsive to dynamically changing real-world environments, an intelligent agent needs to perform complex sequential decision-making tasks that are often guided by commonsense knowledge. The previous work on this line of research led to the framework called interleaved commonsense reasoning and probabilistic planning (i corpp ), which used P-log for representing commmonsense knowledge and Markov Decision Processes (MDPs) or Partially Observable MDPs (POMDPs) for planning under uncertainty. A main limitation of i corpp is that its implementation requires non-trivial engineering efforts to bridge the commonsense reasoning and probabilistic planning formalisms. In this paper, we present a unified framework to integrate i corpp ’s reasoning and planning components. In particular, we extend probabilistic action language pBC + to express utility, belief states, and observation as in POMDP models. Inheriting the advantages of action languages, the new action language provides an elaboration tolerant representation of POMDP that reflects commonsense knowledge. The idea led to the design of the system pbcplus2pomdp , which compiles a pBC + action description into a POMDP model that can be directly processed by off-the-shelf POMDP solvers to compute an optimal policy of the pBC + action description. Our experiments show that it retains the advantages of i corpp while avoiding the manual efforts in bridging the commonsense reasoner and the probabilistic planner.