Symbol Correctness in Deep Neural Networks Containing Symbolic Layers

• URL: http://arxiv.org/abs/2402.03663v1
• Date: Tue, 6 Feb 2024 03:33:50 GMT
• Title: Symbol Correctness in Deep Neural Networks Containing Symbolic Layers
• Authors: Aaron Bembenek, Toby Murray
• Abstract summary: We formalize a high-level principle that can guide the design and analysis of NS-DNNs. We show that symbol correctness is a necessary property for NS-DNN explainability and transfer learning.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: To handle AI tasks that combine perception and logical reasoning, recent work introduces Neurosymbolic Deep Neural Networks (NS-DNNs), which contain -- in addition to traditional neural layers -- symbolic layers: symbolic expressions (e.g., SAT formulas, logic programs) that are evaluated by symbolic solvers during inference. We identify and formalize an intuitive, high-level principle that can guide the design and analysis of NS-DNNs: symbol correctness, the correctness of the intermediate symbols predicted by the neural layers with respect to a (generally unknown) ground-truth symbolic representation of the input data. We demonstrate that symbol correctness is a necessary property for NS-DNN explainability and transfer learning (despite being in general impossible to train for). Moreover, we show that the framework of symbol correctness provides a precise way to reason and communicate about model behavior at neural-symbolic boundaries, and gives insight into the fundamental tradeoffs faced by NS-DNN training algorithms. In doing so, we both identify significant points of ambiguity in prior work, and provide a framework to support further NS-DNN developments.

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