Symbol Correctness in Deep Neural Networks Containing Symbolic Layers
CoRR(2024)
摘要
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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