Symbol Correctness in Deep Neural Networks Containing Symbolic Layers
<|reference_start|>Symbol Correctness in Deep Neural Networks Containing Symbolic Layers: 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.<|reference_end|>
@article{bembenek2024symbol,
    title={Symbol Correctness in Deep Neural Networks Containing Symbolic Layers},
    author={Aaron Bembenek, Toby Murray},
    journal={arXiv preprint arXiv:2402.03663},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.03663},
    primaryClass={cs.LG cs.AI}
}