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About this paper
Pedro Domingos
Tensor Logic proposes a common language for neural computation and symbolic reasoning by expressing both as tensor equations. It represents relations as sparse Boolean tensors and rules as operations that join matching facts, sum over shared variables, and apply a threshold. Worked translations cover transformers, graph neural networks, and graphical models, but the paper reports no performance evaluations.
Key insights
- Diverse AI paradigms, including deep learning architectures (CNNs, GNNs, Transformers), symbolic Datalog, and probabilistic graphical models, can be uniformly expressed using the single tensor equation construct.
- The inherent mathematical connection between symbolic logic and tensor operations enables sound and reliable reasoning directly within embedding spaces.
- A controllable "temperature" parameter within activation functions allows for a spectrum from purely deductive (hallucination-free) reasoning at zero temperature to analogical (similarity-based) reasoning at higher temperatures.
Summary by alphaXiv.
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