Extracting formulae in many-valued logic from deep neural networks

Authors

Yani Zhang and Helmut Bölcskei

Reference

IEEE Transactions on Signal Processing, Mar. 2025, submitted.

Abstract

We propose a new perspective on deep rectified linear unit (ReLU) networks, namely as circuit counterparts of Łukasiewicz infinite-valued logic—--a many-valued (MV) generalization of Boolean logic. An algorithm for extracting formulae in MV logic from trained deep ReLU networks is presented. The algorithm respects the network architecture, in particular compositionality, thereby honoring algebraic information present in the training data. We also establish the representation benefits of deep networks from a mathematical logic perspective.

Keywords

Mathematical logic, many-valued logic, McNaughton functions, deep neural networks

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