Learning Arbitrary Logical Formula as a Sparse Neural Network Module

Jiacheng Yin

Keywords: Neuro-Symbolic AI; System 2 intelligence; Deep Symbolic Learning (DSL); Equation Learner (EQL); differentiable Neural Logic Networks (dNL)

TL;DR: We propose the Logical Formula Learner framework, a general framework of network modules that explicitly equate a logical formula after convergence.

Abstract: NeSy (Neuro-Symbolic) predictors are hybrid models composed of symbolic predictive models chained after neural networks. Most existing NeSy predictors require either given symbolic knowledge or iterative training. DSL (Deep Symbolic Learning) is the first NeSy predictor that supports fully end-to-end training from scratch, but it learns a look-up table rather than arbitrary programs or formulas. We propose the Logical Formula Learner framework, a general framework of network modules that explicitly equate a logical formula after convergence. We then propose 3 novel designs within the LFL framework with different levels of combinatorial search freedom: LFL-Type1 learns arbitrary logical formula, LFL-Type2 learns a look-up table, and LFL-Type3 has combinatorial search freedom between them. LFL-Type1 and LFL-Type2 show improvements over previous designs, and all three types can be wrapped into NeSy predictors. To our knowledge, LFL-Type1-based NeSy predictor is the first NeSy predictor that supports fully end-to-end training from scratch and explicitly learns arbitrary logical formulas.

Primary Area: neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.

Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2025/AuthorGuide.

Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.

No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.

Submission Number: 3826