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Variable Assignment Invariant Neural Networks for Learning Logic Programs

Yin Jun Phua, Katsumi Inoue

TL;DR

Learning dynamics from observed state transitions is difficult when data are noisy or incomplete. The paper introduces delta‑LFIT2, a neural‑symbolic extension of LFIT that enforces variable assignment invariance and uses dynamic rule heads to directly output concise logic rules from transitions. Empirical results on PyBoolNet networks show that delta‑LFIT2, especially the $^3$ configuration, achieves lower MSE and more succinct rules than NN‑LFIT and prior delta‑LFIT variants, while scaling to systems with up to 18 variables. The approach offers a robust, scalable path toward recovering interpretable symbolic models from noisy data, with potential extensions to asynchronous dynamics and first‑order logic.

Abstract

Learning from interpretation transition (LFIT) is a framework for learning rules from observed state transitions. LFIT has been implemented in purely symbolic algorithms, but they are unable to deal with noise or generalize to unobserved transitions. Rule extraction based neural network methods suffer from overfitting, while more general implementation that categorize rules suffer from combinatorial explosion. In this paper, we introduce a technique to leverage variable permutation invariance inherent in symbolic domains. Our technique ensures that the permutation and the naming of the variables would not affect the results. We demonstrate the effectiveness and the scalability of this method with various experiments. Our code is publicly available at https://github.com/phuayj/delta-lfit-2

Variable Assignment Invariant Neural Networks for Learning Logic Programs

TL;DR

Learning dynamics from observed state transitions is difficult when data are noisy or incomplete. The paper introduces delta‑LFIT2, a neural‑symbolic extension of LFIT that enforces variable assignment invariance and uses dynamic rule heads to directly output concise logic rules from transitions. Empirical results on PyBoolNet networks show that delta‑LFIT2, especially the configuration, achieves lower MSE and more succinct rules than NN‑LFIT and prior delta‑LFIT variants, while scaling to systems with up to 18 variables. The approach offers a robust, scalable path toward recovering interpretable symbolic models from noisy data, with potential extensions to asynchronous dynamics and first‑order logic.

Abstract

Learning from interpretation transition (LFIT) is a framework for learning rules from observed state transitions. LFIT has been implemented in purely symbolic algorithms, but they are unable to deal with noise or generalize to unobserved transitions. Rule extraction based neural network methods suffer from overfitting, while more general implementation that categorize rules suffer from combinatorial explosion. In this paper, we introduce a technique to leverage variable permutation invariance inherent in symbolic domains. Our technique ensures that the permutation and the naming of the variables would not affect the results. We demonstrate the effectiveness and the scalability of this method with various experiments. Our code is publicly available at https://github.com/phuayj/delta-lfit-2
Paper Structure (24 sections, 7 equations, 3 figures, 4 tables, 1 algorithm)

This paper contains 24 sections, 7 equations, 3 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Extraction-based Methods
  4. Differentiable Programming-based Methods
  5. Integration-based Methods
  6. Invariance in Deep Learning
  7. Background
  8. Normal Logic Program for State Transitions
  9. LFIT
  10. $\delta$LFIT+
  11. Proposed Method
  12. Variable Assignment Invariance
  13. Dynamic Rule Heads
  14. Overview of $\delta$LFIT2
  15. Scaling to Larger Systems
  16. ...and 9 more sections

Figures (3)

  • Figure 1: Overview of the $\delta$LFIT2 Framework.
  • Figure 2: Overview of the $\delta$LFIT+ Framework.
  • Figure 3: Two identical systems with the labels of the top nodes swapped. Arrows signify activation, whereas flat-edged symbols signify inhibition.