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Efficient rule induction by ignoring pointless rules

Andrew Cropper, David M. Cerna

TL;DR

This work introduces Reducer, an ILP system that dramatically speeds up rule induction by identifying pointless rules—reducible and indiscriminate—and pruning the hypothesis space with ASP-derived constraints. The authors prove soundness and optimality guarantees, showing Reducer returns an optimal hypothesis if one exists. Empirical results across diverse domains show up to a 99% reduction in learning time while preserving predictive accuracy, with only modest overhead for detecting pointless rules. The approach offers a practical and generalizable enhancement to ILP, with potential applicability to recursive hypotheses and broader neuro-symbolic settings.

Abstract

The goal of inductive logic programming (ILP) is to find a set of logical rules that generalises training examples and background knowledge. We introduce an ILP approach that identifies pointless rules. A rule is pointless if it contains a redundant literal or cannot discriminate against negative examples. We show that ignoring pointless rules allows an ILP system to soundly prune the hypothesis space. Our experiments on multiple domains, including visual reasoning and game playing, show that our approach can reduce learning times by 99% whilst maintaining predictive accuracies.

Efficient rule induction by ignoring pointless rules

TL;DR

This work introduces Reducer, an ILP system that dramatically speeds up rule induction by identifying pointless rules—reducible and indiscriminate—and pruning the hypothesis space with ASP-derived constraints. The authors prove soundness and optimality guarantees, showing Reducer returns an optimal hypothesis if one exists. Empirical results across diverse domains show up to a 99% reduction in learning time while preserving predictive accuracy, with only modest overhead for detecting pointless rules. The approach offers a practical and generalizable enhancement to ILP, with potential applicability to recursive hypotheses and broader neuro-symbolic settings.

Abstract

The goal of inductive logic programming (ILP) is to find a set of logical rules that generalises training examples and background knowledge. We introduce an ILP approach that identifies pointless rules. A rule is pointless if it contains a redundant literal or cannot discriminate against negative examples. We show that ignoring pointless rules allows an ILP system to soundly prune the hypothesis space. Our experiments on multiple domains, including visual reasoning and game playing, show that our approach can reduce learning times by 99% whilst maintaining predictive accuracies.

Paper Structure

This paper contains 21 sections, 7 theorems, 4 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Problem Setting
  4. Inductive Logic Programming
  5. Pointless Rules
  6. Algorithm
  7. Correctness
  8. Experiments
  9. Setup
  10. Reproducibility.
  11. Domains
  12. Results
  13. Q1. Can pruning Pointless Rules Reduce Learning Times Whilst Maintaining Predictive Accuracies?
  14. Q2. What Is the Overhead of Finding Pointless Rules?
  15. Q3. Can pruning Reducible or Indiscriminate Rules Alone Reduce Learning Times?
  16. ...and 6 more sections

Key Result

Lemma 1

Let $r_1$ and $r_2$ be rules such that $r_2\subseteq r_1$, $l\in body(r_2)$, and $l$ be $r_2$-captured. Then $l$ is $r_1$-captured.

Figures (4)

  • Figure 1: Learning time improvement of Reducer over Popper. Values above the zero line indicate that Reducer reduces learning times. The tasks are ordered by the learning time improvement. For legibility, we only show tasks where the learning times differ by more than 1 second.
  • Figure 2: Predictive accuracy improvement of Reducer compared to Popper, i.e. when ignoring pointless rules.
  • Figure 3: Overhead of finding pointless rules.
  • Figure 4: Learning time improvement (minutes) when pruning reducible and indiscriminate rules. Values in the upper right quadrant indicate that pruning either reducible rules or indiscriminate rules alone reduces learning time.

Theorems & Definitions (23)

  • Definition 1: Subrule
  • Definition 2: Sub-hypothesis
  • Definition 3: Basic
  • Definition 4: ILP input
  • Definition 5: Cost function
  • Definition 6: Optimal hypothesis
  • Definition 7: Captured literal
  • Lemma 1
  • proof
  • Definition 8: Reducible
  • ...and 13 more