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Differentiable Rule Induction from Raw Sequence Inputs

ICLR 2025 · Time series › Foundation models for time series · approach: Time series classification · 0 citations (OpenAlex)

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Proposes Neural Rule Learner (NeurRL), a fully differentiable ILP pipeline that couples a self-supervised differentiable k-means over autoencoder subsequence embeddings with a deep dense-layer rule learner to induce rules directly from raw time series and flattened images without label leakage.

Problem

Differentiable ILP methods rely on symbolic inputs and pre-trained supervised networks to produce symbols, causing explicit label leakage; learning logic rules directly from raw sequences (time series, images) without intermediate feature labels is hard.

Approach

Discretize raw sequences into cluster-based ground atoms via a self-supervised autoencoder with differentiable k-means, and jointly train this with a novel dense-layer neural rule-learning module (softmax-weighted conjunctions and a fuzzy disjunction) using only the class label, then extract rules from the program tensor with precision/recall thresholds.

Key results

• On 13 binary UCR datasets, NeurRL(N) achieves mean accuracy 0.891 vs 0.859 for SSSL, 0.842 for NeurRL(R), 0.801 for BoW, and 0.718 for Xu, with the best result on 7 datasets.
• Differentiable k-means reduces running time versus non-differentiable k-means (e.g., Coffee 42s vs 313s, Lighting2 120s vs 1166s), with accuracy similar in most cases but worse on Gun point (0.740 vs 0.807).
• Learned rule on ECG reaches precision 0.83 and recall 0.89; rule on ItalyPow.Dem. reaches precision 0.99 and recall 0.90.

Measured effects reported in the paper

Surprising findings

• Pre-training the autoencoder and clustering model improves accuracy but on Coffee the no-pretraining variant is much faster (30s vs 42s), and on some datasets the non-differentiable k-means is more accurate (Gun point).

Limitations

• Rules are extracted via thresholds and kept only if high precision; rule-extracted accuracy NeurRL(R) is lower than the neural module NeurRL(N) on several datasets.
• Accuracy is sensitive to hyperparameters (subsequence length, number of clusters, regions), especially for short series like ItalyPow.Dem.
• Evaluated only on binary-class tasks and small-scale image data (MNIST one-vs-one pairs).

Experimental setup

Datasets: UCR time series archive (13 datasets) MNIST synthetic triangular pulse and trigonometric signals

Benchmarks: UCR time series archive (13 binary datasets) MNIST (one-vs-one digit tasks) synthetic signals

Metrics: classification accuracy precision recall running time (s)

Baselines: SSSL Xu BoW non-differentiable k-means pipeline

Builds on: differentiable ILP (neural ILP from interpretation transitions) differentiable k-means ∂ILP SSSL

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