Learning Interpretable Differentiable Logic Networks for Time-Series Classification

Chang Yue; Niraj K. Jha

cs.LGAug 24, 2025

Learning Interpretable Differentiable Logic Networks for Time-Series Classification

Authors: Chang Yue, Niraj K. Jha

Organizations: Department of Electrical and Computer Engineering, Princeton University, Princeton, NJ 08544, USA

Abstract

Differentiable logic networks (DLNs) have shown promising results in tabular domains by combining accuracy, interpretability, and computational efficiency. In this work, we apply DLNs to the domain of TSC for the first time, focusing on univariate datasets. To enable DLN application in this context, we adopt feature-based representations relying on Catch22 and TSFresh, converting sequential time series into vectorized forms suitable for DLN classification. Unlike prior DLN studies that fix the training configuration and vary various settings in isolation via ablation, we integrate all such configurations into the hyperparameter search space, enabling the search process to select jointly optimal settings. We then analyze the distribution of selected configurations to better understand DLN training dynamics. We evaluate our approach on 51 publicly available univariate TSC benchmarks. The results confirm that classification DLNs maintain their core strengths in this new domain: they deliver competitive accuracy, retain low inference cost, and provide transparent, interpretable decision logic, thus aligning well with previous DLN findings in the realm of tabular classification and regression tasks.

Figures & tables

Figure 1 : Overview of the TSC-DLN architecture. The feature front-end transforms each raw time series into a fixed-dimensional vector, with continuous features scaled to $[0,1]$ and categorical features represented as binary values. The ThresholdLayer converts continuous features into learned binary predicates, while categorical features enter the logical network directly. Each LogicLayer neuron selects two incoming signals, denoted by $A$ and $B$ (red and green connections, respectively), and implements one of the 16 two-input Boolean operations. The SumLayer aggregates selected logic outputs into one score per class, and the class with the highest score is predicted.

Figure 2 : Experimental workflow for TSC-DLN.

ID	Operator	Real-valued	00	01	10	11
0	False	$0$	0	0	0	0
1	$A\land B$	$A\cdot B$	0	0	0	1
2	$\neg(A\Rightarrow B)$	$A-AB$	0	0	1	0
3	$A$	$A$	0	0	1	1
4	$\neg(A\Leftarrow B)$	$B-AB$	0	1	0	0
5	$B$	$B$	0	1	0	1

Table 2: List of all real-valued binary logic operations. Adapted from LGN [ 1 ] .

Figure 3 : Average balanced accuracy (best of 10 runs) versus inference operation cost for all models across 51 datasets. Results are shown for the Catch22, TSFresh-10, TSFresh-20, and TSFresh-40 transformations, with the Pareto frontier drawn for each case. SOTA time-series specific methods (the full TSFresh implementation, MiniRocket, and MultiRocket) are also included to contextualize the broader accuracy-cost landscape. Notably, DLN with TSFresh-40 outperforms the full TSFresh implementation in both accuracy and computational efficiency. The DLN is Pareto-optimal in every instance, and is the top-performing model with the TSFresh-40 transformation among the general classifiers

Figure 4 : Best@k curves for the five strongest models using the TSFresh-40 transformation. The DLN curve exhibits the fastest growth and achieves the best overall performance, given a sufficient number of independent HPO-and-training runs (

k\geq 7

Batch Size	MLP	DLN
Batch = 1	72.0 $\mu\text{s}$	23.8 $\mu\text{s}$
Batch = 32	3.15 $\mu\text{s}$	2.78 $\mu\text{s}$

Table 5 : Classifier-stage inference latency (

\mu

s/sample) on CPU. Values are the geometric mean across all dataset-seed pairs, measured using single-threaded execution.

Figure 5 : Distribution of model training configurations selected by the HPO algorithm for each of the four transformation methods. The statistics are aggregated across all (dataset, random seed) pairs, with each bar representing results from

51\times 10=510

experiments.

Panel of Figure 6 — Figure 6 : Illustration of decision processes for DLN models trained on the FreezerRegularTrain dataset: (a) DLN resulting from the Catch22 feature set, (b) DLN resulting from the TSFresh-20 feature set.

Appendix figures & tables14 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 7 : The Best@k curves for the five strongest models on Catch22. DLN’s curve grows the fastest.

Figure 8 : The Best@k curves for the five strongest models on TSFresh-10.

Figure 9 : The Best@k curves for the five strongest models on TSFresh-20.

	KNN	NB	LR	SVM	DT	RF	AB	MLP	DLN
ACSF1	0.758 $\pm$ 0.030	0.698 $\pm$ 0.018	0.687 $\pm$ 0.052	0.697 $\pm$ 0.028	0.655 $\pm$ 0.028	0.807 $\pm$ 0.033	0.441 $\pm$ 0.081	0.715 $\pm$ 0.028	0.728 $\pm$ 0.026
ChlorineConcentration	0.488 $\pm$ 0.010	0.394 $\pm$ 0.0	0.373 $\pm$ 8.5e-03	0.475 $\pm$ 0.031	0.411 $\pm$ 5.9e-03	0.435 $\pm$ 0.013	0.396 $\pm$ 5.0e-03	0.464 $\pm$ 0.011	0.440 $\pm$ 0.018
Computers	0.683 $\pm$ 0.024	0.684 $\pm$ 0.0	0.704 $\pm$ 0.015	0.723 $\pm$ 0.020	0.682 $\pm$ 0.029	0.711 $\pm$ 0.011	0.710 $\pm$ 0.017	0.682 $\pm$ 0.028	0.690 $\pm$ 0.024
CricketX	0.585 $\pm$ 0.011	0.451 $\pm$ 0.0	0.477 $\pm$ 0.017	0.561 $\pm$ 0.016	0.427 $\pm$ 0.034	0.550 $\pm$ 0.017	0.384 $\pm$ 0.017	0.507 $\pm$ 0.023	0.554 $\pm$ 0.017
CricketY	0.537 $\pm$ 7.2e-03	0.411 $\pm$ 0.0	0.472 $\pm$ 6.1e-03	0.534 $\pm$ 0.011	0.362 $\pm$ 0.013	0.515 $\pm$ 0.012	0.360 $\pm$ 0.019	0.476 $\pm$ 0.018	0.509 $\pm$ 0.026
CricketZ	0.591 $\pm$ 7.0e-03	0.443 $\pm$ 0.0	0.509 $\pm$ 6.4e-03	0.540 $\pm$ 0.016	0.417 $\pm$ 0.011	0.590 $\pm$ 0.015	0.344 $\pm$ 0.013	0.492 $\pm$ 0.031	0.530 $\pm$ 0.022

Appendix

Table 10 : Mean and standard deviation of balanced accuracy for Catch22 across 10 random seeds.

	KNN	NB	LR	SVM	DT	RF	AB	MLP	DLN
ACSF1	1.15M	2.52M	1.81M	8.20M	915	115K	190K	8.13M	31.9K
ChlorineConcentration	7.85M	679K	518K	29.8M	1.65K	176K	222K	7.53M	38.6K
Computers	1.64M	445K	171K	10.7M	695	137K	205K	2.52M	26.5K
CricketX	2.69M	2.71M	2.07M	63.1M	1.23K	186K	252K	4.66M	85.2K
CricketY	2.69M	2.71M	2.07M	49.1M	1.34K	193K	239K	5.43M	67.8K
CricketZ	2.69M	2.71M	2.07M	52.5M	1.74K	170K	240K	6.81M	68.8K

Appendix

Table 11 : Geometric mean of inference OPs for Catch22 across 10 random seeds assuming FP16 for floating-point and INT16 for integer arithmetic.

	KNN	NB	LR	SVM	DT	RF	AB	MLP	DLN
ACSF1	0.780	0.690	0.640	0.750	0.670	0.810	0.610	0.730	0.780
ChlorineConcentration	0.647	0.431	0.448	0.709	0.552	0.531	0.462	0.655	0.549
Computers	0.680	0.668	0.708	0.676	0.656	0.692	0.664	0.652	0.700
CricketX	0.559	0.417	0.511	0.577	0.416	0.545	0.358	0.522	0.522
CricketY	0.594	0.481	0.557	0.627	0.480	0.602	0.419	0.577	0.576
CricketZ	0.579	0.472	0.515	0.569	0.443	0.530	0.402	0.506	0.531

Appendix

Table 12 : Best-of-10 test balanced accuracy for TSFresh-10.

	KNN	NB	LR	SVM	DT	RF	AB	MLP	DLN
ACSF1	0.739 $\pm$ 0.033	0.690 $\pm$ 0.0	0.618 $\pm$ 0.019	0.708 $\pm$ 0.034	0.597 $\pm$ 0.058	0.732 $\pm$ 0.058	0.525 $\pm$ 0.047	0.694 $\pm$ 0.027	0.723 $\pm$ 0.047
ChlorineConcentration	0.637 $\pm$ 0.021	0.431 $\pm$ 0.0	0.446 $\pm$ 2.3e-03	0.697 $\pm$ 0.011	0.482 $\pm$ 0.044	0.514 $\pm$ 0.013	0.451 $\pm$ 9.9e-03	0.618 $\pm$ 0.028	0.526 $\pm$ 0.014
Computers	0.649 $\pm$ 0.038	0.668 $\pm$ 0.0	0.693 $\pm$ 6.3e-03	0.658 $\pm$ 0.017	0.608 $\pm$ 0.035	0.673 $\pm$ 0.013	0.648 $\pm$ 7.9e-03	0.637 $\pm$ 0.014	0.654 $\pm$ 0.024
CricketX	0.547 $\pm$ 0.012	0.417 $\pm$ 0.0	0.507 $\pm$ 2.2e-03	0.563 $\pm$ 8.9e-03	0.385 $\pm$ 0.014	0.533 $\pm$ 8.0e-03	0.330 $\pm$ 0.017	0.500 $\pm$ 0.013	0.489 $\pm$ 0.016
CricketY	0.584 $\pm$ 0.011	0.481 $\pm$ 0.0	0.556 $\pm$ 4.4e-03	0.613 $\pm$ 0.016	0.458 $\pm$ 0.025	0.577 $\pm$ 0.014	0.395 $\pm$ 0.014	0.539 $\pm$ 0.027	0.546 $\pm$ 0.028
CricketZ	0.562 $\pm$ 0.013	0.472 $\pm$ 0.0	0.508 $\pm$ 7.1e-03	0.549 $\pm$ 0.019	0.435 $\pm$ 9.9e-03	0.509 $\pm$ 0.019	0.370 $\pm$ 0.019	0.483 $\pm$ 0.020	0.503 $\pm$ 0.018

Appendix

Table 13 : Mean and standard deviation of balanced accuracy for TSFresh-10 across 10 random seeds.

	KNN	NB	LR	SVM	DT	RF	AB	MLP	DLN
ACSF1	1.14M	1.82M	1.58M	8.21M	1.13K	132K	219K	1.26M	24.2K
ChlorineConcentration	6.57M	544K	473K	43.2M	1.56K	170K	247K	2.26M	25.7K
Computers	1.79M	363K	158K	23.5M	714	95.9K	158K	792K	10.8K
CricketX	2.84M	2.18M	1.89M	50.4M	1.56K	170K	229K	1.60M	38.9K
CricketY	1.97M	2.18M	1.89M	48.1M	1.54K	152K	222K	1.46M	39.4K
CricketZ	1.97M	2.18M	1.89M	51.1M	1.56K	180K	256K	1.43M	33.6K

Appendix

Table 14 : Geometric mean of inference OPs for TSFresh-10 across 10 random seeds assuming FP16 for floating-point and INT16 for integer arithmetic.

	KNN	NB	LR	SVM	DT	RF	AB	MLP	DLN
ACSF1	0.790	0.720	0.750	0.800	0.660	0.860	0.690	0.780	0.800
ChlorineConcentration	0.664	0.423	0.475	0.749	0.574	0.581	0.467	0.682	0.599
Computers	0.652	0.576	0.700	0.676	0.608	0.712	0.728	0.644	0.708
CricketX	0.654	0.542	0.594	0.671	0.463	0.647	0.465	0.626	0.594
CricketY	0.670	0.531	0.633	0.690	0.534	0.648	0.444	0.631	0.647
CricketZ	0.655	0.567	0.581	0.664	0.491	0.590	0.452	0.605	0.606

Appendix

Table 15 : Best-of-10 test balanced accuracy for TSFresh-20.

	KNN	NB	LR	SVM	DT	RF	AB	MLP	DLN
ACSF1	0.763 $\pm$ 0.024	0.720 $\pm$ 0.0	0.734 $\pm$ 9.7e-03	0.778 $\pm$ 0.018	0.630 $\pm$ 0.029	0.837 $\pm$ 0.019	0.554 $\pm$ 0.063	0.763 $\pm$ 0.016	0.745 $\pm$ 0.038
ChlorineConcentration	0.662 $\pm$ 1.1e-03	0.423 $\pm$ 0.0	0.468 $\pm$ 6.9e-03	0.744 $\pm$ 9.7e-03	0.518 $\pm$ 0.043	0.536 $\pm$ 0.028	0.455 $\pm$ 7.4e-03	0.662 $\pm$ 0.014	0.570 $\pm$ 0.023
Computers	0.641 $\pm$ 7.6e-03	0.576 $\pm$ 0.0	0.692 $\pm$ 3.0e-03	0.663 $\pm$ 0.015	0.576 $\pm$ 0.026	0.683 $\pm$ 0.018	0.696 $\pm$ 0.017	0.621 $\pm$ 0.020	0.650 $\pm$ 0.024
CricketX	0.637 $\pm$ 0.020	0.542 $\pm$ 0.0	0.583 $\pm$ 6.7e-03	0.636 $\pm$ 0.022	0.447 $\pm$ 0.017	0.601 $\pm$ 0.029	0.417 $\pm$ 0.025	0.590 $\pm$ 0.019	0.574 $\pm$ 0.018
CricketY	0.665 $\pm$ 3.1e-03	0.531 $\pm$ 0.0	0.600 $\pm$ 0.025	0.674 $\pm$ 0.012	0.495 $\pm$ 0.029	0.622 $\pm$ 0.029	0.410 $\pm$ 0.024	0.621 $\pm$ 7.9e-03	0.583 $\pm$ 0.031
CricketZ	0.649 $\pm$ 6.2e-03	0.567 $\pm$ 0.0	0.549 $\pm$ 0.035	0.644 $\pm$ 0.019	0.472 $\pm$ 0.013	0.570 $\pm$ 0.010	0.412 $\pm$ 0.021	0.571 $\pm$ 0.023	0.574 $\pm$ 0.019

Appendix

Table 16 : Mean and standard deviation of balanced accuracy for TSFresh-20 across 10 random seeds.

	KNN	NB	LR	SVM	DT	RF	AB	MLP	DLN
ACSF1	829K	2.19M	1.70M	7.10M	897	161K	227K	3.68M	43.1K
ChlorineConcentration	11.4M	656K	511K	17.6M	1.83K	116K	244K	6.03M	50.2K
Computers	1.57M	438K	170K	11.7M	897	121K	195K	2.91M	28.1K
CricketX	2.50M	2.63M	2.04M	37.7M	1.50K	171K	248K	4.79M	64.7K
CricketY	4.25M	2.63M	2.04M	60.9M	1.45K	182K	258K	4.30M	63.5K
CricketZ	2.50M	2.63M	2.04M	64.4M	1.56K	152K	274K	4.71M	68.9K

Appendix

Table 17 : Geometric mean of inference OPs for TSFresh-20 across 10 random seeds assuming FP16 for floating-point and INT16 for integer arithmetic.

	KNN	NB	LR	SVM	DT	RF	AB	MLP	DLN
ACSF1	0.750	0.740	0.730	0.770	0.710	0.880	0.630	0.770	0.810
ChlorineConcentration	0.682	0.408	0.574	0.784	0.560	0.583	0.500	0.736	0.665
Computers	0.688	0.584	0.680	0.700	0.660	0.696	0.688	0.676	0.716
CricketX	0.642	0.555	0.624	0.657	0.478	0.624	0.458	0.632	0.631
CricketY	0.721	0.544	0.657	0.765	0.532	0.664	0.484	0.697	0.679
CricketZ	0.683	0.615	0.619	0.643	0.501	0.615	0.443	0.628	0.642

Appendix

Table 18 : Best-of-10 test balanced accuracy for TSFresh-40.

	KNN	NB	LR	SVM	DT	RF	AB	MLP	DLN
ACSF1	0.733 $\pm$ 0.023	0.737 $\pm$ 6.7e-03	0.685 $\pm$ 0.037	0.742 $\pm$ 0.021	0.660 $\pm$ 0.033	0.848 $\pm$ 0.019	0.521 $\pm$ 0.048	0.726 $\pm$ 0.033	0.761 $\pm$ 0.020
ChlorineConcentration	0.682 $\pm$ 3.3e-05	0.408 $\pm$ 0.0	0.566 $\pm$ 0.010	0.776 $\pm$ 0.010	0.525 $\pm$ 0.031	0.556 $\pm$ 0.026	0.474 $\pm$ 0.015	0.705 $\pm$ 0.018	0.646 $\pm$ 0.014
Computers	0.672 $\pm$ 0.013	0.584 $\pm$ 0.0	0.667 $\pm$ 7.8e-03	0.674 $\pm$ 0.013	0.620 $\pm$ 0.032	0.679 $\pm$ 9.8e-03	0.672 $\pm$ 0.012	0.656 $\pm$ 0.014	0.659 $\pm$ 0.035
CricketX	0.636 $\pm$ 5.3e-03	0.555 $\pm$ 0.0	0.607 $\pm$ 0.017	0.644 $\pm$ 9.1e-03	0.452 $\pm$ 0.015	0.597 $\pm$ 0.017	0.408 $\pm$ 0.028	0.603 $\pm$ 0.014	0.602 $\pm$ 0.022
CricketY	0.705 $\pm$ 0.013	0.544 $\pm$ 0.0	0.641 $\pm$ 0.018	0.740 $\pm$ 0.025	0.504 $\pm$ 0.016	0.646 $\pm$ 0.012	0.446 $\pm$ 0.019	0.678 $\pm$ 0.018	0.644 $\pm$ 0.024
CricketZ	0.666 $\pm$ 0.010	0.615 $\pm$ 0.0	0.589 $\pm$ 0.028	0.613 $\pm$ 0.022	0.471 $\pm$ 0.029	0.596 $\pm$ 0.022	0.404 $\pm$ 0.020	0.590 $\pm$ 0.026	0.611 $\pm$ 0.020

Appendix

Table 19 : Mean and standard deviation of balanced accuracy for TSFresh-40 across 10 random seeds.

	KNN	NB	LR	SVM	DT	RF	AB	MLP	DLN
ACSF1	1.10M	2.93M	1.95M	11.2M	1.10K	149K	198K	12.9M	83.5K
ChlorineConcentration	22.1M	880K	585K	20.8M	1.79K	176K	243K	15.5M	81.1K
Computers	2.81M	587K	195K	12.0M	1.19K	151K	180K	5.22M	52.1K
CricketX	4.43M	3.52M	2.34M	69.5M	1.65K	160K	255K	13.7M	120K
CricketY	4.43M	3.52M	2.34M	70.3M	1.39K	179K	260K	21.6M	140K
CricketZ	4.43M	3.52M	2.34M	61.4M	1.52K	148K	259K	13.1M	122K

Appendix

Table 20 : Geometric mean of inference OPs for TSFresh-40 across 10 random seeds assuming FP16 for floating-point and INT16 for integer arithmetic.

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May 29, 2025, cs.LGJ/K move · Enter open · S save

Learning Interpretable Differentiable Logic Networks for Tabular Regression

Chang Yue, Niraj K. Jha

Department of Electrical and Computer Engineering, Princeton University, Princeton, NJ 08544, USA

Differentiable Logic Gate Networks Tabular Learning Logistic Regression Differentiable Optimization

Open paper AskPDF arXiv

Neural networks (NNs) achieve outstanding performance in many domains; however, their decision processes are often opaque and their inference can be computationally expensive in resource-constrained environments. We recently proposed Differentiable Logic Networks (DLNs) to address these issues for tabular classification based on relaxing discrete logic into a differentiable form, thereby enabling gradient-based learning of networks built from binary logic operations. DLNs offer interpretable reasoning and substantially lower inference cost. We extend the DLN framework to supervised tabular regression. We first redesign the final output layer (the SumLayer) to support continuous targets. More critically, we find the original two-phase training procedure used for classification is suboptimal for regression, and thus develop a unified, single-stage optimization procedure. We also demonstrate that temperature annealing of the network's differentiable relaxations is decisive for achieving stable convergence and high accuracy. We evaluate the resulting model on 15 public regression benchmarks, comparing it with modern neural networks and classical regression baselines. Regression DLNs match or exceed baseline accuracy while preserving interpretability and fast inference. Our results show that DLNs are a viable, cost-effective alternative for regression tasks, especially where model transparency and computational efficiency are important.

Abstract

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Learning Interpretable Differentiable Logic Networks for Tabular Regression

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