Pith. sign in

REVIEW 3 major objections 4 minor 1 cited by

Learning Interpretable Differentiable Logic Networks for Tabular Regression

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read This paper claims that a logic circuit whose final layer computes a weighted sum of binary rule activations can match random forests and multilayer perceptrons on tabular regression while staying interpretable and cheap to run.

desk verdict A competent, honest extension of the authors' classification DLN to regression, with broad benchmarks and a defensible central claim, but the accuracy parity is within noise on several datasets and the capacity/interpretability trade-off deserves a sharper test. read the letter →

arxiv 2505.23615 v1 pith:SURUM3K5 submitted 2025-05-29 cs.LG

Chang Yue , Niraj K. Jha This is my paper
classification cs.LG
keywords differentiablelogicnetworkstabularregressioninterpretablemachinelearninggateefficientinferenceruleextractioncontinuousrelaxationSumLayer
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper extends Differentiable Logic Networks (DLNs) from classification to tabular regression by replacing the final class-vote layer with a SumLayer that computes a weighted sum of binary logic-rule activations. The central claim is that this output change lets a network of two-input Boolean gates predict continuous targets with accuracy comparable to random forests and multilayer perceptrons, while keeping the model transparent and its inference cost orders of magnitude lower. On 15 public regression benchmarks the regression DLN ranks second overall in mean $R^2$ and sits on the Pareto frontier of accuracy versus operations under every hyperparameter budget tested. If true, this makes DLNs a practical option for regression settings where model transparency and deployment on resource-constrained hardware matter.

What carries the argument

The load-bearing mechanism is the SumLayer, which replaces the classification DLN's discrete class voting with a weighted sum $y=\sum_j \mathbb{1}\{\mathrm{Sigmoid}(s_j/\tau)\ge\theta_{\mathrm{sum-th}}\}\cdot c_j\cdot x_j$ over the binary outputs $x_j$ of the final LogicLayer. Each $x_j$ is a two-input Boolean function of earlier binary signals, so the model is a logic circuit whose prediction is an intelligible weighted sum of rule firings. Around this output layer, the paper keeps the DLN machinery: a ThresholdLayer binarizes continuous inputs through learned biases and slopes, LogicLayer neurons choose among the 16 two-input Boolean functions and their two incoming connections by temperature-annealed softmax logits, and straight-through estimators keep the discrete forward pass differentiable. The learned rules are then simplified symbolically, shrinking the circuit and making the extracted rules easier to read.

What would settle it

Train the regression DLN on a one-dimensional dataset whose target is a high-frequency smooth function, such as $y=\sin(20x)$ on $[0,1]$ with thresholds chosen from the data; if its $R^2$ stays far below a simple MLP's unless the number of thresholds per feature is raised far beyond ten, the capacity assumption fails.

Watch

Extended reading notes

Core claim

The authors' core discovery is that continuous regression does not require abandoning logic circuits: the activations of the final logic layer are binary rule evaluations, and a differentiable SumLayer that learns a real-valued coefficient per rule maps those binaries to a continuous prediction. At inference the connections are binarized by thresholding learnable gates, the coefficients stay in floating point, and the output is an explicit weighted sum of logic rules, so the whole model can be read as a small set of if-then rules. Across 15 tabular datasets, this architecture achieves a mean test $R^2$ of 0.810 with an average rank of 3.47, ahead of the MLP's 3.67 and behind random forest's 2.67, while its geometric-mean inference cost is 5.8 times lower than random forest and 86 times lower than the MLP. The paper also shows that a single end-to-end training phase with annealed temperatures outperforms the two-phase schedule used for classification DLNs.

Load-bearing premise

The method assumes that turning each continuous feature into a handful of binary thresholds (six or ten) and combining them with two-input logic gates is expressive enough to approximate the target function as accurately as a neural network.

Editorial extensions

If this is right

  • If the central claim holds, transparent rule-based regression can reach the accuracy of black-box neural models on many tabular tasks without post-hoc explanation.
  • Because inference uses only binary logic gates and a short weighted sum, regression DLNs can be deployed where floating-point-heavy MLPs are too slow or too power-hungry.
  • The learned circuit is itself the explanation: each prediction is a readable weighted sum of binary conditions on the original features.
  • Unified single-phase training with temperature annealing means the same end-to-end gradient pipeline used for classification can be reused for regression, simplifying adoption.
  • Implicit feature selection in the learned rules can reduce the input features a deployed model needs to measure.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper leaves implicit that the number of thresholds per feature is the main capacity dial; an adaptive threshold-count selection could extend the method to smoother targets.
  • A natural next step, not pursued here, is to attach the SumLayer to convolutional or temporal logic networks for continuous forecasting.
  • Because the output is linear in binary rules, classical sparsity penalties on the SumLayer coefficients could shrink the rule set further.
  • The Pareto analysis suggests that on strict inference budgets the DLN's advantage over random forest grows; a hardware benchmark on FPGAs or microcontrollers would quantify this.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper extends Differentiable Logic Networks (DLNs) from classification to tabular regression by replacing the classification output with a SumLayer that computes a continuous weighted sum of the binary activations of the last logic layer. It also unifies the previously two-phase training procedure into a single differentiable stage, introduces temperature annealing, and reuses subspace search, straight-through estimators, and input concatenation from the classification DLN. The method is evaluated on 15 public regression datasets against nine baselines, with 10 random seeds and 32/64/128 hyperparameter-search trials. The main claims are that regression DLNs match or exceed baseline accuracy while retaining interpretability and low inference cost, with a mean test R2 of 0.810, a geometric-mean inference cost 5.8x lower than random forest and 86x lower than MLP, and interpretability illustrated on three datasets.

Significance. If substantiated, the paper would broaden the applicability of logic-gate networks to a major task family (regression) while preserving the transparency and inference-efficiency advantages demonstrated for classification. The work is clearly presented and the evaluation is broad: 15 datasets, 10 seeds, and an HPO protocol with up to 128 trials, plus ablation studies for four design choices. The architecture description is detailed enough to reimplement, and the interpretability examples (Figures 7-9) are concrete and informative. However, the central accuracy claim currently rests on aggregate means and ranks without significance testing, the efficiency comparison uses an unvalidated float16 assumption for all models, and the representational-capacity assumption about binarization granularity is not tested. These gaps make the headline claims stronger than the evidence.

major comments (3)
  1. [§4.2, Table 3] The claim that DLN 'matches or exceeds' baseline accuracy rests on the aggregate mean R2 (0.810 vs. RF 0.815 and MLP 0.808) and on average rank, but no significance test is reported across the 15 datasets. The mean differences are smaller than the per-dataset standard errors, and DLN is noticeably worse than MLP on several datasets (e.g., Airfoil 0.889 vs. 0.943, Electrical 0.936 vs. 0.968, Housing 0.766 vs. 0.796). Without a paired test across datasets (e.g., Wilcoxon signed-rank on per-dataset R2 or RMSE) or corrected confidence intervals, the aggregate parity claim is not statistically supported. Please add such tests, or explicitly soften the claim to 'comparable accuracy on these benchmarks.'
  2. [§4.3, Table 5 and Figure 4] The efficiency comparison assumes float16 for floating-point arithmetic and int16 for integers for every model, and maps all high-level operations to gate-level OPs. However, training uses float32 for MLP and DLN and float64 for most traditional models, and no evidence is provided that every baseline retains accuracy at float16. Since the reported geometric-mean OP counts for SVR and MLP are 129M and 2.59M, respectively, versus 29.8K for DLN, the claimed margins and the Pareto-frontier conclusion in Figure 4 could change materially if float32 or float64 operation counts were used. Please justify the precision assumption per model, or report OP counts under the precisions actually used.
  3. [§3.1.1 and §4.6, Table 6] The binarization granularity is a load-bearing representational assumption: with six or ten threshold neurons per continuous feature, the final predictor is piecewise constant in the continuous features, and Section 4.6 concedes that DLN 'lag[s] behind the MLP on several datasets, indicating limited capacity when the target function has highly complex decision boundaries.' The paper does not vary the number of thresholds per feature, does not test synthetic targets with known smoothness or steepness, and does not quantify how threshold count interacts with accuracy. Please add a sensitivity study over the number of thresholds per feature (e.g., 6, 10, 20, 30) and, ideally, a synthetic experiment where target complexity is controlled, so that the reported parity is not an artifact of a fixed discretization budget.
minor comments (4)
  1. [Algorithm 1, line 7 vs. Eq. (1) and Table 1] The ThresholdLayer forward pass in Algorithm 1 is written as Sigmoid(si * (xi - bi)), omitting the division by temperature tau that appears in Eq. (1) and Table 1. Please make the algorithm consistent with the equations.
  2. [Figure 4] The Pareto-frontier plot would benefit from error bars or confidence bands on the R2 values, since each point is an average over 10 seeds, and the legend entries 'Interpretable' and 'Not interpretable' should be clarified in the caption.
  3. [Table 4] The arrows (↑, ↓, →) used to indicate changes across HPO budgets are not explained in the caption; please define them or remove the arrows.
  4. [§4.5, Table 6] For the 'No concat' ablation, the mean R2 drop is 0.802 to 0.782, but the per-dataset drop is much larger on Parkinson's (0.798 to 0.649); reporting the per-dataset changes alongside the mean would better characterize the effect.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the regression DLN accuracy claim is supported by external benchmarks and independent evaluation, not by a fitted quantity or self-citation chain.

full rationale

The paper's central claim is that a SumLayer over binary logic activations yields competitive regression accuracy. That output is, by definition, a weighted sum of the final logic layer's binary outputs, but this is the model's definition, not a derived prediction whose inputs secretly encode the result. Accuracy is measured on held-out test portions of 15 public benchmarks after Optuna-based hyperparameter search with cross-validation and 10 random seeds, so no parameter is fitted to the test set and no reported accuracy reduces to a fitted constant. The ThresholdLayer biases are initialized from decision-tree bin edges on the training split, but they are subsequently trained end-to-end, so the initialization is not a fitted input renamed as a prediction. The paper does borrow several methodological choices from the authors' earlier classification DLN [3], including real-valued logic, subspace search, straight-through estimators, input concatenation, and the SumLayer gate threshold 0.8; these are engineering transfers and not evidence for the regression accuracy result, which stands on the independent comparison against RF, MLP, SVR, and other baselines. No uniqueness theorem is invoked, and no load-bearing premise relies on the authors' prior work as proof of the regression claim. The paper's own limitation statement concedes that DLN lags behind the MLP on some datasets, but that is an honest capacity caveat, not a circular step. The only noteworthy discrepancy is rhetorical: the abstract says DLNs 'match or exceed baseline accuracy,' whereas Table 3 shows random forest with a slightly higher mean R2 and better average rank; that is an overstatement relative to the paper's own table, not a circular derivation. Consequently, there is no reduction of a prediction to its own inputs by construction, and the central result is self-contained against external benchmarks.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The model is an empirical method, not a derivation. The central claim depends on the representational power of binarized logic circuits, the effectiveness of continuous relaxation for discrete search, and the validity of the OP-based efficiency metric. These are domain assumptions rather than free-fitting constants. No new physical or conceptual entities are postulated.

free parameters (4)
  • SumLayer link threshold θsum-th = 0.8
    Chosen by hand following the classification DLN; controls how many logic rules are kept after discretization. Affects inference cost and accuracy.
  • Threshold neurons per continuous feature = 6 or 10
    Chosen by hand; controls binarization resolution. More thresholds improve regression accuracy but increase cost.
  • Temperature schedule (initial τ, decay γ, minimum τmin) = tuned per dataset via Optuna
    Initial temperature, decay factor, and minimum temperature; annealing is critical for convergence according to the ablation study in Section 4.5.
  • HPO budget and architecture hyperparameters = not reported in detail
    Number of LogicLayers, hidden dimensions, learning rate, epochs, and optimizer are tuned but not listed, making exact replication difficult.
assumptions (4)
  • domain assumption Real-valued logic relaxation of the 16 Boolean functions permits effective gradient-based optimization
    Inherited from LGN [1] and DLN [3]; used throughout Section 3.1.2. If this relaxation fails to guide discrete choices, training would not converge to good hard logic circuits.
  • domain assumption Binarizing continuous features with 6-10 learned thresholds preserves enough information for regression
    Section 3.1.1. The whole model operates on binary inputs; if thresholds are too coarse, the final rules cannot fit the target.
  • domain assumption The defined gate-level OP count is a valid proxy for real inference cost
    Section 4.3. Efficiency claims rest on this mapping, which assumes float16 arithmetic is lossless for all models and that each logic gate maps to a fixed number of OPs.
  • domain assumption Straight-through estimators keep the discretized forward pass aligned with training gradients
    Section 3.2. The STEs are used to reduce train/inference mismatch; if they fail, the reported accuracy of the hard-logic model could diverge.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Learning Interpretable Differentiable Logic Networks for Tabular Regression." pith.science (2026). https://pith.science/paper/SURUM3K5

@misc{pith2026250523615,
  author       = {Pith},
  title        = {Pith review of: Learning Interpretable Differentiable Logic Networks for Tabular Regression},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SURUM3K5}},
  note         = {Machine review of arXiv:2505.23615}
}
read the original abstract

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. Specifically, we redesign the final output layer to support continuous targets and unify the original two-phase training procedure into a single differentiable stage. 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.

Figures

Figures reproduced from arXiv: 2505.23615 by the authors.

Figure 1
Figure 1. A simplified regression DLN example. Continuous input features are first binarized by a [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Training workflow for a regression DLN [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Illustration of the training process. The network learns neuron functions and connections [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Comparison of R2 and the number of operations required for inference across models. We plot results for 32, 64, and 128 hyperparameter-search trials and draw the Pareto frontier for each case; DLN is Pareto-optimal in all three. 1. Remove rows with missing values. The …
Figure 5
Figure 5. Figure 5: Distribution of R2 across datasets for each model, averaged over 10 random seeds and 128 hyperparameter-search trials. excels on some complex datasets but is less consistent overall. The MLP performs well on datasets that challenge most other methods (e.g., Airfoil and…
Figure 6
Figure 6. Figure 6: Pearson correlation matrix of model R2 scores, averaged over 10 random seeds and 128 hyperparameter-search trials. Finally, we compare performance under different hyperparameter-search budgets [PITH_FULL_IMAGE:figures/full_fig_p014_6.png]
Figure 7
Figure 7. Figure 7: Decision process learned by a DLN on the [PITH_FULL_IMAGE:figures/full_fig_p016_7.png]
Figure 8
Figure 8. Figure 8: Decision process learned by a DLN on the [PITH_FULL_IMAGE:figures/full_fig_p017_8.png]
Figure 9
Figure 9. Figure 9: Decision process learned by a DLN on the [PITH_FULL_IMAGE:figures/full_fig_p017_9.png]

Discussion (0). Sign in to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Learning Interpretable Differentiable Logic Networks for Time-Series Classification

    cs.LG 2025-08 unverdicted novelty 4.0 of 10

    Differentiable logic networks trained on Catch22 and TSFresh features match competitive accuracy on 51 univariate time-series benchmarks while keeping readable Boolean decision logic.

Reference graph

Works this paper leans on

52 extracted references · 49 canonical work pages · cited by 1 Pith paper

  1. [3]

    Learning interpretable differentiable logic networks,

    C. Yue and N. K. Jha, “Learning interpretable differentiable logic networks,”IEEE Trans. Circuits Syst. Artif. Intell. , vol. 1, no. 1, pp. 69–82, 2024

    work page 2024

  2. [1]

    Deep differentiable logic gate networks,

    F. Petersen, C. Borgelt, H. Kuehne, and O. Deussen, “Deep differentiable logic gate networks,” in Adv. Neural Inf. Process. Syst. , vol. 35, 2022

    work page 2022

  3. [2]

    Convolutional differentiable logic gate networks,

    F. Petersen, H. Kuehne, C. Borgelt, J. Welzel, and S. Ermon, “Convolutional differentiable logic gate networks,” in Adv. Neural Inf. Process. Syst. , vol. 37, 2024

    work page 2024

  4. [4]

    Fuzzy sets as a basis for a theory of possibility,

    L. A. Zadeh, “Fuzzy sets as a basis for a theory of possibility,” Fuzzy Sets Syst., vol. 1, no. 1, pp. 3–28, 1978. 19 Table 8: Average test MAE across 10 random seeds and 128 hyperparameter trials per model Linear Ridge Lasso KNN DT AB RF SVR MLP DLN Abalone 1.57 1.57 1.57 1.54 1.62 1.76 1.50 1.47 1.48 1.57 Airfoil 3.69 3.69 3.69 1.63 2.34 2.83 1.91 2.05 ...

    work page 1978

  5. [5]

    Statistical metrics,

    K. Menger, “Statistical metrics,” Selecta Math., vol. 2, pp. 433–435, 2003

    work page 2003

  6. [6]

    Goertzel, M

    B. Goertzel, M. Ikl´ e, I. F. Goertzel, and A. Heljakka, Probabilistic Logic Networks: A Compre- hensive Framework for Uncertain Inference . Springer, 2008

    work page 2008

  7. [7]

    Distilling a neural network into a soft decision tree,

    N. Frosst and G. Hinton, “Distilling a neural network into a soft decision tree,” in Proc. Int. Workshop Comprehensibility & Explanation in Artif. Intell. & Mach. Learn. , 2017

    work page 2017

  8. [8]

    Deep neural decision trees,

    Y. Yang, I. G. Morillo, and T. M. Hospedales, “Deep neural decision trees,” in Proc. ICML Workshop Human Interpretability in Mach. Learn. , 2018

    work page 2018

Show all 52 references
  1. [9]

    Deep neural decision forests,

    P. Kontschieder, M. Fiterau, A. Criminisi, and S. R. Bulo, “Deep neural decision forests,” in Proc. IEEE Int. Conf. Comput. Vis. , 2015, pp. 1467–1475

    2015

  2. [10]

    Adaptive neural trees,

    R. Tanno, K. Arulkumaran, D. Alexander, A. Criminisi, and A. Nori, “Adaptive neural trees,” in Proc. Int. Conf. Mach. Learn. , 2019, pp. 6166–6175

    2019

  3. [11]

    Neural oblivious decision ensembles for deep learning on tabular data,

    S. Popov, S. Morozov, and A. Babenko, “Neural oblivious decision ensembles for deep learning on tabular data,” in Proc. Int. Conf. Learn. Represent. , 2020

    2020

  4. [12]

    KAN: Kolmogorov-Arnold networks,

    Z. Liu, Y. Wang, S. Vaidya, F. Ruehle, J. Halverson, M. Soljaˇ ci´ c, T. Y. Hou, and M. Tegmark, “KAN: Kolmogorov-Arnold networks,” in Proc. Int. Conf. Learn. Represent. , 2025

    2025

  5. [13]

    Physics-informed neural networks: A deep learn- ing framework for solving forward and inverse problems involving nonlinear partial differential equations,

    M. Raissi, P. Perdikaris, and G. E. Karniadakis, “Physics-informed neural networks: A deep learn- ing framework for solving forward and inverse problems involving nonlinear partial differential equations,” J. Comput. Phys. , vol. 378, pp. 686–707, 2019. 20

    2019

  6. [14]

    DiffTaichi: Differentiable programming for physical simulation,

    Y. Hu, L. Anderson, T.-M. Li, Q. Sun, N. Carr, J. Ragan-Kelley, and F. Durand, “DiffTaichi: Differentiable programming for physical simulation,” in Proc. Int. Conf. Learn. Represent., 2020

    2020

  7. [15]

    Discovering symbolic models from deep learning with inductive biases,

    M. Cranmer, A. Sanchez Gonzalez, P. Battaglia, R. Xu, K. Cranmer, D. Spergel, and S. Ho, “Discovering symbolic models from deep learning with inductive biases,” in Adv. Neural Inf. Process. Syst., vol. 33, 2020, pp. 17 429–17 442

    2020

  8. [16]

    Automatic differentiation in machine learning: A survey,

    A. G. Baydin, B. A. Pearlmutter, A. A. Radul, and J. M. Siskind, “Automatic differentiation in machine learning: A survey,” J. Mach. Learn. Res. , vol. 18, no. 153, pp. 1–43, 2018

    2018

  9. [17]

    Learning with differentiable algorithms,

    F. Petersen, “Learning with differentiable algorithms,” Ph.D. dissertation, University of Konstanz, 2022

    2022

  10. [18]

    Soft-DTW: A differentiable loss function for time-series,

    M. Cuturi and M. Blondel, “Soft-DTW: A differentiable loss function for time-series,” in Proc. Int. Conf. Mach. Learn. , 2017, pp. 894–903

    2017

  11. [19]

    ”Why should I trust you?

    M. T. Ribeiro, S. Singh, and C. Guestrin, “”Why should I trust you?” Explaining the predictions of any classifier,” in Proc. ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. , 2016, pp. 1135– 1144

    2016

  12. [20]

    A unified approach to interpreting model predictions,

    S. M. Lundberg and S.-I. Lee, “A unified approach to interpreting model predictions,” in Adv. Neural Inf. Process. Syst. , vol. 30, 2017

    2017

  13. [21]

    Deep inside convolutional networks: Visualising image classification models and saliency maps,

    K. Simonyan, A. Vedaldi, and A. Zisserman, “Deep inside convolutional networks: Visualising image classification models and saliency maps,” in Proc. Int. Conf. Learn. Represent., Workshop Track, 2014

    2014

  14. [22]

    Feature visualization,

    C. Olah, A. Mordvintsev, and L. Schubert, “Feature visualization,” Distill, vol. 2, no. 11, p. e7, 2017

    2017

  15. [23]

    Peeking inside the black box: Visualizing statistical learning with plots of individual conditional expectation,

    A. Goldstein, A. Kapelner, J. Bleich, and E. Pitkin, “Peeking inside the black box: Visualizing statistical learning with plots of individual conditional expectation,” J. Comput. Graph. Stat. , vol. 24, no. 1, pp. 44–65, 2015

    2015

  16. [24]

    Stop explaining black box machine learning models for high stakes decisions and use interpretable models instead,

    C. Rudin, “Stop explaining black box machine learning models for high stakes decisions and use interpretable models instead,” Nat. Mach. Intell. , vol. 1, no. 5, pp. 206–215, 2019

    2019

  17. [25]

    Ridge regression: Biased estimation for nonorthogonal prob- lems,

    A. E. Hoerl and R. W. Kennard, “Ridge regression: Biased estimation for nonorthogonal prob- lems,” Technometrics, vol. 12, no. 1, pp. 55–67, 1970

    1970

  18. [26]

    Regression shrinkage and selection via the Lasso,

    R. Tibshirani, “Regression shrinkage and selection via the Lasso,” J. R. Statist. Soc. Series B Methodol., vol. 58, no. 1, pp. 267–288, 1996

    1996

  19. [27]

    Generalized additive models,

    T. J. Hastie, “Generalized additive models,” in Statistical Models in S . Routledge, 2017, pp. 249–307

    2017

  20. [28]

    Predictive learning via rule ensembles,

    J. H. Friedman and B. E. Popescu, “Predictive learning via rule ensembles,” Ann. Appl. Stat. , vol. 2, no. 3, pp. 916–954, 2008

    2008

  21. [29]

    Generalized and scalable optimal sparse decision trees,

    J. Lin, C. Zhong, D. Hu, C. Rudin, and M. Seltzer, “Generalized and scalable optimal sparse decision trees,” in Proc. Int. Conf. Mach. Learn. , 2020, pp. 6150–6160

    2020

  22. [30]

    Supersparse linear integer models for optimized medical scoring sys- tems,

    B. Ustun and C. Rudin, “Supersparse linear integer models for optimized medical scoring sys- tems,” Mach. Learn., vol. 102, pp. 349–391, 2016. 21

    2016

  23. [31]

    Logical neural networks,

    R. Riegel, A. Gray, F. Luus, N. Khan, N. Makondo, I. Y. Akhalwaya, H. Qian, R. Fagin, F. Bara- hona, U. Sharma et al. , “Logical neural networks,” arXiv preprint arXiv:2006.13155 , 2020

    2006 arXiv

  24. [32]

    Scalable rule-based representation learning for inter- pretable classification,

    Z. Wang, W. Zhang, N. Liu, and J. Wang, “Scalable rule-based representation learning for inter- pretable classification,” in Adv. Neural Inf. Process. Syst. , vol. 34, 2021

    2021

  25. [33]

    Neural logic machines,

    H. Dong, J. Mao, T. Lin, C. Wang, L. Li, and D. Zhou, “Neural logic machines,” in Proc. Int. Conf. Learn. Represent., 2019

    2019

  26. [34]

    Neural logic networks,

    S. Shi, H. Chen, M. Zhang, and Y. Zhang, “Neural logic networks,” arXiv preprint arXiv:1910.08629, 2019

    1910 arXiv

  27. [35]

    Learning both weights and connections for efficient neural network,

    S. Han, J. Pool, J. Tran, and W. Dally, “Learning both weights and connections for efficient neural network,” in Adv. Neural Inf. Process. Syst. , vol. 28, 2015

    2015

  28. [36]

    The lottery ticket hypothesis: Finding sparse, trainable neural net- works,

    J. Frankle and M. Carbin, “The lottery ticket hypothesis: Finding sparse, trainable neural net- works,” in Proc. Int. Conf. Learn. Represent. , 2019

    2019

  29. [37]

    Binarized neural networks: Training deep neural networks with weights and activations constrained to +1 or -1,

    M. Courbariaux, I. Hubara, D. Soudry, R. El-Yaniv, and Y. Bengio, “Binarized neural networks: Training deep neural networks with weights and activations constrained to +1 or -1,” in Adv. Neural Inf. Process. Syst. , vol. 29, 2016

    2016

  30. [38]

    XNOR-Net: Imagenet classification using binary convolutional neural networks,

    M. Rastegari, V. Ordonez, J. Redmon, and A. Farhadi, “XNOR-Net: Imagenet classification using binary convolutional neural networks,” in Proc. Eur. Conf. Comput. Vis. , 2016, pp. 525–542

    2016

  31. [39]

    GPTQ: Accurate post-training quantiza- tion for generative pre-trained transformers,

    E. Frantar, S. Ashkboos, T. Hoefler, and D. Alistarh, “GPTQ: Accurate post-training quantiza- tion for generative pre-trained transformers,” in Proc. Int. Conf. Learn. Represent. , 2023

    2023

  32. [40]

    Atom: Low-bit quantization for efficient and accurate LLM serving,

    Y. Zhao, C.-Y. Lin, K. Zhu, Z. Ye, L. Chen, S. Zheng, L. Ceze, A. Krishnamurthy, T. Chen, and B. Kasikci, “Atom: Low-bit quantization for efficient and accurate LLM serving,” in Proc. Mach. Learn. Syst., vol. 6, 2024, pp. 196–209

    2024

  33. [41]

    Distilling the knowledge in a neural network,

    G. Hinton, O. Vinyals, and J. Dean, “Distilling the knowledge in a neural network,” in Proc. Neural Inf. Process. Syst. Deep Learn. & Represent. Learn. Workshop , 2015

    2015

  34. [42]

    MiniLLM: Knowledge distillation of large language models,

    Y. Gu, L. Dong, F. Wei, and M. Huang, “MiniLLM: Knowledge distillation of large language models,” in Proc. Int. Conf. Learn. Represent. , 2023

    2023

  35. [43]

    FINN: A framework for fast, scalable binarized neural network inference,

    Y. Umuroglu, N. J. Fraser, G. Gambardella, M. Blott, P. Leong, M. Jahre, and K. Vissers, “FINN: A framework for fast, scalable binarized neural network inference,” in Proc. ACM/SIGDA Int. Symp. Field-Program. Gate Arrays, 2017, pp. 65–74

    2017

  36. [44]

    Estimating or propagating gradients through stochastic neurons for conditional computation,

    Y. Bengio, N. L´ eonard, and A. Courville, “Estimating or propagating gradients through stochastic neurons for conditional computation,” arXiv preprint arXiv:1308.3432 , 2013

    2013 arXiv

  37. [45]

    Wide & deep learning for recommender systems,

    H.-T. Cheng, L. Koc, J. Harmsen, T. Shaked, T. Chandra, H. Aradhye, G. Anderson, G. Corrado, W. Chai, M. Ispir et al., “Wide & deep learning for recommender systems,” in Proc. 1st Workshop Deep Learn. Recommender Syst., 2016

    2016

  38. [46]

    SymPy: Symbolic computing in Python,

    A. Meurer, C. P. Smith, M. Paprocki, O. ˇCert ´ ık, S. B. Kirpichev, M. Rocklin, A. Kumar, S. Ivanov, J. K. Moore, S. Singh, T. Rathnayake, S. Vig, B. E. Granger, R. P. Muller, F. Bonazzi, H. Gupta, S. Vats, F. Johansson, F. Pedregosa, M. J. Curry, A. R. Terrel, v. Rouˇ cka, A...

    2017 doi

  39. [47]

    The UCI machine learning repository,

    M. Kelly, R. Longjohn, and K. Nottingham, “The UCI machine learning repository,” https: //archive.ics.uci.edu, accessed: May 01, 2025

    2025

  40. [48]

    Kaggle, “Kaggle,” https://www.kaggle.com, accessed: May 01, 2025

    2025

  41. [49]

    Optuna: A next-generation hyperpa- rameter optimization framework,

    T. Akiba, S. Sano, T. Yanase, T. Ohta, and M. Koyama, “Optuna: A next-generation hyperpa- rameter optimization framework,” in Proc. ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. , 2019, pp. 2623–2631

    2019

  42. [50]

    Scikit-learn: Machine learning in Python,

    F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Pret- tenhofer, R. Weiss, V. Dubourg et al. , “Scikit-learn: Machine learning in Python,” J. Mach. Learn. Res., vol. 12, pp. 2825–2830, 2011

    2011

  43. [51]

    Pytorch: An imperative style, high-performance deep learn- ing library,

    A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antiga et al. , “Pytorch: An imperative style, high-performance deep learn- ing library,” in Adv. Neural Inf. Process. Syst. , vol. 32, 2019

    2019

  44. [52]

    Ray: A distributed framework for emerging AI applications,

    P. Moritz, R. Nishihara, S. Wang, A. Tumanov, R. Liaw, E. Liang, M. Elibol, Z. Yang, W. Paul, M. I. Jordan et al. , “Ray: A distributed framework for emerging AI applications,” in Proc. USENIX Symp. Oper. Syst. Des. Implement. , 2018, pp. 561–577. 23

    2018

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.