Application of Sensitivity Analysis Methods for Studying Neural Network Models

Jiaxuan Miao; Sergey Matveev

REVIEW 4 major objections 5 minor 34 references

Application of Sensitivity Analysis Methods for Studying Neural Network Models

T0 review · 4 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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

Pith's one-line read This paper demonstrates that sensitivity-analysis methods can identify which inputs a neural network actually depends on, from glucose, BMI, and age in a diabetes model to B-lines, consolidations, and A-lines in lung ultrasound.

desk verdict A straightforward, reproducible demonstration of standard sensitivity/interpretability tools on small models; the diabetes feature-ranking part holds up reasonably, but the lung-ultrasound claim needs held-out accuracy before it earns its conclusion. read the letter →

arxiv 2504.15100 v1 pith:FMZXY2LK submitted 2025-04-21 math.NA cs.LGcs.NA

Jiaxuan Miao , Sergey Matveev This is my paper · ORCID

classification math.NAcs.LGcs.NA MSC 65C0568T07

keywords convolutionalnetworksSobolsensitivityanalysisactivationmaximizationfeedforwardlocalexplainableAIfeatureselectionlungultrasound

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

This paper sets out to show that sensitivity analysis can make neural networks interpretable without specialized machinery: standard variance-based and gradient-based tools reveal which inputs actually drive a network's output. On a small fully connected network for an open diabetes dataset, Sobol global sensitivity indices rank glucose, BMI, and age as the leading features, and retraining on just four of the eight inputs keeps test accuracy near 80% versus 82.5% with all inputs. On convolutional networks, where global analysis is too expensive, the paper turns to local pixel-perturbation sensitivity and activation maximization, finding that sensitivity fades with depth in VGG-16, that residual connections in ResNet-18 preserve deep-layer sensitivity, and that activation maximization brings out clinically recognized signs in lung ultrasound. If correct, these results make a practical case: sensitivity analysis can support feature selection in small tabular models and sanity-check what a medical image classifier actually looks at.

What carries the argument

The machinery is fourfold, each tied to a measurement. First, Sobol's variance decomposition splits the network output $f(x_1,\dots,x_k)$ into $f_0 + \sum_i f_i(x_i) + \sum_{i<j} f_{ij}(x_i,x_j) + \cdots$, with first-order index $S_i = V_i/V(y)$ and total index $S_{Ti} = 1 - V_{\sim i}/V(y)$; this is what produces the Glucose/BMI/Age ranking. Second, local sensitivity computes, for each pixel and color channel, the change in the block output norm when that pixel is perturbed: $s_{ij}^C = \|B_q(\dots,x_{ij}+\varepsilon,\dots)\|_2 - \|B_q(\dots,x_{ij},\dots)\|_2$, giving the heatmaps that show depth-dependent decay. Third, activation maximization solves $x^* = \arg\max_x a_{ij}(\theta,x)$ by gradient ascent, regularized by total variation so the synthetic images stay close to natural ones; this yields the feature-visualization and lung-ultrasound images. Fourth, the residual block $\mathrm{Res}(x)=x+F_{\mathrm{act}}(x)$ is the structural reason ResNet-18 preserves sensitivity in deep layers, since the identity shortcut lets input perturbations survive propagation.

What would settle it

Recompute the Sobol indices using samples drawn from the empirical joint distribution of the eight clinical variables (for example, resampling from the actual dataset or a fitted copula) instead of independent uniform ranges, then retrain the four-feature network. If Glucose, BMI, and Age stop dominating the ranking, or if the four-feature accuracy falls well below the reported 80%, the feature-selection conclusion is an artifact of the independence assumption rather than a stable property of the diabetes data.

Watch

Extended reading notes

Core claim

The central discovery is that sensitivity analysis is not just a diagnostic curiosity but a usable tool for deciding what a network really uses. For the eight-input fully connected diabetes network, Sobol global sensitivity indices rank Glucose, BMI, and Age as the dominant first-order contributors; retraining the same architecture on the four most influential features (Glucose, BMI, Age, Insulin) keeps test accuracy at about 80% against 82.5% with all eight inputs, while the four least influential features alone reach only about 69%. In the convolutional setting, the paper finds that local perturbation sensitivity in VGG-16 declines through the five blocks (reaching scale $10^{-2}$), that ResNet-18's residual blocks keep later-layer sensitivity near $10^0$, and that activation maximization with total-variation regularization produces class images that capture distinctive contours (airplane wings, deer antlers, cat ears). Applied to lung ultrasound, the same activation-maximization method highlights B-lines for COVID-19, consolidations for bacterial pneumonia, and A-lines for healthy lungs, matching clinical signs and Grad-CAM heatmaps but with a more focused sensitive area.

Load-bearing premise

The ranking of Glucose, BMI, and Age as the dominant diabetes features rests on treating the eight clinical inputs as independent random variables sampled uniformly over their observed ranges, and on assuming this particular small network's sensitivities mirror the true relationship between those features and diabetes.

Editorial extensions

If this is right

On tabular clinical data with few features, Sobol indices can serve as a feature-selection step: the paper's four-feature network retains roughly 80% test accuracy, only about 2.5 points below the full model.
VGG-16's sensitivity falls from scale $10^0$ in early blocks to $10^{-2}$ in the fifth block, implying that adding ever-deeper plain convolutional blocks has diminishing returns for capturing input-level features.
ResNet-18's residual blocks maintain deep-layer sensitivity around $10^0$, so the identity shortcut is a concrete mechanism that keeps later layers responsive to input perturbations.
Activation maximization on lung ultrasound highlights clinically named signs—B-lines, consolidations, A-lines—and matches Grad-CAM observations, but with narrower high-sensitivity regions, suggesting it can complement gradient-based attribution in medical imaging.
When a class image is activated by parameters of another class, the network inserts features of the target class (e.g., antlers into a deer image), showing how activation maximization can reveal class-confusing cues that adversarial attacks might exploit.

Reading between the lines

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

A natural next test the paper does not run: recompute the Sobol indices with correlated sampling from the empirical joint distribution. If the Glucose/BMI/Age ranking survives, the method becomes a low-cost screening tool for other small clinical models; if not, the ranking is an artifact of the independence assumption.
The depth-sensitivity decay in VGG-16 suggests a quantitative architectural heuristic: plot the mean local-sensitivity magnitude per block and stop adding blocks once it drops below a threshold. This is implied by the paper's data but not stated as a design rule.
The paper's claim that activation maximization is more effective than Grad-CAM on ultrasound is qualitative; a localization benchmark (e.g., comparing highlighted regions against expert-annotated A/B-lines) would turn that comparison into a measurable claim.
Because the same activation-maximization procedure exposes boundary artifacts that mimic B-lines, it could double as a data-audit tool: run it before training a medical classifier to see which image features are spuriously learnable.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

First thing you should know: this is not a new method paper. It applies Sobol global sensitivity, local sensitivity heatmaps, and activation maximization to a tiny diabetes net, VGG-16/ResNet-18 on CIFAR-10, and a VGG-16 on lung ultrasound. That's fine; its value is as a careful worked demonstration with code.

The Sobol analysis on the 8-input diabetes network is the cleanest part. The convergence plot across sample sizes 128 to 65536 is a nice touch, and the feature-subset experiment (four most sensitive features ~80% vs four least ~69% test accuracy) directly supports the claim that the sensitivity ranking is usable for feature reduction. The PCA comparison is also honest and useful. The CIFAR-10 visualizations are standard, but the exposition is clear.

The load-bearing problem is the lung-ultrasound section. The paper reports only 94% training accuracy and never gives test or validation accuracy, nor the split used. The AM heatmaps in Figures 15-16 might be picking up genuine B-lines, A-lines, and consolidations, but they might equally be artifacts of a model that memorized probe position, gain settings, or text overlays. The authors themselves write that 'some boundaries might be mistakenly recognized as significant medical features,' so they see the risk, but they don't close it with a held-out evaluation. That is fixable but essential before claiming the method 'successfully distinguishes' the three classes.

Second: the diabetes ablative experiments appear to be a single run. 82.5% vs 80% vs 69% has no confidence intervals or seeds, so we don't know whether the 4-feature model is statistically equivalent to the full model. The Sobol ranking also assumes the inputs are independent and uniformly sampled over observed ranges; clinical variables like BMI, age, and blood pressure are correlated, so the indices are conditional on that assumption. The paper doesn't flag this, and it matters for the feature-ranking claim.

The CIFAR-10 sensitivity-depth observations are qualitative. They reproduce known results about early layers encoding edges and color and residual connections preserving gradient flow, so they are plausible but not quantified.

Overall, the paper is honest, reproducible, and scoped correctly except for the LUS overreach. The math is standard and the claims are mostly aligned with what the experiments support. I would send it to a serious referee, but I would expect a substantial revision: report held-out accuracy on the LUS data, add uncertainty estimates or multi-seed runs for the diabetes experiment, and soften the 'successfully distinguishing' language.

The likely audience is practitioners in applied ML and medical imaging who want a worked example of sensitivity-based interpretation, not method developers. My recommendation: treat it as a revise-and-resubmit candidate and give it referee time.

Referee Report

4 major / 5 minor

Summary. The paper demonstrates three sensitivity-analysis tools on neural-network models: Sobol global sensitivity analysis on a small fully connected network trained on tabular diabetes data; local input-pixel perturbation sensitivity heatmaps on VGG-16 and ResNet-18 trained on CIFAR-10; and activation maximization (AM) on the same convolutional models, applied finally to a lung-ultrasound (LUS) classification task. The central claims are that Sobol indices identify Glucose, BMI, and Age as the leading diabetes predictors and that reducing the input features from eight to the four most influential (Glucose, BMI, Age, Insulin) loses little accuracy; that local sensitivity maps show decreasing sensitivity with depth in VGG-16 and preserved sensitivity in ResNet-18; and that AM highlights clinically plausible features (B-lines, consolidations, A-lines) in LUS images, more focused than Grad-CAM. The authors provide code repositories for the experiments.

Significance. If the claims hold, the paper would provide a useful empirical illustration that global sensitivity analysis can guide feature pruning in small tabular MLPs and that activation maximization can localize diagnostically relevant ultrasound features. The strengths are the availability of code, the use of established libraries (SALib), the convergence check of Sobol indices with increasing sample size, and the comparisons with PCA and Grad-CAM. However, the load-bearing evidence is qualitative and single-run in the convolutional and medical-imaging parts, and the feature-reduction claim is not supported by statistical confidence measures. As it stands, the contribution is a set of demonstrations rather than a validated methodology.

major comments (4)

[Section 4 and Conclusion] The claim that the VGG-16 model 'successfully distinguishes' COVID-19, bacterial pneumonia, and normal lungs in Section 4, and that activation maximization 'effectively highlights the medical features', rests on a model for which only 94% training accuracy is reported. Without a held-out test accuracy, per-class metrics, the train/test split, and class balance, the AM heatmaps in Figures 15-16 cannot be separated from patterns learned on dataset artifacts such as probe positioning, gain settings, or text overlays. The manuscript itself acknowledges that 'some boundaries might be mistakenly recognized as significant medical features,' but this does not rescue the claim. Please report test/validation accuracy and per-class performance, and ideally quantify or blind-evaluate the AM and Grad-CAM localizations against clinician annotations.
[Section 2.2-2.3] The Sobol analysis treats the eight clinical inputs as independent random variables sampled uniformly over their observed ranges via SALib. Clinical variables such as Glucose and Insulin, or Age and BMI, are correlated, and Sobol indices are not uniquely interpretable under dependent inputs; the ranking of Glucose, BMI, Age, and Insulin, and consequently the feature-subset experiment, could change under the true joint distribution. Please state explicitly the sampling ranges and either sample from a dependence-aware distribution (e.g., an empirical copula or a Gaussian copula fitted to the data) or provide a sensitivity check showing that the ranking is robust to the independence assumption. This is load-bearing for the paper's main feature-identification claim.
[Section 2.3] The feature-reduction comparison reports test accuracy of 82.5% for the full model, 'about 80%' for the four-feature model, and 'about 69%' for the remaining four features, without confidence intervals, number of seeds, or run-to-run variability. At the dataset size used, these differences are within typical training noise, so the statement that feature reduction occurs 'without significant loss of the accuracy' is not supported by the presented evidence. Please report means and standard deviations over multiple random seeds and a statistical comparison (e.g., a paired test or McNemar's test).
[Section 3.1 and 3.4] The conclusion that sensitivity 'gradually decreases with depth' in VGG-16 and that ResNet-18 preserves sensitivity is based on visual inspection of heatmaps for a single class (airplanes) from a single model, and the plotted scales in Figures 5-10 differ by orders of magnitude (10^0 down to 10^-2). This trend may be partly an artifact of the chosen normalization or output scaling rather than a property of the models. Please provide quantitative summary statistics (e.g., mean or quantiles of the sensitivity per block or layer, aggregated over multiple classes) under a fixed normalization across layers, before drawing conclusions about depth-dependent sensitivity.

minor comments (5)

[Throughout] There are several typos and grammatical errors, including 'ust' for 'use', 'Iy' for 'It', 'classily' for 'classify', and inconsistent capitalization of 'Grad-Cam' versus 'Grad-CAM'; a thorough proofread is needed.
[Section 3] The local-sensitivity formula in Section 3 is typeset poorly and is not numbered; the notation for the block operator B_q and the perturbation epsilon should be defined more carefully, including the norm used (the formula shows a squared L2 norm, but the surrounding text says 'sensitivity of the pixel').
[Section 3.3] The activation maximization update in equation (4) uses two coefficients epsilon_1 and epsilon_2, while equation (5) only has epsilon_1; the relationship between these coefficients and the reported values (epsilon_1 = 0.1, epsilon_2 = 0.1) should be clarified.
[Section 2.4] The PCA comparison is reported without methodological details, such as whether the features were standardized before PCA, how many components were retained, and how 'most important indicators' were derived from the loadings; please add these details.
[References] Some references appear mismatched: reference [13] is cited for the diabetes dataset but appears to describe the ADAP learning algorithm, and reference [14] is listed as a Kaggle dataset; please verify the citation-to-source correspondence.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the sensitivity and activation-maximization results are post-hoc calculations on fixed trained networks, and the feature-ranking claim is validated by an independent retraining experiment.

full rationale

The paper's central claims are (i) Sobol indices computed on a fixed two-layer network rank Glucose, BMI, and Age as leading inputs; (ii) retraining on the four top-ranked features gives roughly 80% test accuracy versus about 69% for the remaining features; (iii) local sensitivity heatmaps and activation maximization on VGG-16/ResNet-18 reveal depth-dependent sensitivity and class-typical patterns, including lung ultrasound features. Each of these steps computes a statistic of an already-trained network or tests a feature ranking by an independent retraining experiment; no sensitivity index, heatmap value, or activation-maximized image is fed back to adjust network parameters, nor is any fitted constant later renamed as a prediction. The self-citations [7, 12, 20, 27] are background references to visualization and sensitivity methodology and are not load-bearing: they do not supply a uniqueness theorem, an ansatz, or a fitted value that the present experiments merely restate. The absence of reported held-out accuracy for the lung ultrasound model is a correctness or validation concern, not a circularity concern, because even a memorizing model would still produce activation-maximization outputs that are computed from the trained weights rather than being equivalent to the input labels or to a fitted target. Accordingly, no step in the derivation chain reduces by construction to its own inputs.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The paper's claims rest mainly on trained-model sensitivity rather than on a derivation. The input ranges for Sobol sampling and the network hyperparameters are chosen by hand; no sensitivity of the conclusions to these choices is reported. The medical section assumes the lung ultrasound labels are trustworthy. No new entities are introduced.

free parameters (3)

Sobol input ranges for each clinical feature = min-max from the diabetes dataset
SALib requires a range per feature; these bounds and the assumption of independent uniform sampling shape the resulting sensitivity indices.
Network hyperparameters (hidden size 10, lambda 0.001, learning rate 0.01, batch size, epochs) = chosen by parameter tuning, exact values not fully specified
The sensitivity maps depend on the trained network; changing architecture or training details changes the results. The paper does not report a search procedure.
Number of Sobol samples = 65,536
Higher sample counts give tighter confidence intervals; the paper notes convergence. This is a compute choice, not a fitted constant.

assumptions (4)

domain assumption Sobol analysis assumes input features are independent random variables with specified ranges.
SALib generates independent quasi-random points; clinical features are likely correlated, so Sobol indices may be approximate or misleading.
domain assumption The sensitivity of the trained network reflects the true relation between clinical features and diabetes outcome.
The paper interprets network sensitivity as medical feature importance; this presumes the network is a good proxy for the underlying disease process, not just the training set.
domain assumption Local pixel perturbations and activation maximization reveal features the network actually uses.
These are standard interpretability heuristics, not formal explanations; the paper relies on visual and qualitative confirmation.
domain assumption The lung ultrasound labels in the COVID-19 repository are correct.
The medical conclusion depends on the quality of the external dataset labels, which the paper does not independently verify.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Application of Sensitivity Analysis Methods for Studying Neural Network Models." pith.science (2026). https://pith.science/paper/FMZXY2LK

@misc{pith2026250415100,
  author       = {Pith},
  title        = {Pith review of: Application of Sensitivity Analysis Methods for Studying Neural Network Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FMZXY2LK}},
  note         = {Machine review of arXiv:2504.15100}
}

read the original abstract

This study demonstrates the capabilities of several methods for analyzing the sensitivity of neural networks to perturbations of the input data and interpreting their underlying mechanisms. The investigated approaches include the Sobol global sensitivity analysis, the local sensitivity method for input pixel perturbations and the activation maximization technique. As examples, in this study we consider a small feedforward neural network for analyzing an open tabular dataset of clinical diabetes data, as well as two classical convolutional architectures, VGG-16 and ResNet-18, which are widely used in image processing and classification. Utilization of the global sensitivity analysis allows us to identify the leading input parameters of the chosen tiny neural network and reduce their number without significant loss of the accuracy. As far as global sensitivity analysis is not applicable to larger models we try the local sensitivity analysis and activation maximization method in application to the convolutional neural networks. These methods show interesting patterns for the convolutional models solving the image classification problem. All in all, we compare the results of the activation maximization method with popular Grad-CAM technique in the context of ultrasound data analysis.

Figures

Figures reproduced from arXiv: 2504.15100 by the authors.

**Figure 2.** The second-order Sobol indices S2 for the output. It is evident that increasing the sample size significantly improves the research results, making the sensitivity indices clearer and more distinct [19, 20]. Our sample data ranged from 128 to 65536, and we observed a gradual convergence of the first and total sensitivity indices ( [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** S1 for the first hidden layer. Based on the above, it can be concluded that the Sobol method is suitable for working with neural networks that have a small number of features [21, 22]. These neural networks are suitable for tabular data and relatively small training samples. As the volume of the data for sampling increases, the width of the confidence intervals gradually converges to zero in accordance with theory… view at source ↗

Figures from the paper (12 more)

**Figure 4.** Figure 4: S1 and ST for various physiological indicators and sample sizes N. The shaded areas represent the corresponding confidence intervals. One may wonder if nice results could be achieved by using only the most important features to build the neural network. Therefore, whil…

**Figure 6.** Figure 6: The sensitivity heatmap for the three color [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]

**Figure 7.** Figure 7: The sensitivity heatmap for the three color [PITH_FULL_IMAGE:figures/full_fig_p005_7.png]

**Figure 8.** Figure 8: The sensitivity heatmap for the three color [PITH_FULL_IMAGE:figures/full_fig_p005_8.png]

**Figure 5.** Figure 5: The sensitivity heatmap for the three color [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

**Figure 9.** Figure 9: The sensitivity heatmap for the three color [PITH_FULL_IMAGE:figures/full_fig_p006_9.png]

**Figure 10.** Figure 10: The sensitivity heatmap for the three color [PITH_FULL_IMAGE:figures/full_fig_p006_10.png]

**Figure 11.** Figure 11: The activation maximization pictures with [PITH_FULL_IMAGE:figures/full_fig_p007_11.png]

**Figure 13.** Figure 13: Sensitivity heatmaps for the red channel of [PITH_FULL_IMAGE:figures/full_fig_p007_13.png]

**Figure 14.** Figure 14: Application of AM with TV-regularization [PITH_FULL_IMAGE:figures/full_fig_p007_14.png]

**Figure 15.** Figure 15: AM for COVID-19 (highlights B-lines), bac [PITH_FULL_IMAGE:figures/full_fig_p008_15.png]

**Figure 16.** Figure 16: The images of lungs with COVID-19, bacterial pneumonia, and healthy lungs are arranged from top to bottom. On the right is the Grad-Cam image. 6https://github.com/jacobgil/pytorch-grad-cam.git 8 [PITH_FULL_IMAGE:figures/full_fig_p008_16.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

34 extracted references · 27 canonical work pages

[1]

Neural networks and physical sys- tems with emergent collective computational abil- ities.,

J. J. Hopfield, “Neural networks and physical sys- tems with emergent collective computational abil- ities.,” Proceedings of the national academy of sci- ences, vol. 79, no. 8, pp. 2554–2558, 1982

work page 1982
[2]

Highly accurate protein structure prediction with AlphaFold,

J. Jumper, R. Evans, A. Pritzel, T. Green, M. Figurnov, O. Ronneberger, K. Tunyasuvu- nakool, R. Bates, A. ˇZ´ ıdek, A. Potapenko,et al., “Highly accurate protein structure prediction with AlphaFold,” nature, vol. 596, no. 7873, pp. 583– 589, 2021

work page 2021
[3]

Video compression dataset and benchmark of learning- based video-quality metrics,

A. Antsiferova, S. Lavrushkin, M. Smirnov, A. Gushchin, D. Vatolin, and D. Kulikov, “Video compression dataset and benchmark of learning- based video-quality metrics,” Advances in Neu- ral Information Processing Systems , vol. 35, pp. 13814–13825, 2022

work page 2022
[4]

Neural video compression using spatio-temporal priors,

H. Liu, T. Chen, M. Lu, Q. Shen, and Z. Ma, “Neural video compression using spatio-temporal priors,” arXiv preprint arXiv:1902.07383 , 2019

arXiv 1902
[5]

Attention is all you need,

A. Vaswani, “Attention is all you need,” Advances in Neural Information Processing Systems , 2017

2017
[6]

Employing fingerprinting of medicinal plants by means of lc-ms and machine learning for species identification task,

P. Kharyuk, D. Nazarenko, I. Oseledets, I. Rodin, O. Shpigun, A. Tsitsilin, and M. Lavrentyev, “Employing fingerprinting of medicinal plants by means of lc-ms and machine learning for species identification task,” Scientific reports , vol. 8, no. 1, p. 17053, 2018

work page 2018
[7]

Overview of visualization methods for artificial neural networks,

S. A. Matveev, I. V. Oseledets, E. S. Ponomarev, and A. V. Chertkov, “Overview of visualization methods for artificial neural networks,” Compu- tational Mathematics and Mathematical Physics , vol. 61, no. 5, pp. 887–899, 2021. 9

work page 2021
[8]

Hop- field networks is all you need,

H. Ramsauer, B. Sch¨ afl, J. Lehner, P. Seidl, M. Widrich, T. Adler, L. Gruber, M. Holzleit- ner, M. Pavlovi´ c, G. K. Sandve, et al. , “Hop- field networks is all you need,” arXiv preprint arXiv:2008.02217, 2020

arXiv 2008

Show all 34 references

[9]

Art of singular vec- tors and universal adversarial perturbations,

V. Khrulkov and I. Oseledets, “Art of singular vec- tors and universal adversarial perturbations,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition , pp. 8562–8570, 2018

2018
[10]

Fast feature fool: A data independent approach to uni- versal adversarial perturbations,

K. R. Mopuri, U. Garg, and R. V. Babu, “Fast feature fool: A data independent approach to uni- versal adversarial perturbations,” arXiv preprint arXiv:1707.05572, 2017

2017 arXiv
[11]

Explainable artificial in- telligence: an analytical review,

P. P. Angelov, E. A. Soares, R. Jiang, N. I. Arnold, and P. M. Atkinson, “Explainable artificial in- telligence: an analytical review,” Wiley Interdis- ciplinary Reviews: Data Mining and Knowledge Discovery, vol. 11, no. 5, p. e1424, 2021

2021
[12]

Ex- ploring specialization and sensitivity of convolu- tional neural networks in the context of simul- taneous image augmentations,

P. Kharyuk, S. Matveev, and I. Oseledets, “Ex- ploring specialization and sensitivity of convolu- tional neural networks in the context of simul- taneous image augmentations,” arXiv preprint arXiv:2503.03283, 2025

2025
[13]

Using the ADAP learning algorithm to forecast the onset of diabetes mellitus,

J. W. Smith, J. E. Everhart, W. Dickson, W. C. Knowler, and R. S. Johannes, “Using the ADAP learning algorithm to forecast the onset of diabetes mellitus,” in Proceedings of the annual symposium on computer application in medical care , p. 261, American Medical Informatics Ass...

1988
[14]

Diabetes dataset,

M. Akturk, “Diabetes dataset,” Kaggle. com , 2020

2020
[15]

J. C. Spall, Introduction to stochastic search and optimization: estimation, simulation, and control . John Wiley & Sons, 2005

2005
[16]

Global sensitivity indices for nonlin- ear mathematical models and their Monte Carlo estimates,

I. M. Sobol, “Global sensitivity indices for nonlin- ear mathematical models and their Monte Carlo estimates,” Mathematics and computers in simu- lation, vol. 55, no. 1-3, pp. 271–280, 2001

2001
[17]

A fully multiple-criteria implementation of the sobol method for parameter sensitivity analysis,

R. Rosolem, H. V. Gupta, W. J. Shuttle- worth, X. Zeng, and L. G. G. de Gon¸ calves, “A fully multiple-criteria implementation of the sobol method for parameter sensitivity analysis,” Journal of Geophysical Research: Atmospheres , vol. 117, no. D7, 2012

2012
[18]

SALib: An open- source python library for sensitivity analysis,

J. Herman and W. Usher, “SALib: An open- source python library for sensitivity analysis,” Journal of Open Source Software , vol. 2, no. 9, p. 97, 2017

2017
[19]

On quasi-monte carlo integrations,

I. M. Sobol, “On quasi-monte carlo integrations,” Mathematics and computers in simulation, vol. 47, no. 2-5, pp. 103–112, 1998

1998
[20]

Sensitivity analysis of soil parameters in crop model supported with high-throughput computing,

M. Gasanov, A. Petrovskaia, A. Nikitin, S. Matveev, P. Tregubova, M. Pukalchik, and I. Oseledets, “Sensitivity analysis of soil parameters in crop model supported with high-throughput computing,” in International Conference on Computational Science , pp. 731– 741, Springer, 2020

2020
[21]

Sensitivity analysis of neural net- work models: Applying methods of analysis of finite fluctuations,

A. Sysoev, A. Ciurlia, R. Sheglevatych, and S. Blyumin, “Sensitivity analysis of neural net- work models: Applying methods of analysis of finite fluctuations,” Periodica polytechnica Elec- trical engineering and computer science , vol. 63, no. 4, pp. 306–311, 2019

2019
[22]

Sensi- tivity analysis of weather factors affecting pv mod- ule output power based on artificial neural net- work and sobol algorithm,

C. Zhang, Y. Zhang, J. Zhao, and J. Luo, “Sensi- tivity analysis of weather factors affecting pv mod- ule output power based on artificial neural net- work and sobol algorithm,” in 2020 IEEE/IAS Industrial and Commercial Power System Asia (I&CPS Asia), pp. 246–250, IEEE, 2020

2020
[23]

Very deep convolutional networks for large-scale image recognition,

K. Simonyan, “Very deep convolutional networks for large-scale image recognition,” arXiv preprint arXiv:1409.1556, 2014

2014 arXiv
[24]

Learning multiple layers of features from tiny images,

K. Alex, “Learning multiple layers of features from tiny images,” https://www. cs. toronto. edu/kriz/learning-features-2009-TR. pdf, 2009

2009
[25]

Neu- ralSens: Sensitivity Analysis of Neural Networks,

J. Pizarroso, J. Portela, and A. Mu˜ noz, “Neu- ralSens: Sensitivity Analysis of Neural Networks,” Journal of Statistical Software , vol. 102, no. 7, p. 1–36, 2022

2022
[26]

Do cifar-10 classifiers generalize to cifar-10?,

B. Recht, R. Roelofs, L. Schmidt, and V. Shankar, “Do cifar-10 classifiers generalize to cifar-10?,” arXiv preprint arXiv:1806.00451 , 2018

2018 arXiv
[27]

Fast gradient-free acti- vation maximization for neurons in spiking neural networks,

N. Pospelov, A. Chertkov, M. Beketov, I. Os- eledets, and K. Anokhin, “Fast gradient-free acti- vation maximization for neurons in spiking neural networks,” Neurocomputing, vol. 618, p. 129070, 2025

2025
[28]

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,” arXiv preprint arXiv:1312.6034 , 2013

2013 arXiv
[29]

Deep resid- ual learning for image recognition,

K. He, X. Zhang, S. Ren, and J. Sun, “Deep resid- ual learning for image recognition,” in Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 770–778, 2016

2016
[30]

Accelerating de- tection of lung pathologies with explainable ultra- sound image analysis,

J. Born, N. Wiedemann, M. Cossio, C. Buhre, G. Br¨ andle, K. Leidermann, J. Goulet, A. Au- jayeb, M. Moor, B. Rieck, et al., “Accelerating de- tection of lung pathologies with explainable ultra- sound image analysis,” Applied Sciences, vol. 11, no. 2, p. 672, 2021. 10

2021
[31]

Gan ran xing fei yan chao sheng zhen duan zhuan jia jian yi,

C. U. G. of Ultrasound Medicine Committee, C. M. E. Association, et al., “Gan ran xing fei yan chao sheng zhen duan zhuan jia jian yi,” Zhong Hua Yi Xue Chao Sheng Za Zhi(Dian Zi Ban) , vol. 17, no. 03, p. 244, 2020

2020
[32]

Grad-cam: Visual explanations from deep networks via gradient-based localization,

R. R. Selvaraju, M. Cogswell, A. Das, R. Vedan- tam, D. Parikh, and D. Batra, “Grad-cam: Visual explanations from deep networks via gradient-based localization,” in Proceedings of the IEEE international conference on computer vi- sion, pp. 618–626, 2017

2017
[33]

Explainable AI for clinical and remote health applications: a sur- vey on tabular and time series data,

F. Di Martino and F. Delmastro, “Explainable AI for clinical and remote health applications: a sur- vey on tabular and time series data,” Artificial Intelligence Review, vol. 56, no. 6, pp. 5261–5315, 2023

2023
[34]

Sobol tensor trains for global sensitiv- ity analysis,

R. Ballester-Ripoll, E. G. Paredes, and R. Pa- jarola, “Sobol tensor trains for global sensitiv- ity analysis,” Reliability Engineering & System Safety, vol. 183, pp. 311–322, 2019. 11

2019

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.

[1] [1]

Neural networks and physical sys- tems with emergent collective computational abil- ities.,

J. J. Hopfield, “Neural networks and physical sys- tems with emergent collective computational abil- ities.,” Proceedings of the national academy of sci- ences, vol. 79, no. 8, pp. 2554–2558, 1982

work page 1982

[2] [2]

Highly accurate protein structure prediction with AlphaFold,

J. Jumper, R. Evans, A. Pritzel, T. Green, M. Figurnov, O. Ronneberger, K. Tunyasuvu- nakool, R. Bates, A. ˇZ´ ıdek, A. Potapenko,et al., “Highly accurate protein structure prediction with AlphaFold,” nature, vol. 596, no. 7873, pp. 583– 589, 2021

work page 2021

[3] [3]

Video compression dataset and benchmark of learning- based video-quality metrics,

A. Antsiferova, S. Lavrushkin, M. Smirnov, A. Gushchin, D. Vatolin, and D. Kulikov, “Video compression dataset and benchmark of learning- based video-quality metrics,” Advances in Neu- ral Information Processing Systems , vol. 35, pp. 13814–13825, 2022

work page 2022

[4] [4]

Neural video compression using spatio-temporal priors,

H. Liu, T. Chen, M. Lu, Q. Shen, and Z. Ma, “Neural video compression using spatio-temporal priors,” arXiv preprint arXiv:1902.07383 , 2019

arXiv 1902

[5] [5]

Attention is all you need,

A. Vaswani, “Attention is all you need,” Advances in Neural Information Processing Systems , 2017

2017

[6] [6]

Employing fingerprinting of medicinal plants by means of lc-ms and machine learning for species identification task,

P. Kharyuk, D. Nazarenko, I. Oseledets, I. Rodin, O. Shpigun, A. Tsitsilin, and M. Lavrentyev, “Employing fingerprinting of medicinal plants by means of lc-ms and machine learning for species identification task,” Scientific reports , vol. 8, no. 1, p. 17053, 2018

work page 2018

[7] [7]

Overview of visualization methods for artificial neural networks,

S. A. Matveev, I. V. Oseledets, E. S. Ponomarev, and A. V. Chertkov, “Overview of visualization methods for artificial neural networks,” Compu- tational Mathematics and Mathematical Physics , vol. 61, no. 5, pp. 887–899, 2021. 9

work page 2021

[8] [8]

Hop- field networks is all you need,

H. Ramsauer, B. Sch¨ afl, J. Lehner, P. Seidl, M. Widrich, T. Adler, L. Gruber, M. Holzleit- ner, M. Pavlovi´ c, G. K. Sandve, et al. , “Hop- field networks is all you need,” arXiv preprint arXiv:2008.02217, 2020

arXiv 2008