{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T20:06:28Z","timestamp":1768421188611,"version":"3.49.0"},"reference-count":73,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2025,1,2]],"date-time":"2025-01-02T00:00:00Z","timestamp":1735776000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computers"],"abstract":"<jats:p>Despite the recent success of deep-learning models, traditional models are overconfident and poorly calibrated. This poses a serious problem when applied to high-stakes applications. To solve this issue, uncertainty quantification (UQ) models have been developed to allow the detection of misclassifications. Meta-model-based UQ methods are promising due to the lack of predictive model re-training and low resource requirement. However, there are still several issues present in the training process. (1) Most current meta-models are trained using hard labels that do not allow quantification of the uncertainty associated with a given data sample; and (2) in most cases, the base model has a high test accuracy. Therefore, the samples used to train the meta-model primarily consist of correctly classified samples. This leads the meta-model to learn a poor approximation of the true decision boundary. To address these problems, we propose a novel soft-label formulation that better differentiates between correct and incorrect classifications, thereby allowing the meta-model to distinguish between correct and incorrect classifications with high uncertainty (i.e., low confidence). In addition, a novel training framework using adversarial samples is proposed to explore the decision boundary of the base model and mitigate issues related to training datasets with label imbalance. To validate the effectiveness of our approach, we use two predictive models trained on SVHN and CIFAR10 and evaluate performance according to sensitivity, specificity, an F1-score-style metric, average precision, and the Area Under the Receiver Operating Characteristic curve. We find the soft-label approach can significantly increase the model\u2019s sensitivity and specificity, while the training with adversarial samples can noticeably improve the balance between sensitivity and specificity. We also compare our method against four state-of-the-art meta-model-based UQ methods, where we achieve significantly better performance than most models.<\/jats:p>","DOI":"10.3390\/computers14010012","type":"journal-article","created":{"date-parts":[[2025,1,2]],"date-time":"2025-01-02T06:05:10Z","timestamp":1735797910000},"page":"12","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Soft-Label Supervised Meta-Model with Adversarial Samples for Uncertainty Quantification"],"prefix":"10.3390","volume":"14","author":[{"given":"Kyle","family":"Lucke","sequence":"first","affiliation":[{"name":"Department of Computer Science, University of Idaho, Idaho Falls, ID 83402, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3365-1291","authenticated-orcid":false,"given":"Aleksandar","family":"Vakanski","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Idaho, Idaho Falls, ID 83402, USA"},{"name":"Department of Nuclear Engineering and Industrial Management, University of Idaho, Idaho Falls, ID 83402, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6098-4441","authenticated-orcid":false,"given":"Min","family":"Xian","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Idaho, Idaho Falls, ID 83402, USA"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1259","DOI":"10.1038\/s41467-021-21466-z","article-title":"Ensembled deep learning model outperforms human experts in diagnosing biliary atresia from sonographic gallbladder images","volume":"12","author":"Zhou","year":"2021","journal-title":"Nat. Commun."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"He, K., Zhang, X., Ren, S., and Sun, J. (2015, January 7\u201313). Delving deep into rectifiers: Surpassing human-level performance on imagenet classification. Proceedings of the IEEE International Conference on Computer Vision, Santiago, Chile.","DOI":"10.1109\/ICCV.2015.123"},{"key":"ref_3","unstructured":"Bengio, S., Wallach, H., Larochelle, H., Grauman, K., Cesa-Bianchi, N., and Garnett, R. (2018, January 3\u20138). Generalisation in humans and deep neural networks. Proceedings of the 32nd International Conference on Neural Information Processing Systems, Montr\u00e9al, QC, Canada. Advances in Neural Information Processing."},{"key":"ref_4","first-page":"15288","article-title":"Calibrating deep neural networks using focal loss","volume":"33","author":"Mukhoti","year":"2020","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_5","unstructured":"Chen, T., Navratil, J., Iyengar, V., and Shanmugam, K. (2019, January 16\u201318). Confidence Scoring Using Whitebox Meta-models with Linear Classifier Probes. Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, Naha, Okinawa, Japan. Proceedings of Machine Learning Research."},{"key":"ref_6","unstructured":"Aigrain, J., and Detyniecki, M. (2019, January 9\u201315). Detecting adversarial examples and other misclassifications in neural networks by introspection. Proceedings of the International Conference on Machine Learning Workshop on Uncertainty and Robustness in Deep Learning, Long Beach, CA, USA."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"He, K., Zhang, X., Ren, S., and Sun, J. (2016, January 27\u201330). Deep residual learning for image recognition. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Las Vegas, NV, USA.","DOI":"10.1109\/CVPR.2016.90"},{"key":"ref_8","unstructured":"Blundell, C., Cornebise, J., Kavukcuoglu, K., and Wierstra, D. (2015, January 6\u201311). Weight uncertainty in neural networks. Proceedings of the International Conference on Machine Learning, Lille, France."},{"key":"ref_9","unstructured":"Gal, Y., and Ghahramani, Z. (2016, January 20\u201322). Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning. Proceedings of the 33rd International Conference on Machine Learning, New York, NY, USA. Proceedings of Machine Learning Research."},{"key":"ref_10","unstructured":"Lakshminarayanan, B., Pritzel, A., and Blundell, C. (2017, January 4\u20139). Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles. Proceedings of the 31st Conference on Neural Information Processing Systems (NIPS 2017), Long Beach, CA, USA. Advances in Neural Information Processing Systems."},{"key":"ref_11","first-page":"1010","article-title":"Bayesian deep ensembles via the neural tangent kernel","volume":"33","author":"He","year":"2020","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_12","first-page":"4697","article-title":"Bayesian deep learning and a probabilistic perspective of generalization","volume":"33","author":"Wilson","year":"2020","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Durasov, N., Bagautdinov, T., Baque, P., and Fua, P. (2021, January 20\u201325). Masksembles for uncertainty estimation. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Nashville, TN, USA.","DOI":"10.1109\/CVPR46437.2021.01333"},{"key":"ref_14","first-page":"4264","article-title":"Maximizing Overall Diversity for Improved Uncertainty Estimates in Deep Ensembles","volume":"34","author":"Jain","year":"2020","journal-title":"Proc. AAAI Conf. Artif. Intell."},{"key":"ref_15","first-page":"15152","article-title":"Toward Robust Uncertainty Estimation with Random Activation Functions","volume":"37","author":"Stoyanova","year":"2023","journal-title":"Proc. AAAI Conf. Artif. Intell."},{"key":"ref_16","unstructured":"Wen, Y., Tran, D., and Ba, J. (May, January 26). BatchEnsemble: An Alternative Approach to Efficient Ensemble and Lifelong Learning. Proceedings of the International Conference on Learning Representations, Online."},{"key":"ref_17","unstructured":"Laurent, O., Lafage, A., Tartaglione, E., Daniel, G., Marc Martinez, J., Bursuc, A., and Franchi, G. (2023, January 1\u20135). Packed Ensembles for efficient uncertainty estimation. Proceedings of the Eleventh International Conference on Learning Representations, Kigali, Rwanda."},{"key":"ref_18","unstructured":"Havasi, M., Jenatton, R., Fort, S., Liu, J.Z., Snoek, J., Lakshminarayanan, B., Dai, A.M., and Tran, D. (2021, January 4). Training independent subnetworks for robust prediction. Proceedings of the International Conference on Learning Representations, Vienna, Austria."},{"key":"ref_19","unstructured":"Van Amersfoort, J., Smith, L., Teh, Y.W., and Gal, Y. (2020, January 13\u201318). Uncertainty estimation using a single deep deterministic neural network. Proceedings of the International Conference on Machine Learning, Online."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Mukhoti, J., Kirsch, A., van Amersfoort, J., Torr, P.H., and Gal, Y. (2023, January 17\u201324). Deep Deterministic Uncertainty: A New Simple Baseline. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Los Alamitos, CA, USA.","DOI":"10.1109\/CVPR52729.2023.02336"},{"key":"ref_21","first-page":"7498","article-title":"Simple and principled uncertainty estimation with deterministic deep learning via distance awareness","volume":"33","author":"Liu","year":"2020","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_22","unstructured":"van Amersfoort, J., Smith, L., Jesson, A., Key, O., and Gal, Y. (2021, January 6\u201314). On Feature Collapse and Deep Kernel Learning for Single Forward Pass Uncertainty. Proceedings of the Thirty-Fifth Conference on Neural Information Processing Systems Bayesian Deep Learning Workshop, Online."},{"key":"ref_23","unstructured":"Miyato, T., Kataoka, T., Koyama, M., and Yoshida, Y. (May, January 30). Spectral Normalization for Generative Adversarial Networks. Proceedings of the International Conference on Learning Representations, Vancouver, BC, Canada."},{"key":"ref_24","first-page":"5769","article-title":"Improved training of wasserstein gans","volume":"30","author":"Gulrajani","year":"2017","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_25","unstructured":"Arjovsky, M., Chintala, S., and Bottou, L. (2017, January 6\u201311). Wasserstein Generative Adversarial Networks. Proceedings of the 34th International Conference on Machine Learning, PMLR, Sydney, Australia. Proceedings of Machine Learning Research."},{"key":"ref_26","unstructured":"Sehwag, V., Chiang, M., and Mittal, P. (2021, January 4). SSD: A Unified Framework for Self-Supervised Outlier Detection. Proceedings of the International Conference on Learning Representations, Vienna, Austria."},{"key":"ref_27","first-page":"S1","article-title":"On the Generalised Distance in Statistics (Reprint, 2018)","volume":"80","author":"Mahalanobis","year":"1936","journal-title":"Sankhya A"},{"key":"ref_28","unstructured":"Corbi\u00e8re, C., THOME, N., Bar-Hen, A., Cord, M., and P\u00e9rez, P. (2019, January 8\u201314). Addressing Failure Prediction by Learning Model Confidence. Proceedings of the Advances in Neural Information Processing Systems, Vancouver, BC, Canada."},{"key":"ref_29","first-page":"9772","article-title":"Post-hoc Uncertainty Learning Using a Dirichlet Meta-Model","volume":"37","author":"Shen","year":"2023","journal-title":"Proc. AAAI Conf. Artif. Intell."},{"key":"ref_30","unstructured":"Alain, G., and Bengio, Y. (2017, January 24\u201326). Understanding intermediate layers using linear classifier probes. Proceedings of the International Conference on Learning Representations, Toulon, France."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1189","DOI":"10.1214\/aos\/1013203451","article-title":"Greedy function approximation: A gradient boosting machine","volume":"29","author":"Friedman","year":"2001","journal-title":"Ann. Stat."},{"key":"ref_32","unstructured":"Joo, T., Chung, U., and Seo, M.G. (2020, January 13\u201318). Being Bayesian about Categorical Probability. Proceedings of the 37th International Conference on Machine Learning, Online. Proceedings of Machine Learning Research."},{"key":"ref_33","first-page":"8017","article-title":"Detecting Misclassification Errors in Neural Networks with a Gaussian Process Model","volume":"36","author":"Qiu","year":"2022","journal-title":"Proc. AAAI Conf. Artif. Intell."},{"key":"ref_34","first-page":"514","article-title":"Gaussian processes for regression","volume":"8","author":"Williams","year":"1995","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_35","unstructured":"Hendrycks, D., and Gimpel, K. (2017, January 24\u201326). A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks. Proceedings of the International Conference on Learning Representations, Toulon, France."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"6390","DOI":"10.1109\/TNNLS.2021.3136503","article-title":"DeepSMOTE: Fusing Deep Learning and SMOTE for Imbalanced Data","volume":"34","author":"Dablain","year":"2023","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Sahoo, A., Singh, A., Panda, R., Feris, R., and Das, A. (2020, January 23\u201328). Mitigating Dataset Imbalance via Joint Generation and Classification. Proceedings of the ECCV Workshop on Imbalance Problems in Computer Vision, Glasgow, UK.","DOI":"10.1007\/978-3-030-65414-6_14"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Qu, H., Li, Y., Foo, L.G., Kuen, J., Gu, J., and Liu, J. (2022, January 23\u201327). Improving the reliability for confidence estimation. Proceedings of the European Conference on Computer Vision, Tel Aviv, Israel.","DOI":"10.1007\/978-3-031-19812-0_23"},{"key":"ref_39","first-page":"21533","article-title":"Learning to predict trustworthiness with steep slope loss","volume":"34","author":"Luo","year":"2021","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_40","unstructured":"Lee, K., Lee, H., Lee, K., and Shin, J. (May, January 30). Training Confidence-calibrated Classifiers for Detecting Out-of-Distribution Samples. Proceedings of the International Conference on Learning Representations, Vancouver, BC, Canada."},{"key":"ref_41","first-page":"21371","article-title":"UQGAN: A Unified Model for Uncertainty Quantification of Deep Classifiers trained via Conditional GANs","volume":"Volume 35","author":"Oberdiek","year":"2022","journal-title":"Proceedings of the Advances in Neural Information Processing Systems"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Tang, K., Miao, D., Peng, W., Wu, J., Shi, Y., Gu, Z., Tian, Z., and Wang, W. (2021, January 10\u201317). CODEs: Chamfer Out-of-Distribution Examples Against Overconfidence Issue. Proceedings of the IEEE\/CVF International Conference on Computer Vision (ICCV), Los Alamitos, CA, USA.","DOI":"10.1109\/ICCV48922.2021.00119"},{"key":"ref_43","unstructured":"Hendrycks, D., Mazeika, M., and Dietterich, T. (2019, January 6\u20139). Deep Anomaly Detection with Outlier Exposure. Proceedings of the International Conference on Learning Representations, New Orleans, LA, USA."},{"key":"ref_44","unstructured":"Wang, Q., Ye, J., Liu, F., Dai, Q., Kalander, M., Liu, T., HAO, J., and Han, B. (2023, January 1\u20135). Out-of-distribution Detection with Implicit Outlier Transformation. Proceedings of the Eleventh International Conference on Learning Representations, Kigali, Rwanda."},{"key":"ref_45","unstructured":"Arjovsky, M., and Bottou, L. (2017, January 24\u201326). Towards Principled Methods for Training Generative Adversarial Networks. Proceedings of the International Conference on Learning Representations, Toulon, France."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Yang, J., Wang, H., Feng, L., Yan, X., Zheng, H., Zhang, W., and Liu, Z. (2021, January 10\u201317). Semantically Coherent Out-of-Distribution Detection. Proceedings of the IEEE\/CVF International Conference on Computer Vision (ICCV), Los Alamitos, CA, USA.","DOI":"10.1109\/ICCV48922.2021.00819"},{"key":"ref_47","unstructured":"Du, X., Wang, Z., Cai, M., and Li, Y. (2022, January 25\u201329). VOS: Learning What You Don\u2019t Know by Virtual Outlier Synthesis. Proceedings of the International Conference on Learning Representations, Virtual."},{"key":"ref_48","first-page":"14608","article-title":"Using Mixup as a Regularizer Can Surprisingly Improve Accuracy & Out-of-Distribution Robustness","volume":"Volume 35","author":"Pinto","year":"2022","journal-title":"Proceedings of the Advances in Neural Information Processing Systems"},{"key":"ref_49","unstructured":"Sun, Y., Ming, Y., Zhu, X., and Li, Y. (2022, January 17\u201323). Out-of-distribution Detection with Deep Nearest Neighbors. Proceedings of the 39th International Conference on Machine Learning, Baltimore, MD, USA."},{"key":"ref_50","first-page":"36308","article-title":"Nonparametric uncertainty quantification for single deterministic neural network","volume":"35","author":"Kotelevskii","year":"2022","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_51","unstructured":"Northcutt, C.G., Athalye, A., and Mueller, J. (2021, January 6\u201316). Pervasive Label Errors in Test Sets Destabilize Machine Learning Benchmarks. Proceedings of the 35th Conference on Neural Information Processing Systems Track on Datasets and Benchmarks, Virtual Event."},{"key":"ref_52","unstructured":"V\u0103dineanu, \u015e., Pelt, D.M., Dzyubachyk, O., and Batenburg, K.J. (2022, January 6\u20138). An analysis of the impact of annotation errors on the accuracy of deep learning for cell segmentation. Proceedings of the International Conference on Medical Imaging with Deep Learning, PMLR, Zurich, Switzerland."},{"key":"ref_53","unstructured":"Hinton, G., Vinyals, O., and Dean, J. (2014, January 8\u201313). Distilling the knowledge in a neural network. Proceedings of the The Twenty-Eighth Annual Conference on Neural Information Processing Systems Deep Learning Workshop, Montr\u00e9al, QC, Canada."},{"key":"ref_54","unstructured":"Goodfellow, I.J., Shlens, J., and Szegedy, C. (2015, January 7\u20139). Explaining and harnessing adversarial examples. Proceedings of the International Conference on Learning Representations, San Diego, CA, USA."},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Chen, J., and Gu, Q. (2020, January 6\u201310). RayS: A Ray Searching Method for Hard-label Adversarial Attack. Proceedings of the 26rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Virtual Event.","DOI":"10.1145\/3394486.3403225"},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Ma, Y., Lucke, K., Xian, M., and Vakanski, A. (2024). Semantic-Aware Adaptive Binary Search for Hard-Label Black-Box Attack. Computers, 13.","DOI":"10.3390\/computers13080203"},{"key":"ref_57","unstructured":"Netzer, Y., Wang, T., Coates, A., Bissacco, A., Wu, B., and Ng, A.Y. (2011, January 16). Reading digits in natural images with unsupervised feature learning. Proceedings of the NIPS Workshop on Deep Learning and Unsupervised Feature Learning, Granada, Spain."},{"key":"ref_58","unstructured":"Krizhevsky, A., and Hinton, G. (2009). Learning Multiple Layers of Features from Tiny Images, University of Toronto. Technical Report."},{"key":"ref_59","doi-asserted-by":"crossref","unstructured":"Baeza-Yates, R., and Ribeiro-Neto, B. (2011). Modern Information Retrieval, Addison Wesley.","DOI":"10.1145\/2009916.2010172"},{"key":"ref_60","unstructured":"Ruder, S. (2016). An overview of gradient descent optimization algorithms. arXiv."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1111\/j.2517-6161.1952.tb00104.x","article-title":"Rational Decisions","volume":"14","author":"Good","year":"1952","journal-title":"J. R. Stat. Society. Ser. B (Methodol.)"},{"key":"ref_62","unstructured":"Kingma, D.P. (2015, January 7\u20139). Adam: A method for stochastic optimization. Proceedings of the International Conference for Learning Representations, San Diego, CA, USA."},{"key":"ref_63","first-page":"1929","article-title":"Dropout: A Simple Way to Prevent Neural Networks from Overfitting","volume":"15","author":"Srivastava","year":"2014","journal-title":"J. Mach. Learn. Res."},{"key":"ref_64","unstructured":"Glorot, X., Bordes, A., and Bengio, Y. (2011, January 11\u201313). Deep Sparse Rectifier Neural Networks. Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics, Fort Lauderdale, FL, USA. Proceedings of Machine Learning Research."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1007\/BF02295996","article-title":"Note on the sampling error of the difference between correlated proportions or percentages","volume":"12","author":"McNemar","year":"1947","journal-title":"Psychometrika"},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1007\/BF02289261","article-title":"Note on the \u201ccorrection for continuity\u201d in testing the significance of the difference between correlated proportions","volume":"13","author":"Edwards","year":"1948","journal-title":"Psychometrika"},{"key":"ref_67","unstructured":"Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., and Antiga, L. (2019, January 8\u201314). PyTorch: An imperative style, high-performance deep learning library. Proceedings of the 33rd International Conference on Neural Information Processing Systems, Vancouver, BC, Canada."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"638","DOI":"10.21105\/joss.00638","article-title":"MLxtend: Providing machine learning and data science utilities and extensions to Python\u2019s scientific computing stack","volume":"3","author":"Raschka","year":"2018","journal-title":"J. Open Source Softw."},{"key":"ref_69","doi-asserted-by":"crossref","unstructured":"Sun, S., Xian, M., Vakanski, A., and Ghanem, H. (2022, January 18\u201322). MIRST-DM: Multi-instance RST with drop-max layer for robust classification of breast cancer. Proceedings of the International Conference on Medical Image Computing and Computer-Assisted Intervention, Singapore.","DOI":"10.1007\/978-3-031-16440-8_39"},{"key":"ref_70","doi-asserted-by":"crossref","unstructured":"Deng, J., Dong, W., Socher, R., Li, L.J., Li, K., and Fei-Fei, L. (2009, January 20\u201325). ImageNet: A large-scale hierarchical image database. Proceedings of the 2009 IEEE Conference on Computer Vision and Pattern Recognition, Miami, FL, USA.","DOI":"10.1109\/CVPR.2009.5206848"},{"key":"ref_71","doi-asserted-by":"crossref","unstructured":"Cui, Y., Song, Y., Sun, C., Howard, A., and Belongie, S. (2018, January 18\u201323). Large scale fine-grained categorization and domain-specific transfer learning. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Salt Lake City, UT, USA.","DOI":"10.1109\/CVPR.2018.00432"},{"key":"ref_72","unstructured":"Gupta, K., Pesquet-Popescu, B., Kaakai, F., Pesquet, J.C., and Malliaros, F.D. (2021, January 19\u201320). An adversarial attacker for neural networks in regression problems. Proceedings of the IJCAI Workshop on Artificial Intelligence Safety (AI Safety), Virtual Event."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"7827","DOI":"10.1109\/TSMC.2023.3302838","article-title":"Adversarial Attacks on Regression Systems via Gradient Optimization","volume":"53","author":"Kong","year":"2023","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."}],"container-title":["Computers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-431X\/14\/1\/12\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T15:23:38Z","timestamp":1759850618000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-431X\/14\/1\/12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,2]]},"references-count":73,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,1]]}},"alternative-id":["computers14010012"],"URL":"https:\/\/doi.org\/10.3390\/computers14010012","relation":{},"ISSN":["2073-431X"],"issn-type":[{"value":"2073-431X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,1,2]]}}}