Abstract
Modern algorithms based on artificial neural networks (ANNs) are extremely useful in solving a variety of complicated problems in computer vision, robust control, and natural language analysis of sound and texts as applied to data processing, robotics, etc. However, for the ANN approach to be successfully incorporated into critically important systems, for example, in medicine or jurisprudence, a clear interpretation is required for the internal architecture of ANN and for ANN-based decision-making processes. In recent years, analysis methods based on various visualization techniques applied to computation graphs, loss function profiles, parameters of single network layers, and even single neurons have become especially popular as tools for creating explainable deep learning models. This survey systematizes existing mathematical analysis methods and explanations of the behavior of underlying algorithms and presents formulations of corresponding problems in computational mathematics. The study and visualization of deep neural networks are new poorly studied yet rapidly developing areas. The considered methods give a deeper insight into the operation of neural network algorithms.
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REFERENCES
Y. LeCun, Y. Bengio, and G. Hinton, “Deep learning,” Nature 521, 436–444 (2015).
N. Shahid, T. Rappon, and W. Berta, “Applications of artificial neural networks in health care organizational decision-making: A scoping review,” PLoS ONE 14 (2), e0212356 (2019).
A. B. Nassif, I. Shahin, I. Attili, M. Azzeh, and K. Shaalan, “Speech recognition using deep neural networks: A systematic review,” IEEE Access 7, 19143–19165 (2019).
H. H. Alkinani, A. T. T. Al-Hameedi, S. Dunn-Norman, R. E. Flori, M. T. Alsaba, and A. S. Amer, “Applications of artificial neural networks in the petroleum industry: A review,” SPE Middle East Oil and Gas Show and Conference (Society of Petroleum Engineers, 2019).
E. Tjoa and C. Guan, “A survey on explainable artificial intelligence (XAI): Toward medical XAI,” Proceedings of the IEEE Transactions on Neural Networks and Learning Systems (2020).
F. Xu, H. Uszkoreit, Y. Du, W. Fan, D. Zhao, and J. Zhu, “Explainable AI: A brief survey on history, research areas, approaches and challenges,” CCF International Conference on Natural Language Processing and Chinese Computing (2019), pp. 563–574.
Explainable AI: Interpreting, Explaining, and Visualizing Deep Learning, Ed. by W. Samek, G. Montavon, A. Vedaldi, L. K. Hansen, and K.-R. Müller (Springer, Berlin, 2019).
Z. C. Lipton, “The mythos of model interpretability,” Queue 16 (3), 31–57 (2018).
N. Cowan, “The many faces of working memory and short-term storage,” Psychon. Bull. Rev. 24 (4), 1158–1170 (2017).
K. Anokhin, O. Ivashkina, K. Toropova, A. Gruzdeva, O. B. Rogozhnikova, V. Plushnin, and I. Fedotov, “Neuronal encoding of object-type and object-place memories in hippocampus and neocortex of young and old mice,” FASEB J. 34 (S1), 1 (2020).
P. Zhigulina, V. Ushakov, S. Kartashov, D. Malakhov, V. Orlov, K. Novikov, A. Korotkova, K. Anokhin, and V. Nourkova, “The architecture of neural networks for enhanced autobiographical memory access: A functional MRI study,” Proc. Comput. Sci. 169, 787–794 (2020).
A. A. Tiunova, N. V. Komissarova, and K. V. Anokhin, “Mapping the neural substrates of recent and remote visual imprinting memory in the chick brain,” Frontiers Physiol. 10, 351–351 (2019).
J. H. Marshel, Y. S. Kim, T. A. Machado, S. Quirin, B. Benson, J. Kadmon, C. Raja, A. Chibukhchyan, C. Ramakrishnan, and M. Inoue, “Cortical layer-specific critical dynamics triggering perception,” Science 365 (6453) (2019).
D. Erhan, Y. Bengio, A. Courville, and P. Vincent, “Visualizing higher-layer features of a deep network,” Technical Report, ICML 2009 Workshop on Learning Feature Hierarchies (Montréal, Canada, 2009).
D. Hubel and T. Wiesel, “Receptive fields of single neurons in the cat’s striate cortex,” J. Physiol. 148, 574–591 (1959).
A. Nguyen, J. Yosinski, and J. Clune, “Understanding neural networks via feature visualization: A survey,” in Explainable AI: Interpreting, Explaining, and Visualizing Deep Learning (2019), pp. 55–76.
A. Nguyen, A. Dosovitskiy, J. Yosinski, T. Brox, and J. Clune, “Synthesizing the preferred inputs for neurons in neural networks via deep generator networks,” Advances in Neural Information Processing Systems 30 (2016), pp. 3395–3403.
K. Simonyan, A. Vedaldi, and A. Zisserman, “Deep inside convolutional networks: Visualizing image classification models and saliency maps,” Workshop at International Conference on Learning Representations (2014).
J. Yosinski, J. Clune, A. Nguyen, T. Fuchs, and H. Lipson, “Understanding neural networks through deep visualization,” Deep Learning Workshop at ICML 2015 (2015).
D. Wei, B. Zhou, A. Torrabla, and W. Freeman, “Understanding intra-class knowledge inside CNN” (2015). https://arxiv.org/abs/1507.02379.
A. Mahendran and A. Vedaldi, “Visualizing deep convolutional neural networks using natural pre-images,” Int. J. Comput. Vision 120 (3), 233–255 (2016).
A. Nguyen, J. Yosinski, and J. Clune, “Multifaceted feature visualization: Uncovering the different types of features learned by each neuron in deep neural networks” (2016). https://arxiv.org/abs/1602.03616.
I. J. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y. Bengio, “Generative adversarial nets,” Proceedings of the 27th International Conference on Neural Information Processing Systems (2014), Vol. 2, pp. 2672–2680.
S. Lapuschkin, S. Wӓldchen, A. Binder, G. Montavon, W. Samek, and K.-R. Müller, “Unmasking Clever Hans predictors and assessing what machines really learn,” Nat. Commun. 10 (1) (2019). https://doi.org/10.1038/s41467-019-08987-4
M. Everingham, S. M. A. Eslami, L. Van Gool, C. K. I. Williams, J. Winn, and A. Zisserman, “The Pascal visual object classes challenge: A retrospective,” Int. J. Comput. Vision 111 (1), 98–136 (2015).
S. Lapuschkin, A. Binder, G. Montavon, F. Klauschen, K.-R. Müller, and W. Samek, “On pixel-wise explanations for non-linear classifier decisions by layer-wise relevance propagation,” PLoS ONE 10 (2015).
W. Samek, T. Wiegand, and K.-R. Müller, “Explainable artificial intelligence: Understanding, visualizing, and interpreting deep learning models,” ITU J. ICT Discoveries 1, 39–48 (2019).
W. Samek, A. Binder, G. Montavon, S. Lapushckin, and K.-R. Müller, “Evaluating the visualization of what a deep neural network has learned,” IEEE Trans. Neural Networks Learn. Syst. 28 (11), 2660–2673 (2017).
A. Shrikumar, P. Greenside, and A. Kundaje, “Learning important features through propagating activation differences,” Proceedings of the 34th International Conference on Machine Learning, PLMR (2017), pp. 3145–3153.
J. T. Springenberg, A. Dosovitskiy, T. Brox, and R. Riedmiller, “Striving for simplicity: The all convolutional net” (2014). https://arxiv.org/abs/1412.6806.
M. Sundararajan, A. Taly, and Q. Yan, “Axiomatic attribution for deep networks,” Proceedings of the International Conference on Machine Learning, ICML (2017), pp. 3319–3328.
D. Smilkov, N. Thorat, B. Kim, F. Viégas, and M. Wattenberg, “Smoothgrad: Removing noise by adding noise,” Workshop on Visualization for Deep Learning, ICML (2017).
B. Zhou, A. Khosla, A. Lapedriza, A. Oliva, and A. Torralba, “Learning deep features for discriminative localization,” Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (2016), pp. 2921–2929.
R. R. Selvaraju, M. Cogswell, A. Das, R. Vedantam, D. Parikh, and D. Batra, “Grad-CAM: Visual explanations from deep networks via gradient-based localization,” Proceedings of the IEEE International Conference on Computer Vision (2017), pp. 618–626.
H. Wang, Z. Wang, M. Du, F. Yang, Z. Zhang, S. Ding, P. Mardziel, and X. Hu, “Score-CAM: Score-weighted visual explanations for convolutional neural networks,” Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (2020), pp. 24–25.
S. M. Lundberg and S.-I. Lee, “A unified approach to interpreting model predictions,” Advances in Neural Information Processing Systems 30 (2017), pp. 4765–4774.
M. D. Zeiler and R. Fergus, “Visualizing and understanding convolutional networks,” European Conference on Computer Vision (Springer, 2014), pp. 818–833.
A. Choromanska, M. Henaff, M. Mathieu, G. B. Arous, and Y. LeCun, “The loss surfaces of multilayer networks,” J. Mach. Learn. Res. 38, 192–204 (2015).
H. Li, Z. Xu, G. Taylor, C. Studer, and T. Goldstein, “Visualizing the loss landscape of neural nets,” Advances in Neural Information Processing Systems 31 (2018), pp. 6389–6399.
L. Dinh, R. Pascanu, S. Bengio, and Y. Bengio, “Sharp minima can generalize for deep nets,” Proceedings of the 34th International Conference on Machine Learning (PMLR) (2017), pp. 1019–1028.
N. S. Keskar, D. Mudigere, J. Nocedal, M. Smelyanskiy, and P. T. P. Tang, “On large-batch training for deep learning: Generalization gap and sharp minima,” 5th International Conference on Learning Representations (ICLR) (2017).
I. J. Goodfellow, O. Vinyals, and A. M. Saxe, “Qualitatively characterizing neural network optimization problems,” International Conference on Learning Representations (2015).
D. J. Im, M. Tao, and K. Branson, “An empirical analysis of deep network loss surfaces” (2016). https://arxiv.org/abs/1612.04010.
M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, “TensorFlow: Large-scale machine learning on heterogeneous systems” (2016). https://arxiv.org/abs/1603.04467.
A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antiga, A. Desmaison, A. Kopf, E. Yang, Z. DeVito, M. Raison, A. Tejani, S. Chilamkurthy, B. Steiner, L. Fang, J. Bai, and S. Chintala, “Pytorch: An imperative style, high-performance deep learning library,” Advances in Neural Information Processing Systems 32 (2019), pp. 8024–8035.
A. Kapishnikov, T. Bolukbasi, F. Viégas, and M. Terry, “Xrai: Better attributions through regions,” Proceedings of the IEEE International Conference on Computer Vision (2019), pp. 4948–4957.
B. Kim, M. Wattenberg, J. Gilmer, C. Cai, J. Wexler, F. Viegas, et al., “Interpretability beyond feature attribution: Quantitative testing with concept activation vectors (TCAV),” International Conference on Machine Learning (PMLR) (2018), pp. 2668–2677.
S. Liu, X. Wang, M. Liu, and J. Zhu, “Towards better analysis of machine learning models: A visual analytics perspective,” Visual Inf. 1 (1), 48–56 (2017).
C. Seifert, A. Aamir, A. Balagopalan, D. Jain, A. Sharma, S. Grottel, and S. Gumhold, “Visualizations of deep neural networks in computer vision: A survey,” Transparent Data Mining for Big and Small Data (2017), pp. 123–144.
R. Yu and L. Shi, “A user-based taxonomy for deep learning visualization,” Visual Inf. 2 (3), 147–154 (2018).
Q.-S. Zhang and S.-C. Zhu, “Visual interpretability for deep learning: A survey,” Front. Inf. Technol. Electron. Eng. 19 (1), 27–39 (2018).
Z. Qin, F. Yu, C. Liu, and X. Chen, “How convolutional neural network see the world: A survey of convolutional neural network visualization methods,” Math. Found. Comput. 1 (2), 149–180 (2018).
J. Choo and S. Liu, “Visual analytics for explainable deep learning,” IEEE Comput. Graphics Appl. 38 (4), 84–92 (2018).
F. Hohman, M. Kahng, R. Pienta, and D. H. Chau, “Visual analytics in deep learning: An interrogative survey for the next frontiers,” IEEE Trans. Visualization Comput. Graphics 25 (8), 2674–2693 (2018).
R. Garcia, A. C. Telea, B. C. da Silva, J. Tørresen, and J. L. D. Comba, “A task-and-technique centered survey on visual analytics for deep learning model engineering,” Comput. Graphics 77, 30–49 (2018).
J. Yuan, C. Chen, W. Yang, M. Liu, J. Xia, and S. Liu, “A survey of visual analytics techniques for machine learning,” Comput. Visual Media 7, 3–36 (2021).
A. Chatzimparmpas, R. M. Martins, I. Jusufi, and A. Kerren, “A survey of surveys on the use of visualization for interpreting machine learning models,” Inf. Visualization 19 (3), 207–233 (2020).
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This work was supported by the Ministry of Science and Higher Education of the Russian Federation, grant no. 075-15-2020-801.
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Matveev, S.A., Oseledets, I.V., Ponomarev, E.S. et al. Overview of Visualization Methods for Artificial Neural Networks. Comput. Math. and Math. Phys. 61, 887–899 (2021). https://doi.org/10.1134/S0965542521050134
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DOI: https://doi.org/10.1134/S0965542521050134