收缩、分离和聚合: 面向长尾视觉识别的特征平衡方法

杨佳鑫; 于淼淼; 李虹颖; 李硕豪; 范灵毓; 张军

doi:10.16383/j.aas.c230288

收缩、分离和聚合: 面向长尾视觉识别的特征平衡方法

doi: 10.16383/j.aas.c230288

杨佳鑫^{1, 2,},
于淼淼^{1, 2,},
李虹颖^{1, 2,},
李硕豪^{1, 2,},
范灵毓^3,,
张军^{1, 2,}

1.
国防科技大学系统工程学院长沙 410073
2.
大数据与决策实验室长沙 410073
3.
中国人民解放军 96962 部队北京 102206

基金项目: 国家自然科学基金 (62101571), 湖南省自然科学基金 (2021JJ40685)资助

详细信息

作者简介:
杨佳鑫：国防科技大学系统工程学院硕士研究生. 主要研究方向为长尾识别技术. E-mail: yangjiaxin21@nudt.edu.cn

于淼淼：国防科技大学系统工程学院博士研究生. 主要研究方向为人脸伪造检测. E-mail: yumiaomiaonudt@nudt.edu.cn

李虹颖：国防科技大学系统工程学院硕士研究生. 主要研究方向为对抗攻击. E-mail: lihongying@nudt.edu.cn

李硕豪：国防科技大学系统工程学院副教授. 主要研究方向为场景图生成. E-mail: lishuohao@nudt.edu.cn

范灵毓：中国人民解放军96962部队工程师. 主要研究方向为伪装目标检测与分析. E-mail: 13810576175@139.com

张军：国防科技大学系统工程学院教授. 主要研究方向为视觉数据计算与分析. 本文通信作者. E-mail: zhangjun1975@nudt.edu.cn

计量
- 文章访问数: 434
- HTML全文浏览量: 287
- PDF下载量: 168
- 被引次数: 0
出版历程
- 收稿日期: 2023-05-18
- 录用日期: 2023-11-03
- 网络出版日期: 2024-04-23
- 刊出日期: 2024-05-29

Shrink, Separate and Aggregate: A Feature Balancing Method for Long-tailed Visual Recognition

YANG Jia-Xin^{1, 2
,},
YU Miao-Miao^{1, 2
,},
LI Hong-Ying^{1, 2
,},
LI Shuo-Hao^{1, 2
,},
FAN Ling-Yu^3
,,
ZHANG Jun^{1, 2
,}

1.
College of System Engineering, National University of Defense Technology, Changsha 410073
2.
Laboratory for Big Data and Decision, Changsha 410073
3.
Unit 96962 of the PLA, Beijing 102206

Funds: Supported by National Natural Science Foundation of China (62101571) and Natural Science Foundation of Hunan Province (2021JJ40685)

More Information

Author Bio:
YANG Jia-Xin　Master student at the College of System Engineering, National University of Defense Technology. His main research interest is long-tailed recognition

YU Miao-Miao　Ph.D. candidate at the College of System Engineering, National University of Defense Technology. Her main research interest is face forgery detection

LI Hong-Ying　Master student at the College of System Engineering, National University of Defense Technology. His main research interest is adversarial attacks

LI Shuo-Hao　Associate professor at the College of System Engineering, National University of Defense Technology. His main research interest is scene graph generation

FAN Ling-Yu　Engineer at the Unit 96962 of the PLA. Her research interest covers camouflaged object detection and analysis

ZHANG Jun　Professor at the College of System Engineering, National University of Defense Technology. Her research interest covers visual data computation and analysis. Corresponding author of this paper

摘要

摘要: 数据在现实世界中通常呈现长尾分布, 即, 少数类别拥有大量样本, 而多数类别仅有少量样本. 这种数据不均衡的情况会导致在该数据集上训练的模型对于样本数量较少的尾部类别产生过拟合. 面对长尾视觉识别这一任务, 提出一种面向长尾视觉识别的特征平衡方法, 通过对样本在特征空间中的收缩、分离和聚合操作, 增强模型对于难样本的识别能力. 该方法主要由特征平衡因子和难样本特征约束两个模块组成. 特征平衡因子利用类样本数量来调整模型的输出概率分布, 使得不同类别之间的特征距离更加均衡, 从而提高模型的分类准确率. 难样本特征约束通过对样本特征进行聚类分析, 增加不同类别之间的边界距离, 使得模型能够找到更合理的决策边界. 该方法在多个常用的长尾基准数据集上进行实验验证, 结果表明不但提高了模型在长尾数据上的整体分类精度, 而且显著提升了尾部类别的识别性能. 与基准方法BS相比较, 该方法在CIFAR100-LT、ImageNet-LT和iNaturalist 2018数据集上的性能分别提升了7.40%、6.60%和2.89%.
- 长尾识别 /
- 损失设计 /
- 特征平衡 /
- 特征约束
Abstract: Data in the real world often exhibits a long-tailed distribution, where a few classes have a large number of samples, while most classes have only a few samples. This data imbalance can lead to overfitting in the model trained on this dataset for tail classes with fewer samples. To address this problem, we propose a feature balancing method for long-tailed visual recognition, which enhances the model＇s ability to recognize hard samples by shrinking, separating and aggregating samples in the feature space. The method consists of two modules: Feature balance factor and hard sample feature constraint. The feature balance factor uses the sample number of classes to adjust the model＇s output probability distribution, making the feature distance between different classes more balanced, thereby improving the model＇s classification accuracy. The hard sample feature constraint performs clustering analysis on the sample features, increasing the boundary distance between different classes, enabling the model to find a more reasonable decision boundary. We conduct experiments on several common long-tailed benchmark datasets, experimental results show that the proposed method not only improves the model＇s overall classification accuracy on long-tailed data, but also significantly enhances the recognition performance of tail classes. Compared with baseline method BS, the proposed method achieves performance improvements of 7.40%, 6.60% and 2.89% on CIFAR100-LT, ImageNet-LT and iNaturalist 2018 datasets respectively.
- Long-tailed recognition /
- loss design /
- feature balance /
- feature constraint

HTML全文

图 1 长尾分布

Fig. 1 Long-tailed distribution

下载: 全尺寸图片幻灯片

图 2 长尾与均衡数据的特征可视化

Fig. 2 Feature visualization of long-tailed and balanced data

下载: 全尺寸图片幻灯片

图 3 基于类别的分类器权重$L_2 $范数

Fig. 3 Class-based classifier weight $L_2 $ norm

下载: 全尺寸图片幻灯片

图 4 面向长尾视觉识别的特征平衡方法

Fig. 4 A feature balancing method for long-tailed visual recognition

下载: 全尺寸图片幻灯片

图 5 难样本特征约束

Fig. 5 Hard sample feature constraint

下载: 全尺寸图片幻灯片

图 6 特征可视化对比

Fig. 6 Comparison of feature visualization

下载: 全尺寸图片幻灯片

图 7 特征$L_2 $范数对比

Fig. 7 Feature $L_2 $ norm comparison

下载: 全尺寸图片幻灯片

图 8 参数$\psi $分析

Fig. 8 Analysis of the parameter$\psi $

下载: 全尺寸图片幻灯片

表 1 数据集的基本信息

Table 1 Basic information of the datasets

数据集	类数量 (个)	训练样本 (张)	测试样本 (张)	$IF$
CIFAR100-LT	100	10847	10000	100
ImageNet-LT	1000	115846	500000	256
iNaturalist 2018	8142	437513	24426	435

下载: 导出CSV

表 2 模型的基本设定

Table 2 Basic settings of the model

数据集	CIFAR100-LT	ImageNet-LT	iNaturalist 2018
骨干网络	ResNet-32	ResNet-50	ResNeXt-50
batch size	64	256	512
权重衰减	0.0040	0.0002	0.0002
初始学习率	0.1	0.2	0.2
调整策略	warmup	cosine	cosine
动量	0.9	0.9	0.9

下载: 导出CSV

表 3 CIFAR100-LT上的Top-1准确率 (%)

Table 3 Top-1 accuracy on CIFAR100-LT (%)

方法	来源	年份	CIFAR100-LT
方法	来源	年份	10	50	100
CE^[41]			55.7	43.9	38.6
CE-DRW^[41]	NeurIPS	2022	57.9	47.9	41.1
LDAM-DRW^[37]	NeurIPS	2019	58.7	46.3	42.0
Causal Norm^[42]	NeurIPS	2020	59.6	50.3	44.1
BS^[12]	NeurIPS	2020	63.0		50.8
Remix^[43]	ECCV	2020	59.2	49.5	45.8
RIDE(3E)^[14]	ICLR	2020			48.0
MiSLAS^[44]	CVPR	2021	63.2	52.3	47.0
TSC^[11]	CVPR	2022	59.0	47.4	43.8
WD^[29]	CVPR	2022	68.7	57.7	53.6
KPS^[9]	PAMI	2023		49.2	45.0
PC^[40]	IJCAI	2023	69.1	57.8	53.4
SuperDisco^[39]	CVPR	2023	69.3	58.3	53.8
SHIKE^[38]	CVPR	2023		59.8	56.3
特征平衡方法	本文		73.3	63.0	58.2

下载: 导出CSV

表 4 ImageNet-LT上的Top-1准确率 (%)

Table 4 Top-1 accuracy on ImageNet-LT (%)

方法	来源	年份	骨干网络	头部类	中部类	尾部类	总计
CE^[41]			ResNet-50	64.0	33.8	5.8	41.60
CE-DRW^[41]	NeurIPS	2022	ResNet-50	61.7	47.3	28.8	50.10
LDAM-DRW^[37]	NeurIPS	2019	ResNet-50	60.4	46.9	30.7	49.80
Causal Norm^[42]	NeurIPS	2020	ResNeXt-50	62.7	48.8	31.6	51.80
BS^[12]	NeurIPS	2020	ResNet-50	60.9	48.8	32.1	51.00
Remix^[43]	ECCV	2020	ResNet-18	60.4	46.9	30.7	48.60
RIDE(3E)^[14]	ICLR	2020	ResNeXt-50	66.2	51.7	34.9	55.40
MiSLAS^[44]	CVPR	2021	ResNet-50	61.7	51.3	35.8	52.70
CMO^[41]	CVPR	2022	ResNet-50	66.4	53.9	35.6	56.20
TSC^[11]	CVPR	2022	ResNet-50	63.5	49.7	30.4	52.40
WD^[29]	CVPR	2022	ResNeXt-50	62.5	50.4	41.5	53.90
KPS^[9]	PAMI	2023	ResNet-50				51.28
PC^[40]	IJCAI	2023	ResNeXt-50	63.5	50.8	42.7	54.90
SuperDisco^[39]	CVPR	2023	ResNeXt-50	66.1	53.3	37.1	57.10
SHIKE^[38]	CVPR	2023	ResNet-50				59.70
特征平衡方法	本文		ResNet-50	67.9	54.3	40.1	57.60
特征平衡方法	本文		ResNeXt-50	67.6	55.3	41.7	58.19

下载: 导出CSV

表 5 iNaturalist 2018上的Top-1准确率 (%)

Table 5 Top-1 accuracy on iNaturalist 2018 (%)

方法	来源	年份	骨干网络	头部类	中部类	尾部类	总计
CE^[41]			ResNet-50	73.9	63.5	55.5	61.00
LDAM-DRW^[37]	NeurIPS	2019	ResNet-50				66.10
BS^[12]	NeurIPS	2020	ResNet-50	70.0	70.2	69.9	70.00
Remix^[43]	ECCV	2020	ResNet-50				70.50
RIDE(3E)^[14]	ICLR	2020	ResNet-50	70.2	72.2	72.7	72.20
MiSLAS^[44]	CVPR	2021	ResNet-50	73.2	72.4	70.4	71.60
CMO^[41]	CVPR	2022	ResNet-50	68.7	72.6	73.1	72.80
TSC^[11]	CVPR	2022	ResNet-50	72.6	70.6	67.8	69.70
WD^[29]	CVPR	2022	ResNet-50	71.2	70.4	69.7	70.20
KPS^[9]	PAMI	2023	ResNet-50				70.35
PC^[40]	IJCAI	2023	ResNet-50	71.6	70.6	70.2	70.60
SuperDisco^[39]	CVPR	2023	ResNet-50	72.3	72.9	71.3	73.60
SHIKE^[38]	CVPR	2023	ResNet-50				74.50
特征平衡方法	本文		ResNet-50	74.9	72.2	73.2	72.89
特征平衡方法	本文		ResNeXt-50	74.6	72.3	72.2	72.53

下载: 导出CSV

表 6 模块的消融实验

Table 6 Ablation experiments of the module

数据增强	权重衰减	特征平衡因子	难样本特征约束	CE				BS
数据增强	权重衰减	特征平衡因子	难样本特征约束	头部	中部	尾部	总体	头部	中部	尾部	总体
							38.6				50.8
√				76.0	45.6	16.9	47.6	72.0	51.5	28.0	51.6
√	√			82.2	52.3	13.3	51.0	78.2	55.3	31.6	56.2
√	√	√		79.9	56.5	16.1	52.6	76.1	56.8	36.8	57.6
√	√	√	√	80.1	57.6	17.1	53.3	76.6	57.9	37.4	58.2

下载: 导出CSV

参考文献(45)

[1]	Zoph B, Vasudevan V, Shlens J, Le Q V. Learning transferable architectures for scalable image recognition. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. Salt Lake City, USA: IEEE, 2018. 8697−8710
[2]	Redmon J, Divvala S, Girshick R, Farhadi A. You only look once: Unified, real-time object detection. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR). Las Vegas, USA: IEEE, 2016. 779−788
[3]	Deng J, Dong W, Socher R, Li L J, Li K, Li F F. ImageNet: A large-scale hierarchical image database. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. Miami, USA: IEEE, 2009. 248−255
[4]	Russakovsky O, Deng J, Su H, Krause J, Satheesh S, Ma S, et al. ImageNet large scale visual recognition challenge. International Journal of Computer Vision, 2015, 115: 211−252 doi: 10.1007/s11263-015-0816-y
[5]	Lin T Y, Maire M, Belongie S, Hays J, Perona P, Ramanan D, et al. Microsoft COCO: Common objects in context. In: Proceedings of the 13th European Conference on Computer Vision. Zurich, Switzerland: Springer, 2014. 740−755
[6]	Zhou B L, Lapedriza A, Khosla A, Oliva A, Torralba A. Places: A 10 million image database for scene recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2018, 40(6): 1452−1464 doi: 10.1109/TPAMI.2017.2723009
[7]	Anwar S M, Majid M, Qayyum A, Awais M, Alnowami M, Khan M K. Medical image analysis using convolutional neural networks: A review. Journal of Medical Systems, 2018, 42: Article No. 226 doi: 10.1007/s10916-018-1088-1
[8]	Liu Z W, Miao Z Q, Zhan X H, Wang J Y, Gong B Q, Yu S X. Large-scale long-tailed recognition in an open world. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. Long Beach, USA: IEEE, 2019. 2537−2546
[9]	Li M K, Cheung Y M, Hu Z K. Key point sensitive loss for long-tailed visual recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2023, 45(4): 4812−4825
[10]	Tian C Y, Wang W H, Zhu X Z, Dai J F, Qiao Y. VL-LTR: Learning class-wise visual-linguistic representation for long-tailed visual recognition. In: Proceedings of the 17th European Conference on Computer Vision. Tel Aviv, Israel: Springer, 2022. 73–91
[11]	Li T H, Cao P, Yuan Y, Fan L J, Yang Y Z, Feris R, et al. Targeted supervised contrastive learning for long-tailed recognition. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). New Orleans, USA: IEEE, 2022. 6908−6918
[12]	Ren J W, Yu C J, Sheng S A, Ma X, Zhao H Y, Yi S, et al. Balanced meta-softmax for long-tailed visual recognition. Advances in Neural Information Processing Systems, 2020, 33: 4175−4186
[13]	Hong Y, Han S, Choi K, Seo S, Kim B, Chang B. Disentangling label distribution for long-tailed visual recognition. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Nashville, USA: IEEE, 2021. 6622−6632
[14]	Wang X D, Lian L, Miao Z Q, Liu Z W, Yu S X. Long-tailed recognition by outing diverse distribution-aware experts. arXiv preprint arXiv: 2010.01809, 2020.
[15]	Li T H, Wang L M, Wu G S. Self supervision to distillation for long-tailed visual recognition. In: Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV). Montreal, Canada: IEEE, 2021. 610−619
[16]	Wang Y R, Gan W H, Yang J, Wu W, Yan J J. Dynamic curriculum learning for imbalanced data classication. In: Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV). Seoul, South Korea: IEEE, 2019. 5016−5025
[17]	Zang Y H, Huang C, Loy C C. FASA: Feature augmentation and sampling adaptation for long-tailed instance segmentation. In: Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV). Montreal, Canada: IEEE, 2021. 3457−3466
[18]	Cui Y, Jia M L, Lin T Y, Song Y, Belongie S. Class-balanced loss based on effective number of samples. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Long Beach, USA: IEEE, 2019. 9268−9277
[19]	Lin T Y, Goyal P, Girshick R, He K M, Dollár P. Focal loss for dense object detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2020, 42(2): 318−327 doi: 10.1109/TPAMI.2018.2858826
[20]	Tan J R, Wang C B, Li B Y, Li Q Q, Ouyang W L, Yin C Q, et al. Equalization loss for long-tailed object recognition. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Seattle, USA: IEEE, 2020. 11659−11668
[21]	Wang J Q, Zhang W W, Zang Y H, Cao Y H, Pang J M, Gong T, et al. Seesaw loss for long-tailed instance segmentation. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Nashville, USA: IEEE, 2021. 9690−9699
[22]	Zhao Y, Chen W C, Tan X, Huang K, Zhu J H. Adaptive logit adjustment loss for long-tailed visual recognition. arXiv preprint arXiv: 2104.06094, 2021.
[23]	Guo H, Wang S. Long-tailed multi-label visual recognition by collaborative training on uniform and re-balanced samplings. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Nashville, USA: IEEE, 2021. 15084−15093
[24]	Zhou B Y, Cui Q, Wei X S, Chen Z M. BBN: Bilateral-branch network with cumulative learning for long-tailed visual recognition. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Seattle, USA: IEEE, 2020. 9716−9725
[25]	Li Y, Wang T, Kang B Y, Tang S, Wang C F, Li J T, et al. Overcoming classier imbalance for long-tail object detection with balanced group softmax. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Seattle, USA: IEEE, 2020. 10988−10997
[26]	Cui J Q, Liu S, Tian Z T, Zhong Z S, Jia J Y. ResLT: Residual learning for long-tailed recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2023, 45(3): 3695−3706
[27]	Li J, Tan Z C, Wan J, Lei Z, Guo G D. Nested collaborative learning for long-tailed visual recognition. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). New Orleans, USA: IEEE, 2022. 6939−6948
[28]	Cui J Q, Zhong Z S, Liu S, Yu B, Jia J Y. Parametric contrastive learning. In: Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV). Montreal, Canada: IEEE, 2021. 695−704
[29]	Alshammari S, Wang Y X, Ramanan D, Kong S. Long-tailed recognition via weight balancing. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). New Orleans, USA: IEEE, 2022. 6887−6897
[30]	Li M K, Cheung Y M, Jiang J Y. Feature-balanced loss for long-tailed visual recognition. In: Proceedings of the IEEE International Conference on Multimedia and Expo (ICME). Taiwan, China: IEEE, 2022. 1−6
[31]	Goodfellow I, Bengio Y, Courville A. Deep Learning. Massachusetts: MIT Press, 2016.
[32]	Schroff F, Kalenichenko D, Philbin J. FaceNet: A unified embedding for face recognition and clustering. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Boston, USA: IEEE, 2015. 815−823
[33]	Krizhevsky A. Learning Multiple Layers of Features From Tiny Images [Master thesis], University of Toronto, Canada, 2009.
[34]	Horn G V, Aodha O M, Song Y, Cui Y, Sun C, Shepard A, et al. The iNaturalist species classication and detection dataset. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Salt Lake City, USA: IEEE, 2018. 8769−8778
[35]	He K M, Zhang X Y, Ren S Q, Sun J. Deep residual learning for image recognition. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Las Vegas, USA: IEEE, 2016. 770−778
[36]	Xie S N, Girshick R, Dollar P, Tu Z W, He K M. Aggregated residual transformations for deep neural networks. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Honolulu, USA: IEEE, 2017. 5987−5995
[37]	Cao K D, Wei C, Gaidon A, Arechiga N, Ma T Y. Learning imbalanced datasets with label-distribution-aware margin loss. In: Proceedings of the 33rd International Conference on Neural Information Processing Systems. Vancouver, Canada: Curran Associates Inc., 2019. 1567–1578
[38]	Jin Y, Li M K, Lu Y, Cheung Y M, Wang H Z. Long-tailed visual recognition via self-heterogeneous integration with knowledge excavation. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Vancouver, Canada: IEEE, 2023. 23695−23704
[39]	Du Y J, Shen J Y, Zhen X T, Snoek C G M. SuperDisco: Super-class discovery improves visual recognition for the long-tail. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Vancouver, Canada: IEEE, 2023. 19944−19954
[40]	Sharma S, Xian Y Q, Yu N, Singh A. Learning prototype classiers for long-tailed recognition. In: Proceedings of the Thirty-second International Joint Conference on Articial Intelligence. Macao, China: ACM, 2023. 1360−1368
[41]	Park S, Hong Y, Heo B, Yun S, Choi J Y. The majority can help the minority: Context-rich minority oversampling for long-tailed classication. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). New Orleans, USA: IEEE, 2022. 6877−6886
[42]	Tang K H, Huang J Q, Zhang H W. Long-tailed classication by keeping the good and removing the bad momentum causal effect. arXiv preprint arXiv: 2009.12991, 2020.
[43]	Chou H P, Chang S C, Pan J Y, Wei W, Juan D C. Remix: Rebalanced mixup. In: Proceedings of the European Conference on Computer Vision. Glasgow, UK: Springer, 2020. 95−110
[44]	Zhong Z S, Cui J Q, Liu S, Jia J Y. Improving calibration for long-tailed recognition. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Nashville, USA: IEEE, 2021. 16484−16493
[45]	McInnes L, Healy J, Melville J. UMAP: Uniform manifold approximation and projection for dimension reduction. arXiv preprint arXiv: 1802.03426, 2020.