Learning method of residual network for heavy-tailed noisy image classification

doi:10.11772/j.issn.1001-9081.2024101407

Abstract

Abstract:

To address the problem that image classification accuracy of Residual Network （ResNet） drops due to influence of unknown heavy-tailed noise， a Multi-distribution Heavy-Tailed Noise Adaptive ResNet （MHTNA-ResNet） model was proposed. Firstly， to reduce impact of heavy-tailed noise on final predictions， a Multi-distribution Heavy-Tailed Noise Adaptive layer （MHTNA） was designed， which created noise templates using various heavy-tailed distributions to perturb clean training data， thereby enabling ResNet to get recognition capabilities for heavy-tailed noisy images through training. Secondly， MHTNA was trained adaptively， updated noise template parameters were solved by using the maximum likelihood estimation method， and the noise templates were regenerated according to these parameters， so as to ensure that the noise is always heavy-tailedly distributed. Finally， during testing， the MHTNA was abandoned and heavy-tailed noise attacks were performed to test images， thereby evaluating the model’s capability of noise resistance. Experimental results demonstrate that compared to PRIME model， the proposed model has the classification accuracy improved by an average of 3.86， 7.10 and 5.46 percentage points， respectively， on the CIFAR10， CIFAR100 and MINI-ImageNet datasets facing heavy-tailed noise attacks. It can be seen that the proposed model can improve ResNet’s robustness against heavy-tailed noise interference effectively.

Key words: heavy-tailed noise, image classification, Residual Network (ResNet), multi-distribution, deep learning

摘要：

针对残差网络（ResNet）在图像分类中容易受未知重尾噪声影响导致识别准确率下降的问题，提出一种多分布重尾噪声自适应残差网络（MHTNA-ResNet）模型。首先，为抑制重尾噪声对最终预测的影响，设计一个多分布重尾噪声自适应层（MHTNA），该层使用多种重尾分布创建噪声模板，扰动干净的训练数据，使ResNet通过训练获得对重尾噪声图像的识别能力；其次，MHTNA在训练中进行自适应训练，使用最大似然估计法求解更新的噪声模板参数，并根据求解参数重新生成噪声模板，控制噪声始终遵循重尾分布；最后，测试时屏蔽MHTNA，对测试图像进行重尾噪声攻击，从而检验模型的抗噪能力。实验结果表明，与PRIME模型相比，面对重尾噪声的攻击，在CIFAR10、CIFAR100和MINI-ImageNet数据集上所提模型的分类准确率分别平均提升了3.86、7.10和5.46个百分点。可见，所提模型可以有效提高ResNet面对重尾噪声干扰时的鲁棒性。

关键词: 重尾噪声, 图像分类, 残差网络, 多分布, 深度学习

CLC Number:

TP181

Zhiyu GONG, Shitong WANG. Learning method of residual network for heavy-tailed noisy image classification[J]. Journal of Computer Applications, 2025, 45(10): 3091-3100.

宫智宇, 王士同. 面向重尾噪声图像分类的残差网络学习方法[J]. 《计算机应用》唯一官方网站, 2025, 45(10): 3091-3100.

Figures/Tables 12

Fig. 1 Prediction changes with heavy-tailed noise added to images

Fig. 2 Blocks for ResNet

Tab. 1 Network structures of ResNet18 and ResNet50

网络层	ResNet18	ResNet50
conv1_x	7×7，64，stride=2
conv1_x	3×3 max pool，stride=2
conv2_x	$3 × 3 64 3 × 3 64 × 2$	$1 × 1 64 3 × 3 64 1 × 1 256 × 3$
conv3_x	$3 × 3 128 3 × 3 128 × 2$	$1 × 1 128 3 × 3 128 1 × 1 512 × 4$
conv4_x	$3 × 3 256 3 × 3 256 × 2$	$1 × 1 256 3 × 3 256 1 × 1 1024 × 6$
conv5_x	$3 × 3 512 3 × 3 512 × 2$	$1 × 1 512 3 × 3 512 1 × 1 2048 × 3$
其他	average pool，fc，Softmax

Tab. 1 Network structures of ResNet18 and ResNet50

网络层	ResNet18	ResNet50
conv1_x	7×7，64，stride=2
conv1_x	3×3 max pool，stride=2
conv2_x	$3 × 3 64 3 × 3 64 × 2$	$1 × 1 64 3 × 3 64 1 × 1 256 × 3$
conv3_x	$3 × 3 128 3 × 3 128 × 2$	$1 × 1 128 3 × 3 128 1 × 1 512 × 4$
conv4_x	$3 × 3 256 3 × 3 256 × 2$	$1 × 1 256 3 × 3 256 1 × 1 1024 × 6$
conv5_x	$3 × 3 512 3 × 3 512 × 2$	$1 × 1 512 3 × 3 512 1 × 1 2048 × 3$
其他	average pool，fc，Softmax

Fig. 3 Curves of four types of heavy-tailed distributions

Fig. 4 Images before and after adding heavy-tailed noise

Fig. 5 Structure of MHTNA-ResNet model

Tab. 2 Ablation experimental results

方法	Clean/%	不同分布和不同参数重尾噪声攻击下的准确率/%
		Cauchy			Student-t			Laplace			Erlang
		γ=5	γ=10	γ=15	v=0.5	v=0.4	v=0.3	σ=10	σ=15	σ=30	a=0.100，b=3	a=0.050，b=3	a=0.045，b=3
ResNet18	95.19	23.79	15.31	13.17	17.01	14.03	11.78	53.79	28.24	14.31	43.05	18.59	17.20
M	94.12	88.54	71.81	51.23	87.48	75.76	46.21	90.63	83.49	50.91	86.28	60.16	49.35
MHTNA-M	94.59	90.18	76.67	58.91	90.17	82.79	60.54	90.98	85.15	53.76	87.13	63.27	53.51
A	93.19	91.57	78.94	58.71	90.38	83.23	57.41	92.17	87.83	50.39	89.37	59.35	52.87
MHTNA-A	93.27	91.95	81.23	62.03	91.21	84.71	61.37	92.85	88.53	51.88	89.93	61.46	54.16
MA	93.79	91.73	82.91	69.83	91.02	86.06	65.72	92.41	88.41	64.53	90.42	68.14	61.52
MHTNA-MA	93.65	92.68	86.15	73.29	91.59	88.63	71.59	92.87	89.45	66.72	91.25	70.52	64.93

Tab. 3 Test results of non-heavy-tailed noise attacks

网络	MHTNA	Clean/%	不同分布和不同参数非重尾噪声攻击下的准确率/%
			Gaussian			Pepper			Poisson
			v=5	v=10	v=20	r=0.005	r=0.010	r=0.050	p=0.2	p=0.5	p=1.0
ResNet18	w/o	95.19	90.18	72.77	29.45	86.88	70.56	25.94	53.79	28.24	14.31
ResNet18	w/	93.65	94.18	92.22	79.21	90.57	83.62	43.70	93.48	90.83	79.98
ResNet50	w/o	75.33	60.46	36.30	11.98	66.37	51.35	6.97	71.38	55.76	32.01
ResNet50	w/	75.31	75.03	69.17	45.86	72.39	67.68	26.85	73.25	64.39	44.63

Tab. 4 Test results of various methods on CIFAR10 dataset

方法	Clean/%	不同分布和不同参数重尾噪声攻击下的准确率/%
		Cauchy			Student-t			Laplace			Erlang
		γ=1.0	γ=1.5	γ=5.0	v=1.0	v=0.8	v=0.5	σ=5	σ=10	σ=15	a=0.5，b=3	a=0.5，b=10	a=0.1，b=3
LAS-AT	85.66	82.98	81.19	71.95	82.76	79.41	63.93	84.95	83.02	79.30	85.62	85.04	81.27
DAJAT	85.71	83.82	82.87	74.71	83.79	81.20	66.99	85.18	83.45	79.63	85.55	85.18	82.34
PD	89.76	88.14	86.92	78.33	88.10	85.57	69.09	89.39	87.28	83.49	89.63	89.08	85.78
NoL	94.17	89.59	86.09	55.06	89.62	80.74	32.20	93.61	86.72	71.15	92.98	92.33	80.06
PRIME	92.96	91.01	89.94	82.30	91.05	88.32	74.87	92.06	90.25	87.86	92.74	92.15	90.09
MHTNA	93.65	92.68	92.93	91.87	93.07	93.51	91.59	93.41	92.87	89.45	93.41	92.87	91.25

Tab. 5 Test results of various methods on CIFAR100 dataset

方法	Clean/%	不同分布和不同参数重尾噪声攻击下的准确率/%
		Cauchy			Student-t			Laplace			Erlang
		γ=1.0	γ=1.5	γ=5.0	v=1.0	v=0.8	v=0.5	σ=5	σ=10	σ=15	a=0.5，b=3	a=0.5，b=10	a=0.1，b=3
LAS-AT	67.31	60.40	56.08	28.58	60.95	48.97	14.59	66.87	62.46	51.00	67.30	66.89	58.78
DAJAT	68.74	63.36	60.09	39.08	63.22	54.73	23.92	68.03	64.42	55.19	68.56	67.77	61.08
PD	65.72	62.84	61.44	47.33	63.22	58.92	35.88	65.42	63.27	57.14	65.67	65.21	60.66
NoL	75.08	71.02	67.83	28.71	70.83	59.62	28.47	74.53	64.26	53.61	74.28	72.09	53.17
PRIME	74.59	69.05	67.04	53.94	71.78	65.46	42.20	74.15	70.67	65.49	73.93	70.29	65.52
MHTNA	75.31	75.57	75.32	68.79	75.23	75.16	69.47	75.04	72.29	67.64	75.37	74.81	69.97

Tab. 6 Test results of various methods on MINI-ImageNet dataset

方法	Clean/%	不同分布和不同参数重尾噪声攻击下的准确率/%
		Cauchy			Student-t			Laplace			Erlang
		γ=1.0	γ=1.5	γ=5.0	v=1.0	v=0.8	v=0.5	σ=5	σ=10	σ=15	a=0.5，b=3	a=0.5，b=10	a=0.1，b=3
LAS-AT	71.43	67.50	65.23	50.62	67.53	60.13	27.61	65.97	61.37	58.05	67.74	67.23	57.43
DAJAT	71.61	68.27	64.04	51.58	67.92	59.97	28.16	67.16	61.81	58.63	67.28	66.87	60.31
PD	73.24	70.37	68.39	54.21	71.62	63.87	30.18	70.86	67.84	63.81	71.53	70.91	63.37
NoL	81.31	75.87	73.59	43.26	73.98	60.21	31.52	80.18	72.37	62.83	79.26	77.27	58.73
PRIME	79.36	76.08	73.26	61.85	76.71	71.48	35.13	79.58	77.51	70.14	78.89	77.91	70.43
MHTNA	81.43	81.41	81.12	68.08	81.26	79.93	48.69	81.1	80.15	74.23	80.64	80.18	77.64

Fig. 6 Influence of noise template quantity

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