数据增强下深度卷积网络不变性机理的可解释性研究

Interpretability Study of the Invariance Mechanism of Deep Convolutional Networks under Data Augmentation

摘要

针对目前数据增强提升深度卷积网络不变性的研究缺乏对其实现不变性的机理进行阐释的问题，对其位置、方向等信息的表征机制和特征综合机理展开研究。首先，采用圆形和方形二分类任务构建简化实验场景，使用其增强数据训练网络；然后，通过最大激活方法对全连接层和全局平均池化层进行特征可视化，并采用t-SNE降维揭示了全连接层间高维权重向量的分类决策机理。结果表明：全连接层首层通过逐步扩大位置感知域的方式实现平移不变性；在圆方数据集平移增强实验中，Fc2层平移不变性得分为0.99，较Conv5层提升了45%；全连接层通过线性加权机制综合圆形和方形的局部特征，遵循同类别特性正向激发、异类别特征负向抑制的连接逻辑；ResNet架构中平均池化层展现更优的平移不变性，在圆方数据集增强实验中，平均池化层得分为0.93，高于全连接层的0.79，而级联全连接结构则表现出更强的旋转和尺度不变性。以上结论在MNIST数据集的扩展实验上也得到了验证。

Abstract

Addressing the issue that current research on enhancing the invariance of deep convolutional networks through data augmentation lacks an explanation of the mechanisms underlying its implementation,this paper explores the representation and pooling mechanisms of position,orientation,and other information.First,a simplified experimental scenario is constructed using a binary classification task of circles and squares,which is employed to augment data for network training.Then,feature visualization is conducted for the fully connected layer and global average pooling layer using the maximum activation method,and t-SNE dimensionality reduction is adopted to reveal the classification decision-making mechanism of high-dimensional weight vectors within the fully connected layers.It is shown that translation invariance is achieved by the first fully connected layer through the gradual expansion of the position-aware receptive field.In the translation augmentation experiment on the circle-and-square dataset,a translation invariance score of 0.99 is obtained by the Fc2 layer,representing a 45% improvement over that of the Conv5 layer.The local features of circles and squares are synthesized by the fully connected layers through a linear weighting mechanism,following a connection logic in which same-category features are positively activated and different-category features are negatively suppressed.Better translation invariance is exhibited by the average pooling layer in the ResNet architecture.In the augmentation experiment on the circle-and-square dataset,a score of 0.93 is obtained by the AvgPool layer,higher than the 0.79 obtained by the fully connected layer,whereas stronger rotation and scale invariance is exhibited by the cascaded fully connected structure.These conclusions are also verified through extended experiments on the MNIST dataset.

关键词

深度卷积网络 / 数据增强 / 平移不变性 / 特征可视化

Key words

deep convolutional network / data augmentation / translation invariance / feature visualization

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基金资助

国家自然科学基金区域创新发展联合基金资助项目(U23A20682)

国家自然科学基金区域创新发展联合基金资助项目(U22A20247)

陕西省自然科学基础研究计划资助项目(2024JC-YBMS-566)