《Zero Stability Well Predicts Performance of Convolutional Neural Networks》

# 《Zero Stability Well Predicts Performance of Convolutional Neural Networks》

## 文章结构
1. 摘要
2. 引言
3. 预备知识
4. 来自现存CNNs的观察
5. 零稳定性网络ZeroSNet
6. 实验
-- 通过零稳定预测性能
-- 和其它网络比较
-- 验证鲁棒性
-- 泛化Gap实验
-- 计算效率
-- 实验设置
7. 相关工作
-- neural ODEs的鲁棒性
-- CNNs的稳定性
-- 基于高阶离散化的结构
8. 讨论
9. 结论
10. 附录
-- 额外的实验
-- ZeroSNet的推导
-- 理论证明

### 摘要
**原文：**`The question of what kind of convolutional neural network (CNN) structure performs well is fascinating. In this work, we move toward the answer with one more step by connecting zero stability and model performance. Specifically, we found that if a discrete solver of an ordinary differential equation is zero stable, the CNN corresponding to that solver performs well. We first give the interpretation of zero stability in the context of deep learning and then investigate the performance of existing first- and second-order CNNs under different zero-stable circumstances. Based on the preliminary observation, we provide a higher-order discretization to construct CNNs and then propose a zero-stable network (ZeroSNet). To guarantee zero stability of the ZeroSNet, we first deduce a structure that meets consistency conditions and then give a zero stable region of a training-free parameter. By analyzing the roots of a characteristic equation, we theoretically obtain the optimal coefficients of feature maps. Empirically, we present our results from three aspects: We provide extensive empirical evidence of different depth on different datasets to show that the moduli of the characteristic equation’s roots are the keys for the performance of CNNs that require historical features; Our experiments show that ZeroSNet outperforms existing CNNs which is based on high-order discretization; ZeroSNets show better robustness against noises on the input. The source code is available at https://github.com/LongJin-lab/ZeroSNet.`

**翻译：**`哪种卷积神经网络(CNN)结构表现良好的问题令人着迷。本文通过将零稳定性和模型性能联系起来，向答案又迈进了一步。具体来说，我们发现，如果常微分方程的离散求解器是零稳定的，则该求解器对应的CNN表现良好。首先给出了深度学习背景下零稳定性的解释，然后研究了现有的一阶和二阶cnn在不同零稳定情况下的性能。基于初步观察，本文提供了一种高阶离散化来构建cnn，然后提出了一种零稳定网络(ZeroSNet)。为保证ZeroSNet的零稳定性，首先推导出满足一致性条件的结构，然后给出免训练参数的零稳定区域。通过分析特征方程的根，理论上可以得到最优的特征映射系数。从三个方面展示了结果:在不同的数据集上提供了不同深度的广泛经验证据，表明特征方程根的模是需要历史特征的cnn性能的关键;实验表明，ZeroSNet优于现有的基于高阶离散化的cnn;ZeroSNets对输入噪声表现出更好的鲁棒性。源代码可以在https://github.com/LongJin-lab/ZeroSNet上找到。`

**句型：**
1. The question of [something] is fascinating.
2. In this work, [we] [do something].
3. [We] move toward [something] by [doing something].
4. [We] connect [something] and [something else].
5. Specifically, [we] found that [statement].
6. If [condition], [result].
7. We first give [something].
8. [We] interpret [something] in the context of [something].
9. [We] investigate the performance of [something] under [conditions].
10. Based on [something], [we] [do something].
11. To guarantee [something], [we] [do something].
12. By analyzing [something], [we] [do something].
13. We theoretically obtain [something] by [doing something].
14. Empirically, [we] present [our results] from [aspects].
15. [We] provide extensive empirical evidence of [something] to show [something].
16. Our experiments show [something].
17. [Something] outperforms [something else].
18. [Something] shows better [quality] against [something].
19. The source code is available at [URL].

**短语：**``

**行文思路：**
1. 引入问题和背景：段落开头提出了一个有趣的问题，即何种CNN结构能够表现出良好性能。
2. 关联零稳定性和模型性能：接下来，提到作者通过将零稳定性与模型性能相连接，向回答这个问题迈出了一步。
3. 调查现有CNN的性能：研究了现有的一阶和二阶CNN在不同零稳定条件下的性能。
4. 提出ZeroSNet：提出了一种高阶离散化方法构建CNN，命名为ZeroSNet。
5. 理论和实证结果：通过分析特征方程的根并从理论上得出了特征图的最优系数。接下来，通过广泛的实验从三个方面验证了ZeroSNet的性能优势：不同深度在不同数据集上的实证结果，ZeroSNet相对于基于高阶离散化的现有CNN的性能优势，以及ZeroSNet对输入噪声的鲁棒性。
6. 提供源代码：最后一句提供了源代码的链接，方便读者获取更多细节或进行复现实验。

**论文摘要写作指导：**
- 在论文摘要中，应该简明扼要地介绍研究的背景、问题、方法和结果，让读者能够了解研究的核心内容。
- 引言部分可以提出一个引人入胜的问题或现实应用场景，引起读者的兴趣。
- 在介绍研究方法时，要突出创新点和研究的重要性，说明为什么这个方法或理论对解决问题或推动领域发展具有重要意义。
- 在结果部分，重点突出实证结果的重要性和发现的新见解，可以使用定量数据或具体例子来支持。
- 最后，提供相关资源的链接或引用，如源代码、数据集或其他参考资料，以便读者进一步了解或复现研究。

### 引言
### 预备知识
### 来自现存CNNs的观察
### 零稳定性网络ZeroSNet
### 实验
-- 通过零稳定预测性能
-- 和其它网络比较
-- 验证鲁棒性
-- 泛化Gap实验
-- 计算效率
-- 实验设置
### 相关工作
-- neural ODEs的鲁棒性
-- CNNs的稳定性
-- 基于高阶离散化的结构
### 讨论
### 结论
### 附录
-- 额外的实验
-- ZeroSNet的推导
-- 理论证明

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Convolutional Performance Stability Predicts Networksconvolutional performance stability predicts convolutional segmentation biomedical networks classification convolutional imagenet networks convolutional stochastic reduction networks convolutional segmentation networks semantic recommendation convolutional networks hamming convolutional distilling knowledge networks convolutional networks neural cnn skeleton-based convolutional recognition networks 卷积convolutional网路networks