Training Very Deep Networks论文笔记

本文提出了一种名为“高速公路网络”的新型神经网络架构,旨在解决深度神经网络训练过程中信息流动受阻的问题。该架构借鉴了长短期记忆(LSTM)网络的概念,通过自适应门控单元调节信息流,确保信息在多层间顺畅传递,即使网络深度达到数百层,也能通过简单梯度下降进行有效训练。

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Abstract
Theoretical and empirical evidence indicates that the depth of neural networks is crucial for their success. However, training becomes more difficult as depth increases, and training of very deep networks remains an open problem. Here we introduce a new architecture designed to overcome this. Our so-called highway networks allow unimpeded information flow across many layers on information highways. They are inspired by Long Short-Term Memory recurrent networks and use adaptive gating units to regulate the information flow. Even with hundreds of layers, highway networks can be trained directly through simple gradient descent. This enables the study of extremely deep and efficient architectures.

摘要
理论和实证证据表明,神经网络的深度对其性能至关重要。 然而,随着深度的增加,训练变得更加困难,这对于深度网络的训练来说仍然是一个悬而未决的问题。 在这里,我们介绍一种旨在克服这一点的新架构。 我们称其为高速公路网络,此网络允许信息在高速公路网络的多层中畅通无阻。 这个网络是受到LSTM的启发,并使用自适应门控单元来调节信息流。 即使有数百层,也可以通过简单的梯度下降直接训练高速公路网络。 这使得研究极其深入和高效的架构成为可能。

2 Highway Networks
Notation We use boldface letters for vectors and matrices, and italicized capital letters to denote transformation functions. 0 and 1 denote vectors of zeros and ones respectively, and I denotes an identity matrix. The function σ(x) is defined as σ(x)=11+e−x\sigma \left ( x \right )=\frac{1}{1+e^{-x}}σ(x)=1+ex1;xϵRx\epsilon RxϵR. The dot operator (·) is used to denote element-wise multiplication.
A plain feedforward neural network typically consists of L layers where the lthl^{th}lth layer (lϵ{1,2,...,L}l\epsilon \left \{ 1,2,...,L \right \}lϵ{1,2,...,L}) applies a non-linear transformation H (parameterized by WH,lW_{H,l}WH,l) on its input xlx_{l}xl to produce its output yly_{l}yl. Thus, x1x_{1}x1 is the input to the network and yLy_{L}yL is the network’s output. Omitting the layer index and biases for clarity,
y=H(x,WH)y=H\left ( x,W_{H} \right )y=H(x,WH) (1)
H is usually an affine transform followed by a non-linear activation function, but in general it may take other forms, possibly convolutional or recurrent. For a highway network, we additionally define two non-linear transforms T(x,WT)T\left ( x,W_{T} \right )T(x,WT)and C(x,WC)C\left ( x,W_{C} \right )C(x,WC) such that
y=H(x,WH)⋅T(x,WT)+x⋅C(x,WC)y=H\left ( x,W_{H} \right ) \cdot T\left ( x,W_{T} \right )+x\cdot C\left ( x,W_{C} \right )y=H(x,WH)T(x,WT)+xC(x,WC) (2)
We refer to T as the transform gate and C as the carry gate, since they express how much of the output is produced by transforming the input and carrying it, respectively. For simplicity, in this paper we set C = 1 − T, giving
y=H(x,WH)⋅T(x,WT)+x⋅(1−T(x,WT))y=H\left ( x,W_{H} \right ) \cdot T\left ( x,W_{T} \right )+x\cdot (1-T\left ( x,W_{T} \right ))y=H(x,WH)T(x,WT)+x(1T(x,WT)) (3)
The dimensionality of x; y; H(x,WH)H\left ( x,W_{H} \right )H(x,WH) and T(x,WT)T\left ( x,W_{T} \right )T(x,WT) must be the same for Equation 3 to be valid.
Note that this layer transformation is much more flexible than Equation 1. In particular, observe that for particular values of T,
y={x,ifT(x,WT)=0H(x,WH),ifT(x,WT)=1y=\left\{\begin{matrix} x,& ifT\left ( x,W_{T} \right )= 0\\ H\left ( x,W_{H} \right),& if T\left ( x,W_{T} \right )=1 \end{matrix}\right.y={x,H(x,WH),ifT(x,WT)=0ifT(x,WT)=1 (4)

Similarly, for the Jacobian of the layer transform,
dydx={IifT(x,WT)=0H′(x,WH)ifT(x,WT)=1\frac{dy}{dx}=\left\{\begin{matrix} I& if T\left ( x,W_{T} \right )=0\\ H^{'}\left ( x,W_{H} \right ) & if T\left ( x,W_{T} \right )=1 \end{matrix}\right.dxdy={IH(x,WH)ifT(x,WT)=0ifT(x,WT)=1(5)
Thus, depending on the output of the transform gates, a highway layer can smoothly vary its behavior between that of H and that of a layer which simply passes its inputs through. Just as a plain layer consists of multiple computing units such that the ithi^{th}ith unit computes yi=Hi(x)y_{i}=H_{i}(x)yi=Hi(x), a highway network consists of multiple blocks such that the ithi^{th}ith block computes a block state Hi(x)H_{i}(x)Hi(x) and transform gate output Ti(x)T_{i}(x)Ti(x). Finally, it produces the block output yi=Hi(x)∗Ti(x)+xi∗(1−Ti(x))y_{i}=H_{i}(x)\ast T_{i}(x)+x_{i}\ast (1-T_{i}(x))yi=Hi(x)Ti(x)+xi(1Ti(x)), which is connected to the next layer.2

### 关于人工智能监督学习的论文 监督学习是机器学习领域的重要分支之一,它通过已标注的数据集进行训练,使得模型能够预测未见过的数据。以下是一些与人工智能监督学习相关的经典论文及其下载方式: 1. **AlexNet**: AlexNet 是深度学习领域的一个里程碑式的工作,首次展示了卷积神经网络(CNN)在图像分类任务中的强大性能[^3]。 - 论文标题:ImageNet Classification with Deep Convolutional Neural Networks - 下载地址:[https://papers.nips.cc/paper/2012/file/c399862d3b4d68b29e70845fa1c898ae-Paper.pdf](https://papers.nips.cc/paper/2012/file/c399862d3b4d68b29e70845fa1c898ae-Paper.pdf) 2. **VGGNet**: VGGNet 通过加深网络层数展示了深度对模型性能的影响,同时引入了更小的卷积核[^4]。 - 论文标题:Very Deep Convolutional Networks for Large-Scale Image Recognition - 下载地址:[https://arxiv.org/pdf/1409.1556.pdf](https://arxiv.org/pdf/1409.1556.pdf) 3. **ResNet**: ResNet 提出了残差网络的概念,解决了深层网络中的梯度消失问题,使训练更深的网络成为可能[^5]。 - 论文标题:Deep Residual Learning for Image Recognition - 下载地址:[https://arxiv.org/pdf/1512.03385.pdf](https://arxiv.org/pdf/1512.03385.pdf) 4. **胶囊网络(Capsule Network)**: 虽然胶囊网络的实际应用效果不如理论预期,但它对监督学习和卷积的理解具有革命性意义[^2]。 - 论文标题:Dynamic Routing Between Capsules - 下载地址:[https://arxiv.org/pdf/1710.09829.pdf](https://arxiv.org/pdf/1710.09829.pdf) 5. **BERT**: BERT 是自然语言处理领域的突破性工作,虽然其预训练阶段是无监督的,但微调阶段通常采用监督学习的方式[^6]。 - 论文标题:BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding - 下载地址:[https://arxiv.org/pdf/1810.04805.pdf](https://arxiv.org/pdf/1810.04805.pdf) ### 如何获取更多论文 - **Google Scholar**:可以通过搜索关键词如“supervised learning”或“deep learning supervised”找到相关论文,并尝试从官方链接或第三方网站下载。 - **arXiv**:这是许多机器学习和人工智能论文的开源平台,可以直接搜索并下载PDF文件。 - **学术会议官网**:例如 NeurIPS、ICML、CVPR 等会议官网,通常会提供论文的下载链接。 ```python # 示例代码:如何使用 Python 自动化下载 PDF 文件 import requests def download_paper(url, filename): response = requests.get(url) if response.status_code == 200: with open(filename, 'wb') as f: f.write(response.content) print(f"Paper downloaded successfully as {filename}") else: print("Failed to download paper") # 使用示例 download_paper('https://arxiv.org/pdf/1512.03385.pdf', 'resnet_paper.pdf') ```
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