Feedforward Neural Networks Basics

Deep Learning

• A branch of machine learning 机器学习的一个分支

• Re-branded name for neural networks 神经网络的重命名

• Deep: Many layers are chained together in modern deep learning models 深度：现在深度学习模型中的链式链接的多层

• Neural Networks: Historically inspired by the way computation works in the brain 神经网络：历史上受大脑计算方式的启发

  • Consists of computation units called neurons 由称为神经元的计算单元组成

Feedforward Neural Network 前馈神经网络

• Also called multilayer perceptron 也被称为多层感知机

• E.g. of architecture: 架构示例

  

• Each arrow carries a weight, reflecting its importance 每个箭头都会携带一个权重，以反应其重要性

• Certain layers have non-linear activation functions 某些层具有非线性的激活函数

Neuron 神经元

• Each neuron is a function: 每个神经元是一个函数

  • Given input x, compute real-value h: 给定输入x，计算实值h

  
  
  

  • Scales input (with weights, w) and adds offset (bias, b) 通过权重w缩放输入并添加偏移量（偏置，b）
  • Applies non-linear function, such as logistic sigmoid, hyperbolic sigmoid(tanh), or rectified linear unit 应用非线性函数，如逻辑sigmoid、双曲sigmoid（tanh）或修正线性单元
  • w and b are parameters of the model w 和 b 是模型的参数

• Typically hava several hidden units 通常有几个隐藏单元. E.g.

  • Each with its own weights w_i, and bias terms b_i 每个单元都有自己的权重 w_i，和偏置项 b_i

  • Can be expressed using matrix and vector operators 可以使用矩阵和向量运算符表示:

  • Where is a matrix comprising the weight vectors and 是一个包含权重向量的矩阵 is a vector of all bias terms 是所有偏置项的向量

  • Non-linear function applied element-wise 非线性函数逐元素应用

Output Layer 输出层

• For binary classification problem: Sigmoid Activation Function 对于二元分类问题：Sigmoid 激活函数

• Multi-class classification problem: Softmax Activation Function ensures probabilities are greater than 0 and sum to 1 多类分类问题：Softmax 激活函数确保概率大于0且和为1:

Optimization

• Consider how well the model fits the training data, in terms of the probability it assigns to the correct output 考虑模型如何拟合训练数据，即它对正确输出所分配的概率

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  • Want to maximize total probability L 想要最大化总概率 L

  • Equivalently minimize -log L with respect to parameters 等价地，以参数最小化 -log L

• Trained using gradient descent 使用梯度下降进行训练

  • Tools like tensorflow, pytorch, dynet use autodiff to compute gradients automatically 像 tensorflow, pytorch, dynet 这样的工具用于自动计算梯度

Regularization 正则化

• Have many parameters, so the model overfits easily 有许多参数，所以模型很容易过拟合

• Low bias, high variance 偏差较低，方差较高

• Regularization is very import in neural networks 在神经网络中，正则化非常重要

• L1-norm: sum of absolute values of all parameters L1范数：所有参数的绝对值之和

• L2-norm: sum of squares of all parameters L2范数：所有参数的平方之和

• Dropout: randomly zero-out some neurons of a layer Dropout：随机将某一层的部分神经元值设为零

  • If a dropout rate = 0.1, a random 10% of neurons now have 0 values 如果Dropout比率 = 0.1，那么随机10%的神经元现在的值为0

  

  • Can apply dropout to any layer, but in practice, mostly to the hidden layers 可以在任何层应用dropout，但实际上，主要应用于隐藏层

Applications in NLP

Topic Classification 主题分类

• Given a document, classify it into a predefined set of topics. E.g. economy, politics, sports 给定一个文档，将其分类到预定义的主题集合中。例如：经济，政治，体育

• Input: Bag-of-words 输入：词袋模型

  Example input:
  
  

• Training:

  Architecture:
  
  
  
  
  Hidden Layers:
  
  
  
  
  
  
  

  • Randomly initialize W and b
  • E.g:

    Input:
    
    Output: : Probability distribution over
    
    Loss: if true label is
    

• Prediction:

  • E.g.

    Input:
    
    Output:
    
    Predicted class is
    

• Potential Improvements: 可能的改进

  • Use Bag of bigrams as input 使用bigrams的词袋作为输入
  • Preprocess text to lemmatize words and remove stopwords 预处理文本，对词进行词元化并去除停用词
  • Instead of raw counts, can weight words using TF-IDF or indicators 可以使用TF-IDF或指标来权衡单词，而不是原始计数

Language Model as Classifiers 语言模型作为分类器

• Language Models can be considered simple classifiers 语言模型可以被视为简单的分类器.

  • E.g. For a trigram model: classifies the likely next word in a sequence, given salt and and 给出了在给定 salt 和 and 的情况下，可能的下一个词的分类

• Feedforward Neural Network Language Model 前向传播神经网络语言模型

  • Use neural network as a classifier to model 使用神经网络作为分类器来模型
  • Input features: The previous words 输入特征：前面的单词
  • Output classes: the next word 输出类别：下一个单词
  • Use Word Embeddings to represent each word 使用词嵌入来表示每个单词
    • E.g. of Word Embeddings: 词嵌入的例子

      

Word Embeddings 词嵌入

• Maps discrete word symbols to continuous vectors in a relatively low dimensional space 将离散的词符号映射到相对较低维度的连续向量空间中

• Word embeddings allow the model to capture similarity between words 词嵌入允许模型捕获单词之间的相似性

• In feed-forward neural network language model, the first layer is the sum of input word embeddings 在前向传播神经网络语言模型中，第一层是输入词嵌入的和

Training a Feed-Forward Neural Network Language Model 训练前向传播神经网络语言模型

• E.g.

• Lookup word embeddings () for a, cow, and eats

• Concatenate them and feed it to the network 将它们连接起来并输入网络:

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• gives the probability distribution over all words in the vocabulary 给出了所有词汇表中单词的概率分布

  • E.g.

  
  
  
  

• Loss:

• Most parameters are in the word embeddings W₁ (size = d * |V|) and the output embeddings W₃ (size = |V| * d) 大部分参数都在词嵌入 W₁ (大小 = d * |V|) 和输出嵌入 W₃ (大小 = |V| * d)

• Example Architecture:

  
  
  

• Problem of Count-based N-gram models: 基于计数的N-gram模型的问题

  • Cheap to train 便宜的训练
  • Problems with sparsity and scaling to larger contexts 在稀疏性和大规模上下文的扩展性上存在问题
  • Don’t adequately capture properties of words 不能充分捕获单词的属性

• Advantages of Feed-Forward Neural Network Language Model: 前向传播神经网络语言模型的优点

  • Automatically capture word properties, leading to more robust estimates 自动捕获单词的属性，导致更稳健的估计

Feed-Forward Neural Network for POS Tagging 用于词性标注的前向传播神经网络

• POS tagging can also be framed as classification: 词性标注也可以被框定为分类

  • -> classifies the likely POS tag for eats 对eats的可能的词性标签进行分类

• Feed-Forward Neural Network Language Model architecture can be adapted to the task directly 前向传播神经网络语言模型的架构可以直接适应这个任务

• Inputs:

  • recent words 最近的词:
  • recent tags 最近的标签:

• Outputs:

  • current tags:

• Frame as neural network with:

  • 5 inputs: 3 word embeddings and 2 tag embeddings 5个输入：3个词嵌入和2个标签嵌入
  • 1 output: vector of size |T|, using softmax 1个输出：大小为|T|的向量，其中|T|是词性标签集的大小

• Training to minimize:

• Example Architecture:

  
  
  

Convolutional Networks

Convolutional Networks 卷积网络

• Commonly used in computer vision 常用于计算机视觉

• Identify indicative local predictors 确定指示性本地预测因子

• Combine them to produce a fixed-size representation 将它们合并，形成固定大小的表示

Convolutional Networks for NLP

• Sliding window over sequence 按顺序滑动窗口

• W = convolution filter (linear transformation + tanh) W = 卷积滤波器（线性变换+tanh）。

• max-pool to produce a fixed-size representation max-pool来产生一个固定大小的表示

• Example architecture: