Ref: CS231n Winter 2016: Lecture 4: Backpropagation Ref: How to implement a NN:中文翻译版本 Ref: Jacobian矩阵和Hessian矩阵 关于这部分内容,请详看链接二内容,并请自在本上手动推导. Chain Rule: 根据Chain Rule进行梯度传递:  x = 1.37 代入1/x的导数 --> -0.53  x = 0.37 代入1的导数 乘以 (-0.53) --> -0.53  x = -1,…

1. Feedforward and cost function; 2.Regularized cost function: 3.Sigmoid gradient The gradient for the sigmoid function can be computed as: where: 4.Random initialization randInitializeWeights.m function W = randInitializeWeights(L_in, L_out) %RANDIN…

https://page.mi.fu-berlin.de/rojas/neural/chapter/K7.pdf 7.1 Learning as gradient descent We saw in the last chapter that multilayered networks are capable of computing a wider range of Boolean functions than networks with a single layer of computing…

In the last chapter we saw how neural networks can learn their weights and biases using the gradient descent algorithm. There was, however, a gap in our explanation: we didn't discuss how to compute the gradient of the cost function. That's quite a g…

假设我们有一个固定样本集,它包含 个样例.我们可以用批量梯度下降法来求解神经网络.具体来讲,对于单个样例(x,y),其代价函数为:这是一个(二分之一的)方差代价函数.给定一个包含 个样例的数据集,我们可以定义整体代价函数为: 以上公式中的第一项 是一个均方差项.第二项是一个规则化项(也叫权重衰减项),其目的是减小权重的幅度,防止过度拟合. [注:通常权重衰减的计算并不使用偏置项 ,比如我们在 的定义中就没有使用.一般来说,将偏置项包含在权重衰减项中只会对最终的神经网络产生很小的影响.在贝叶斯规则…

Backpropagation algorithm(反向传播算法) Θij(l) is a real number. Forward propagation 上图是给出一个training example(x,y),是怎么进行forward propagation的. Backpropagation algorithm(一个trainning example) 因为我们是先求的δ(4),再求δ(3),再一层层往input layer那边推,所以叫做Backpropagation algorith…

在下图所示的Neural Network中,我们将拥有三个节点的layer1及layer4分别称为输入和输出层,而中间的两层layer2,layer3称为隐藏层(hidden layer).输入数据X,从左侧进入神经网络,经过层层传播最终从右侧输出的过程,称为Feedforward.而根据training set来调整参数的算法,称为Backpropagation Algorithm,即反向传播算法. 在Hidden layer的每个Node中,都存在一个non-linear unit,常用的是…

最近在看深度学习的东西,一开始看的吴恩达的UFLDL教程,有中文版就直接看了,后来发现有些地方总是不是很明确,又去看英文版,然后又找了些资料看,才发现,中文版的译者在翻译的时候会对省略的公式推导过程进行补充,但是补充的又是错的,难怪觉得有问题.反向传播法其实是神经网络的基础了,但是很多人在学的时候总是会遇到一些问题,或者看到大篇的公式觉得好像很难就退缩了,其实不难,就是一个链式求导法则反复用.如果不想看公式,可以直接把数值带进去,实际的计算一下,体会一下这个过程之后再来推导公式,这样就会觉得很容…

今天得主题是BP算法.大规模的神经网络可以使用batch gradient descent算法求解,也可以使用 stochastic gradient descent 算法,求解的关键问题在于求得每层中每个参数的偏导数,BP算法正是用来求解网络中参数的偏导数问题的. 先上一张吊炸天的图,可以看到BP的工作原理: 下面来看BP算法,用m个训练样本集合来train一个神经网络,对于该模型,首先需要定义一个代价函数,常见的代价函数有以下几种: 1)0-1损失函数:(0-1 loss function)…

之前我们在计算神经网络预测结果的时候我们采用了一种正向传播方法,我们从第一层开始正向一层一层进行计算,直到最后一层的ℎ…

今天得主题是BP算法.大规模的神经网络可以使用batch gradient descent算法求解,也可以使用 stochastic gradient descent 算法,求解的关键问题在于求得每层中每个参数的偏导数,BP算法正是用来求解网络中参数的偏导数问题的. 先上一张吊炸天的图,可以看到BP的工作原理: 下面来看BP算法,用m个训练样本集合来train一个神经网络,对于该模型,首先需要定义一个代价函数,常见的代价函数有以下几种: 1)0-1损失函数:(0-1 loss function)…

搞卷积神经网络的时候突然发现自己不清楚神经网络怎么训练了,满脸黑线,借此机会复习一下把. 首先放一位知乎大佬的解释.https://www.zhihu.com/question/27239198?rf=24827633 链式法则大一的时候高数就学会了,不过如果直接利用链式法则的化冗余的计算可是发杂的网络接受不了的,bp算法的特点便是通过反向计算的方式来解决冗余计算的问题.…

Relevant Readable Links Name Interesting topic Comment Edwin Chen 非参贝叶斯   徐亦达老板 Dirichlet Process 学习目标:Dirichlet Process, HDP, HDP-HMM, IBP, CRM Alex Kendall Geometry and Uncertainty in Deep Learning for Computer Vision 语义分割 colah's blog Feature Visu…

二十三(Convolution和Pooling练习)  三十八(Stacked CNN简单介绍) 三十六(关于构建深度卷积SAE网络的一点困惑) 五十(Deconvolution Network简单理解) 五十一(CNN的反向求导及练习)   Stacked Convolutional Auto-Encoders for Hierarchical Feature Extraction中提到的一个实验 作者认为加噪声用处不大,且max-pooling功能特别强大,大到像作者说的那样有了max-po…

Deep learning:三十七(Deep learning中的优化方法) Deep learning:四十一(Dropout简单理解) Deep learning:四十三(用Hessian Free方法训练Deep Network) Deep learning:四十五(maxout简单理解) Deep learning:四十六(DropConnect简单理解) Deep learning:四十七(Stochastic Pooling简单理解)   这部分内容应属于以下[Converge]系列…

摘要 本文是对 Andrew Ng 在 Coursera 上的机器学习课程中 Backpropagation Algorithm 一小节的延伸.文章分三个部分:第一部分给出一个简单的神经网络模型和 Backpropagation(以下简称 BP)算法的具体流程.第二部分以分别计算第一层和第二层中的第一个参数(parameters,在神经网络中也称之为 weights)的梯度为例来解释 BP 算法流程,并给出了具体的推导过程.第三个部分采用了更加直观的图例来解释 BP 算法的工作流程. 注:1.…

Principles of training multi-layer neural network using backpropagation http://galaxy.agh.edu.pl/~vlsi/AI/backp_t_en/backprop.html The project describes teaching process of multi-layer neural network employing backpropagation algorithm. To illustrate…

The goal of backpropagation is to compute the partial derivatives ∂C/∂w and ∂C/∂b of the cost function C with respect to any weight ww or bias b in the network. we use the quadratic cost function   two assumptions : 1: The first assumption we need is…

几个有助于加深对反向传播算法直观理解的网页,包括普通前向神经网络,卷积神经网络以及利用BP对一般性函数求导 A Visual Explanation of the Back Propagation Algorithm for Neural Networks By Sebastian Raschka, Michigan State University. Let's assume we are really into mountain climbing, and to add a little e…

Let's make a DQN 系列 Let's make a DQN: Theory September 27, 2016DQN This article is part of series Let's make a DQN. 1. Theory2. Implementation3. Debugging4. Full DQN5. Double DQN and Prioritized experience replay (available soon) Introduction In Febr…

When a golf player is first learning to play golf, they usually spend most of their time developing a basic swing. Only gradually do they develop other shots, learning to chip, draw and fade the ball, building on and modifying their basic swing. In a…

R2RT   Written Memories: Understanding, Deriving and Extending the LSTM Tue 26 July 2016 When I was first introduced to Long Short-Term Memory networks (LSTMs), it was hard to look past their complexity. I didn’t understand why they were designed the…

Week1: Machine Learning: A computer program is said to learn from experience E with respect to some class of tasks T and performance measure P, if its performance at tasks in T, as measured by P, improves with experience E. Supervised Learning:We alr…

Machine Learning Crash Course  |  Google Developers https://developers.google.com/machine-learning/crash-course/ Google's fast-paced, practical introduction to machine learning ML Concepts Introduction to Machine Learning As you'll discover, machine…

java神经网络组件Joone.Encog和Neuroph https://github.com/deeplearning4j/deeplearning4j http://muchong.com/html/201611/10796085.html Comparing Neural Networks in Neuroph, Encog and JOONE https://www.codeproject.com/articles/85385/comparing-neural-networks-in-…

Click here for a newer version (Knet7) of this tutorial. The code used in this version (KUnet) has been deprecated. There are a number of deep learning packages out there. However most sacrifice readability for efficiency. This has two disadvantages:…

Week 1: Machine Learning: A computer program is said to learn from experience E with respect to some class of tasks T and performance measure P, if its performance at tasks in T, as measured by P, improves with experience E. Supervised Learning:We al…

Machine Learning Note Introduction Introduction What is Machine Learning? Two definitions of Machine Learning are offered. Arthur Samuel described it as:"the filed of study that gives computers the ability to learn without being explicitly programmed…

About this Course If you want to break into cutting-edge AI, this course will help you do so. Deep learning engineers are highly sought after, and mastering deep learning will give you numerous new career opportunities. Deep learning is also a new "s…

##Linear Regression with One Variable Linear regression predicts a real-valued output based on an input value. We discuss the application of linear regression to housing price prediction, present the notion of a cost function, and introduce the gradi…