DOCSLIB.ORG

CSE 152: Computer Vision Manmohan Chandraker

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

CSE 152: Computer Vision Manmohan Chandraker Lecture 15: Optimization in CNNs Recap Engineered against learned features Label Convolutional filters are trained in a Dense supervised manner by back-propagating classification error Dense Dense Convolution + pool Label Convolution + pool Classifier Convolution + pool Pooling Convolution + pool Feature extraction Convolution + pool Image Image Jia-Bin Huang and Derek Hoiem, UIUC Two-layer perceptron network Slide credit: Pieter Abeel and Dan Klein Neural networks Non-linearity Activation functions Multi-layer neural network From fully connected to convolutional networks next layer image Convolutional layer Slide: Lazebnik Spatial filtering is convolution Convolutional Neural Networks [Slides credit: Efstratios Gavves] 2D spatial filters Filters over the whole image Weight sharing Insight: Images have similar features at various spatial locations! Key operations in a CNN Feature maps Spatial pooling Non-linearity Convolution (Learned) . Input Image Input Feature Map Source: R. Fergus, Y. LeCun Slide: Lazebnik Convolution as a feature extractor Key operations in a CNN Feature maps Rectified Linear Unit (ReLU) Spatial pooling Non-linearity Convolution (Learned) Input Image Source: R. Fergus, Y. LeCun Slide: Lazebnik Key operations in a CNN Feature maps Spatial pooling Max Non-linearity Convolution (Learned) Input Image Source: R. Fergus, Y. LeCun Slide: Lazebnik Pooling operations • Aggregate multiple values into a single value • Invariance to small transformations • Keep only most important information for next layer • Reduces the size of the next layer • Fewer parameters, faster computations • Observe larger receptive field in next layer • Hierarchically extract more abstract features Key operations in a CNN Feature maps Spatial pooling Non-linearity Convolution (Learned) . Input Image Input Feature Map Source: R. Fergus, Y. LeCun Slide: Lazebnik Convolution as a feature extractor 1 x 1 convolutions 1 x 1 convolution layers also possible, equivalent to a dot product. Types of Neural Networks Convolutional Neural Networks Optimization in CNNs Learning w § Training examples § Objective: a misclassification loss § Procedure: § Gradient descent or hill climbing Slide credit: Pieter Abeel and Dan Klein A 3-layer network for digit recognition MNIST dataset Cost function • The network tries to approximate the function y(x) and its output is a • We use a quadratic cost function, or MSE, or “L2-loss”. Gradient descent Stochastic gradient descent Update rules for each parameter: Cost function is a sum over all the training samples: Gradient from entire training set: Usually, n is very large. Stochastic gradient descent Gradient from entire training set: • For large training data, gradient computation takes a long time • Leads to “slow learning” • Instead, consider a mini-batch with m samples • If sample size is large enough, properties approximate the dataset Stochastic gradient descent Stochastic gradient descent Stochastic gradient descent Stochastic gradient descent Build up velocity as a running mean of gradients. Layer to layer relationship Cost and gradient computation Chain rule of differentiation This is all you need to know to get the gradients in a neural network! Backpropagation This is all you need to know to get the gradients in a neural network! Backpropagation: application of chain rule in certain order, taking advantage of forward propagation to efficiently compute gradients. Backpropagation example [Slides credit: Fei-Fei Li] Backpropagation example Backpropagation example Backpropagation example Backpropagation example Backpropagation example Backpropagation example Backpropagation example Backpropagation example Backpropagation example Backpropagation example Backpropagation example Backpropagation example Backpropagation example Backpropagation example Backpropagation example Backpropagation example Add gate: gradient distributor Mul gate: gradient switcher Patterns in backpropagation Convolutional layer is differentiable Max Pooling Average Pooling Transfer Learning in CNNs Transfer Learning • Improvement of learning in a new task through the transfer of knowledge from a related task that has already been learned. • Weight initialization for CNN Learning and Transferring Mid-Level Image Representations using Convolutional Neural Networks [Oquab et al. CVPR 2014] Slide: Jiabin Huang Transfer Learning CNNs are good at transfer learning Fine-tune hT using hS as initialization Initializng hT with hS Initializng hT with hS Initializng hT with hS Initializng hT with hS Strategy for fine-tuning of data needed Amount Use hS as a feature extractor for hT Transfer learning is a common choice CNN Architectures AlexNet architecture Architectural details of AlexNet • Similar framework to LeCun 1998 but: • Bigger model (7 hidden layers, 650k units, 60M parameters) • More data (106 images instead of 103 images) • GPU implementation (50 times speedup over CPU) Removing layer 7 Removing layers 6 and 7 Removing layers 3 and 4 Removing layers 3, 4, 6 and 7 VGGNet architecture • Much more accurate • AlexNet : 18.2% top-5 error • VGGNet: 6.8% top-5 error • More than twice as many layers • Filters are much smaller • Harder and slower to train ResNet: going real deep Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun, Deep Residual Learning for Image Recognition, CVPR 2016 Bigger not better: innovations typically reduce parameters, despite deeper nets Simply stacking layers Deep residual learning Deep residual learning Deep residual learning Deep residual learning Plain Net • Simple design • Use only 3x3 conv (like VGG) • No hidden FC Deep residual learning Key ideas for CNN architectures • Convolutional layers – Same local functions evaluated everywhere – Much fewer parameters • Pooling – Larger receptive field • ReLU – Maintain a gradient signal over large portion of domain • Limit parameters – Sequence of 3x3 filters instead of large filters – 1x1 convolutions to reduce feature dimensions • Skip network – Easier optimization with greater depth.
Recommended publications
  • Synthesizing Images of Humans in Unseen Poses

    Synthesizing Images of Humans in Unseen Poses

    Synthesizing Images of Humans in Unseen Poses Guha Balakrishnan Amy Zhao Adrian V. Dalca Fredo Durand MIT MIT MIT and MGH MIT [email protected] [email protected] [email protected] [email protected] John Guttag MIT [email protected] Abstract We address the computational problem of novel human pose synthesis. Given an image of a person and a desired pose, we produce a depiction of that person in that pose, re- taining the appearance of both the person and background. We present a modular generative neural network that syn- Source Image Target Pose Synthesized Image thesizes unseen poses using training pairs of images and poses taken from human action videos. Our network sepa- Figure 1. Our method takes an input image along with a desired target pose, and automatically synthesizes a new image depicting rates a scene into different body part and background lay- the person in that pose. We retain the person’s appearance as well ers, moves body parts to new locations and refines their as filling in appropriate background textures. appearances, and composites the new foreground with a hole-filled background. These subtasks, implemented with separate modules, are trained jointly using only a single part details consistent with the new pose. Differences in target image as a supervised label. We use an adversarial poses can cause complex changes in the image space, in- discriminator to force our network to synthesize realistic volving several moving parts and self-occlusions. Subtle details conditioned on pose. We demonstrate image syn- details such as shading and edges should perceptually agree thesis results on three action classes: golf, yoga/workouts with the body’s configuration.
  • Training Autoencoders by Alternating Minimization

    Training Autoencoders by Alternating Minimization

    Under review as a conference paper at ICLR 2018 TRAINING AUTOENCODERS BY ALTERNATING MINI- MIZATION Anonymous authors Paper under double-blind review ABSTRACT We present DANTE, a novel method for training neural networks, in particular autoencoders, using the alternating minimization principle. DANTE provides a distinct perspective in lieu of traditional gradient-based backpropagation techniques commonly used to train deep networks. It utilizes an adaptation of quasi-convex optimization techniques to cast autoencoder training as a bi-quasi-convex optimiza- tion problem. We show that for autoencoder configurations with both differentiable (e.g. sigmoid) and non-differentiable (e.g. ReLU) activation functions, we can perform the alternations very effectively. DANTE effortlessly extends to networks with multiple hidden layers and varying network configurations. In experiments on standard datasets, autoencoders trained using the proposed method were found to be very promising and competitive to traditional backpropagation techniques, both in terms of quality of solution, as well as training speed. 1 INTRODUCTION For much of the recent march of deep learning, gradient-based backpropagation methods, e.g. Stochastic Gradient Descent (SGD) and its variants, have been the mainstay of practitioners. The use of these methods, especially on vast amounts of data, has led to unprecedented progress in several areas of artificial intelligence. On one hand, the intense focus on these techniques has led to an intimate understanding of hardware requirements and code optimizations needed to execute these routines on large datasets in a scalable manner. Today, myriad off-the-shelf and highly optimized packages exist that can churn reasonably large datasets on GPU architectures with relatively mild human involvement and little bootstrap effort.
  • Learning to Learn by Gradient Descent by Gradient Descent

    Learning to Learn by Gradient Descent by Gradient Descent

    Learning to learn by gradient descent by gradient descent Marcin Andrychowicz1, Misha Denil1, Sergio Gómez Colmenarejo1, Matthew W. Hoffman1, David Pfau1, Tom Schaul1, Brendan Shillingford1,2, Nando de Freitas1,2,3 1Google DeepMind 2University of Oxford 3Canadian Institute for Advanced Research [email protected] {mdenil,sergomez,mwhoffman,pfau,schaul}@google.com [email protected], [email protected] Abstract The move from hand-designed features to learned features in machine learning has been wildly successful. In spite of this, optimization algorithms are still designed by hand. In this paper we show how the design of an optimization algorithm can be cast as a learning problem, allowing the algorithm to learn to exploit structure in the problems of interest in an automatic way. Our learned algorithms, implemented by LSTMs, outperform generic, hand-designed competitors on the tasks for which they are trained, and also generalize well to new tasks with similar structure. We demonstrate this on a number of tasks, including simple convex problems, training neural networks, and styling images with neural art. 1 Introduction Frequently, tasks in machine learning can be expressed as the problem of optimizing an objective function f(✓) defined over some domain ✓ ⇥. The goal in this case is to find the minimizer 2 ✓⇤ = arg min✓ ⇥ f(✓). While any method capable of minimizing this objective function can be applied, the standard2 approach for differentiable functions is some form of gradient descent, resulting in a sequence of updates ✓ = ✓ ↵ f(✓ ) . t+1 t − tr t The performance of vanilla gradient descent, however, is hampered by the fact that it only makes use of gradients and ignores second-order information.
  • Memristor-Based Approximated Computation

    Memristor-Based Approximated Computation

    Memristor-based Approximated Computation Boxun Li1, Yi Shan1, Miao Hu2, Yu Wang1, Yiran Chen2, Huazhong Yang1 1Dept. of E.E., TNList, Tsinghua University, Beijing, China 2Dept. of E.C.E., University of Pittsburgh, Pittsburgh, USA 1 Email: [email protected] Abstract—The cessation of Moore’s Law has limited further architectures, which not only provide a promising hardware improvements in power efficiency. In recent years, the physical solution to neuromorphic system but also help drastically close realization of the memristor has demonstrated a promising the gap of power efficiency between computing systems and solution to ultra-integrated hardware realization of neural net- works, which can be leveraged for better performance and the brain. The memristor is one of those promising devices. power efficiency gains. In this work, we introduce a power The memristor is able to support a large number of signal efficient framework for approximated computations by taking connections within a small footprint by taking the advantage advantage of the memristor-based multilayer neural networks. of the ultra-integration density [7]. And most importantly, A programmable memristor approximated computation unit the nonvolatile feature that the state of the memristor could (Memristor ACU) is introduced first to accelerate approximated computation and a memristor-based approximated computation be tuned by the current passing through itself makes the framework with scalability is proposed on top of the Memristor memristor a potential, perhaps even the best, device to realize ACU. We also introduce a parameter configuration algorithm of neuromorphic computing systems with picojoule level energy the Memristor ACU and a feedback state tuning circuit to pro- consumption [8], [9].
  • A Survey of Autonomous Driving: Common Practices and Emerging Technologies

    A Survey of Autonomous Driving: Common Practices and Emerging Technologies

    Accepted March 22, 2020 Digital Object Identifier 10.1109/ACCESS.2020.2983149 A Survey of Autonomous Driving: Common Practices and Emerging Technologies EKIM YURTSEVER1, (Member, IEEE), JACOB LAMBERT 1, ALEXANDER CARBALLO 1, (Member, IEEE), AND KAZUYA TAKEDA 1, 2, (Senior Member, IEEE) 1Nagoya University, Furo-cho, Nagoya, 464-8603, Japan 2Tier4 Inc. Nagoya, Japan Corresponding author: Ekim Yurtsever (e-mail: [email protected]). ABSTRACT Automated driving systems (ADSs) promise a safe, comfortable and efficient driving experience. However, fatalities involving vehicles equipped with ADSs are on the rise. The full potential of ADSs cannot be realized unless the robustness of state-of-the-art is improved further. This paper discusses unsolved problems and surveys the technical aspect of automated driving. Studies regarding present challenges, high- level system architectures, emerging methodologies and core functions including localization, mapping, perception, planning, and human machine interfaces, were thoroughly reviewed. Furthermore, many state- of-the-art algorithms were implemented and compared on our own platform in a real-world driving setting. The paper concludes with an overview of available datasets and tools for ADS development. INDEX TERMS Autonomous Vehicles, Control, Robotics, Automation, Intelligent Vehicles, Intelligent Transportation Systems I. INTRODUCTION necessary here. CCORDING to a recent technical report by the Eureka Project PROMETHEUS [11] was carried out in A National Highway Traffic Safety Administration Europe between 1987-1995, and it was one of the earliest (NHTSA), 94% of road accidents are caused by human major automated driving studies. The project led to the errors [1]. Against this backdrop, Automated Driving Sys- development of VITA II by Daimler-Benz, which succeeded tems (ADSs) are being developed with the promise of in automatically driving on highways [12].
  • Training Neural Networks Without Gradients: a Scalable ADMM Approach

    Training Neural Networks Without Gradients: a Scalable ADMM Approach

    Training Neural Networks Without Gradients: A Scalable ADMM Approach Gavin Taylor1 [email protected] Ryan Burmeister1 Zheng Xu2 [email protected] Bharat Singh2 [email protected] Ankit Patel3 [email protected] Tom Goldstein2 [email protected] 1United States Naval Academy, Annapolis, MD USA 2University of Maryland, College Park, MD USA 3Rice University, Houston, TX USA Abstract many parameters. Because big datasets provide results that With the growing importance of large network (often dramatically) outperform the prior state-of-the-art in models and enormous training datasets, GPUs many machine learning tasks, researchers are willing to have become increasingly necessary to train neu- purchase specialized hardware such as GPUs, and commit ral networks. This is largely because conven- large amounts of time to training models and tuning hyper- tional optimization algorithms rely on stochastic parameters. gradient methods that don’t scale well to large Gradient-based training methods have several properties numbers of cores in a cluster setting. Further- that contribute to this need for specialized hardware. First, more, the convergence of all gradient methods, while large amounts of data can be shared amongst many including batch methods, suffers from common cores, existing optimization methods suffer when paral- problems like saturation effects, poor condition- lelized. Second, training neural nets requires optimizing ing, and saddle points. This paper explores an highly non-convex objectives that exhibit saddle points, unconventional training method that uses alter- poor conditioning, and vanishing gradients, all of which nating direction methods and Bregman iteration slow down gradient-based methods such as stochastic gra- to train networks without gradient descent steps.
  • Training Deep Networks with Stochastic Gradient Normalized by Layerwise Adaptive Second Moments

    Training Deep Networks with Stochastic Gradient Normalized by Layerwise Adaptive Second Moments

    Training Deep Networks with Stochastic Gradient Normalized by Layerwise Adaptive Second Moments Boris Ginsburg 1 Patrice Castonguay 1 Oleksii Hrinchuk 1 Oleksii Kuchaiev 1 Ryan Leary 1 Vitaly Lavrukhin 1 Jason Li 1 Huyen Nguyen 1 Yang Zhang 1 Jonathan M. Cohen 1 Abstract We started with Adam, and then (1) replaced the element- wise second moment with the layer-wise moment, (2) com- We propose NovoGrad, an adaptive stochastic puted the first moment using gradients normalized by layer- gradient descent method with layer-wise gradient wise second moment, (3) decoupled weight decay (WD) normalization and decoupled weight decay. In from normalized gradients (similar to AdamW). our experiments on neural networks for image classification, speech recognition, machine trans- The resulting algorithm, NovoGrad, combines SGD’s and lation, and language modeling, it performs on par Adam’s strengths. We applied NovoGrad to a variety of or better than well-tuned SGD with momentum, large scale problems — image classification, neural machine Adam, and AdamW. Additionally, NovoGrad (1) translation, language modeling, and speech recognition — is robust to the choice of learning rate and weight and found that in all cases, it performs as well or better than initialization, (2) works well in a large batch set- Adam/AdamW and SGD with momentum. ting, and (3) has half the memory footprint of Adam. 2. Related Work NovoGrad belongs to the family of Stochastic Normalized 1. Introduction Gradient Descent (SNGD) optimizers (Nesterov, 1984; Hazan et al., 2015). SNGD uses only the direction of the The most popular algorithms for training Neural Networks stochastic gradient gt to update the weights wt: (NNs) are Stochastic Gradient Descent (SGD) with mo- gt mentum (Polyak, 1964; Sutskever et al., 2013) and Adam wt+1 = wt − λt · (Kingma & Ba, 2015).
  • Automated Source Code Generation and Auto-Completion Using Deep Learning: Comparing and Discussing Current Language Model-Related Approaches

    Automated Source Code Generation and Auto-Completion Using Deep Learning: Comparing and Discussing Current Language Model-Related Approaches

    Article Automated Source Code Generation and Auto-Completion Using Deep Learning: Comparing and Discussing Current Language Model-Related Approaches Juan Cruz-Benito 1,* , Sanjay Vishwakarma 2,†, Francisco Martin-Fernandez 1 and Ismael Faro 1 1 IBM Quantum, IBM T.J. Watson Research Center, Yorktown Heights, NY 10598, USA; [email protected] (F.M.-F.); [email protected] (I.F.) 2 Electrical and Computer Engineering, Carnegie Mellon University, Mountain View, CA 94035, USA; [email protected] * Correspondence: [email protected] † Intern at IBM Quantum at the time of writing this paper. Abstract: In recent years, the use of deep learning in language models has gained much attention. Some research projects claim that they can generate text that can be interpreted as human writ- ing, enabling new possibilities in many application areas. Among the different areas related to language processing, one of the most notable in applying this type of modeling is programming languages. For years, the machine learning community has been researching this software engi- neering area, pursuing goals like applying different approaches to auto-complete, generate, fix, or evaluate code programmed by humans. Considering the increasing popularity of the deep learning- enabled language models approach, we found a lack of empirical papers that compare different deep learning architectures to create and use language models based on programming code. This paper compares different neural network architectures like Average Stochastic Gradient Descent (ASGD) Weight-Dropped LSTMs (AWD-LSTMs), AWD-Quasi-Recurrent Neural Networks (QRNNs), and Citation: Cruz-Benito, J.; Transformer while using transfer learning and different forms of tokenization to see how they behave Vishwakarma, S.; Martin- Fernandez, F.; Faro, I.
  • GEE: a Gradient-Based Explainable Variational Autoencoder for Network Anomaly Detection

    GEE: a Gradient-Based Explainable Variational Autoencoder for Network Anomaly Detection

    GEE: A Gradient-based Explainable Variational Autoencoder for Network Anomaly Detection Quoc Phong Nguyen Kar Wai Lim Dinil Mon Divakaran National University of Singapore National University of Singapore Trustwave [email protected] [email protected] [email protected] Kian Hsiang Low Mun Choon Chan National University of Singapore National University of Singapore [email protected] [email protected] Abstract—This paper looks into the problem of detecting number of factors, such as end-user behavior, customer busi- network anomalies by analyzing NetFlow records. While many nesses (e.g., banking, retail), applications, location, time of the previous works have used statistical models and machine learning day, and are expected to evolve with time. Such diversity and techniques in a supervised way, such solutions have the limitations that they require large amount of labeled data for training and dynamism limits the utility of rule-based detection systems. are unlikely to detect zero-day attacks. Existing anomaly detection Next, as capturing, storing and processing raw traffic from solutions also do not provide an easy way to explain or identify such high capacity networks is not practical, Internet routers attacks in the anomalous traffic. To address these limitations, today have the capability to extract and export meta data such we develop and present GEE, a framework for detecting and explaining anomalies in network traffic. GEE comprises of two as NetFlow records [3]. With NetFlow, the amount of infor- components: (i) Variational Autoencoder (VAE) — an unsuper- mation captured is brought down by orders of magnitude (in vised deep-learning technique for detecting anomalies, and (ii) a comparison to raw packet capture), not only because a NetFlow gradient-based fingerprinting technique for explaining anomalies.
  • Optimization and Gradient Descent INFO-4604, Applied Machine Learning University of Colorado Boulder

    Optimization and Gradient Descent INFO-4604, Applied Machine Learning University of Colorado Boulder

    Optimization and Gradient Descent INFO-4604, Applied Machine Learning University of Colorado Boulder September 11, 2018 Prof. Michael Paul Prediction Functions Remember: a prediction function is the function that predicts what the output should be, given the input. Prediction Functions Linear regression: f(x) = wTx + b Linear classification (perceptron): f(x) = 1, wTx + b ≥ 0 -1, wTx + b < 0 Need to learn what w should be! Learning Parameters Goal is to learn to minimize error • Ideally: true error • Instead: training error The loss function gives the training error when using parameters w, denoted L(w). • Also called cost function • More general: objective function (in general objective could be to minimize or maximize; with loss/cost functions, we want to minimize) Learning Parameters Goal is to minimize loss function. How do we minimize a function? Let’s review some math. Rate of Change The slope of a line is also called the rate of change of the line. y = ½x + 1 “rise” “run” Rate of Change For nonlinear functions, the “rise over run” formula gives you the average rate of change between two points Average slope from x=-1 to x=0 is: 2 f(x) = x -1 Rate of Change There is also a concept of rate of change at individual points (rather than two points) Slope at x=-1 is: f(x) = x2 -2 Rate of Change The slope at a point is called the derivative at that point Intuition: f(x) = x2 Measure the slope between two points that are really close together Rate of Change The slope at a point is called the derivative at that point Intuition: Measure the
  • 1 Convolution

    1 Convolution

    CS1114 Section 6: Convolution February 27th, 2013 1 Convolution Convolution is an important operation in signal and image processing. Convolution op- erates on two signals (in 1D) or two images (in 2D): you can think of one as the \input" signal (or image), and the other (called the kernel) as a “filter” on the input image, pro- ducing an output image (so convolution takes two images as input and produces a third as output). Convolution is an incredibly important concept in many areas of math and engineering (including computer vision, as we'll see later). Definition. Let's start with 1D convolution (a 1D \image," is also known as a signal, and can be represented by a regular 1D vector in Matlab). Let's call our input vector f and our kernel g, and say that f has length n, and g has length m. The convolution f ∗ g of f and g is defined as: m X (f ∗ g)(i) = g(j) · f(i − j + m=2) j=1 One way to think of this operation is that we're sliding the kernel over the input image. For each position of the kernel, we multiply the overlapping values of the kernel and image together, and add up the results. This sum of products will be the value of the output image at the point in the input image where the kernel is centered. Let's look at a simple example. Suppose our input 1D image is: f = 10 50 60 10 20 40 30 and our kernel is: g = 1=3 1=3 1=3 Let's call the output image h.
  • Deep Clustering with Convolutional Autoencoders

    Deep Clustering with Convolutional Autoencoders

    Deep Clustering with Convolutional Autoencoders Xifeng Guo1, Xinwang Liu1, En Zhu1, and Jianping Yin2 1 College of Computer, National University of Defense Technology, Changsha, 410073, China [email protected] 2 State Key Laboratory of High Performance Computing, National University of Defense Technology, Changsha, 410073, China Abstract. Deep clustering utilizes deep neural networks to learn fea- ture representation that is suitable for clustering tasks. Though demon- strating promising performance in various applications, we observe that existing deep clustering algorithms either do not well take advantage of convolutional neural networks or do not considerably preserve the local structure of data generating distribution in the learned feature space. To address this issue, we propose a deep convolutional embedded clus- tering algorithm in this paper. Specifically, we develop a convolutional autoencoders structure to learn embedded features in an end-to-end way. Then, a clustering oriented loss is directly built on embedded features to jointly perform feature refinement and cluster assignment. To avoid feature space being distorted by the clustering loss, we keep the decoder remained which can preserve local structure of data in feature space. In sum, we simultaneously minimize the reconstruction loss of convolutional autoencoders and the clustering loss. The resultant optimization prob- lem can be effectively solved by mini-batch stochastic gradient descent and back-propagation. Experiments on benchmark datasets empirically validate