Incorporating Nesterov Momentum Into Adam

Total Page:16

File Type:pdf, Size:1020Kb

Incorporating Nesterov Momentum Into Adam Incorporating Nesterov Momentum into Adam Timothy Dozat 1 Introduction Algorithm 1 Gradient Descent gt ∇q f (q t−1) When attempting to improve the performance of a t−1 q t q t−1 − hgt deep learning system, there are more or less three approaches one can take: the first is to improve the structure of the model, perhaps adding another layer, sum (with decay constant m) of the previous gradi- switching from simple recurrent units to LSTM cells ents into a momentum vector m, and using that in- [4], or–in the realm of NLP–taking advantage of stead of the true gradient. This has the advantage of syntactic parses (e.g. as in [13, et seq.]); another ap- accelerating gradient descent learning along dimen- proach is to improve the initialization of the model, sions where the gradient remains relatively consis- guaranteeing that the early-stage gradients have cer- tent across training steps and slowing it along turbu- tain beneficial properties [3], or building in large lent dimensions where the gradient is significantly amounts of sparsity [6], or taking advantage of prin- oscillating. ciples of linear algebra [15]; the final approach is to try a more powerful learning algorithm, such as in- Algorithm 2 Classical Momentum cluding a decaying sum over the previous gradients gt ∇qt−1 f (q t−1) in the update [12], by dividing each parameter up- mt mmt−1 + gt date by the L2 norm of the previous updates for that q t q t−1 − hmt parameter [2], or even by foregoing first-order algo- rithms for more powerful but more computationally [14] show that Nesterov’s accelerated gradient costly second order algorithms [9]. This paper has (NAG) [11]–which has a provably better bound than as its goal the third option—improving the quality gradient descent–can be rewritten as a kind of im- of the final solution by using a faster, more powerful proved momentum. If we can substitute the defini- learning algorithm. tion for mt in place of the symbol mt in the parame- ter update as in (2) 2 Related Work q q − hm (1) 2.1 Momentum-based algorithms t t−1 t q t q t−1 − hmmt−1 − hgt (2) Gradient descent is a simple, well-known, and gen- erally very robust optimization algorithm where the we can see that the term mt−1 doesn’t depend on gradient of the function to be minimized with re- the current gradient gt —so in principle, we can get spect to the parameters (∇ f (q t−1)) is computed, and a superior step direction by applying the momentum a portion h of that gradient is subtracted off of the vector to the parameters before computing the gradi- parameters: ent. The authors provide empirical evidence that this Classical momentum [12] accumulates a decaying algorithm is superior to the gradient descent, classi- Algorithm 3 Nesterov’s accelerated gradient with adaptive moment estimation (Adam), combin- gt ∇qt−1 f (q t−1 − hmmt−1) ing classical momentum (using a decaying mean in- mt mmt−1 + gt stead of a decaying sum) with RMSProp to improve q t q t−1 − hmt performance on a number of benchmarks. In their algorithm, they include initialization bias correction terms, which offset some of the instability that ini- cal momentum, and Hessian-Free [9] algorithms for tializing m and n to 0 can create. conventionally difficult optimization objectives. Algorithm 6 Adam 2.2 L2 norm-based algorithms gt ∇qt−1 f (q t−1) [2] present adaptive subgradient descent (Ada- mt mmt−1 + (1 − m)gt L mt Grad), which divides h of every step by the 2 norm mˆ t 1−mt of all previous gradients; this slows down learning 2 nt nnt−1 + (1 − n)gt along dimensions that have already changed signifi- nt nˆt 1−nt cantly and speeds up learning along dimensions that mˆ t q t q t−1 − h p have only changed slightly, stabilizing the model’s nˆt +e representation of common features and allowing it to rapidly “catch up” its representation of rare fea- [5] also include an algorithm AdaMax that re- 1 tures. places the L2 norm with the L¥ norm, removing the need for nˆt and replacing nt and q t with the follow- Algorithm 4 AdaGrad ing updates: gt ∇ f (q t− ) qt−1 1 nt max(nnt− ;jgt j) 2 1 nt nt−1 + g mˆ t t q t q t−1 − h gt nt +e q t q t−1 − h p nt +e We can generalize this to RMSProp as well, using the L¥ norm in the denominator instead of the L2 One notable problem with AdaGrad is that the norm, giving what might be called the MaxaProp norm vector n eventually becomes so large that algorithm. training slows to a halt, preventing the model from 3 Methods reaching the local minimum; [16] go on to motivate RMSProp, an alternative to AdaGrad that replaces 3.1 NAG revisited the sum in n with a decaying mean parameterized t Adam combines RMSProp with classical momen- here by n. This allows the model to continue to learn tum. But as [14] show, NAG is in general supe- indefinitely. rior to classical momentum—so how would we go Algorithm 5 RMSProp about modifying Adam to use NAG instead? First, we rewrite the NAG algorithm to be more straight- gt ∇qt−1 f (q t−1) 2 forward and efficient to implement at the cost of nt nnt−1 + (1 − n)gt gt some intuitive readability. Momentum is most ef- q t q t−1 − h p nt +e fective with a warming schedule, so for complete- ness we parameterize m by t as well. Here, the 2.3 Combination Algorithm 7 NAG rewritten One might ask if combining the momentum-based gt ∇qt−1 f (q t−1) and norm-based methods might provide the ad- mt mt mt−1 + gt vantages of both. In fact, [5] successfully do so m¯ t gt + mt+1mt q t q t−1 − hm¯ t 1Most implementations of this kind of algorithm include an e parameter to keep the denominator from being too small and resulting in an irrecoverably large step vector m¯ contains the gradient update for the cur- rent timestep gt in addition to the momentum vector Algorithm 8 Nesterov-accelerated adaptive moment update for the next timestep mt+1mt , which needs estimation to be applied before taking the gradient at the next gt ∇qt−1 f (q t−1) gt timestep. We don’t need to apply the momentum gˆ t 1−∏i=1 mi vector for the current timestep anymore because we mt mmt−1 + (1 − m)gt mt already applied it in the last update of the parame- mˆ t t+1 1−∏i=1 mi ters, at timestep t − 1. 2 nt nnt−1 + (1 − n)gt nˆ nt 3.2 Applying NAG to Adam t 1−nt m¯ t (1 − mt )gˆt + mt+1mˆ t Ignoring the initialization bias correction terms for m¯ t q t q t−1 − h p the moment, Adam’s update rule can be written in nˆt +e terms of the previous momentum/norm vectors and current gradient update as in (3). 4 Experiments mmt−1 q t q t−1 − h p (3) To test this algorithm, we compared the perfor- nn + (1 − n)g2 + e t−1 t mance of nine algorithms–GD, Momentum, NAG, (1 − m)g − h t RMSProp, Adam, Nadam, MaxaProp, AdaMax, p 2 nnt−1 + (1 − n)gt + e and Nadamax–on three benchmarks–word2vec [10], MNIST image classification [7], and LSTM lan- In rewritten NAG, we would take the first part of the guage models [17]. All algorithms used n = :999 step and apply it before taking the gradient of the and e = 1e−8 as suggested in [5], with a momen- cost function f –however, the denominator depends t tum schedule given by mt = m(1 − :5 × :96 250 ) with on gt , so we can’t take advantage of the trick used m = :99, similar to the recommendation in [14]. in NAG for this equation. However, n is generally Only the learning rate h differed across algorithms chosen to be very large (normally > :9), so the dif- and experiments. The algorithms were all coded us- ference between nt−1 and nt will in general be very ing Google’s TensorFlow [1] API and the experi- small. We can then replace nt with nt−1 without los- ments were done using the built-in TensorFlow mod- ing too much accuracy: els, making only small edits to the default settings. mmt−1 All algorithms used initialization bias correction. q t q t−1 − h p (4) nt− + e 1 4.1 Word2Vec (1 − m)g − h t p 2 Word2vec [10] word embeddings were trained us- nnt− + (1 − n)g + e 1 t ing each of the nine algorithms. Approximately The the first term in the expression in (4) no longer 100MB of cleaned text2 from Wikipedia were used depends on gt , meaning here we can use the Nes- as the source text, and any word not in the top 50000 terov trick; this give us the following expressions for words was replaced with UNK. 128-dimensional vec- m¯ t and q t : tors with a left and right context size of 1 were trained using noise-contrastive estimation with 64 m¯ t (1 − mt )gt + mt+1mt m¯ t negative samples. Validation was done using the q t q t−1 − h p vt +e word analogy task; we report the average cosine dif- All that’s left is to determine how to include the ferene ( 1−cossim(x;y) ) between the analogy vector and initialization bias correction terms, taking into con- 2 the embedding of the correct answer to the analogy.
Recommended publications
  • Improved Policy Networks for Computer Go
    Improved Policy Networks for Computer Go Tristan Cazenave Universite´ Paris-Dauphine, PSL Research University, CNRS, LAMSADE, PARIS, FRANCE Abstract. Golois uses residual policy networks to play Go. Two improvements to these residual policy networks are proposed and tested. The first one is to use three output planes. The second one is to add Spatial Batch Normalization. 1 Introduction Deep Learning for the game of Go with convolutional neural networks has been ad- dressed by [2]. It has been further improved using larger networks [7, 10]. AlphaGo [9] combines Monte Carlo Tree Search with a policy and a value network. Residual Networks improve the training of very deep networks [4]. These networks can gain accuracy from considerably increased depth. On the ImageNet dataset a 152 layers networks achieves 3.57% error. It won the 1st place on the ILSVRC 2015 classifi- cation task. The principle of residual nets is to add the input of the layer to the output of each layer. With this simple modification training is faster and enables deeper networks. Residual networks were recently successfully adapted to computer Go [1]. As a follow up to this paper, we propose improvements to residual networks for computer Go. The second section details different proposed improvements to policy networks for computer Go, the third section gives experimental results, and the last section con- cludes. 2 Proposed Improvements We propose two improvements for policy networks. The first improvement is to use multiple output planes as in DarkForest. The second improvement is to use Spatial Batch Normalization. 2.1 Multiple Output Planes In DarkForest [10] training with multiple output planes containing the next three moves to play has been shown to improve the level of play of a usual policy network with 13 layers.
    [Show full text]
  • Lecture Notes Geoffrey Hinton
    Lecture Notes Geoffrey Hinton Overjoyed Luce crops vectorially. Tailor write-ups his glasshouse divulgating unmanly or constructively after Marcellus barb and outdriven squeakingly, diminishable and cespitose. Phlegmatical Laurance contort thereupon while Bruce always dimidiating his melancholiac depresses what, he shores so finitely. For health care about working memory networks are the class and geoffrey hinton and modify or are A practical guide to training restricted boltzmann machines Lecture Notes in. Trajectory automatically learn about different domains, geoffrey explained what a lecture notes geoffrey hinton notes was central bottleneck form of data should take much like a single example, geoffrey hinton with mctsnets. Gregor sieber and password you may need to this course that models decisions. Jimmy Ba Geoffrey Hinton Volodymyr Mnih Joel Z Leibo and Catalin Ionescu. YouTube lectures by Geoffrey Hinton3 1 Introduction In this topic of boosting we combined several simple classifiers into very complex classifier. Separating Figure from stand with a Parallel Network Paul. But additionally has efficient. But everett also look up. You already know how the course that is just to my assignment in the page and writer recognition and trends in the effect of the motivating this. These perplex the or free liquid Intelligence educational. Citation to lose sight of language. Sparse autoencoder CS294A Lecture notes Andrew Ng Stanford University. Geoffrey Hinton on what's nothing with CNNs Daniel C Elton. Toronto Geoffrey Hinton Advanced Machine Learning CSC2535 2011 Spring. Cross validated is sparse, a proof of how to list of possible configurations have to see. Cnns that just download a computational power nor the squared error in permanent electrode array with respect to the.
    [Show full text]
  • Deep Learning Is Robust to Massive Label Noise
    Deep Learning is Robust to Massive Label Noise David Rolnick * 1 Andreas Veit * 2 Serge Belongie 2 Nir Shavit 3 Abstract Thus, annotation can be expensive and, for tasks requiring expert knowledge, may simply be unattainable at scale. Deep neural networks trained on large supervised datasets have led to impressive results in image To address this limitation, other training paradigms have classification and other tasks. However, well- been investigated to alleviate the need for expensive an- annotated datasets can be time-consuming and notations, such as unsupervised learning (Le, 2013), self- expensive to collect, lending increased interest to supervised learning (Pinto et al., 2016; Wang & Gupta, larger but noisy datasets that are more easily ob- 2015) and learning from noisy annotations (Joulin et al., tained. In this paper, we show that deep neural net- 2016; Natarajan et al., 2013; Veit et al., 2017). Very large works are capable of generalizing from training datasets (e.g., Krasin et al.(2016); Thomee et al.(2016)) data for which true labels are massively outnum- can often be obtained, for example from web sources, with bered by incorrect labels. We demonstrate remark- partial or unreliable annotation. This can allow neural net- ably high test performance after training on cor- works to be trained on a much wider variety of tasks or rupted data from MNIST, CIFAR, and ImageNet. classes and with less manual effort. The good performance For example, on MNIST we obtain test accuracy obtained from these large, noisy datasets indicates that deep above 90 percent even after each clean training learning approaches can tolerate modest amounts of noise example has been diluted with 100 randomly- in the training set.
    [Show full text]
  • CSC321 Lecture 23: Go
    CSC321 Lecture 23: Go Roger Grosse Roger Grosse CSC321 Lecture 23: Go 1 / 22 Final Exam Monday, April 24, 7-10pm A-O: NR 25 P-Z: ZZ VLAD Covers all lectures, tutorials, homeworks, and programming assignments 1/3 from the first half, 2/3 from the second half If there's a question on this lecture, it will be easy Emphasis on concepts covered in multiple of the above Similar in format and difficulty to the midterm, but about 3x longer Practice exams will be posted Roger Grosse CSC321 Lecture 23: Go 2 / 22 Overview Most of the problem domains we've discussed so far were natural application areas for deep learning (e.g. vision, language) We know they can be done on a neural architecture (i.e. the human brain) The predictions are inherently ambiguous, so we need to find statistical structure Board games are a classic AI domain which relied heavily on sophisticated search techniques with a little bit of machine learning Full observations, deterministic environment | why would we need uncertainty? This lecture is about AlphaGo, DeepMind's Go playing system which took the world by storm in 2016 by defeating the human Go champion Lee Sedol Roger Grosse CSC321 Lecture 23: Go 3 / 22 Overview Some milestones in computer game playing: 1949 | Claude Shannon proposes the idea of game tree search, explaining how games could be solved algorithmically in principle 1951 | Alan Turing writes a chess program that he executes by hand 1956 | Arthur Samuel writes a program that plays checkers better than he does 1968 | An algorithm defeats human novices at Go 1992
    [Show full text]
  • The History Began from Alexnet: a Comprehensive Survey on Deep Learning Approaches
    > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 1 The History Began from AlexNet: A Comprehensive Survey on Deep Learning Approaches Md Zahangir Alom1, Tarek M. Taha1, Chris Yakopcic1, Stefan Westberg1, Paheding Sidike2, Mst Shamima Nasrin1, Brian C Van Essen3, Abdul A S. Awwal3, and Vijayan K. Asari1 Abstract—In recent years, deep learning has garnered I. INTRODUCTION tremendous success in a variety of application domains. This new ince the 1950s, a small subset of Artificial Intelligence (AI), field of machine learning has been growing rapidly, and has been applied to most traditional application domains, as well as some S often called Machine Learning (ML), has revolutionized new areas that present more opportunities. Different methods several fields in the last few decades. Neural Networks have been proposed based on different categories of learning, (NN) are a subfield of ML, and it was this subfield that spawned including supervised, semi-supervised, and un-supervised Deep Learning (DL). Since its inception DL has been creating learning. Experimental results show state-of-the-art performance ever larger disruptions, showing outstanding success in almost using deep learning when compared to traditional machine every application domain. Fig. 1 shows, the taxonomy of AI. learning approaches in the fields of image processing, computer DL (using either deep architecture of learning or hierarchical vision, speech recognition, machine translation, art, medical learning approaches) is a class of ML developed largely from imaging, medical information processing, robotics and control, 2006 onward. Learning is a procedure consisting of estimating bio-informatics, natural language processing (NLP), cybersecurity, and many others.
    [Show full text]
  • Uncertainty in Deep Learning
    References Martín Abadi, Ashish Agarwal, Paul Barham, Eugene Brevdo, Zhifeng Chen, Craig Citro, Greg S. Corrado, Andy Davis, Jefrey Dean, Matthieu Devin, Sanjay Ghemawat, Ian Goodfellow, Andrew Harp, Geofrey Irving, Michael Isard, Yangqing Jia, Rafal Jozefowicz, Lukasz Kaiser, Manjunath Kudlur, Josh Levenberg, Dan Mané, Rajat Monga, Sherry Moore, Derek Murray, Chris Olah, Mike Schuster, Jonathon Shlens, Benoit Steiner, Ilya Sutskever, Kunal Talwar, Paul Tucker, Vincent Vanhoucke, Vijay Vasudevan, Fernanda Viégas, Oriol Vinyals, Pete Warden, Martin Wattenberg, Martin Wicke, Yuan Yu, and Xiaoqiang Zheng. TensorFlow: Large-scale machine learning on heterogeneous systems, 2015. URL http://tensorĆow.org/. Software available from tensorĆow.org. Dario Amodei, Chris Olah, Jacob Steinhardt, Paul Christiano, John Schulman, and Dan Mane. Concrete problems in ai safety. arXiv preprint arXiv:1606.06565, 2016. C Angermueller and O Stegle. Multi-task deep neural network to predict CpG methylation proĄles from low-coverage sequencing data. In NIPS MLCB workshop, 2015. O Anjos, C Iglesias, F Peres, J Martínez, Á García, and J Taboada. Neural networks applied to discriminate botanical origin of honeys. Food chemistry, 175:128Ű136, 2015. Christopher Atkeson and Juan Santamaria. A comparison of direct and model-based reinforcement learning. In In International Conference on Robotics and Automation. Citeseer, 1997. Jimmy Ba and Brendan Frey. Adaptive dropout for training deep neural networks. In Advances in Neural Information Processing Systems, pages 3084Ű3092, 2013. P Baldi, P Sadowski, and D Whiteson. Searching for exotic particles in high-energy physics with deep learning. Nature communications, 5, 2014. Pierre Baldi and Peter J Sadowski. Understanding dropout. In Advances in Neural Information Processing Systems, pages 2814Ű2822, 2013.
    [Show full text]
  • Mesh-Tensorflow: Deep Learning for Supercomputers
    Mesh-TensorFlow: Deep Learning for Supercomputers Noam Shazeer, Youlong Cheng, Niki Parmar, Dustin Tran, Ashish Vaswani, Penporn Koanantakool, Peter Hawkins, HyoukJoong Lee Mingsheng Hong, Cliff Young, Ryan Sepassi, Blake Hechtman Google Brain {noam, ylc, nikip, trandustin, avaswani, penporn, phawkins, hyouklee, hongm, cliffy, rsepassi, blakehechtman}@google.com Abstract Batch-splitting (data-parallelism) is the dominant distributed Deep Neural Network (DNN) training strategy, due to its universal applicability and its amenability to Single-Program-Multiple-Data (SPMD) programming. However, batch-splitting suffers from problems including the inability to train very large models (due to memory constraints), high latency, and inefficiency at small batch sizes. All of these can be solved by more general distribution strategies (model-parallelism). Unfortunately, efficient model-parallel algorithms tend to be complicated to dis- cover, describe, and to implement, particularly on large clusters. We introduce Mesh-TensorFlow, a language for specifying a general class of distributed tensor computations. Where data-parallelism can be viewed as splitting tensors and op- erations along the "batch" dimension, in Mesh-TensorFlow, the user can specify any tensor-dimensions to be split across any dimensions of a multi-dimensional mesh of processors. A Mesh-TensorFlow graph compiles into a SPMD program consisting of parallel operations coupled with collective communication prim- itives such as Allreduce. We use Mesh-TensorFlow to implement an efficient data-parallel, model-parallel version of the Transformer [16] sequence-to-sequence model. Using TPU meshes of up to 512 cores, we train Transformer models with up to 5 billion parameters, surpassing state of the art results on WMT’14 English- to-French translation task and the one-billion-word language modeling benchmark.
    [Show full text]
  • Using Neural Networks for Image Classification Tim Kang San Jose State University
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by SJSU ScholarWorks San Jose State University SJSU ScholarWorks Master's Projects Master's Theses and Graduate Research Spring 5-18-2015 Using Neural Networks for Image Classification Tim Kang San Jose State University Follow this and additional works at: https://scholarworks.sjsu.edu/etd_projects Part of the Artificial Intelligence and Robotics Commons Recommended Citation Kang, Tim, "Using Neural Networks for Image Classification" (2015). Master's Projects. 395. DOI: https://doi.org/10.31979/etd.ssss-za3p https://scholarworks.sjsu.edu/etd_projects/395 This Master's Project is brought to you for free and open access by the Master's Theses and Graduate Research at SJSU ScholarWorks. It has been accepted for inclusion in Master's Projects by an authorized administrator of SJSU ScholarWorks. For more information, please contact [email protected]. Using Neural Networks for Image Classification San Jose State University, CS298 Spring 2015 Author: Tim Kang ([email protected]), San Jose State University ​ ​ Advisor: Robert Chun ([email protected]), San Jose State University ​ ​ Committee: Thomas Austin ([email protected]), San Jose State University ​ ​ Committee: Thomas Howell ([email protected]), San Jose State University ​ ​ Abstract This paper will focus on applying neural network machine learning methods to images for the purpose of automatic detection and classification. The main advantage of using neural network methods in this project is its adeptness at fitting non­linear data and its ability to work as an unsupervised algorithm. The algorithms will be run on common, publically available datasets, namely the MNIST and CIFAR­10, so that our results will be easily reproducible.
    [Show full text]
  • Combining Tactical Search and Deep Learning in the Game of Go
    Combining tactical search and deep learning in the game of Go Tristan Cazenave PSL-Universite´ Paris-Dauphine, LAMSADE CNRS UMR 7243, Paris, France [email protected] Abstract Elaborated search algorithms have been developed to solve tactical problems in the game of Go such as capture problems In this paper we experiment with a Deep Convo- [Cazenave, 2003] or life and death problems [Kishimoto and lutional Neural Network for the game of Go. We Muller,¨ 2005]. In this paper we propose to combine tactical show that even if it leads to strong play, it has search algorithms with deep learning. weaknesses at tactical search. We propose to com- Other recent works combine symbolic and deep learn- bine tactical search with Deep Learning to improve ing approaches. For example in image surveillance systems Golois, the resulting Go program. A related work [Maynord et al., 2016] or in systems that combine reasoning is AlphaGo, it combines tactical search with Deep with visual processing [Aditya et al., 2015]. Learning giving as input to the network the results The next section presents our deep learning architecture. of ladders. We propose to extend this further to The third section presents tactical search in the game of Go. other kind of tactical search such as life and death The fourth section details experimental results. search. 2 Deep Learning 1 Introduction In the design of our network we follow previous work [Mad- Deep Learning has been recently used with a lot of success dison et al., 2014; Tian and Zhu, 2015]. Our network is fully in multiple different artificial intelligence tasks.
    [Show full text]
  • The MNIST Database of Handwritten Digit Images for Machine Learning Research
    best of THE WEB Li Deng [ ] The MNIST Database of Handwritten Digit Images for Machine Learning Research n this issue, “Best of the Web” pres- The MNIST database was constructed their results that were obtained using the ents the modified National Institute of out of the original NIST database; hence, MNIST database. In most experiments, the Standards and Technology (MNIST) modified NIST or MNIST. There are existing training data from the database resources, consisting of a collection of 60,000 training images (some of these were used in learning the classifiers, where handwritten digit images used exten- training images can also be used for cross- “none” is entered in the “Preprocessing” Isively in optical character recognition and validation purposes) and 10,000 test column of the table on the Web site. In machine learning research. images, both drawn from the same distri- some experiments, the training set was Handwritten digit recognition is an bution. All these black and white digits are augmented with artificially distorted ver- important problem in optical character size normalized, and centered in a fixed- sions of the original training samples. The recognition, and it has been used as a test size image where the center of gravity of distortions include random combinations case for theories of pattern recognition the intensity lies at the center of the of jittering, shifts, scaling, deskewing, and machine learning algorithms for image with 28 # 28 pixels. Thus, the deslanting, blurring, and compression. The many years. Historically, to promote dimensionality of each image sample vec- type(s) of these and other distortions are machine learning and pattern recognition tor is 28 * 28 = 784, where each element specified in the “Preprocessing” column of research, several standard databases have is binary.
    [Show full text]
  • Data Augmentation for Supervised Learning with Generative Adversarial Networks Manaswi Podduturi Iowa State University
    Iowa State University Capstones, Theses and Graduate Theses and Dissertations Dissertations 2018 Data augmentation for supervised learning with generative adversarial networks Manaswi Podduturi Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/etd Part of the Computer Sciences Commons Recommended Citation Podduturi, Manaswi, "Data augmentation for supervised learning with generative adversarial networks" (2018). Graduate Theses and Dissertations. 16439. https://lib.dr.iastate.edu/etd/16439 This Thesis is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Graduate Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Data augmentation for supervised learning with generative adversarial networks by Manaswi Podduturi A thesis submitted to the graduate faculty in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Major: Computer Science Program of Study Committee: Chinmay Hegde, Co-major Professor Jin Tian, Co-major Professor Pavan Aduri The student author, whose presentation of the scholarship herein was approved by the program of study committee, is solely responsible for the content of this thesis. The Graduate College will ensure this thesis is globally accessible and will not permit alterations after a degree is conferred. Iowa State University Ames, Iowa 2018 Copyright c Manaswi Podduturi, 2018. All rights reserved. ii DEDICATION I would like to dedicate this thesis to my late father Prasad who pushed his boundaries to make me what I am today.
    [Show full text]
  • Improved Handwritten Digit Recognition Using Convolutional Neural Networks (CNN)
    sensors Article Improved Handwritten Digit Recognition Using Convolutional Neural Networks (CNN) Savita Ahlawat 1, Amit Choudhary 2, Anand Nayyar 3, Saurabh Singh 4 and Byungun Yoon 4,* 1 Department of Computer Science and Engineering, Maharaja Surajmal Institute of Technology, New Delhi 110058, India; [email protected] 2 Department of Computer Science, Maharaja Surajmal Institute, New Delhi 110058, India; [email protected] 3 Graduate School, Duy Tan University, Da Nang 550000, Vietnam; [email protected] 4 Department of Industrial & Systems Engineering, Dongguk University, Seoul 04620, Korea; [email protected] * Correspondence: [email protected] Received: 25 May 2020; Accepted: 9 June 2020; Published: 12 June 2020 Abstract: Traditional systems of handwriting recognition have relied on handcrafted features and a large amount of prior knowledge. Training an Optical character recognition (OCR) system based on these prerequisites is a challenging task. Research in the handwriting recognition field is focused around deep learning techniques and has achieved breakthrough performance in the last few years. Still, the rapid growth in the amount of handwritten data and the availability of massive processing power demands improvement in recognition accuracy and deserves further investigation. Convolutional neural networks (CNNs) are very effective in perceiving the structure of handwritten characters/words in ways that help in automatic extraction of distinct features and make CNN the most suitable approach for solving handwriting recognition problems. Our aim in the proposed work is to explore the various design options like number of layers, stride size, receptive field, kernel size, padding and dilution for CNN-based handwritten digit recognition. In addition, we aim to evaluate various SGD optimization algorithms in improving the performance of handwritten digit recognition.
    [Show full text]