Variable Activation Functions and Spawning in Neuroevolution
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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. -
Artificial Neural Networks Part 2/3 – Perceptron
Artificial Neural Networks Part 2/3 – Perceptron Slides modified from Neural Network Design by Hagan, Demuth and Beale Berrin Yanikoglu Perceptron • A single artificial neuron that computes its weighted input and uses a threshold activation function. • It effectively separates the input space into two categories by the hyperplane: wTx + b = 0 Decision Boundary The weight vector is orthogonal to the decision boundary The weight vector points in the direction of the vector which should produce an output of 1 • so that the vectors with the positive output are on the right side of the decision boundary – if w pointed in the opposite direction, the dot products of all input vectors would have the opposite sign – would result in same classification but with opposite labels The bias determines the position of the boundary • solve for wTp+b = 0 using one point on the decision boundary to find b. Two-Input Case + a = hardlim(n) = [1 2]p + -2 w1, 1 = 1 w1, 2 = 2 - Decision Boundary: all points p for which wTp + b =0 If we have the weights and not the bias, we can take a point on the decision boundary, p=[2 0]T, and solving for [1 2]p + b = 0, we see that b=-2. p w wT.p = ||w||||p||Cosθ θ Decision Boundary proj. of p onto w proj. of p onto w T T w p + b = 0 w p = -bœb = ||p||Cosθ 1 1 = wT.p/||w|| • All points on the decision boundary have the same inner product (= -b) with the weight vector • Therefore they have the same projection onto the weight vector; so they must lie on a line orthogonal to the weight vector ADVANCED An Illustrative Example Boolean OR ⎧ 0 ⎫ ⎧ 0 ⎫ ⎧ 1 ⎫ ⎧ 1 ⎫ ⎨p1 = , t1 = 0 ⎬ ⎨p2 = , t2 = 1 ⎬ ⎨p3 = , t3 = 1⎬ ⎨p4 = , t4 = 1⎬ ⎩ 0 ⎭ ⎩ 1 ⎭ ⎩ 0 ⎭ ⎩ 1 ⎭ Given the above input-output pairs (p,t), can you find (manually) the weights of a perceptron to do the job? Boolean OR Solution 1) Pick an admissable decision boundary 2) Weight vector should be orthogonal to the decision boundary. -
CS 189 Introduction to Machine Learning Spring 2021 Jonathan Shewchuk HW6
CS 189 Introduction to Machine Learning Spring 2021 Jonathan Shewchuk HW6 Due: Wednesday, April 21 at 11:59 pm Deliverables: 1. Submit your predictions for the test sets to Kaggle as early as possible. Include your Kaggle scores in your write-up (see below). The Kaggle competition for this assignment can be found at • https://www.kaggle.com/c/spring21-cs189-hw6-cifar10 2. The written portion: • Submit a PDF of your homework, with an appendix listing all your code, to the Gradescope assignment titled “Homework 6 Write-Up”. Please see section 3.3 for an easy way to gather all your code for the submission (you are not required to use it, but we would strongly recommend using it). • In addition, please include, as your solutions to each coding problem, the specific subset of code relevant to that part of the problem. Whenever we say “include code”, that means you can either include a screenshot of your code, or typeset your code in your submission (using markdown or LATEX). • You may typeset your homework in LaTeX or Word (submit PDF format, not .doc/.docx format) or submit neatly handwritten and scanned solutions. Please start each question on a new page. • If there are graphs, include those graphs in the correct sections. Do not put them in an appendix. We need each solution to be self-contained on pages of its own. • In your write-up, please state with whom you worked on the homework. • In your write-up, please copy the following statement and sign your signature next to it. -
Can Temporal-Difference and Q-Learning Learn Representation? a Mean-Field Analysis
Can Temporal-Difference and Q-Learning Learn Representation? A Mean-Field Analysis Yufeng Zhang Qi Cai Northwestern University Northwestern University Evanston, IL 60208 Evanston, IL 60208 [email protected] [email protected] Zhuoran Yang Yongxin Chen Zhaoran Wang Princeton University Georgia Institute of Technology Northwestern University Princeton, NJ 08544 Atlanta, GA 30332 Evanston, IL 60208 [email protected] [email protected] [email protected] Abstract Temporal-difference and Q-learning play a key role in deep reinforcement learning, where they are empowered by expressive nonlinear function approximators such as neural networks. At the core of their empirical successes is the learned feature representation, which embeds rich observations, e.g., images and texts, into the latent space that encodes semantic structures. Meanwhile, the evolution of such a feature representation is crucial to the convergence of temporal-difference and Q-learning. In particular, temporal-difference learning converges when the function approxi- mator is linear in a feature representation, which is fixed throughout learning, and possibly diverges otherwise. We aim to answer the following questions: When the function approximator is a neural network, how does the associated feature representation evolve? If it converges, does it converge to the optimal one? We prove that, utilizing an overparameterized two-layer neural network, temporal- difference and Q-learning globally minimize the mean-squared projected Bellman error at a sublinear rate. Moreover, the associated feature representation converges to the optimal one, generalizing the previous analysis of [21] in the neural tan- gent kernel regime, where the associated feature representation stabilizes at the initial one. The key to our analysis is a mean-field perspective, which connects the evolution of a finite-dimensional parameter to its limiting counterpart over an infinite-dimensional Wasserstein space. -
Neural Networks Shuai Li John Hopcroft Center, Shanghai Jiao Tong University
Lecture 6: Neural Networks Shuai Li John Hopcroft Center, Shanghai Jiao Tong University https://shuaili8.github.io https://shuaili8.github.io/Teaching/VE445/index.html 1 Outline • Perceptron • Activation functions • Multilayer perceptron networks • Training: backpropagation • Examples • Overfitting • Applications 2 Brief history of artificial neural nets • The First wave • 1943 McCulloch and Pitts proposed the McCulloch-Pitts neuron model • 1958 Rosenblatt introduced the simple single layer networks now called Perceptrons • 1969 Minsky and Papert’s book Perceptrons demonstrated the limitation of single layer perceptrons, and almost the whole field went into hibernation • The Second wave • 1986 The Back-Propagation learning algorithm for Multi-Layer Perceptrons was rediscovered and the whole field took off again • The Third wave • 2006 Deep (neural networks) Learning gains popularity • 2012 made significant break-through in many applications 3 Biological neuron structure • The neuron receives signals from their dendrites, and send its own signal to the axon terminal 4 Biological neural communication • Electrical potential across cell membrane exhibits spikes called action potentials • Spike originates in cell body, travels down axon, and causes synaptic terminals to release neurotransmitters • Chemical diffuses across synapse to dendrites of other neurons • Neurotransmitters can be excitatory or inhibitory • If net input of neuro transmitters to a neuron from other neurons is excitatory and exceeds some threshold, it fires an action potential 5 Perceptron • Inspired by the biological neuron among humans and animals, researchers build a simple model called Perceptron • It receives signals 푥푖’s, multiplies them with different weights 푤푖, and outputs the sum of the weighted signals after an activation function, step function 6 Neuron vs. -
Artificial Neuron Using Mos2/Graphene Threshold Switching Memristor
University of Central Florida STARS Electronic Theses and Dissertations, 2004-2019 2018 Artificial Neuron using MoS2/Graphene Threshold Switching Memristor Hirokjyoti Kalita University of Central Florida Part of the Electrical and Electronics Commons Find similar works at: https://stars.library.ucf.edu/etd University of Central Florida Libraries http://library.ucf.edu This Masters Thesis (Open Access) is brought to you for free and open access by STARS. It has been accepted for inclusion in Electronic Theses and Dissertations, 2004-2019 by an authorized administrator of STARS. For more information, please contact [email protected]. STARS Citation Kalita, Hirokjyoti, "Artificial Neuron using MoS2/Graphene Threshold Switching Memristor" (2018). Electronic Theses and Dissertations, 2004-2019. 5988. https://stars.library.ucf.edu/etd/5988 ARTIFICIAL NEURON USING MoS2/GRAPHENE THRESHOLD SWITCHING MEMRISTOR by HIROKJYOTI KALITA B.Tech. SRM University, 2015 A thesis submitted in partial fulfilment of the requirements for the degree of Master of Science in the Department of Electrical and Computer Engineering in the College of Engineering and Computer Science at the University of Central Florida Orlando, Florida Summer Term 2018 Major Professor: Tania Roy © 2018 Hirokjyoti Kalita ii ABSTRACT With the ever-increasing demand for low power electronics, neuromorphic computing has garnered huge interest in recent times. Implementing neuromorphic computing in hardware will be a severe boost for applications involving complex processes such as pattern recognition. Artificial neurons form a critical part in neuromorphic circuits, and have been realized with complex complementary metal–oxide–semiconductor (CMOS) circuitry in the past. Recently, insulator-to-metal-transition (IMT) materials have been used to realize artificial neurons. -
Dynamic Modification of Activation Function Using the Backpropagation Algorithm in the Artificial Neural Networks
(IJACSA) International Journal of Advanced Computer Science and Applications, Vol. 10, No. 4, 2019 Dynamic Modification of Activation Function using the Backpropagation Algorithm in the Artificial Neural Networks Marina Adriana Mercioni1, Alexandru Tiron2, Stefan Holban3 Department of Computer Science Politehnica University Timisoara, Timisoara, Romania Abstract—The paper proposes the dynamic modification of These functions represent the main activation functions, the activation function in a learning technique, more exactly being currently the most used by neural networks, representing backpropagation algorithm. The modification consists in from this reason a standard in building of an architecture of changing slope of sigmoid function for activation function Neural Network type [6,7]. according to increase or decrease the error in an epoch of learning. The study was done using the Waikato Environment for The activation functions that have been proposed along the Knowledge Analysis (WEKA) platform to complete adding this time were analyzed in the light of the applicability of the feature in Multilayer Perceptron class. This study aims the backpropagation algorithm. It has noted that a function that dynamic modification of activation function has changed to enables differentiated rate calculated by the neural network to relative gradient error, also neural networks with hidden layers be differentiated so and the error of function becomes have not used for it. differentiated [8]. Keywords—Artificial neural networks; activation function; The main purpose of activation function consists in the sigmoid function; WEKA; multilayer perceptron; instance; scalation of outputs of the neurons in neural networks and the classifier; gradient; rate metric; performance; dynamic introduction a non-linear relationship between the input and modification output of the neuron [9]. -
Using the Modified Back-Propagation Algorithm to Perform Automated Downlink Analysis by Nancy Y
Using The Modified Back-propagation Algorithm To Perform Automated Downlink Analysis by Nancy Y. Xiao Submitted to the Department of Electrical Engineering and Computer Science in partial fulfillment of the requirements for the degrees of Bachelor of Science and Master of Engineering in Electrical Engineering and Computer Science at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 1996 Copyright Nancy Y. Xiao, 1996. All rights reserved. The author hereby grants to MIT permission to reproduce and distribute publicly paper and electronic copies of this thesis document in whole or in part, and to grant others the right to do so. A uthor ....... ............ Depar -uter Science May 28, 1996 Certified by. rnard C. Lesieutre ;rical Engineering Thesis Supervisor Accepted by.. F.R. Morgenthaler Chairman, Departmental Committee on Graduate Students OF TECH NOLOCG JUN 111996 Eng, Using The Modified Back-propagation Algorithm To Perform Automated Downlink Analysis by Nancy Y. Xiao Submitted to the Department of Electrical Engineering and Computer Science on May 28, 1996, in partial fulfillment of the requirements for the degrees of Bachelor of Science and Master of Engineering in Electrical Engineering and Computer Science Abstract A multi-layer neural network computer program was developed to perform super- vised learning tasks. The weights in the neural network were found using the back- propagation algorithm. Several modifications to this algorithm were also implemented to accelerate error convergence and optimize search procedures. This neural network was used mainly to perform pattern recognition tasks. As an initial test of the system, a controlled classical pattern recognition experiment was conducted using the X and Y coordinates of the data points from two to five possibly overlapping Gaussian distributions, each with a different mean and variance. -
A Deep Reinforcement Learning Neural Network Folding Proteins
DeepFoldit - A Deep Reinforcement Learning Neural Network Folding Proteins Dimitra Panou1, Martin Reczko2 1University of Athens, Department of Informatics and Telecommunications 2Biomedical Sciences Research Center “Alexander Fleming” ABSTRACT Despite considerable progress, ab initio protein structure prediction remains suboptimal. A crowdsourcing approach is the online puzzle video game Foldit [1], that provided several useful results that matched or even outperformed algorithmically computed solutions [2]. Using Foldit, the WeFold [3] crowd had several successful participations in the Critical Assessment of Techniques for Protein Structure Prediction. Based on the recent Foldit standalone version [4], we trained a deep reinforcement neural network called DeepFoldit to improve the score assigned to an unfolded protein, using the Q-learning method [5] with experience replay. This paper is focused on model improvement through hyperparameter tuning. We examined various implementations by examining different model architectures and changing hyperparameter values to improve the accuracy of the model. The new model’s hyper-parameters also improved its ability to generalize. Initial results, from the latest implementation, show that given a set of small unfolded training proteins, DeepFoldit learns action sequences that improve the score both on the training set and on novel test proteins. Our approach combines the intuitive user interface of Foldit with the efficiency of deep reinforcement learning. KEYWORDS: ab initio protein structure prediction, Reinforcement Learning, Deep Learning, Convolution Neural Networks, Q-learning 1. ALGORITHMIC BACKGROUND Machine learning (ML) is the study of algorithms and statistical models used by computer systems to accomplish a given task without using explicit guidelines, relying on inferences derived from patterns. ML is a field of artificial intelligence. -
Deep Multiphysics and Particle–Neuron Duality: a Computational Framework Coupling (Discrete) Multiphysics and Deep Learning
applied sciences Article Deep Multiphysics and Particle–Neuron Duality: A Computational Framework Coupling (Discrete) Multiphysics and Deep Learning Alessio Alexiadis School of Chemical Engineering, University of Birmingham, Birmingham B15 2TT, UK; [email protected]; Tel.: +44-(0)-121-414-5305 Received: 11 November 2019; Accepted: 6 December 2019; Published: 9 December 2019 Featured Application: Coupling First-Principle Modelling with Artificial Intelligence. Abstract: There are two common ways of coupling first-principles modelling and machine learning. In one case, data are transferred from the machine-learning algorithm to the first-principles model; in the other, from the first-principles model to the machine-learning algorithm. In both cases, the coupling is in series: the two components remain distinct, and data generated by one model are subsequently fed into the other. Several modelling problems, however, require in-parallel coupling, where the first-principle model and the machine-learning algorithm work together at the same time rather than one after the other. This study introduces deep multiphysics; a computational framework that couples first-principles modelling and machine learning in parallel rather than in series. Deep multiphysics works with particle-based first-principles modelling techniques. It is shown that the mathematical algorithms behind several particle methods and artificial neural networks are similar to the point that can be unified under the notion of particle–neuron duality. This study explains in detail the particle–neuron duality and how deep multiphysics works both theoretically and in practice. A case study, the design of a microfluidic device for separating cell populations with different levels of stiffness, is discussed to achieve this aim. -
Neural Network Architectures and Activation Functions: a Gaussian Process Approach
Fakultät für Informatik Neural Network Architectures and Activation Functions: A Gaussian Process Approach Sebastian Urban Vollständiger Abdruck der von der Fakultät für Informatik der Technischen Universität München zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.) genehmigten Dissertation. Vorsitzender: Prof. Dr. rer. nat. Stephan Günnemann Prüfende der Dissertation: 1. Prof. Dr. Patrick van der Smagt 2. Prof. Dr. rer. nat. Daniel Cremers 3. Prof. Dr. Bernd Bischl, Ludwig-Maximilians-Universität München Die Dissertation wurde am 22.11.2017 bei der Technischen Universtät München eingereicht und durch die Fakultät für Informatik am 14.05.2018 angenommen. Neural Network Architectures and Activation Functions: A Gaussian Process Approach Sebastian Urban Technical University Munich 2017 ii Abstract The success of applying neural networks crucially depends on the network architecture being appropriate for the task. Determining the right architecture is a computationally intensive process, requiring many trials with different candidate architectures. We show that the neural activation function, if allowed to individually change for each neuron, can implicitly control many aspects of the network architecture, such as effective number of layers, effective number of neurons in a layer, skip connections and whether a neuron is additive or multiplicative. Motivated by this observation we propose stochastic, non-parametric activation functions that are fully learnable and individual to each neuron. Complexity and the risk of overfitting are controlled by placing a Gaussian process prior over these functions. The result is the Gaussian process neuron, a probabilistic unit that can be used as the basic building block for probabilistic graphical models that resemble the structure of neural networks. -
A Study of Activation Functions for Neural Networks Meenakshi Manavazhahan University of Arkansas, Fayetteville
University of Arkansas, Fayetteville ScholarWorks@UARK Computer Science and Computer Engineering Computer Science and Computer Engineering Undergraduate Honors Theses 5-2017 A Study of Activation Functions for Neural Networks Meenakshi Manavazhahan University of Arkansas, Fayetteville Follow this and additional works at: http://scholarworks.uark.edu/csceuht Part of the Other Computer Engineering Commons Recommended Citation Manavazhahan, Meenakshi, "A Study of Activation Functions for Neural Networks" (2017). Computer Science and Computer Engineering Undergraduate Honors Theses. 44. http://scholarworks.uark.edu/csceuht/44 This Thesis is brought to you for free and open access by the Computer Science and Computer Engineering at ScholarWorks@UARK. It has been accepted for inclusion in Computer Science and Computer Engineering Undergraduate Honors Theses by an authorized administrator of ScholarWorks@UARK. For more information, please contact [email protected], [email protected]. A Study of Activation Functions for Neural Networks An undergraduate thesis in partial fulfillment of the honors program at University of Arkansas College of Engineering Department of Computer Science and Computer Engineering by: Meena Mana 14 March, 2017 1 Abstract: Artificial neural networks are function-approximating models that can improve themselves with experience. In order to work effectively, they rely on a nonlinearity, or activation function, to transform the values between each layer. One question that remains unanswered is, “Which non-linearity is optimal for learning with a particular dataset?” This thesis seeks to answer this question with the MNIST dataset, a popular dataset of handwritten digits, and vowel dataset, a dataset of vowel sounds. In order to answer this question effectively, it must simultaneously determine near-optimal values for several other meta-parameters, including the network topology, the optimization algorithm, and the number of training epochs necessary for the model to converge to good results.