1 Adversarial Examples and the Deeper Riddle of Induction
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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. -
Deep Learning Based Computer Generated Face Identification Using
applied sciences Article Deep Learning Based Computer Generated Face Identification Using Convolutional Neural Network L. Minh Dang 1, Syed Ibrahim Hassan 1, Suhyeon Im 1, Jaecheol Lee 2, Sujin Lee 1 and Hyeonjoon Moon 1,* 1 Department of Computer Science and Engineering, Sejong University, Seoul 143-747, Korea; [email protected] (L.M.D.); [email protected] (S.I.H.); [email protected] (S.I.); [email protected] (S.L.) 2 Department of Information Communication Engineering, Sungkyul University, Seoul 143-747, Korea; [email protected] * Correspondence: [email protected] Received: 30 October 2018; Accepted: 10 December 2018; Published: 13 December 2018 Abstract: Generative adversarial networks (GANs) describe an emerging generative model which has made impressive progress in the last few years in generating photorealistic facial images. As the result, it has become more and more difficult to differentiate between computer-generated and real face images, even with the human’s eyes. If the generated images are used with the intent to mislead and deceive readers, it would probably cause severe ethical, moral, and legal issues. Moreover, it is challenging to collect a dataset for computer-generated face identification that is large enough for research purposes because the number of realistic computer-generated images is still limited and scattered on the internet. Thus, a development of a novel decision support system for analyzing and detecting computer-generated face images generated by the GAN network is crucial. In this paper, we propose a customized convolutional neural network, namely CGFace, which is specifically designed for the computer-generated face detection task by customizing the number of convolutional layers, so it performs well in detecting computer-generated face images. -
Matrix Calculus
Appendix D Matrix Calculus From too much study, and from extreme passion, cometh madnesse. Isaac Newton [205, §5] − D.1 Gradient, Directional derivative, Taylor series D.1.1 Gradients Gradient of a differentiable real function f(x) : RK R with respect to its vector argument is defined uniquely in terms of partial derivatives→ ∂f(x) ∂x1 ∂f(x) , ∂x2 RK f(x) . (2053) ∇ . ∈ . ∂f(x) ∂xK while the second-order gradient of the twice differentiable real function with respect to its vector argument is traditionally called the Hessian; 2 2 2 ∂ f(x) ∂ f(x) ∂ f(x) 2 ∂x1 ∂x1∂x2 ··· ∂x1∂xK 2 2 2 ∂ f(x) ∂ f(x) ∂ f(x) 2 2 K f(x) , ∂x2∂x1 ∂x2 ··· ∂x2∂xK S (2054) ∇ . ∈ . .. 2 2 2 ∂ f(x) ∂ f(x) ∂ f(x) 2 ∂xK ∂x1 ∂xK ∂x2 ∂x ··· K interpreted ∂f(x) ∂f(x) 2 ∂ ∂ 2 ∂ f(x) ∂x1 ∂x2 ∂ f(x) = = = (2055) ∂x1∂x2 ³∂x2 ´ ³∂x1 ´ ∂x2∂x1 Dattorro, Convex Optimization Euclidean Distance Geometry, Mεβoo, 2005, v2020.02.29. 599 600 APPENDIX D. MATRIX CALCULUS The gradient of vector-valued function v(x) : R RN on real domain is a row vector → v(x) , ∂v1(x) ∂v2(x) ∂vN (x) RN (2056) ∇ ∂x ∂x ··· ∂x ∈ h i while the second-order gradient is 2 2 2 2 , ∂ v1(x) ∂ v2(x) ∂ vN (x) RN v(x) 2 2 2 (2057) ∇ ∂x ∂x ··· ∂x ∈ h i Gradient of vector-valued function h(x) : RK RN on vector domain is → ∂h1(x) ∂h2(x) ∂hN (x) ∂x1 ∂x1 ··· ∂x1 ∂h1(x) ∂h2(x) ∂hN (x) h(x) , ∂x2 ∂x2 ··· ∂x2 ∇ . -
AI for Health Examples from Industry, Government, and Academia Table of Contents
guidehouse.com AI for Health Examples from industry, government, and academia Table of Contents Abstract 3 Introduction to artificial intelligence 4 Introduction to health data 7 Molecules: AI for understanding biology and developing therapies 10 Fundamental research 10 Drug development 11 Patients: AI for predicting disease and improving care 13 Diagnostics and outcome risks 13 Personalized medicine 14 Groups: AI for optimizing clinical trials and safeguarding public health 15 Clinical trials 15 Public health 17 Conclusion and outlook 18 2 Guidehouse Abstract This paper is directed toward a health-informed reader who is curious about the developments and potential of artificial intelligence (AI) in the health space, but could equally be read by AI practitioners curious about how their knowledge and methods are being used to advance human health. We present a brief, equation-free introduction to AI and its major subfields in order to provide a framework for understanding the technical context of the examples that follow. We discuss the various data sources available for questions of health and life sciences, as well as the unique challenges inherent to these fields. We then consider recent (past five years) applications of AI that have already had tangible, measurable impact to the advancement of biomedical knowledge and the development of new and improved treatments. These examples are organized by scale, ranging from the molecule (fundamental research and drug development) to the patient (diagnostics, risk-scoring, and personalized medicine) to the group (clinical trials and public health). Finally, we conclude with a brief summary and our outlook for the future of AI for health. -
Pre-Training of Deep Bidirectional Protein Sequence Representations with Structural Information
Date of publication xxxx 00, 0000, date of current version xxxx 00, 0000. Digital Object Identifier 10.1109/ACCESS.2017.DOI Pre-training of Deep Bidirectional Protein Sequence Representations with Structural Information SEONWOO MIN1,2, SEUNGHYUN PARK3, SIWON KIM1, HYUN-SOO CHOI4, BYUNGHAN LEE5 (Member, IEEE), and SUNGROH YOON1,6 (Senior Member, IEEE) 1Department of Electrical and Computer engineering, Seoul National University, Seoul 08826, South Korea 2LG AI Research, Seoul 07796, South Korea 3Clova AI Research, NAVER Corp., Seongnam 13561, South Korea 4Department of Computer Science and Engineering, Kangwon National University, Chuncheon 24341, South Korea 5Department of Electronic and IT Media Engineering, Seoul National University of Science and Technology, Seoul 01811, South Korea 6Interdisciplinary Program in Artificial Intelligence, ASRI, INMC, and Institute of Engineering Research, Seoul National University, Seoul 08826, South Korea Corresponding author: Byunghan Lee ([email protected]) or Sungroh Yoon ([email protected]) This research was supported by the National Research Foundation (NRF) of Korea grants funded by the Ministry of Science and ICT (2018R1A2B3001628 (S.Y.), 2014M3C9A3063541 (S.Y.), 2019R1G1A1003253 (B.L.)), the Ministry of Agriculture, Food and Rural Affairs (918013-4 (S.Y.)), and the Brain Korea 21 Plus Project in 2021 (S.Y.). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. ABSTRACT Bridging the exponentially growing gap between the numbers of unlabeled and labeled protein sequences, several studies adopted semi-supervised learning for protein sequence modeling. In these studies, models were pre-trained with a substantial amount of unlabeled data, and the representations were transferred to various downstream tasks. -
Differentiability in Several Variables: Summary of Basic Concepts
DIFFERENTIABILITY IN SEVERAL VARIABLES: SUMMARY OF BASIC CONCEPTS 3 3 1. Partial derivatives If f : R ! R is an arbitrary function and a = (x0; y0; z0) 2 R , then @f f(a + tj) ¡ f(a) f(x ; y + t; z ) ¡ f(x ; y ; z ) (1) (a) := lim = lim 0 0 0 0 0 0 @y t!0 t t!0 t etc.. provided the limit exists. 2 @f f(t;0)¡f(0;0) Example 1. for f : R ! R, @x (0; 0) = limt!0 t . Example 2. Let f : R2 ! R given by ( 2 x y ; (x; y) 6= (0; 0) f(x; y) = x2+y2 0; (x; y) = (0; 0) Then: @f f(t;0)¡f(0;0) 0 ² @x (0; 0) = limt!0 t = limt!0 t = 0 @f f(0;t)¡f(0;0) ² @y (0; 0) = limt!0 t = 0 Note: away from (0; 0), where f is the quotient of differentiable functions (with non-zero denominator) one can apply the usual rules of derivation: @f 2xy(x2 + y2) ¡ 2x3y (x; y) = ; for (x; y) 6= (0; 0) @x (x2 + y2)2 2 2 2. Directional derivatives. If f : R ! R is a map, a = (x0; y0) 2 R and v = ®i + ¯j is a vector in R2, then by definition f(a + tv) ¡ f(a) f(x0 + t®; y0 + t¯) ¡ f(x0; y0) (2) @vf(a) := lim = lim t!0 t t!0 t Example 3. Let f the function from the Example 2 above. Then for v = ®i + ¯j a unit vector (i.e. -
Lipschitz Recurrent Neural Networks
Published as a conference paper at ICLR 2021 LIPSCHITZ RECURRENT NEURAL NETWORKS N. Benjamin Erichson Omri Azencot Alejandro Queiruga ICSI and UC Berkeley Ben-Gurion University Google Research [email protected] [email protected] [email protected] Liam Hodgkinson Michael W. Mahoney ICSI and UC Berkeley ICSI and UC Berkeley [email protected] [email protected] ABSTRACT Viewing recurrent neural networks (RNNs) as continuous-time dynamical sys- tems, we propose a recurrent unit that describes the hidden state’s evolution with two parts: a well-understood linear component plus a Lipschitz nonlinearity. This particular functional form facilitates stability analysis of the long-term behavior of the recurrent unit using tools from nonlinear systems theory. In turn, this en- ables architectural design decisions before experimentation. Sufficient conditions for global stability of the recurrent unit are obtained, motivating a novel scheme for constructing hidden-to-hidden matrices. Our experiments demonstrate that the Lipschitz RNN can outperform existing recurrent units on a range of bench- mark tasks, including computer vision, language modeling and speech prediction tasks. Finally, through Hessian-based analysis we demonstrate that our Lipschitz recurrent unit is more robust with respect to input and parameter perturbations as compared to other continuous-time RNNs. 1 INTRODUCTION Many interesting problems exhibit temporal structures that can be modeled with recurrent neural networks (RNNs), including problems in robotics, system identification, natural language process- ing, and machine learning control. In contrast to feed-forward neural networks, RNNs consist of one or more recurrent units that are designed to have dynamical (recurrent) properties, thereby enabling them to acquire some form of internal memory. -
Biological Structure and Function Emerge from Scaling Unsupervised Learning to 250 Million Protein Sequences
bioRxiv preprint doi: https://doi.org/10.1101/622803; this version posted May 29, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC-ND 4.0 International license. BIOLOGICAL STRUCTURE AND FUNCTION EMERGE FROM SCALING UNSUPERVISED LEARNING TO 250 MILLION PROTEIN SEQUENCES Alexander Rives ∗y z Siddharth Goyal ∗x Joshua Meier ∗x Demi Guo ∗x Myle Ott x C. Lawrence Zitnick x Jerry Ma y x Rob Fergus y z x ABSTRACT In the field of artificial intelligence, a combination of scale in data and model capacity enabled by unsupervised learning has led to major advances in representation learning and statistical generation. In biology, the anticipated growth of sequencing promises unprecedented data on natural sequence diversity. Learning the natural distribution of evolutionary protein sequence variation is a logical step toward predictive and generative modeling for biology. To this end we use unsupervised learning to train a deep contextual language model on 86 billion amino acids across 250 million sequences spanning evolutionary diversity. The resulting model maps raw sequences to representations of biological properties without labels or prior domain knowledge. The learned representation space organizes sequences at multiple levels of biological granularity from the biochemical to proteomic levels. Unsupervised learning recovers information about protein structure: secondary structure and residue-residue contacts can be identified by linear projections from the learned representations. Training language models on full sequence diversity rather than individual protein families increases recoverable information about secondary structure. -
Neural Networks
School of Computer Science 10-601B Introduction to Machine Learning Neural Networks Readings: Matt Gormley Bishop Ch. 5 Lecture 15 Murphy Ch. 16.5, Ch. 28 October 19, 2016 Mitchell Ch. 4 1 Reminders 2 Outline • Logistic Regression (Recap) • Neural Networks • Backpropagation 3 RECALL: LOGISTIC REGRESSION 4 Using gradient ascent for linear Recall… classifiers Key idea behind today’s lecture: 1. Define a linear classifier (logistic regression) 2. Define an objective function (likelihood) 3. Optimize it with gradient descent to learn parameters 4. Predict the class with highest probability under the model 5 Using gradient ascent for linear Recall… classifiers This decision function isn’t Use a differentiable function differentiable: instead: 1 T pθ(y =1t)= h(t)=sign(θ t) | 1+2tT( θT t) − sign(x) 1 logistic(u) ≡ −u 1+ e 6 Using gradient ascent for linear Recall… classifiers This decision function isn’t Use a differentiable function differentiable: instead: 1 T pθ(y =1t)= h(t)=sign(θ t) | 1+2tT( θT t) − sign(x) 1 logistic(u) ≡ −u 1+ e 7 Recall… Logistic Regression Data: Inputs are continuous vectors of length K. Outputs are discrete. (i) (i) N K = t ,y where t R and y 0, 1 D { }i=1 ∈ ∈ { } Model: Logistic function applied to dot product of parameters with input vector. 1 pθ(y =1t)= | 1+2tT( θT t) − Learning: finds the parameters that minimize some objective function. θ∗ = argmin J(θ) θ Prediction: Output is the most probable class. yˆ = `;Kt pθ(y t) y 0,1 | ∈{ } 8 NEURAL NETWORKS 9 Learning highly non-linear functions f: X à Y l f might be non-linear -
Jointly Clustering with K-Means and Learning Representations
Deep k-Means: Jointly clustering with k-Means and learning representations Maziar Moradi Fard Univ. Grenoble Alpes, CNRS, Grenoble INP – LIG [email protected] Thibaut Thonet Univ. Grenoble Alpes, CNRS, Grenoble INP – LIG [email protected] Eric Gaussier Univ. Grenoble Alpes, CNRS, Grenoble INP – LIG, Skopai [email protected] Abstract We study in this paper the problem of jointly clustering and learning representations. As several previous studies have shown, learning representations that are both faithful to the data to be clustered and adapted to the clustering algorithm can lead to better clustering performance, all the more so that the two tasks are performed jointly. We propose here such an approach for k-Means clustering based on a continuous reparametrization of the objective function that leads to a truly joint solution. The behavior of our approach is illustrated on various datasets showing its efficacy in learning representations for objects while clustering them. 1 Introduction Clustering is a long-standing problem in the machine learning and data mining fields, and thus accordingly fostered abundant research. Traditional clustering methods, e.g., k-Means [23] and Gaussian Mixture Models (GMMs) [6], fully rely on the original data representations and may then be ineffective when the data points (e.g., images and text documents) live in a high-dimensional space – a problem commonly known as the curse of dimensionality. Significant progress has been arXiv:1806.10069v2 [cs.LG] 12 Dec 2018 made in the last decade or so to learn better, low-dimensional data representations [13]. -
Differentiability of the Convolution
Differentiability of the convolution. Pablo Jimenez´ Rodr´ıguez Universidad de Valladolid March, 8th, 2019 Pablo Jim´enezRodr´ıguez Differentiability of the convolution Definition Let L1[−1; 1] be the set of the 2-periodic functions f so that R 1 −1 jf (t)j dt < 1: Given f ; g 2 L1[−1; 1], the convolution of f and g is the function Z 1 f ∗ g(x) = f (t)g(x − t) dt −1 Pablo Jim´enezRodr´ıguez Differentiability of the convolution Definition Let L1[−1; 1] be the set of the 2-periodic functions f so that R 1 −1 jf (t)j dt < 1: Given f ; g 2 L1[−1; 1], the convolution of f and g is the function Z 1 f ∗ g(x) = f (t)g(x − t) dt −1 Pablo Jim´enezRodr´ıguez Differentiability of the convolution Definition Let L1[−1; 1] be the set of the 2-periodic functions f so that R 1 −1 jf (t)j dt < 1: Given f ; g 2 L1[−1; 1], the convolution of f and g is the function Z 1 f ∗ g(x) = f (t)g(x − t) dt −1 Pablo Jim´enezRodr´ıguez Differentiability of the convolution Definition Let L1[−1; 1] be the set of the 2-periodic functions f so that R 1 −1 jf (t)j dt < 1: Given f ; g 2 L1[−1; 1], the convolution of f and g is the function Z 1 f ∗ g(x) = f (t)g(x − t) dt −1 Pablo Jim´enezRodr´ıguez Differentiability of the convolution If f is Lipschitz, then f ∗ g is Lipschitz. -
The Simple Essence of Automatic Differentiation
The Simple Essence of Automatic Differentiation CONAL ELLIOTT, Target, USA Automatic differentiation (AD) in reverse mode (RAD) is a central component of deep learning and other uses of large-scale optimization. Commonly used RAD algorithms such as backpropagation, however, are complex and stateful, hindering deep understanding, improvement, and parallel execution. This paper develops a simple, generalized AD algorithm calculated from a simple, natural specification. The general algorithm is then specialized by varying the representation of derivatives. In particular, applying well-known constructions to a naive representation yields two RAD algorithms that are far simpler than previously known. In contrast to commonly used RAD implementations, the algorithms defined here involve no graphs, tapes, variables, partial derivatives, or mutation. They are inherently parallel-friendly, correct by construction, and usable directly from an existing programming language with no need for new data types or programming style, thanks to use of an AD-agnostic compiler plugin. CCS Concepts: · Mathematics of computing → Differential calculus; · Theory of computation → Program reasoning; Program specifications; Additional Key Words and Phrases: automatic differentiation, program calculation, category theory ACM Reference Format: Conal Elliott. 2018. The Simple Essence of Automatic Differentiation. Proc. ACM Program. Lang. 2, ICFP, Article 70 (September 2018), 29 pages. https://doi.org/10.1145/3236765 1 INTRODUCTION Accurate, efficient, and reliable computation of derivatives has become increasingly important over the last several years, thanks in large part to the successful use of backpropagation in machine learning, including multi-layer neural networks, also known as łdeep learningž [Goodfellow et al. 2016; Lecun et al. 2015]. Backpropagation is a specialization and independent invention of the reverse mode of automatic differentiation (AD) and is used to tune a parametric model to closely match observed data, using gradient descent (or stochastic gradient descent).