Credit Assignment: Beyond Backpropagation
|
|
|
- Joy Powers
- 5 years ago
- Views:
Transcription
1 Credit Assignment: Beyond Backpropagation Yoshua Bengio 11 December 2016 AutoDiff NIPS 2016 Workshop oo b s res P IT g, M e n i arn nlin Le ain o p ee em : D will r G PLU ters p cha k t, u o is
2 Deep Learning Jobs in Montreal Faculty positions at all levels at U. Montreal Researcher positions at Element AI and Google Brain Montreal Researcher positions at U. Montreal (IVADO data science center) Studentships at all levels at U. Montreal 2
3 Some Credit Assignment Principles Chain rule & Backprop: exact gradient wrt parameters, via gradient wrt intermediate states not always computable, or 0 when discrete operations only valuable in infinitesimal ball but can be stochastic (noise viewed as an extra input) requires storing the full forward computation state (alternative: forward accumulation, both memory and compute heavy) Boltzmann machines: stochastic gradient estimator involves sampling from MCMC, which may have high variance, iterative relaxation REINFORCE (or random perturbations / finite differences): very general but very high variance, bad scaling Actor-Critic: trades off some variance for potentially high bias 3
4 Backprop wins In practice, when backprop can be used, it tends to work MUCH better than any of the other principles It can be enhanced by various adaptive techniques (adaptive learning rate, natural gradient, momentum-like techniques) Why? only needs to consider ONE direction in the space of variations of the parameters (the gradient) efficient and exact computation of the gradient 4
5 Limitations of backprop When the computation is DISCRETE or just VERY NONLINEAR we are in trouble with backprop very deep composition of non-linearities, very deep nets (non-resnet) RNNs with long sequences, problem with long-term dependencies, for the same reason The effect of an infinitesimal change does not always tell us what a small but finite change would yield 5
6 Issues with Boltzmann Machines (with the existing learning procedures) Sampling from the MCMC of the model is required in the inner loop of training As the model gets sharper, mixing between well-separated modes stalls Training updates vicious circle Mixing 6
7 Difference Target-Prop (Lee, Zhang, Fischer & Bengio 2014 & 2015) Difference Target Propagatio to Make a correction that guarantees first order that the projection h iestimated gi (h ) + gito (h the is icloser 1 = hi 1target i) correct target than the original value fi (h i 1 ) = fi (hi 1 gi (hi ) + gi (h i )) Difference Target Pro h i = fi (h hi 1 h i fi (h i fi (h i h i if 7 1) fi (h i 0 ) + f 1 i (hi = fi (hi 1) [I 2 fi (hi 1) i < h i i i 0 )g 1 i (hi )(h i h fi (h 0 + g (hi(h )(h i) +hg 1 i ))(h if ig ) h i hi i 1 fi (hi hi i hi ) fi g (h ) + g (h i )) i 0 i i 01 fi (hi 1 )gi (hi )] (h i 0 + g 1 2 i (hi )(h i hi ) hi )) hi if h i h hi h fi (hi 1 ) +0 fi (hi0 1 )gti (hi )(0 h i 0hi ) i 1 > max eigen value (I fi (hi 1 )gi (hi )) (I fi (hi 1 )gi (hi )) 0 0 i
8 Mostly material from: Equilibrium Propagation Bridging the Gap Between Energy-Based Models and Backpropagation arxiv: Benjamin Scellier & Yoshua Bengio Montreal Institute for Learning Algorithms
9 How could we train a continuous time physical system that performs computations? Consider a physical system that performs potentially useful computations through its deterministic or stochastic dynamics It has parameters that could be tuned Tractable cost function C can measure how good are its answers The relationship between parameters and objective J (cost at equilibrium of the dynamics) is implicit (via the dynamics) How to estimate the gradient of the loss wrt parameters? 9
10 Equilibria of the Dynamics Deterministic case: dynamics converge to fixed points which are minima of an UNKNOWN energy function F Stochastic case: dynamics converge in probability to the Boltzmann distribution associated with UNKNOWN F 10
11 Clamping & Nudging The outside world can exert some influence on v Coefficients control how much pressure is put on different elements of v Internal energy External energy E.g. Clamping x: Prediction: clamp x and let y free with Nudge y towards right answer with small 11
12 Traditional Explicit Framework Proposed Implicit Framework
13 Main Theorem Gradient on the objective function (cost at equilibrium) can be obtained by a ONE-DIMENSIONAL finite-difference Small nudging Sufficient statistic after nudging Sufficient statistic before nudging 13
14 Stochastic Version Equilibrium distribution: p Z,v (s) := e F (, Z Z,v,s,v) Objective = expected cost under that distribution: Z Theorem: d J d e 1 (, v) = lim!0 e E +,v apple ej (, v) := apple @ (, +,s,v) E,v (,,s,v) Theorem 3 below, which generalizes Theorem 1 to the stochastic framework. 14
15 Application to Supervised Learning Negative phase: Clamp x with Let y free with Let dynamics converge to minimum of energy Read out the prediction y and measure loss C Measure sufficient statistics Positive phase: Nudge y towards smaller loss by setting Let dynamics converge to nearby modified min of energy Measure sufficient statistics Update parameters towards the difference in suff. stat. 15
16 No Need for Calibration of Physical System wrt Idealized Analytic Model Traditional analog circuits are meant to approximate an analytic model defined by an equation Analog physical implementation are imperfect proxys à need to calibrate and deal with low-precision approximation Alternatively: tune the parameters wrt the ACTUAL energy implemented by the physical system, using Equilibrium Propagation 16
17 Inherits Properties of Backprop Unlike finite-difference methods in parameter space, backprop is equivalent to finite difference IN A SINGLE DIRECTION, THE DIRECTION OF THE COST GRADIENT. Same here. In the case where the network has a multi-layer structure, we can show that the propagation of perturbations (nudges) corresponds to back-propagation of gradients First shot at showing this in Bengio & Fischer, Early Inference in Energy-Based Models Approximates Back-Propagation, arxiv:
18 Propagation of errors = propagation of surprises = getting back in harmony Bengio & Fischer, 2015, arxiv: Variation on the output y is propagated into a variation in h 1 mediated by the feedback weights W T = transpose of feedforward weights W Then the variation in h 1 is transformed into a variation in h 2, etc. W W T And we show that proportional to 18
19 Equilibrium Propagation Includes Ordinary Backprop for Feedforward Nets as Special Case Consider the internal energy function With layered architecture, = l-th layer of activations, = parametrized computation at l-th layer. E has a global minimum at It is also a mode associated with stationary distribution. 19
20 Equilibrium Propagation Includes Ordinary Backprop for Feedforward Nets as Special Case With this feedforward-compatible energy-function Negative phase is EQUIVALENT to feedforward prop. Positive phase: nudge outputs, nudges propagated backwards Equilibrium-propagation estimates the same gradient as backprop in a feedforward net, but using a physical (analog) dynamical system which implements the above energy function, with no need for a separate circuit for backpropagation. 20
21 Connection to Marginal Log-Likelihood (Boltzmann Machine) Define Thm: if F is linear in then Note that Corollary: 21
22 Interpretation for Biological Implementation of Backprop à STDP This was the ini+al mo+va+on Hopfield(-like) energy func+on X X X X X gives rise to neurally plausible dynamics (with 0 gradient descent 1 or Langevin Sufficient sta+s+cs = (,s)= (s i ) (s j ij Update: a form of contras+ve Hebbian update Can be implemented by con+nuously following during the posi+ve phase = STDP update. Remaining issue: need symmetric weights (,s)= 0 (s i X W ij (s j )+b i A s i j6=i W ij / lim!0 1 s i s j s 0 i d dt (s i) (s j ) s 0 j
23 Some Open Problems How to implement this in analog electric circuit? With a voltage source and current flowing, there is no equilibrium in terms of electrons energy (position & momentum), only in terms of currents and voltages: Lyapunov function? Get rid of local minima of energy formulation and generalize to system defined purely by its dynamics, learn the transition operator, thus avoiding the weight symmetry constraint Generalize these ideas to unsupervised learning (ongoing) 23
24 Montreal Institute for Learning Algorithms
Artificial Neural Networks. MGS Lecture 2
Artificial Neural Networks MGS 2018 - Lecture 2 OVERVIEW Biological Neural Networks Cell Topology: Input, Output, and Hidden Layers Functional description Cost functions Training ANNs Back-Propagation
Learning Energy-Based Models of High-Dimensional Data
Learning Energy-Based Models of High-Dimensional Data Geoffrey Hinton Max Welling Yee-Whye Teh Simon Osindero www.cs.toronto.edu/~hinton/energybasedmodelsweb.htm Discovering causal structure as a goal
Neural Networks. Mark van Rossum. January 15, School of Informatics, University of Edinburgh 1 / 28
1 / 28 Neural Networks Mark van Rossum School of Informatics, University of Edinburgh January 15, 2018 2 / 28 Goals: Understand how (recurrent) networks behave Find a way to teach networks to do a certain
Introduction to Neural Networks
Introduction to Neural Networks What are (Artificial) Neural Networks? Models of the brain and nervous system Highly parallel Process information much more like the brain than a serial computer Learning
Need for Deep Networks Perceptron. Can only model linear functions. Kernel Machines. Non-linearity provided by kernels
Need for Deep Networks Perceptron Can only model linear functions Kernel Machines Non-linearity provided by kernels Need to design appropriate kernels (possibly selecting from a set, i.e. kernel learning)
Deep learning in the brain. Deep learning summer school Montreal 2017
Deep learning in the brain Deep learning summer school Montreal 207 . Why deep learning is not just for AI The recent success of deep learning in artificial intelligence (AI) means that most people associate
Deep Feedforward Networks
Deep Feedforward Networks Liu Yang March 30, 2017 Liu Yang Short title March 30, 2017 1 / 24 Overview 1 Background A general introduction Example 2 Gradient based learning Cost functions Output Units 3
Learning Deep Architectures
Learning Deep Architectures Yoshua Bengio, U. Montreal Microsoft Cambridge, U.K. July 7th, 2009, Montreal Thanks to: Aaron Courville, Pascal Vincent, Dumitru Erhan, Olivier Delalleau, Olivier Breuleux,
Data Mining & Machine Learning
Data Mining & Machine Learning CS57300 Purdue University March 1, 2018 1 Recap of Last Class (Model Search) Forward and Backward passes 2 Feedforward Neural Networks Neural Networks: Architectures 2-layer
Neural networks. Chapter 20. Chapter 20 1
Neural networks Chapter 20 Chapter 20 1 Outline Brains Neural networks Perceptrons Multilayer networks Applications of neural networks Chapter 20 2 Brains 10 11 neurons of > 20 types, 10 14 synapses, 1ms
Deep learning / Ian Goodfellow, Yoshua Bengio and Aaron Courville. - Cambridge, MA ; London, Spis treści
Deep learning / Ian Goodfellow, Yoshua Bengio and Aaron Courville. - Cambridge, MA ; London, 2017 Spis treści Website Acknowledgments Notation xiii xv xix 1 Introduction 1 1.1 Who Should Read This Book?
How to do backpropagation in a brain
How to do backpropagation in a brain Geoffrey Hinton Canadian Institute for Advanced Research & University of Toronto & Google Inc. Prelude I will start with three slides explaining a popular type of deep
Lecture 5: Logistic Regression. Neural Networks
Lecture 5: Logistic Regression. Neural Networks Logistic regression Comparison with generative models Feed-forward neural networks Backpropagation Tricks for training neural networks COMP-652, Lecture
Need for Deep Networks Perceptron. Can only model linear functions. Kernel Machines. Non-linearity provided by kernels
Need for Deep Networks Perceptron Can only model linear functions Kernel Machines Non-linearity provided by kernels Need to design appropriate kernels (possibly selecting from a set, i.e. kernel learning)
Part 2. Representation Learning Algorithms
53 Part 2 Representation Learning Algorithms 54 A neural network = running several logistic regressions at the same time If we feed a vector of inputs through a bunch of logis;c regression func;ons, then
Neural Networks for Machine Learning. Lecture 11a Hopfield Nets
Neural Networks for Machine Learning Lecture 11a Hopfield Nets Geoffrey Hinton Nitish Srivastava, Kevin Swersky Tijmen Tieleman Abdel-rahman Mohamed Hopfield Nets A Hopfield net is composed of binary threshold
Neural networks. Chapter 19, Sections 1 5 1
Neural networks Chapter 19, Sections 1 5 Chapter 19, Sections 1 5 1 Outline Brains Neural networks Perceptrons Multilayer perceptrons Applications of neural networks Chapter 19, Sections 1 5 2 Brains 10
Reading Group on Deep Learning Session 4 Unsupervised Neural Networks
Reading Group on Deep Learning Session 4 Unsupervised Neural Networks Jakob Verbeek & Daan Wynen 206-09-22 Jakob Verbeek & Daan Wynen Unsupervised Neural Networks Outline Autoencoders Restricted) Boltzmann
Deep Feedforward Networks
Deep Feedforward Networks Liu Yang March 30, 2017 Liu Yang Short title March 30, 2017 1 / 24 Overview 1 Background A general introduction Example 2 Gradient based learning Cost functions Output Units 3
Neural Nets and Symbolic Reasoning Hopfield Networks
Neural Nets and Symbolic Reasoning Hopfield Networks Outline The idea of pattern completion The fast dynamics of Hopfield networks Learning with Hopfield networks Emerging properties of Hopfield networks
arxiv: v1 [cs.lg] 9 Dec 2016
![arxiv: v1 [cs.lg] 9 Dec 2016](/thumbs/88/114685115.jpg "arxiv: v1 [cs.lg] 9 Dec 2016")
Towards deep learning with spiking neurons in energy based models with contrastive Hebbian plasticity arxiv:1612.03214v1 [cs.lg] 9 Dec 2016 Thomas Mesnard École Normale Supérieure Paris, France thomas.mesnard@ens.fr
Basic Principles of Unsupervised and Unsupervised
Basic Principles of Unsupervised and Unsupervised Learning Toward Deep Learning Shun ichi Amari (RIKEN Brain Science Institute) collaborators: R. Karakida, M. Okada (U. Tokyo) Deep Learning Self Organization
Course Structure. Psychology 452 Week 12: Deep Learning. Chapter 8 Discussion. Part I: Deep Learning: What and Why? Rufus. Rufus Processed By Fetch
Psychology 452 Week 12: Deep Learning What Is Deep Learning? Preliminary Ideas (that we already know!) The Restricted Boltzmann Machine (RBM) Many Layers of RBMs Pros and Cons of Deep Learning Course Structure
Machine Learning. Neural Networks
Machine Learning Neural Networks Bryan Pardo, Northwestern University, Machine Learning EECS 349 Fall 2007 Biological Analogy Bryan Pardo, Northwestern University, Machine Learning EECS 349 Fall 2007 THE
AN INTRODUCTION TO NEURAL NETWORKS. Scott Kuindersma November 12, 2009
AN INTRODUCTION TO NEURAL NETWORKS Scott Kuindersma November 12, 2009 SUPERVISED LEARNING We are given some training data: We must learn a function If y is discrete, we call it classification If it is
Experiments on the Consciousness Prior
Yoshua Bengio and William Fedus UNIVERSITÉ DE MONTRÉAL, MILA Abstract Experiments are proposed to explore a novel prior for representation learning, which can be combined with other priors in order to
Deep unsupervised learning
Deep unsupervised learning Advanced data-mining Yongdai Kim Department of Statistics, Seoul National University, South Korea Unsupervised learning In machine learning, there are 3 kinds of learning paradigm.
A summary of Deep Learning without Poor Local Minima
A summary of Deep Learning without Poor Local Minima by Kenji Kawaguchi MIT oral presentation at NIPS 2016 Learning Supervised (or Predictive) learning Learn a mapping from inputs x to outputs y, given
Artificial Neural Networks
Artificial Neural Networks Oliver Schulte - CMPT 310 Neural Networks Neural networks arise from attempts to model human/animal brains Many models, many claims of biological plausibility We will focus on
COMP9444 Neural Networks and Deep Learning 11. Boltzmann Machines. COMP9444 c Alan Blair, 2017
COMP9444 Neural Networks and Deep Learning 11. Boltzmann Machines COMP9444 17s2 Boltzmann Machines 1 Outline Content Addressable Memory Hopfield Network Generative Models Boltzmann Machine Restricted Boltzmann
arxiv: v3 [cs.lg] 9 Aug 2016
![arxiv: v3 [cs.lg] 9 Aug 2016](/thumbs/72/66297267.jpg "arxiv: v3 [cs.lg] 9 Aug 2016")
Yoshua Bengio 1, Dong-Hyun Lee, Jorg Bornschein, Thomas Mesnard and Zhouhan Lin Montreal Institute for Learning Algorithms, University of Montreal, Montreal, QC, H3C 3J7 1 CIFAR Senior Fellow arxiv:1502.04156v3
AI Programming CS F-20 Neural Networks
AI Programming CS662-2008F-20 Neural Networks David Galles Department of Computer Science University of San Francisco 20-0: Symbolic AI Most of this class has been focused on Symbolic AI Focus or symbols
Artificial Neural Networks Examination, June 2005
Artificial Neural Networks Examination, June 2005 Instructions There are SIXTY questions. (The pass mark is 30 out of 60). For each question, please select a maximum of ONE of the given answers (either
A graph contains a set of nodes (vertices) connected by links (edges or arcs)
BOLTZMANN MACHINES Generative Models Graphical Models A graph contains a set of nodes (vertices) connected by links (edges or arcs) In a probabilistic graphical model, each node represents a random variable,
C4 Phenomenological Modeling - Regression & Neural Networks : Computational Modeling and Simulation Instructor: Linwei Wang
C4 Phenomenological Modeling - Regression & Neural Networks 4040-849-03: Computational Modeling and Simulation Instructor: Linwei Wang Recall.. The simple, multiple linear regression function ŷ(x) = a
Using a Hopfield Network: A Nuts and Bolts Approach
Using a Hopfield Network: A Nuts and Bolts Approach November 4, 2013 Gershon Wolfe, Ph.D. Hopfield Model as Applied to Classification Hopfield network Training the network Updating nodes Sequencing of
Neural Networks. Bishop PRML Ch. 5. Alireza Ghane. Feed-forward Networks Network Training Error Backpropagation Applications
Neural Networks Bishop PRML Ch. 5 Alireza Ghane Neural Networks Alireza Ghane / Greg Mori 1 Neural Networks Neural networks arise from attempts to model human/animal brains Many models, many claims of
Day 3 Lecture 3. Optimizing deep networks
Day 3 Lecture 3 Optimizing deep networks Convex optimization A function is convex if for all α [0,1]: f(x) Tangent line Examples Quadratics 2-norms Properties Local minimum is global minimum x Gradient
Plan. Perceptron Linear discriminant. Associative memories Hopfield networks Chaotic networks. Multilayer perceptron Backpropagation
Neural Networks Plan Perceptron Linear discriminant Associative memories Hopfield networks Chaotic networks Multilayer perceptron Backpropagation Perceptron Historically, the first neural net Inspired
y(x n, w) t n 2. (1)
Network training: Training a neural network involves determining the weight parameter vector w that minimizes a cost function. Given a training set comprising a set of input vector {x n }, n = 1,...N,
Slide credit from Hung-Yi Lee & Richard Socher
Slide credit from Hung-Yi Lee & Richard Socher 1 Review Recurrent Neural Network 2 Recurrent Neural Network Idea: condition the neural network on all previous words and tie the weights at each time step
Neural Networks and Deep Learning
Neural Networks and Deep Learning Professor Ameet Talwalkar November 12, 2015 Professor Ameet Talwalkar Neural Networks and Deep Learning November 12, 2015 1 / 16 Outline 1 Review of last lecture AdaBoost
Artificial Neural Networks Examination, March 2004
Artificial Neural Networks Examination, March 2004 Instructions There are SIXTY questions (worth up to 60 marks). The exam mark (maximum 60) will be added to the mark obtained in the laborations (maximum
Equivalence of Backpropagation and Contrastive Hebbian Learning in a Layered Network
LETTER Communicated by Geoffrey Hinton Equivalence of Backpropagation and Contrastive Hebbian Learning in a Layered Network Xiaohui Xie xhx@ai.mit.edu Department of Brain and Cognitive Sciences, Massachusetts
Introduction to Restricted Boltzmann Machines
Introduction to Restricted Boltzmann Machines Ilija Bogunovic and Edo Collins EPFL {ilija.bogunovic,edo.collins}@epfl.ch October 13, 2014 Introduction Ingredients: 1. Probabilistic graphical models (undirected,
Machine Learning Basics III
Machine Learning Basics III Benjamin Roth CIS LMU München Benjamin Roth (CIS LMU München) Machine Learning Basics III 1 / 62 Outline 1 Classification Logistic Regression 2 Gradient Based Optimization Gradient
CS 6501: Deep Learning for Computer Graphics. Basics of Neural Networks. Connelly Barnes
CS 6501: Deep Learning for Computer Graphics Basics of Neural Networks Connelly Barnes Overview Simple neural networks Perceptron Feedforward neural networks Multilayer perceptron and properties Autoencoders
Neural Networks. William Cohen [pilfered from: Ziv; Geoff Hinton; Yoshua Bengio; Yann LeCun; Hongkak Lee - NIPs 2010 tutorial ]
![Neural Networks. William Cohen [pilfered from: Ziv; Geoff Hinton; Yoshua Bengio; Yann LeCun; Hongkak Lee - NIPs 2010 tutorial ]](/thumbs/88/117565192.jpg "Neural Networks. William Cohen [pilfered from: Ziv; Geoff Hinton; Yoshua Bengio; Yann LeCun; Hongkak Lee - NIPs 2010 tutorial ]")
Neural Networks William Cohen 10-601 [pilfered from: Ziv; Geoff Hinton; Yoshua Bengio; Yann LeCun; Hongkak Lee - NIPs 2010 tutorial ] WHAT ARE NEURAL NETWORKS? William s notation Logis;c regression + 1
SPSS, University of Texas at Arlington. Topics in Machine Learning-EE 5359 Neural Networks
Topics in Machine Learning-EE 5359 Neural Networks 1 The Perceptron Output: A perceptron is a function that maps D-dimensional vectors to real numbers. For notational convenience, we add a zero-th dimension
Neural networks: Unsupervised learning
Neural networks: Unsupervised learning 1 Previously The supervised learning paradigm: given example inputs x and target outputs t learning the mapping between them the trained network is supposed to give
Hamiltonian Monte Carlo for Scalable Deep Learning
Hamiltonian Monte Carlo for Scalable Deep Learning Isaac Robson Department of Statistics and Operations Research, University of North Carolina at Chapel Hill isrobson@email.unc.edu BIOS 740 May 4, 2018
Back-Propagation Algorithm. Perceptron Gradient Descent Multilayered neural network Back-Propagation More on Back-Propagation Examples
Back-Propagation Algorithm Perceptron Gradient Descent Multilayered neural network Back-Propagation More on Back-Propagation Examples 1 Inner-product net =< w, x >= w x cos(θ) net = n i=1 w i x i A measure
Tutorial on Machine Learning for Advanced Electronics
Tutorial on Machine Learning for Advanced Electronics Maxim Raginsky March 2017 Part I (Some) Theory and Principles Machine Learning: estimation of dependencies from empirical data (V. Vapnik) enabling
Don t Decay the Learning Rate, Increase the Batch Size. Samuel L. Smith, Pieter-Jan Kindermans, Quoc V. Le December 9 th 2017
Don t Decay the Learning Rate, Increase the Batch Size Samuel L. Smith, Pieter-Jan Kindermans, Quoc V. Le December 9 th 2017 slsmith@ Google Brain Three related questions: What properties control generalization?
Stochastic Analogues to Deterministic Optimizers
Stochastic Analogues to Deterministic Optimizers ISMP 2018 Bordeaux, France Vivak Patel Presented by: Mihai Anitescu July 6, 2018 1 Apology I apologize for not being here to give this talk myself. I injured
Machine Learning I Continuous Reinforcement Learning
Machine Learning I Continuous Reinforcement Learning Thomas Rückstieß Technische Universität München January 7/8, 2010 RL Problem Statement (reminder) state s t+1 ENVIRONMENT reward r t+1 new step r t
The connection of dropout and Bayesian statistics
The connection of dropout and Bayesian statistics Interpretation of dropout as approximate Bayesian modelling of NN http://mlg.eng.cam.ac.uk/yarin/thesis/thesis.pdf Dropout Geoffrey Hinton Google, University
Machine Learning for Large-Scale Data Analysis and Decision Making A. Neural Networks Week #6
Machine Learning for Large-Scale Data Analysis and Decision Making 80-629-17A Neural Networks Week #6 Today Neural Networks A. Modeling B. Fitting C. Deep neural networks Today s material is (adapted)
Deep Learning & Artificial Intelligence WS 2018/2019
Deep Learning & Artificial Intelligence WS 2018/2019 Linear Regression Model Model Error Function: Squared Error Has no special meaning except it makes gradients look nicer Prediction Ground truth / target
Approximate Bayesian Computation and Particle Filters
Approximate Bayesian Computation and Particle Filters Dennis Prangle Reading University 5th February 2014 Introduction Talk is mostly a literature review A few comments on my own ongoing research See Jasra
How to do backpropagation in a brain. Geoffrey Hinton Canadian Institute for Advanced Research & University of Toronto
1 How to do backpropagation in a brain Geoffrey Hinton Canadian Institute for Advanced Research & University of Toronto What is wrong with back-propagation? It requires labeled training data. (fixed) Almost
Cheng Soon Ong & Christian Walder. Canberra February June 2018
Cheng Soon Ong & Christian Walder Research Group and College of Engineering and Computer Science Canberra February June 2018 Outlines Overview Introduction Linear Algebra Probability Linear Regression
Deep Belief Networks are compact universal approximators
1 Deep Belief Networks are compact universal approximators Nicolas Le Roux 1, Yoshua Bengio 2 1 Microsoft Research Cambridge 2 University of Montreal Keywords: Deep Belief Networks, Universal Approximation
Chapter 20. Deep Generative Models
Peng et al.: Deep Learning and Practice 1 Chapter 20 Deep Generative Models Peng et al.: Deep Learning and Practice 2 Generative Models Models that are able to Provide an estimate of the probability distribution
Multilayer Neural Networks
Multilayer Neural Networks Introduction Goal: Classify objects by learning nonlinearity There are many problems for which linear discriminants are insufficient for minimum error In previous methods, the
Artificial Intelligence
Artificial Intelligence Jeff Clune Assistant Professor Evolving Artificial Intelligence Laboratory Announcements Be making progress on your projects! Three Types of Learning Unsupervised Supervised Reinforcement
Introduction to Machine Learning Spring 2018 Note Neural Networks
CS 189 Introduction to Machine Learning Spring 2018 Note 14 1 Neural Networks Neural networks are a class of compositional function approximators. They come in a variety of shapes and sizes. In this class,
Feed-forward Networks Network Training Error Backpropagation Applications. Neural Networks. Oliver Schulte - CMPT 726. Bishop PRML Ch.
Neural Networks Oliver Schulte - CMPT 726 Bishop PRML Ch. 5 Neural Networks Neural networks arise from attempts to model human/animal brains Many models, many claims of biological plausibility We will
RegML 2018 Class 8 Deep learning
RegML 2018 Class 8 Deep learning Lorenzo Rosasco UNIGE-MIT-IIT June 18, 2018 Supervised vs unsupervised learning? So far we have been thinking of learning schemes made in two steps f(x) = w, Φ(x) F, x
Unsupervised Discovery of Nonlinear Structure Using Contrastive Backpropagation
Cognitive Science 30 (2006) 725 731 Copyright 2006 Cognitive Science Society, Inc. All rights reserved. Unsupervised Discovery of Nonlinear Structure Using Contrastive Backpropagation Geoffrey Hinton,
Artificial Neural Networks
Introduction ANN in Action Final Observations Application: Poverty Detection Artificial Neural Networks Alvaro J. Riascos Villegas University of los Andes and Quantil July 6 2018 Artificial Neural Networks
Simple Techniques for Improving SGD. CS6787 Lecture 2 Fall 2017
Simple Techniques for Improving SGD CS6787 Lecture 2 Fall 2017 Step Sizes and Convergence Where we left off Stochastic gradient descent x t+1 = x t rf(x t ; yĩt ) Much faster per iteration than gradient
4. Multilayer Perceptrons
4. Multilayer Perceptrons This is a supervised error-correction learning algorithm. 1 4.1 Introduction A multilayer feedforward network consists of an input layer, one or more hidden layers, and an output
Bits of Machine Learning Part 1: Supervised Learning
Bits of Machine Learning Part 1: Supervised Learning Alexandre Proutiere and Vahan Petrosyan KTH (The Royal Institute of Technology) Outline of the Course 1. Supervised Learning Regression and Classification
Learning Long Term Dependencies with Gradient Descent is Difficult
Learning Long Term Dependencies with Gradient Descent is Difficult IEEE Trans. on Neural Networks 1994 Yoshua Bengio, Patrice Simard, Paolo Frasconi Presented by: Matt Grimes, Ayse Naz Erkan Recurrent
Artificial Neural Networks 2
CSC2515 Machine Learning Sam Roweis Artificial Neural s 2 We saw neural nets for classification. Same idea for regression. ANNs are just adaptive basis regression machines of the form: y k = j w kj σ(b
Artificial Neural Network : Training
Artificial Neural Networ : Training Debasis Samanta IIT Kharagpur debasis.samanta.iitgp@gmail.com 06.04.2018 Debasis Samanta (IIT Kharagpur) Soft Computing Applications 06.04.2018 1 / 49 Learning of neural
Learning Deep Architectures for AI. Part I - Vijay Chakilam
Learning Deep Architectures for AI - Yoshua Bengio Part I - Vijay Chakilam Chapter 0: Preliminaries Neural Network Models The basic idea behind the neural network approach is to model the response as a
Learning Deep Architectures for AI. Part II - Vijay Chakilam
Learning Deep Architectures for AI - Yoshua Bengio Part II - Vijay Chakilam Limitations of Perceptron x1 W, b 0,1 1,1 y x2 weight plane output =1 output =0 There is no value for W and b such that the model
TUTORIAL PART 1 Unsupervised Learning
TUTORIAL PART 1 Unsupervised Learning Marc'Aurelio Ranzato Department of Computer Science Univ. of Toronto ranzato@cs.toronto.edu Co-organizers: Honglak Lee, Yoshua Bengio, Geoff Hinton, Yann LeCun, Andrew
More Tips for Training Neural Network. Hung-yi Lee
More Tips for Training Neural Network Hung-yi ee Outline Activation Function Cost Function Data Preprocessing Training Generalization Review: Training Neural Network Neural network: f ; θ : input (vector)
UNSUPERVISED LEARNING
UNSUPERVISED LEARNING Topics Layer-wise (unsupervised) pre-training Restricted Boltzmann Machines Auto-encoders LAYER-WISE (UNSUPERVISED) PRE-TRAINING Breakthrough in 2006 Layer-wise (unsupervised) pre-training
Neural Nets Supervised learning
6.034 Artificial Intelligence Big idea: Learning as acquiring a function on feature vectors Background Nearest Neighbors Identification Trees Neural Nets Neural Nets Supervised learning y s(z) w w 0 w
COMP 551 Applied Machine Learning Lecture 14: Neural Networks
COMP 551 Applied Machine Learning Lecture 14: Neural Networks Instructor: Ryan Lowe (ryan.lowe@mail.mcgill.ca) Slides mostly by: Class web page: www.cs.mcgill.ca/~hvanho2/comp551 Unless otherwise noted,
Recurrent Neural Networks. Jian Tang
Recurrent Neural Networks Jian Tang tangjianpku@gmail.com 1 RNN: Recurrent neural networks Neural networks for sequence modeling Summarize a sequence with fix-sized vector through recursively updating
Neural Networks. Hopfield Nets and Auto Associators Fall 2017
Neural Networks Hopfield Nets and Auto Associators Fall 2017 1 Story so far Neural networks for computation All feedforward structures But what about.. 2 Loopy network Θ z = ቊ +1 if z > 0 1 if z 0 y i
Lecture 17: Neural Networks and Deep Learning
UVA CS 6316 / CS 4501-004 Machine Learning Fall 2016 Lecture 17: Neural Networks and Deep Learning Jack Lanchantin Dr. Yanjun Qi 1 Neurons 1-Layer Neural Network Multi-layer Neural Network Loss Functions
Value Function Methods. CS : Deep Reinforcement Learning Sergey Levine
Value Function Methods CS 294-112: Deep Reinforcement Learning Sergey Levine Class Notes 1. Homework 2 is due in one week 2. Remember to start forming final project groups and writing your proposal! Proposal
CSC321 Lecture 10 Training RNNs
CSC321 Lecture 10 Training RNNs Roger Grosse and Nitish Srivastava February 23, 2015 Roger Grosse and Nitish Srivastava CSC321 Lecture 10 Training RNNs February 23, 2015 1 / 18 Overview Last time, we saw
Neural Networks. Yan Shao Department of Linguistics and Philology, Uppsala University 7 December 2016
Neural Networks Yan Shao Department of Linguistics and Philology, Uppsala University 7 December 2016 Outline Part 1 Introduction Feedforward Neural Networks Stochastic Gradient Descent Computational Graph
Comparison of Modern Stochastic Optimization Algorithms
Comparison of Modern Stochastic Optimization Algorithms George Papamakarios December 214 Abstract Gradient-based optimization methods are popular in machine learning applications. In large-scale problems,
Development of Stochastic Artificial Neural Networks for Hydrological Prediction
Development of Stochastic Artificial Neural Networks for Hydrological Prediction G. B. Kingston, M. F. Lambert and H. R. Maier Centre for Applied Modelling in Water Engineering, School of Civil and Environmental
Neural Networks, Computation Graphs. CMSC 470 Marine Carpuat
Neural Networks, Computation Graphs CMSC 470 Marine Carpuat Binary Classification with a Multi-layer Perceptron φ A = 1 φ site = 1 φ located = 1 φ Maizuru = 1 φ, = 2 φ in = 1 φ Kyoto = 1 φ priest = 0 φ
arxiv: v1 [cs.ne] 19 Sep 2015
![arxiv: v1 [cs.ne] 19 Sep 2015](/thumbs/94/122344459.jpg "arxiv: v1 [cs.ne] 19 Sep 2015")
An objective function for STDP arxiv:1509.05936v1 [cs.ne] 19 Sep 2015 Yoshua Bengio 1, Thomas Mesnard, Asja Fischer, Saizheng Zhang and Yuhuai Wu Montreal Institute for Learning Algorithms, University
Topics in AI (CPSC 532L): Multimodal Learning with Vision, Language and Sound. Lecture 3: Introduction to Deep Learning (continued)
Topics in AI (CPSC 532L): Multimodal Learning with Vision, Language and Sound Lecture 3: Introduction to Deep Learning (continued) Course Logistics - Update on course registrations - 6 seats left now -
Recurrent Neural Networks
Recurrent Neural Networks Datamining Seminar Kaspar Märtens Karl-Oskar Masing Today's Topics Modeling sequences: a brief overview Training RNNs with back propagation A toy example of training an RNN Why
EXTENDING THE FRAMEWORK OF EQUILIBRIUM PROPAGATION TO GENERAL DYNAMICS
EXTENDING THE FRAMEWORK OF EQUILIBRIUM PROPAGATION TO GENERAL DYNAMICS Anonymous authors Paper under double-blind review ABSTRACT The biological plausibility of the backpropagation algorithm has long been
Learning and Memory in Neural Networks
Learning and Memory in Neural Networks Guy Billings, Neuroinformatics Doctoral Training Centre, The School of Informatics, The University of Edinburgh, UK. Neural networks consist of computational units
Comments. Assignment 3 code released. Thought questions 3 due this week. Mini-project: hopefully you have started. implement classification algorithms
Neural networks Comments Assignment 3 code released implement classification algorithms use kernels for census dataset Thought questions 3 due this week Mini-project: hopefully you have started 2 Example:
Approximate inference in Energy-Based Models
CSC 2535: 2013 Lecture 3b Approximate inference in Energy-Based Models Geoffrey Hinton Two types of density model Stochastic generative model using directed acyclic graph (e.g. Bayes Net) Energy-based