Neural Networks Module2 : learning with Gradient Descent module 2: - PowerPoint PPT Presentation

Nov 18, 2023 •438 likes •639 views

Neural Networks Module2 : learning with Gradient Descent module 2: numerical optimization LEARNING PERFORMANCE REPRESENTATION DATA PROBLEM EVALUATION RAW DATA CLUSTERING FEATURES housing data train/test error, accuracy spam data Cross

Neural Networks
Module2 : learning with Gradient Descent module 2: numerical optimization LEARNING PERFORMANCE REPRESENTATION DATA PROBLEM EVALUATION RAW DATA CLUSTERING FEATURES housing data train/test error, accuracy spam data Cross Validation SUPERVISED SELECTION ROC LABELS LEARNING ANALYSIS numerical optimization DATA Logistic Regression DIMENSIONS Perceptron PROCESSING TUNING Neural Network • formulate problem by model/parameters • formulate error as mathematical objective • optimize numerically the parameters for the given objective • usually algebraic setup - involves matrices and calculus • probabilistic setup (likelihoods) next module
Module 2 Objectives / Neural Networks • perceptron rules • neural network idea, philosophy, construction • NN weights • Backpropagation : training NN using gradient descent • NN modes, autoencoders • run NN-autoencoder on a simple problem
The perceptron
The perceptron • (like with regression) we are looking for a linear classifier � � • error different than regression: weighted sum over misclassified points set M
Perceptron - geometry • perceptron is a linear (hyperplane) separator • for simplicity, will transform data points with y=-1 (left) to y=1 (right) by reversing the sign
The perceptron • To optimize for perceptron error, use gradient descent � • with update rule � � • batch update: �
perceptron update - intuition • perceptron update: the plane (dotted red) normal w (red arrow) moves in the direction of misclassified p1 until p1 is on the correct side.
Perceptron proof of convergence • if data is indeed linearly separable, the perceptron will find the separator line.
Multilayer perceptrons
Checkpoint : XOR perceptron • build/explain a 3-layer perceptron that give the same classification as the logical XOR function � � � � • your answer is required! Submit via dropbox.
Neural Networks • NN is a stack of connected perceptrons � • bottom up: - input layer - hidden layer - output layer � • multilayer NN very very powerful in that they can approximate almost any function - with enough training data
Neural Networks • Each unit performs first a linear combination of inputs � � • Then applies a nonlinear (ex. logistic) function “f” before outputting a value � • Three layer NN output can be expressed mathematically as �
Training the NN weights ( w ) • one datapoint � � � • set of weights up (close to output): � � � � • we obtain the hidden-output weight update rule
Training the NN weights ( w ) • weight first set of weights (close to input)
NN training
Autoencoders • network is “rotated” - from left to right: input-hidden-ouput • input and output are the same values - hidden layer encodes the input and decodes back to itself
BackPropagation ( Tom Mitchell book )

Recommend

Outline Evolution of neurocomputing Artificial neural networks Feed forward

Introduction to Neural Networks and Deep Learning Ling Guan References: S. Haykin, Neural Networks , 2 nd Edition, New Jersey: Prentice Hall, 1. 2004. C. M. Bishop, Neural Networks for Pattern Re cognition, New York: 2. Oxford University

451 views • 17 slides

Neural Networks 0. Logistics Spring 2019 1 Neural Networks are taking over! Neural networks

Neural Networks 0. Logistics Spring 2019 1 Neural Networks are taking over! Neural networks have become one of the major thrust areas recently in various pattern recognition, prediction, and analysis problems In many problems they have

852 views • 33 slides

Neural Networks 1. Introduction Fall 2017 Neural Networks are taking over! Neural networks

Neural Networks 1. Introduction Fall 2017 Neural Networks are taking over! Neural networks have become one of the major thrust areas recently in various pattern recognition, prediction, and analysis problems In many problems they have

1.17k views • 91 slides

CONVOLUTIONAL AND RECURRENT NEURAL NETWORKS Neural networks Fully connected networks

CONVOLUTIONAL AND RECURRENT NEURAL NETWORKS Neural networks Fully connected networks Neuron Non-linearity Softmax layer DNN training Loss function and regularization SGD and backprop Learning rate Overfitting

1.8k views • 86 slides

Neural Networks 1. Introduction Spring 2019 1 Neural Networks are taking over! Neural

Neural Networks 1. Introduction Spring 2019 1 Neural Networks are taking over! Neural networks have become one of the major thrust areas recently in various pattern recognition, prediction, and analysis problems In many problems they

1.57k views • 124 slides

Neural Networks 1. Introduction Spring 2020 1 Neural Networks are taking over! Neural

Neural Networks 1. Introduction Spring 2020 1 Neural Networks are taking over! Neural networks have become one of the major thrust areas recently in various pattern recognition, prediction, and analysis problems In many problems they

1.63k views • 119 slides

Relaxation and Hopfield Networks Neural Networks Neural Networks - Hopfield 1 Bibliography

Relaxation and Hopfield Networks Neural Networks Neural Networks - Hopfield 1 Bibliography Hopfield, J. J., "Neural networks and physical systems with emergent collective computational abilities," Proceedings of the National Academy

367 views • 19 slides

Neural Networks and their Application to Go Neural Networks Learning Blackjack Theory Training

Neural Networks and their Application to Go A. Bausch Neural Networks and their Application to Go Neural Networks Learning Blackjack Theory Training neural networks Problems AlphaGo Anne-Marie Bausch The Game of Go Policy Network

280 views • 24 slides

(Very) Brief Introduction to Neural Networks IITP-03 Algorithms for NLP 1 / 31 Learning

(Very) Brief Introduction to Neural Networks IITP-03 Algorithms for NLP 1 / 31 Learning objectives What are neural networks? What are deep neural networks? How do we train neural networks? What variants of neural network

331 views • 31 slides

How Neural Networks (NN) Biological Neuron: A . . . Can (Hopefully) Learn Artificial Neural . .

Need for Machine . . . Neural Networks . . . How to Speed Up . . . Neural Networks: A . . . How Neural Networks (NN) Biological Neuron: A . . . Can (Hopefully) Learn Artificial Neural . . . Resulting Algorithm Faster by Taking Into How to

464 views • 17 slides

Outline Why model neural networks? Modeling Neural Networks A brief look at the neuron.

Outline Why model neural networks? Modeling Neural Networks A brief look at the neuron. A look at some current works. Adding an evolutionary strategy. Paul Nuytten CPSC 607 Why Model Neural Networks? The Neuron The nervous

697 views • 4 slides

Introduction to Deep Neural Networks 0. Logistics Spring 2020 1 Neural Networks are taking

Introduction to Deep Neural Networks 0. Logistics Spring 2020 1 Neural Networks are taking over! Neural networks have become one of the major thrust areas recently in various pattern recognition, prediction, and analysis problems In

987 views • 40 slides

Propagating Error Backward Hyperparameters for Neural Networks } Multi-layer (deep) neural

Learning in Neural Networks w 1,3 w 3,5 1 3 5 w w 1,4 3,6 w w 2,3 4,5 2 4 6 w w 2,4 4,6 Class #18: Back-Propagation; } A neural network can learn a classification function by Tuning Hyper-Parameters adjusting its weights to

259 views • 4 slides

Neural Networks Hugo Larochelle ( @hugo_larochelle ) Google Brain 2 NEURAL NETWORKS What

Neural Networks Hugo Larochelle ( @hugo_larochelle ) Google Brain 2 NEURAL NETWORKS What well cover ... f ( x ) computer vision architectures - convolutional networks - data augmentation 1 - residual networks ... ...

1.29k views • 75 slides

Neural Networks Oskar Taubert (SCC) SCC 1 15.01.2020 Oskar Taubert - Neural Networks SCC

Neural Networks Oskar Taubert (SCC) SCC 1 15.01.2020 Oskar Taubert - Neural Networks SCC www.kit.edu KIT The Research University in the Helmholtz Association Neural Network Concept (very) remotely brain inspired computational system

479 views • 25 slides

Introduction to Artificial Intelligence Neural Networks - Deep Learning for NLP Janyl Jumadinova

Introduction to Artificial Intelligence Neural Networks - Deep Learning for NLP Janyl Jumadinova November 21, 2016 Neural Networks 2/20 Neural Networks 3/20 Neural Networks Neural computing requires a number of neurons , to be connected

813 views • 21 slides

7. Artificial neural networks Introduction to neural networks Despite struggling to understand

7. Artificial neural networks Introduction to neural networks Despite struggling to understand intricacies of protein, cell, and network function within the brain, neuroscientists would agree on the following simplistic description of how the

157 views • 11 slides

Neural networks Chapter 20 Chapter 20 1 Outline Brains Neural networks Perceptrons

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, 1ms10ms cycle

804 views • 47 slides

Modeling Neural Networks Paul Nuytten CPSC 607 Outline Why model neural networks? A

Modeling Neural Networks Paul Nuytten CPSC 607 Outline Why model neural networks? A brief look at the neuron. A look at some current works. Adding an evolutionary strategy. Why Model Neural Networks? The nervous system is a

1.22k views • 23 slides

Modular Neural Networks CPSC 533 Franco Lee Ian Ko Modular Neural Networks What is it ? Dif

Modular Neural Networks CPSC 533 Franco Lee Ian Ko Modular Neural Networks What is it ? Dif f erent models of neural net w orks combined int o a single syst em. Each single net w ork is made int o a module t hat can be f reely int

289 views • 25 slides

Convolutional Neural Networks (CNNs) Recurrent Neural Networks (RNNs) L1 Scalar Processor L0

Convolutional Neural Networks (CNNs) Recurrent Neural Networks (RNNs) L1 Scalar Processor L0 L0 M*V Processor N N N N N N Project Brainwave Pretrained DNN Model Scalable DNN Hardware Neural Processing Unit Microservice Extract

525 views • 30 slides

Computa(on through dynamics Using recurrent neural networks to unveil mechanism in neural

Computa(on through dynamics Using recurrent neural networks to unveil mechanism in neural circuits David Sussillo with Valerio Mante and Bill Newsome Table of contents Introduc(on Training recurrent neural networks(RNNs) Understanding how

1.57k views • 105 slides

Neural Networks for Machine Learning Lecture 2a An overview of the main types of neural network

Neural Networks for Machine Learning Lecture 2a An overview of the main types of neural network architecture Geoffrey Hinton with Nitish Srivastava Kevin Swersky Feed-forward neural networks These are the commonest type of neural

534 views • 32 slides

Neural Networks and Handwriting Recognition Background Neural Networks Neural Network Steven

Neural Networks and Handwriting Recognition Steven Sloss Math 164 Neural Networks and Handwriting Recognition Background Neural Networks Neural Network Steven Sloss Structure Training Neural Networks Math 164 Motivation Problem

889 views • 41 slides