Machine Learning for Physicists Lecture 1
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1 Machine Learning for Physicists Lecture 1 Summer 2017 University of Erlangen-Nuremberg Florian Marquardt (Image generated by a net with 20 hidden layers)
2 OUTPUT INPUT (Picture: Wikimedia Commons)
3 OUTPUT (drawing by Ramon y Cajal, ~1900) INPUT (Picture: Wikimedia Commons)
4 OUTPUT Artificial Neural Network INPUT
5 OUTPUT output layer input layer INPUT
6 light bulb output layer input layer (this particular picture has never been seen before!) (Picture: Wikimedia Commons)
7 light bulb output layer input layer (training images) (Picture: Wikimedia Commons)
8 ImageNet competition 1.2 million training pictures (annotated by humans) 1000 object classes 2012: A deep neural network beats competition clearly (16% error rate; since then rapid decrease of error rate, down to about 7%) Picture: ImageNet Large Scale Visual Recognition Challenge, Russakovsky et al. 2014
9 Example applications of (deep) neural networks Recognize images Describe images in sentences Colorize images (see links on website) e.g. Translate languages (French to Spanish, etc.) Answer questions about a brief text Play video games & board games at superhuman level (in physics:) predict properties of materials classify phases of matter represent quantum wave functions
10 Lectures Outline Basic structure of artificial neural networks Training a network (backpropagation) Exploiting translational invariance in image processing (convolutional networks) Unsupervised learning of essential features (autoencoders) Learning temporal data, e.g. sentences (recurrent networks) Learning a probability distribution (Boltzmann machine) Learning from rare rewards (reinforcement learning) Further tricks and concepts Modern applications to physics and science
11 Lectures Outline Basic structure of artificial neural networks Training a network (backpropagation) Python Exploiting translational invariance in image processing (convolutional networks) Unsupervised learning of essential features Learning by doing! Keras (autoencoders) package for Learning temporal data, e.g. sentences (recurrent Python networks) Learning a probability distribution (Boltzmann machine) Learning from rare rewards (reinforcement learning) Further tricks and concepts Modern applications to physics and science
12 Homework Homework: (usually) explore via programming We provide feedback if desired No regular tutorial sessions _Machine_Learning_for_Physicists,_by_Florian_Marquardt
13 Homework First homework: 1.Install python & keras on your computer (see lecture homepage); questions will be resolved after second lecture THIS IS IMPORTANT! 2.Brainstorm: Which problems could you address using neural networks? Next time: installation party after the lecture Bring your laptop, if available (or ask questions)
14 Mo Tu We Th Fr May Mo Tu We Th Fr 1. June Mo Tu We Th July Machine Learning Lecture Schedule (Summer 2017) Mo/Th 18-20
15 Very brief history of artificial neural networks Recurrent networks Deep nets for Convolutional networks image recognition Perceptrons 80s/90s beat the competition 50s/60s 2012 Backpropagation 80s (*1970) 1956 Dartmouth Workshop on early 2000s Deep networks become practical 2015 A deep net reaches expert level in Go Artificial Intelligence
16 Lots of tutorials/info on the web... recommend: online book by Nielsen ("Neural Networks and Deep Learning") at much more detailed book: Deep Learning by Goodfellow, Bengio, Courville; MIT press; see also Software here: python & keras (builds on theano)
17 A neural network = a nonlinear function (of many variables) that depends on many parameters
18 A neural network output layer hidden layers input layer
19 output of a neuron = nonlinear function of weighted sum of inputs input values y 1 y 2 y 3...
20 output of a neuron = nonlinear function of weighted sum of inputs weighted sum z = X j w j y j + b (offset, bias ) output value f(z) weights w 1 w 2 w 3... input values y 1 y 2 y 3...
21 output of a neuron = nonlinear function of weighted sum of inputs f(z) sigmoid weighted sum z w j y j + b output value relu z = X j (offset, bias ) f(z) (rectified linear unit) weights w 1 w 2 w 3... input values y 1 y 2 y 3...
22 A neural network output layer Each connection has a weight w Each neuron has an offset b Each neuron has a nonlinear function f (fixed) hidden layers input layer The values of input layer neurons are fed into the network from the outside
23
24 ?
25 ?
26 f(z) z=0.5* *
27 feedforward pass through the network: calculate output from input
28 feedforward pass through the network: calculate output from input
29 feedforward pass through the network: calculate output from input
30 feedforward pass through the network: calculate output from input
31 One layer output input j=output neuron k=input neuron z j = X k w jk y in k + b j in matrix/vector notation: z = wy in + b elementwise nonlinear function: y out j = f(z j )
32 for j in range(n): do_step(j) u=dot(m,v) def f(x): return(sin(x)/x) x=linspace(-5,5,n) Anaconda Jupyter ython
33 for j in range(n): do_step(j) u=dot(m,v) def f(x): return(sin(x)/x) x=linspace(-5,5,n) Anaconda Jupyter ython
34 A few lines of python! Python code vector (Nout) vector (Nin) z=dot(w,y)+b matrix (Nout x Nin) vector (Nout) z j = X k w jk y in k + b j in matrix/vector notation: z = wy in + b
35 A few lines of python! output N1=2 input N0=3 Random weights and biases Input values Apply network!
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