Ratebased artificial neural networks and error backpropagation learning. Scott Murdison Machine learning journal club May 16, 2016


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1 Ratebased artificial neural networks and error backpropagation learning Scott Murdison Machine learning journal club May 16, 2016 Murdison, Leclercq, Lefèvre and Blohm J Neurophys 2015
2 Neural networks??? Why would we use those?! Some problems are just too complicated (i.e. nonlinear) to solve with simple programming Computer vision/audition applications:  digit recognition  facial recognition  reading  speech recognition  object recognition Others:  detection of medical disorders  industrial process control  stock market predictions  the list goes on Could theoretically write a program to solve each of these problems, but the rules governing such a program would be incredibly complicated! Geoff Hinton sweet intro vid 2
3 Neural networks??? Why would we use those?! Some problems are just too complicated to solve with simple programming Computer vision/audition applications:  facial recognition Paul Debevec. A Neural Network for Facial Feature Location. UC Berkeley CS283 Project Report, December
4 Neural networks??? Why would we use those?! Some problems are just too complicated to solve with simple programming Computer vision/audition applications:  facial recognition manually located left eye, nose and mh polartransformed images around each feature Paul Debevec. A Neural Network for Facial Feature Location. UC Berkeley CS283 Project Report, December subsampled images to feed to neural network A. Avoids local minima Why? B. 4MB RAM in 1992 = $150 USD 4
5 Neural networks??? Why would we use those?! Some problems are just too complicated to solve with simple programming Computer vision/audition applications:  facial recognition After training a simple, feedforward network with backprop using yearbook photos it could successfully detect each eye, nose and mh in previously unseen photo! Paul Debevec. A Neural Network for Facial Feature Location. UC Berkeley CS283 Project Report, December
6 The choice for ratebased over spiking for machine learning spiking ratebased Pros neuronlevel resolution timeresolved (spiking dynamics, variability) several levels of abstraction available (HH, leaky integrateandfire, Izhikevich) Cons computationally expensive for large populations of neurons intractable for simulations of whole brain areas not obviously useful for machine learning Pros describes average firing of functional populations of neurons computationally cheap can address network structure/function mathematical simplicity Universal function approximator Cons lose benefits of spiking spatiotemporal resolution averages over timing/dynamics/variability/ etc. biological analogs not always obvious 6
7 General architecture Simplest network is the perceptron r1 in r2 in w1 w2 g r Transfer function g( ) general engineering term used to describe put of some processing unit as a function of input in if r i = x i and r = y then y = g(w 1 x 1 + w 2 x 2 ) and if g( ) = (i.e. g is purely linear) then y = w1 x1 + w2 x2 General singlelayer mapping r i = g( w ij r in j ) + r = g(wr in ) i 7
8 r1 in The XOR problem w1 XOR x1 x2 y x2 r2 in w2 Boolean OR x1 x2 y x2 g r x not linearly separable: more complicated! x1 linearly separable: can be easily separated with single threshold! g(x)= G 1 if x > H 0 else 8
9 r1 in The XOR problem w1 XOR x1 x2 y x1 r2 in w2 g r becomes not linearly separable: more complicated! x2 With enough hidden units, multilayer perceptron is the universal function approximator! 9
10 The XOR problem r1 in w1 g r r2 in w2 becomes With enough hidden units, multilayer perceptron is the universal function approximator! 10
11 Multilayer perceptron HLU1 HLU2 put HLU3 E.g. sine wave approximation using logistic transfer function With enough hidden units, multilayer perceptron is the universal function approximator! 11
12 Multilayer perceptron Limitations  Brainlike performance doesn t equate with actual performance  Training rules are nonphysiologic Strengths  Hidden layer activity might resemble brain function (with appropriate inputs/puts)  Brain = mapping network  SelfOrganization, like the brain  High flexibility in possible computations Point: MLP is usually good for machine learning purposes, but is not necessarily good for neuroscience theory all the time! 12
13 Two types of NNets feedforward ratebased recurrent Feedforward: information only flows forward, simplest connectivity  Kernel machines  Radial basis function networks  Probabilistic mapping networks  Bayesian nets  Stochastic nets  Modular nets  Committee machines  Associative neural nets  Holographic associative nets (???)  Fuzzy nets  Compositional patternproducing nets  etc. Recurrent: information can flow forward and backward, useful for timeresolved problems 13
14 How do we train a neural network? Minimize some cost function gradient descent! r1 in w1 MSE g r 1 E = 2 r2 in w2 i (r i  y i ) 2 desired put (data, training set) w ij! w ij + Dw ij 2E Dw ij = f( ) 2wij learning gradient of MSE rate wrt weights 14
15 How do we train a neural network? r1 in r2 in w1 w2 g r E = 2 1 i (r i  y i ) 2 w ij! w ij + Dw ij 2E Dw ij = f( ) 2wij 2E 1 2 2w = ij 2 2wij i j in (g( w ij r j )  y i ) hi f change in weight i,j depends on learning rate and dependence of error on weight change at i,j 2f 2w ij 2f = 2g 2g 2h (using chain rule) 2h 2w ij error s dependence on weight i,j, rewritten using MSE equation Dw ij = f(g'(h i )(y i  r i )r j in ) learning rule (derivation?) 15
16 Adding layers Start by finding the put rates 2layer (1 hidden) perceptron r i = g( w r ) r = g( w r ) j h ij h j E = 2 1 i (r i  y i ) 2 Dw ij = f(g'(h i )(y i  r i )r j in ) h h in r = g ( w g ( w r )) 3layer (2 hidden) perceptron h h h h in r = g ( w g 1( w 1g 2( w 2r ))) nlayer (n1 hidden) perceptron h h h h h h h h in r = g ( w g 1( w 1g 2( w g  n+ 1( w  n+ 1g n( w nr ))))) Idea is to nest each layer s put rates within the next 16
17 Training through the layers Generalized delta rule (put wts) 2E 2wij with d i 2E 2w 2E 2w with d h i 1 2 = 2 ( ri y) w  i 2 ij i h = di r j = g '( h h i)( r i yi) h ij h ij = E = ( r ) w 2 = h i yi 2 ij i 1 2 h 2 ( g ( wij g ( w r )) yi) w h = h in jk k  2 ij i j k h in = dir j h g '( h in i ) w k ik d k 2 i delta rule for put weights (r i  y i ) 2 Dw ij = f(g'(h i )(y i  r i )r j in ) Hidden layer weights Error propagates BACKWARDS through the layers! delta rule for hidden wts (depends on delta rule for put wts) 2 17
18 Training protocol (gradient descent) Training set Test set 1. Train until gradient of error function reaches minimum. A. Batch: use full training set with each iteration (smooth convergence, but more prone to local minima) B. Online: use different sample of training set with each iteration (more memory efficient, but messy convergence) 2. Test generalization of network using previously unseen test data set. 18
19 Caveats Local minima Can use momentum term in weight update to incorporate history of weight changes. Overfitting Use heuristics to determine appropriate number of nodes for solving particular problem. Can usually use 2*number of nodes for training set. 19
20 Recurrent networks are a whole new game! but I ll spare you Backprop. through time (BPTT) 20
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