Introduction to Neural Networks
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1 Introduction to Neural Networks Steve Renals Automatic Speech Recognition ASR Lecture February 2014 ASR Lecture 10 Introduction to Neural Networks 1
2 Neural networks for speech recognition Introduction to Neural Networks Training feed-forward networks Hybrid neural network / HMM acoustic models Neural network features Tandem, posteriorgrams Deep neural network acoustic models Neural network language models ASR Lecture 10 Introduction to Neural Networks 2
3 Neural networks for speech recognition Introduction to Neural Networks Training feed-forward networks Hybrid neural network / HMM acoustic models Neural network features Tandem, posteriorgrams Deep neural network acoustic models Neural network language models ASR Lecture 10 Introduction to Neural Networks 3
4 Neural network acoustic models Output layer Hidden layer H Hidden layer H-1... Hidden layer 1 Input layer Input layer takes several consecutive frames of acoustic features Output layer corresponds to classes (e.g. phones, HMM states) Multiple non-linear hidden layers between input and output Neural networks also called multi-layer perceptrons ASR Lecture 10 Introduction to Neural Networks 4
5 NN vs GMM Output layer Hidden layer H Hidden layer H-1... Hidden layer 1 Input layer Potential deep structure through multiple hidden layers (rather than a single layer of GMMs) Operates on multiple frames of input (rather than a single frame) One big network for everything (rather than one HMM per phone) ASR Lecture 10 Introduction to Neural Networks 5
6 Layered neural networks: structure (1) w (2) 10 + Outputs + y1 y K w (2) KM Bias + Hidden + z 0 z 1 z M w (1) 10 w (1) Md Bias Inputs x 0 x 1 x d Neural network with one hidden layer ASR Lecture 10 Introduction to Neural Networks 6
7 Layered neural networks: structure (2) d input units, M hidden units, K output units Hidden layer: each of M units takes a linear combination of the inputs x i : d b j = w (1) ji x i b j : activations w (1) ji : first layer of weights i=0 ASR Lecture 10 Introduction to Neural Networks 7
8 Layered neural networks: structure (2) d input units, M hidden units, K output units Hidden layer: each of M units takes a linear combination of the inputs x i : d b j = w (1) ji x i i=0 b j : activations w (1) ji : first layer of weights Activations transformed by a nonlinear activation function h (e.g. a sigmoid): z j = h(b j ) = exp( b j ) z j : hidden unit outputs ASR Lecture 10 Introduction to Neural Networks 7
9 Logisitic sigmoid activation function g(a) = 1 (1 + exp( a)) 1 Logistic sigmoid activation function g(a) = 1/(1+exp( a)) g(a) a ASR Lecture 10 Introduction to Neural Networks 8
10 Layered neural networks: structure (3) Outputs of the hidden units are linearly combined to give activations of the output units: a k = M j=0 w (2) kj z j ASR Lecture 10 Introduction to Neural Networks 9
11 Layered neural networks: structure (3) Outputs of the hidden units are linearly combined to give activations of the output units: a k = M j=0 w (2) kj z j Output units can be sigmoids, but it is better if they use the softmax activation function: y k = g(a k ) = exp(a k ) K l=1 exp(a l) ASR Lecture 10 Introduction to Neural Networks 9
12 Layered neural networks: structure (3) Outputs of the hidden units are linearly combined to give activations of the output units: a k = M j=0 w (2) kj z j Output units can be sigmoids, but it is better if they use the softmax activation function: y k = g(a k ) = exp(a k ) K l=1 exp(a l) Softmax enforces sum-to-one across outputs ASR Lecture 10 Introduction to Neural Networks 9
13 Layered neural networks: structure (3) Outputs of the hidden units are linearly combined to give activations of the output units: a k = M j=0 w (2) kj z j Output units can be sigmoids, but it is better if they use the softmax activation function: y k = g(a k ) = exp(a k ) K l=1 exp(a l) Softmax enforces sum-to-one across outputs If output unit k corresponds to class C k, then interpret outputs of trained network as posterior probability estimates P(C k x) = y k ASR Lecture 10 Introduction to Neural Networks 9
14 Layered neural networks: training Weights w ji are the trainable parameters Train the weights by adjusting them to minimise a cost function which measures the error the network outputs y n k (for the nth frame) compared with the target output t n k Sum squared error E n = 1 2 K tk n yk n 2 k=1 For multiclass classification, the natural cost function is (negative) log probability of the correct class E n = K tk n log yk n k=1 E = n E n Optimise the cost function using gradient descent (back-propagation of error backprop) ASR Lecture 10 Introduction to Neural Networks 10
15 Gradient descent Gradient descent can be used whenever it is possible to compute the derivatives of the error function E with respect to the parameters to be optimized W Basic idea: adjust the weights to move downhill in weight space Weight space: space defined by all the trainable parameters (weights) Operation of gradient descent: 1 Start with a guess for the weight matrix W (small random numbers) 2 Update the weights by adjusting the weight matrix in the direction of W E. 3 Recompute the error, and iterate The update for weight w ki at iteration τ + 1 is: w τ+1 ki = w τ ki η E w ki The parameter η is the learning rate ASR Lecture 10 Introduction to Neural Networks 11
16 Using neural networks for acoustic modelling Hybrid NN/HMM systems Basic idea: in an HMM, replace the GMMs used to estimate output pdfs with the outputs of neural networks Transform NN posterior probability estimates to scaled likelihoods by dividing by the relative frequencies in the training data of each class P(x t C k ) P(C k x t ) P train (C k ) = y k P train (C k ) NN outputs correspond to phone classes or HMM states Tandem features Use NN probability estimates as an additional input feature stream in an HMM/GMM system (posteriograms) ASR Lecture 10 Introduction to Neural Networks 12
17 End of part 1 Next two lectures Hybrid NN/HMM systems Tandem features Deep neural networks Neural network language models Reading N Morgan and H Bourlard (May 1995). Continuous speech recognition: An introduction to the hybrid HMM/connectionist approach, IEEE Signal Processing Magazine, 12(3), Christopher M Bishop (2006). Pattern Recognition and Machine Learning, Springer. Chapters 4 and 5. ASR Lecture 10 Introduction to Neural Networks 13
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