Based on the original slides of Hung-yi Lee

Transcription

1 Based on the original slides of Hung-yi Lee

2 New Activation Function

3 Rectified Linear Unit (ReLU) σ z a a = z Reason: 1. Fast to compute 2. Biological reason a = 0 [Xavier Glorot, AISTATS 11] [Andrew L. Maas, ICML 13] [Kaiming He, arxiv 15] z 3. Infinite sigmoid with different biases 4. Vanishing gradient problem

4 x 1 x N In x2006, 2 people used RBM pre-training. In 2015, people use ReLU. y 1 y 2 y M Smaller gradients Learn very slow Almost random Larger gradients Learn very fast Already converge based on random!?

5 Smaller gradients x 1 x 2 Small output y 1 y 2 y 1 y 2 x N + w y M C + C Large input y M Intuitive way to compute the gradient C w =? C w

6 a a = z 0 a = 0 z x 1 x y 1 y 2 0

7 a a = z A Thinner linear network a = 0 z x 1 y 1 x 2 y 2 Do not have smaller gradients

8 ReLU is a special cases of Maxout Learnable activation function [Ian J. Goodfellow, ICML 13] + 5 neuron + 1 Input Max 7 x Max 2 x Max Max 4 You can have more than 2 elements in a group.

9 ReLU is a special cases of Maxout Learnable activation function [Ian J. Goodfellow, ICML 13] Activation function in maxout network can be any piecewise linear convex function How many pieces depending on how many elements in a group 2 elements in a 3 elements in a group group

10 Adaptive Learning Rate

11 Set the learning rate η carefully η C θ 0 If learning rate is too large w 2 Cost may not decrease after each update C θ 0 θ 0 w 1

12 Can we give different parameters different learning rates? Set the learning rate η carefully If learning rate is too large w 2 η C θ 0 θ 0 C θ 0 Cost may not decrease after each update If learning rate is too small Training would be too slow w 1

13 Original Gradient Descent θ t θ t 1 η C θ t 1 Each parameter w are considered separately w t+1 w t ߟ w g t g t = C θt w Parameter dependent learning rate ߟ w = η t i=0 g i 2 constant Summation of the square of the previous derivatives

14 g 0 g 1 w 1 w Learning rate: η η = η 0.1 = η 0.22 g 0 g Learning rate: η 20 2 η Observation: 1. Learning rate is smaller and smaller for all parameters 2. Smaller derivatives, larger learning rate, and vice versa = η 20 = η 22 Why?

15 Larger derivatives Smaller Learning Rate Smaller Derivatives Larger Learning Rate 2. Smaller derivatives, larger learning rate, and vice versa Why?

16 Adagrad [John Duchi, JMLR 11] RMSprop Adadelta [Matthew D. Zeiler, arxiv 12] Adam [Diederik P. Kingma, ICLR 15] AdaSecant [Caglar Gulcehre, arxiv 14] No more pesky learning rates [Tom Schaul, arxiv 12]

17 Dropout

18 Pick a mini-batch θ t θ t 1 η C θ t 1 Training: Each time before computing the gradients Each neuron has p% to dropout

19 Pick a mini-batch θ t θ t 1 η C θ t 1 Training: Thinner! Each time before computing the gradients Each neuron has p% to dropout The structure of the network is changed. Using the new network for training For each mini-batch, we resample the dropout neurons

20 Testing: No dropout If the dropout rate at training is p%, all the weights times (1-p)% Assume that the dropout rate is 50%. If a weight w = 1 by training, set w = 0.5 for testing.

21 Partners need to perform When teams up, if everyone expect the partner will do the work, nothing will be done finally. However, if you know your partner will dropout, you will do better. When testing, no one dropout actually, so obtaining good results eventually.

22 Why the weights should multiply (1-p)% (dropout rate) when testing? Training of Dropout Assume dropout rate is 50% w 1 w 2 w 3 w 4 z Testing of Dropout No dropout w 1 w 2 w 3 w 4 Weights from training z 2z z Weights multiply (1-p)% z z

23 Ensemble Training Set Set 1 Set 2 Set 3 Set 4 Network 1 Network 2 Network 3 Network 4 Train a bunch of networks with different structures

24 Ensemble Testing data x Network 1 Network 2 Network 3 Network 4 y 1 y 2 y 3 y 4 average

25 minibatch 1 minibatch 2 minibatch 3 minibatch 4 Training of Dropout M neurons 2 M possible networks Using one mini-batch to train one network Some parameters in the network are shared

26 Testing of Dropout testing data x All the weights multiply (1-p)% y 1 y 2 y 3 average y

27 More reference for dropout [Nitish Srivastava, JMLR 14] [Pierre Baldi, NIPS 13][Geoffrey E. Hinton, arxiv 12] Dropout works better with Maxout [Ian J. Goodfellow, ICML 13] Dropconnect [Li Wan, ICML 13] Dropout delete neurons Dropconnect deletes the connection between neurons Annealed dropout [S.J. Rennie, SLT 14] Dropout rate decreases by epochs Standout [J. Ba, NISP 13] Each neural has different dropout rate

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29 Name Entity Recognition Detecting named entities like name of people, locations, organization, etc. in a sentence. apple DNN people location organization none

30 Name Entity Recognition Detecting named entities like name of people, locations, organization, etc. in a sentence. targe t ORG NONE y 1 y 2 y 3 y 4 y 5 y 6 y 7 DNN DNN DNN DNN DNN DNN DNN x 1 x 2 x 3 x 4 x 5 x 6 x 7 the president of apple eats an apple DNN needs memory! targe t

31 y 1 y 2 The output of hidden layer are stored in the memory. copy a1 a2 Memory can be considered as another input. x1 x2

32 W o y 1 y 2 y 3 W o copy copy W a o 1 a 2 a 3 a 1 a 2 W i W h W W i h W i x 1 x 2 x 3 The same network is used again and again. Output y i depends on x 1, x 2, x i

33 How to train? y 1 target y 2 target y 3 target L 1 L 2 L 3 y 1 y 2 y 3 W o W h W o W h W o W i W i x 1 x 2 x 3 W i Find the network parameters to minimize the total cost: Backpropagation through time (BPTT)

34 y t y t+1 y t+2 x t x t+1 x t+2

35 Both input and output are both sequences, but the output is shorter. E.g. Speech Recognition Output: Why can t it be (character sequence) Problem? Trimming Why can t it be Input: (vector sequence)

36 Both input and output are both sequences, but the output is shorter. Connectionist Temporal Classification (CTC) [Alex Graves, ICML 06][Alex Graves, ICML 14][Haşim Sak, Interspeech 15][Jie Li, Interspeech 15][Andrew Senior, ASRU 15] Add an extra symbol φ representing null φ φ φ φ φ φ φ φ φ φ φ

37 RNN-based network is not always easy to learn Real experiments on Language modeling sometimes Lucky

38 The error surface is either very flat or very steep. Clippin g Cost w 2 w 1 [Razvan Pascanu, ICML 13]

39 w = 1 w = 1.01 y 1000 = 1 y Large gradient Small Learning rate? w = 0.99 w = 0.01 y y small gradient Large Learning rate? =w 999 Toy Example y 1 y 2 y 3 y w w w

40 Nesterov s Accelerated Gradient (NAG): Advance momentum method RMS Prop Advanced approach to give each parameter different learning rates Considering the change of Second derivatives Long Short-term Memory (LSTM) Can deal with gradient vanishing (not exploding gradient)

41 Signal control the output gate (Other part of the network) Signal control the input gate (Other part of the network) Other part of the network Output Gate Memory Cell Input Gate Other part of the network Forget Gate LSTM Special Neuron: 4 inputs, 1 output Signal control the forget gate (Other part of the network)

42 a = h c f z o z o multiply f z o h c Activation function f is usually a sigmoid function c f z f Between 0 and 1 Mimic open and close gate c c z f cf z f z i f z i g z f z i multiply g z c = g z f z i + cf z f z

43 Extension: peephole y t y t+1 c t-1 c t c t z f z i z z o z f z i z z o c t-1 h t-1 x t c t h t x t+1

44 + a 1 a times of parameters x 1 x 2 Input

45 Gated Recurrent Unit (GRU) Structurally Constrained Recurrent Network (SCRN) [Cho, EMNLP 14] Vanilla RNN Initialized with Identity matrix + ReLU activation function [Quoc V. Le, arxiv 15] [Tomas Mikolov, ICLR 15] Outperform or be comparable with LSTM in 4 different tasks

46 Attention-based Model End-To-End Memory Networks. S. Sukhbaatar, A. Szlam, J. Weston, R. Fergus. arxiv Pre-Print, Neural Turing Machines. Alex Graves, Greg Wayne, Ivo Danihelka. arxiv Pre- Print, 2014 Ask Me Anything: Dynamic Memory Networks for Natural Language Processing. Kumar et al. arxiv Pre-Print, 2015 Neural Machine Translation by Jointly Learning to Align and Translate. D. Bahdanau, K. Cho, Y. Bengio; International Conference on Representation Learning Show, Attend and Tell: Neural Image Caption Generation with Visual Attention. Kelvin Xu et. al.. arxiv Pre-Print, Attention-Based Models for Speech Recognition. Jan Chorowski, Dzmitry Bahdanau, Dmitriy Serdyuk, Kyunghyun Cho, Yoshua Bengio. arxiv Pre-Print, Recurrent models of visual attention. V. Mnih, N. Hees, A. Graves and K. Kavukcuoglu. In NIPS, A Neural Attention Model for Abstractive Sentence Summarization. A. M. Rush, S. Chopra and J. Weston. EMNLP LSTM in the context of the Internet of Things (IoT)?

47 Neural Networks and Deep Learning written by Michael Nielsen Deep Learning (not finished yet) Written by Yoshua Bengio, Ian J. Goodfellow and Aaron Courville Understanding LSTM Networks LSTM NEURAL NETWORK FOR TIME SERIES PREDICTION Network-for-Time-Series-Prediction