introduction to deep learning @ startup.ml by andres rodriguez

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Introduction to deeplearning with neon

MAKING MACHINES SMARTER.™

Nervana Systems Proprietary

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• Intel Nervana overview• Machine learning basics

• What is deep learning?

• Basic deep learning concepts

• Example: recognition of handwritten digits

• Model ingredients in-depth

• Deep learning with neon


Intel Nervana‘s deep learning solution stack

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Images

Video

Text

Speech

Tabular

Time series

Solutions


Intel Nervana in action

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Healthcare: Tumor detection

Automotive: Speech interfaces Finance: Time-series search engine

Positive:

Negative:

Agricultural Robotics Oil & Gas

Positive:

Negative:

Proteomics: Sequence analysis

Query:

Results:


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• Intel Nervana overview

• Machine learning basics• What is deep learning?


• Example: recognition of handwritten digits




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Training error


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Training error

x

x

x

x

x

x

x

x x

xx

x xx

x x

xxx

x

x

xxx

xxx

Testing error


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Training Time

Err

or

Training Error

Testing/Validation Error

Underfitting Overfitting

Bias-Variance Trade-off


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• Machine learning basics


• Basic deep learning concepts• Model ingredients in-depth



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(𝑓1, 𝑓2, … , 𝑓𝐾)

SVMRandom ForestNaïve BayesDecision TreesLogistic RegressionEnsemble methods

𝑁 × 𝑁

𝐾 ≪ 𝑁

Arjun


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~60 million parameters

Arjun

But old practices apply: Data Cleaning, Underfit/Overfit, Data exploration, right cost function, hyperparameters, etc.

𝑁 × 𝑁


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𝑦𝑥2

𝑥3

𝑥1

𝑎

max(𝑎, 0)

𝑡𝑎𝑛ℎ(𝑎)

Output of unit

Activation Function

Linear weights Bias unit

Input from unit j

𝒘𝟏𝒘𝟐

𝒘𝟑

𝑔∑


InputHidden

Output

Affine layer: Linear + Bias + Activation


MNIST dataset 70,000 images (28x28 pixels)Goal: classify images into a digit 0-9

N = 28 x 28 pixels = 784 input units

N = 10 output units (one for each digit)

Each unit i encodes the probability of the input image of being of the

digit i

N = 100 hidden units (user-defined parameter)

InputHidden

Output


N=784N=100

N=10

Total parameters:

𝑊𝑖→𝑗, 𝑏𝑗𝑊𝑗→𝑘, 𝑏𝑘

𝑊𝑖→𝑗𝑏𝑗𝑊𝑗→𝑘𝑏𝑘

784 x 100100100 x 1010

= 84,600

𝐿𝑎𝑦𝑒𝑟 𝑖𝐿𝑎𝑦𝑒𝑟 𝑗

𝐿𝑎𝑦𝑒𝑟 𝑘


InputHidden

Output 1. Randomly seed weights2. Forward-pass3. Cost4. Backward-pass5. Update weights


InputHidden

Output

𝑊𝑖→𝑗, 𝑏𝑗 ∼ 𝐺𝑎𝑢𝑠𝑠𝑖𝑎𝑛(0,1)

𝑊𝑗→𝑘, 𝑏𝑘 ∼ 𝐺𝑎𝑢𝑠𝑠𝑖𝑎𝑛(0,1)


0.00.10.00.30.10.10.00.00.40.0

Output (10x1)

28x28

InputHidden

Output


0.00.10.00.30.10.10.00.00.40.0

Output (10x1)

28x28

InputHidden

Output

0001000000

Ground Truth

Cost function

𝑐(𝑜𝑢𝑡𝑝𝑢𝑡, 𝑡𝑟𝑢𝑡ℎ)


0.00.10.00.30.10.10.00.00.40.0

Output (10x1)

InputHidden

Output

0001000000

Ground Truth

Cost function

𝑐(𝑜𝑢𝑡𝑝𝑢𝑡, 𝑡𝑟𝑢𝑡ℎ)

Δ𝑊𝑖→𝑗 Δ𝑊𝑗→𝑘


InputHidden

Output 𝐶 𝑦, 𝑡𝑟𝑢𝑡ℎ

𝑊∗

𝜕𝐶𝜕𝑊∗

compute


InputHidden

Output 𝐶 𝑦, 𝑡𝑟𝑢𝑡ℎ = 𝐶 𝑔 ∑(𝑊𝑗→𝑘𝑥𝑘 + 𝑏𝑘)

𝑊∗


InputHidden

Output 𝐶 𝑦, 𝑡𝑟𝑢𝑡ℎ = 𝐶 𝑔 ∑(𝑊𝑗→𝑘𝑥𝑘 + 𝑏𝑘)

𝑎(𝑊𝑗→𝑘, 𝑥𝑘)=

𝑊𝑗→𝑘∗𝜕𝐶𝜕𝑊∗=𝜕𝐶𝜕𝑔∙𝜕𝑔𝜕𝑎∙𝜕𝑎𝜕𝑊∗

a

𝑔 = max(𝑎, 0)

a

𝑔′(𝑎)

= 𝐶 𝑔(𝑎 𝑊𝑗→𝑘, 𝑥𝑘 )


InputHidden

Output 𝐶 𝑦, 𝑡𝑟𝑢𝑡ℎ = 𝐶 𝑔𝑘(𝑎𝑘 𝑊𝑗→𝑘, 𝑔𝑗(𝑎𝑗(𝑊𝑖→𝑗, 𝑥𝑗))

𝜕𝐶𝜕𝑊∗=𝜕𝐶𝜕𝑔𝑘∙𝜕𝑔𝑘𝜕𝑎𝑘∙𝜕𝑎𝑘𝜕𝑔𝑗∙𝜕𝑔𝑗𝜕𝑎𝑗∙𝜕𝑎𝑗𝜕𝑊∗

𝐶 𝑦, 𝑡𝑟𝑢𝑡ℎ = 𝐶 𝑔𝑘 𝑎𝑘(𝑊𝑗→𝑘, 𝑥𝑘 = 𝑦𝑗

𝑦𝑗

𝑊𝑖→𝑗∗


Szegedy et al, 2015 Schmidhuber, 1997

• Activation functions• Weight initialization• Learning rule• Layer architecture (number of layers,

layer types, depth, etc.)


fprop cost bprop 𝛿𝑊













Update weights via:

Δ𝑊 = 𝛼 ∗1𝑁 𝛿𝑊

Learning rate








minibatch #1 weight update

minibatch #2 weight update


Epoch 0

Epoch 1

Sample numbers:• Learning rate ~0.001• Batch sizes of 32-128• 50-90 epochs


SGDGradient Descent


Krizhevsky, 2012

60 million parameters

120 million parametersTaigman, 2014


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• Model ingredients in-depth• Deep learning with neon


Dataset Model/Layers Activation OptimizerCost

𝐶(𝑦, 𝑡)


Filter + Non-Linearity

Pooling


Fully connected layers

…

“how can I help you?”

cat

Low level features

Mid level features

Object parts, phonemes

Objects, words

*Hinton et al., LeCun, Zeiler, Fergus


Pooling


Tanh Rectified Linear UnitLogistic

-1

11

0

𝑔 𝑎 =𝑒𝑎

∑𝑘 𝑒𝑎𝑘

Softmax


Gaussian Gaussian(mean, sd)

GlorotUniform Uniform(-k, k)

Xavier Uniform(k, k)

Kaiming Gaussian(0, sigma)

𝑘 =6

𝑑𝑖𝑛 + 𝑑𝑜𝑢𝑡

𝑘 =3𝑑𝑖𝑛

𝜎 =2𝑑𝑖𝑛


• Cross Entropy Loss

• Misclassification Rate

• Mean Squared Error

• L1 loss


0.00.10.00.30.10.10.00.00.40.0

Output (10x1)

0001000000

Ground Truth

− 𝑘

𝑡𝑘 × log(𝑦𝑘) = −log(0.3)


0.3 0.3 0.4

0.3 0.4 0.3

0.1 0.2 0.7

0 0 1

0 1 0

1 0 0

Outputs Targets Correct?

Y

Y

N

0.1 0.2 0.7

0.1 0.7 0.2

0.3 0.4 0.3

0 0 1

0 1 0

1 0 0

Y

Y

N

-(log(0.4) + log(0.4) + log(0.1))/3=1.38

-(log(0.7) + log(0.7) + log(0.3))/3=0.64


• SGD with Momentum

• RMS propagation

• Adagrad

• Adadelta

• Adam


Δ𝑊1 Δ𝑊2 Δ𝑊3 Δ𝑊4

training time

𝛼𝑡=4′ =𝛼

Δ𝑊2 2 + Δ𝑊3 2 + Δ𝑊4 2


Δ𝑊1 Δ𝑊2 Δ𝑊3 Δ𝑊4

training time

𝛼𝑡=𝑇′ =𝛼

∑𝑡=0𝑡=𝑇 Δ𝑊𝑡 2


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•Popular, well established, developer familiarity

•Fast to prototype

•Rich ecosystem of existing packages.

•Data Science: pandas, pycuda, ipython, matplotlib, h5py, …

•Good “glue” language: scriptable plus functional and OO support,

plays well with other languages


Backend NervanaGPU, NervanaCPU

Datasets MNIST, CIFAR-10, Imagenet 1K, PASCAL VOC, Mini-Places2, IMDB, Penn Treebank, Shakespeare Text, bAbI, Hutter-prize, UCF101, flickr8k, flickr30k, COCO

Initializers Constant, Uniform, Gaussian, Glorot Uniform, Xavier, Kaiming, IdentityInit, Orthonormal

Optimizers Gradient Descent with Momentum, RMSProp, AdaDelta, Adam, Adagrad,MultiOptimizer

Activations Rectified Linear, Softmax, Tanh, Logistic, Identity, ExpLin

LayersLinear, Convolution, Pooling, Deconvolution, Dropout, Recurrent,Long Short-

Term Memory, Gated Recurrent Unit, BatchNorm, LookupTable,Local Response Normalization, Bidirectional-RNN, Bidirectional-LSTM

Costs Binary Cross Entropy, Multiclass Cross Entropy, Sum of Squares Error

Metrics Misclassification (Top1, TopK), LogLoss, Accuracy, PrecisionRecall, ObjectDetection


1. Generate backend2. Load data3. Specify model architecture4. Define training parameters5. Train model6. Evaluate

NERVANA

[email protected]

introduction to deep learning @ startup.ml by andres rodriguez

Technology