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%install '.package(path: "$cwd/FastaiNotebook_02_fully_connected")' FastaiNotebook_02_fully_connected

Installing packages:
	.package(path: "/home/ubuntu/fastai_docs/dev_swift/FastaiNotebook_02_fully_connected")
		FastaiNotebook_02_fully_connected
With SwiftPM flags: []
Working in: /tmp/tmpxtwrx9n4
Fetching https://github.com/mxcl/Path.swift
Fetching https://github.com/JustHTTP/Just
Completed resolution in 2.04s
Cloning https://github.com/JustHTTP/Just
Resolving https://github.com/JustHTTP/Just at 0.7.1
Cloning https://github.com/mxcl/Path.swift
Resolving https://github.com/mxcl/Path.swift at 0.16.2
Compile Swift Module 'Just' (1 sources)
Compile Swift Module 'Path' (9 sources)
Compile Swift Module 'FastaiNotebook_02_fully_connected' (5 sources)
Compile Swift Module 'jupyterInstalledPackages' (1 sources)
Linking ./.build/x86_64-unknown-linux/debug/libjupyterInstalledPackages.so
Initializing Swift...
Loading library...
Installation complete!

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import FastaiNotebook_02_fully_connected

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// export
import Foundation
import TensorFlow
import Path

Does nn.Conv2d init work well?¶

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var (xTrain, yTrain, xValid, yValid) = loadMNIST(path: Path.home/".fastai"/"data"/"mnist_tst")
let (trainMean, trainStd) = (xTrain.mean(), xTrain.standardDeviation())
xTrain = normalize(xTrain, mean: trainMean, std: trainStd)
xValid = normalize(xValid, mean: trainMean, std: trainStd)

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xTrain = xTrain.reshaped(to: [xTrain.shape[0], 28, 28, 1])
xValid = xValid.reshaped(to: [xValid.shape[0], 28, 28, 1])
print(xTrain.shape, xValid.shape)

TensorShape(dimensions: [60000, 28, 28, 1]) TensorShape(dimensions: [10000, 28, 28, 1])

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let images = xTrain.shape[0]
let classes = xValid.max() + 1
let channels = 32

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var layer1 = FAConv2D<Float>(filterShape: (5, 5, 1, channels)) //Conv2D(1, nh, 5)

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let x = xValid[0..<100]

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x.shape

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▿ TensorShape
  ▿ dimensions : 4 elements
    - 0 : 100
    - 1 : 28
    - 2 : 28
    - 3 : 1

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extension Tensor where Scalar: TensorFlowFloatingPoint {
    func stats() -> (mean: Tensor, std: Tensor) {
        return (mean: self.mean(), std: self.standardDeviation())
    }
}

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(filter: layer1.filter.stats(), bias: layer1.bias.stats())

Out[ ]:

▿ 2 elements
  ▿ filter : 2 elements
    - mean : -0.00026652578
    - std : 0.04966226
  ▿ bias : 2 elements
    - mean : 0.0
    - std : 0.0

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let result = layer1.applied(to: x)

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result.stats()

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▿ 2 elements
  - mean : -0.00050843204
  - std : 0.27653128

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// export
extension Tensor where Scalar: TensorFlowFloatingPoint {
    init(kaimingNormal shape: TensorShape, negativeSlope: Double = 1.0) {
        // Assumes Leaky ReLU nonlinearity
        let gain = Scalar(sqrt(2.0 / (1.0 + pow(negativeSlope, 2))))
        let spatialDimCount = shape.count - 2
        let receptiveField = shape[0..<spatialDimCount].contiguousSize
        let fanIn = shape[shape.count - 2] * receptiveField
        self.init(
            randomNormal: shape,
            stddev: gain / sqrt(Scalar(fanIn)),
            generator: &PhiloxRandomNumberGenerator.global
        )
    }
}

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layer1.filter = Tensor(kaimingNormal: layer1.filter.shape, negativeSlope: 1.0)
layer1.applied(to: x).stats()

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▿ 2 elements
  - mean : 0.0077752783
  - std : 1.1046494

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// export
func leakyRelu<T: TensorFlowFloatingPoint>(
    _ x: Tensor<T>,
    negativeSlope: Double = 0.0
) -> Tensor<T> {
    return max(0, x) + T(negativeSlope) * min(0, x)
}

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layer1.filter = Tensor(kaimingNormal: layer1.filter.shape, negativeSlope: 0.0)
leakyRelu(layer1.applied(to: x)).stats()

Out[ ]:

▿ 2 elements
  - mean : 0.46370196
  - std : 0.8628286

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var layer1 = FAConv2D<Float>(filterShape: (5, 5, 1, channels)) //Conv2D(1, nh, 5)
leakyRelu(layer1.applied(to: x)).stats()

Out[ ]:

▿ 2 elements
  - mean : 0.08939172
  - std : 0.17101486

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layer1.filter.shape

Out[ ]:

▿ TensorShape
  ▿ dimensions : 4 elements
    - 0 : 5
    - 1 : 5
    - 2 : 1
    - 3 : 32

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let spatialDimCount = layer1.filter.rank - 2
let receptiveField = layer1.filter.shape[0..<spatialDimCount].contiguousSize
receptiveField

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let filtersIn = layer1.filter.shape[2]
let filtersOut = layer1.filter.shape[3]
print(filtersIn, filtersOut)

1 32

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let fanIn = filtersIn * receptiveField
let fanOut = filtersOut * receptiveField
print(fanIn, fanOut)

25 800

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func gain(_ negativeSlope: Double) -> Double {
    return sqrt(2.0 / (1.0 + pow(negativeSlope, 2.0)))
}

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(gain(1.0), gain(0.0), gain(0.01), gain(0.1), gain(sqrt(5.0)))

Out[ ]:

▿ 5 elements
  - .0 : 1.0
  - .1 : 1.4142135623730951
  - .2 : 1.4141428569978354
  - .3 : 1.4071950894605838
  - .4 : 0.5773502691896257

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(2 * Tensor<Float>(randomUniform: [10000]) - 1).standardDeviation()

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0.57633716

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1.0 / sqrt(3.0)

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0.5773502691896258

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//export
extension Tensor where Scalar: TensorFlowFloatingPoint {
    init(kaimingUniform shape: TensorShape, negativeSlope: Double = 1.0) {
        // Assumes Leaky ReLU nonlinearity
        let gain = Scalar(sqrt(2.0 / (1.0 + pow(negativeSlope, 2))))
        let spatialDimCount = shape.count - 2
        let receptiveField = shape[0..<spatialDimCount].contiguousSize
        let fanIn = shape[shape.count - 2] * receptiveField
        let bound = sqrt(Scalar(3.0)) * gain / sqrt(Scalar(fanIn))
        self = bound * (2 * Tensor(
            randomUniform: shape,
            generator: &PhiloxRandomNumberGenerator.global
        ) - 1)
    }
}

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layer1.filter = Tensor(kaimingUniform: layer1.filter.shape, negativeSlope: 0.0)
leakyRelu(layer1.applied(to: x)).stats()

Out[ ]:

▿ 2 elements
  - mean : 0.52419895
  - std : 0.9307874

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layer1.filter = Tensor(kaimingUniform: layer1.filter.shape, negativeSlope: sqrt(5.0))
leakyRelu(layer1.applied(to: x)).stats()

Out[ ]:

▿ 2 elements
  - mean : 0.19034371
  - std : 0.33603325

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public struct Model: Layer {
    public var conv1 = FAConv2D<Float>(
        filterShape: (5, 5, 1, 8),   strides: (2, 2), padding: .same, activation: relu
    )
    public var conv2 = FAConv2D<Float>(
        filterShape: (3, 3, 8, 16),  strides: (2, 2), padding: .same, activation: relu
    )
    public var conv3 = FAConv2D<Float>(
        filterShape: (3, 3, 16, 32), strides: (2, 2), padding: .same, activation: relu
    )
    public var conv4 = FAConv2D<Float>(
        filterShape: (3, 3, 32, 1),  strides: (2, 2), padding: .valid
    )
    public var flatten = Flatten<Float>()
    @differentiable
    public func applied(to input: Tensor<Float>) -> Tensor<Float> {
        return input.sequenced(through: conv1, conv2, conv3, conv4, flatten)
    }
}

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let y = Tensor<Float>(yValid[0..<100])
var model = Model()

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let prediction = model.applied(to: x)
prediction.stats()

Out[ ]:

▿ 2 elements
  - mean : 0.07328143
  - std : 0.070444785

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let gradients = gradient(at: model) { model in
    meanSquaredError(predicted: model.applied(to: x), expected: y)
}

gradients.conv1.filter.stats()

Out[ ]:

▿ 2 elements
  - mean : -0.1473091
  - std : 0.27992472

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for keyPath in [\Model.conv1, \Model.conv2, \Model.conv3, \Model.conv4] {
    model[keyPath: keyPath].filter = Tensor(kaimingUniform: model[keyPath: keyPath].filter.shape)
}

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let prediction = model.applied(to: x)
prediction.stats()

Out[ ]:

▿ 2 elements
  - mean : 0.45652133
  - std : 0.2774702

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let gradients = gradient(at: model) { model in
    meanSquaredError(predicted: model.applied(to: x), expected: y)
}

gradients.conv1.filter.stats()

Out[ ]:

▿ 2 elements
  - mean : -0.03488037
  - std : 0.60459524

Export¶

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notebookToScript(fname: (Path.cwd / "02a_why_sqrt5.ipynb").string)

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