Regression

In this example we implement a logistic regression based binary classifier and train it to distinguish between the MNIST digits of 0 and 1.

Loading the data

First, let's start by loading the MNIST training and testing data and arranging these into training, validation, and testing sets.

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open Hype
open Hype.Neural
open DiffSharp.AD.Float32
open DiffSharp.Util

let MNIST = Dataset(Util.LoadMNISTPixels("C:/datasets/MNIST/train-images.idx3-ubyte", 60000),
                    Util.LoadMNISTLabels("C:/datasets/MNIST/train-labels.idx1-ubyte", 60000) |> toDV |> DM.ofDV 1).NormalizeX()



let MNISTtrain = MNIST.[..58999]
let MNISTvalid = MNIST.[59000..]

let MNISTtest = Dataset(Util.LoadMNISTPixels("C:/datasets/MNIST/t10k-images.idx3-ubyte", 10000),
                        Util.LoadMNISTLabels("C:/datasets/MNIST/t10k-labels.idx1-ubyte", 10000) |> toDV |> DM.ofDV 1).NormalizeX()

We shuffle the columns of the datasets and filter them to only keep the digits of 0 and 1.

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let MNISTtrain01 = MNISTtrain.Shuffle().Filter(fun (x, y) -> y.[0] <= D 1.f)
let MNISTvalid01 = MNISTvalid.Shuffle().Filter(fun (x, y) -> y.[0] <= D 1.f)
let MNISTtest01 = MNISTtest.Shuffle().Filter(fun (x, y) -> y.[0] <= D 1.f)

val MNISTtrain01 : Dataset = Hype.Dataset
   X: 784 x 12465
   Y: 1 x 12465
val MNISTvalid01 : Dataset = Hype.Dataset
   X: 784 x 200
   Y: 1 x 200
val MNISTtest01 : Dataset = Hype.Dataset
   X: 784 x 2115
   Y: 1 x 2115

We can visualize individual digits from the dataset.

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MNISTtrain.X.[*,9] |> DV.visualizeAsDM 28 |> printfn "%s"
MNISTtrain.Y.[*,9]

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DM : 28 x 28




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val it : DV = DV [|4.0f|]

We can also visualize a series of digits in grid layout.

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MNISTtrain.[..5].VisualizeXColsAsImageGrid(28) |> printfn "%s"

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Hype.Dataset
   X: 784 x 6
   Y: 1 x 6
X's columns reshaped to (28 x 28), presented in a (2 x 3) grid:
DM : 56 x 84




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MNISTtrain01.[..5].VisualizeXColsAsImageGrid(28) |> printfn "%s"

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Hype.Dataset
   X: 784 x 6
   Y: 1 x 6
X's columns reshaped to (28 x 28), presented in a (2 x 3) grid:
DM : 56 x 84




                 ▴●███-                      ·♦██                                   
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Defining the model

Let's now create our linear regression model. We implement this using the Hype.Neural module, as a linear layer with \(28 \times 28 = 784\) inputs and one output. The output of the layer is passed through the sigmoid function.

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let n = Neural.FeedForward()
n.Add(Linear(28 * 28, 1))
n.Add(sigmoid)

We can visualize the initial state of the linear model weights before the training. For information of about weight initialization parameters, please see the neural networks example.

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let l = (n.[0] :?> Linear)
l.VisualizeWRowsAsImageGrid(28) |> printfn "%s"

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Hype.Neural.Linear
   784 -> 1
   Learnable parameters: 785
   Init: Standard
   W's rows reshaped to (28 x 28), presented in a (1 x 1) grid:
DM : 28 x 28
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   b:
DV : 1

Training

Let's train the model for 10 epochs (full passes through the training data), with a minibatch size of 100, using the training and validation sets we've defined. The validation set will make sure that we're not overfitting the model.

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let p = {Params.Default with 
            Epochs = 10; 
            Batch = Minibatch 100; 
            EarlyStopping = EarlyStopping.DefaultEarly}

n.Train(MNISTtrain01, MNISTvalid01, p)

[12/11/2015 20:21:12] --- Training started
[12/11/2015 20:21:12] Parameters     : 785
[12/11/2015 20:21:12] Iterations     : 1240
[12/11/2015 20:21:12] Epochs         : 10
[12/11/2015 20:21:12] Batches        : Minibatches of 100 (124 per epoch)
[12/11/2015 20:21:12] Training data  : 12465
[12/11/2015 20:21:12] Validation data: 200
[12/11/2015 20:21:12] Valid. interval: 10
[12/11/2015 20:21:12] Method         : Gradient descent
[12/11/2015 20:21:12] Learning rate  : RMSProp a0 = D 0.00100000005f, k = D 0.899999976f
[12/11/2015 20:21:12] Momentum       : None
[12/11/2015 20:21:12] Loss           : L2 norm
[12/11/2015 20:21:12] Regularizer    : L2 lambda = D 9.99999975e-05f
[12/11/2015 20:21:12] Gradient clip. : None
[12/11/2015 20:21:12] Early stopping : Stagnation thresh. = 750, overfit. thresh. = 10
[12/11/2015 20:21:12] Improv. thresh.: D 0.995000005f
[12/11/2015 20:21:12] Return best    : true
[12/11/2015 20:21:12]  1/10 | Batch   1/124 | D  4.748471e-001 [- ] | Valid D  4.866381e-001 [- ] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:12]  1/10 | Batch  11/124 | D  2.772053e-001 [↓▼] | Valid D  3.013612e-001 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:12]  1/10 | Batch  21/124 | D  2.178165e-001 [↓▼] | Valid D  2.304372e-001 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:12]  1/10 | Batch  31/124 | D  2.009703e-001 [↓▼] | Valid D  1.799015e-001 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:12]  1/10 | Batch  41/124 | D  1.352896e-001 [↓▼] | Valid D  1.405802e-001 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:12]  1/10 | Batch  51/124 | D  1.182899e-001 [↓▼] | Valid D  1.108390e-001 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:12]  1/10 | Batch  61/124 | D  1.124191e-001 [↓▼] | Valid D  8.995526e-002 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:12]  1/10 | Batch  71/124 | D  8.975799e-002 [↓▼] | Valid D  7.361954e-002 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:12]  1/10 | Batch  81/124 | D  5.031444e-002 [↓▼] | Valid D  5.941865e-002 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:12]  1/10 | Batch  91/124 | D  5.063754e-002 [↑ ] | Valid D  4.927430e-002 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:12]  1/10 | Batch 101/124 | D  3.842642e-002 [↓▼] | Valid D  4.095582e-002 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:12]  1/10 | Batch 111/124 | D  4.326219e-002 [↑ ] | Valid D  3.452797e-002 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:12]  1/10 | Batch 121/124 | D  2.585407e-002 [↓▼] | Valid D  2.788338e-002 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:12]  2/10 | Batch   1/124 | D  3.069563e-002 [↑ ] | Valid D  2.663207e-002 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:12]  2/10 | Batch  11/124 | D  1.765305e-002 [↓▼] | Valid D  2.332163e-002 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:12]  2/10 | Batch  21/124 | D  2.314118e-002 [↑ ] | Valid D  1.902804e-002 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:12]  2/10 | Batch  31/124 | D  3.177435e-002 [↑ ] | Valid D  1.691620e-002 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:12]  2/10 | Batch  41/124 | D  2.219648e-002 [↓ ] | Valid D  1.455527e-002 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:12]  2/10 | Batch  51/124 | D  1.205402e-002 [↓▼] | Valid D  1.240637e-002 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:12]  2/10 | Batch  61/124 | D  3.891717e-002 [↑ ] | Valid D  1.189688e-002 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:12]  2/10 | Batch  71/124 | D  2.114762e-002 [↓ ] | Valid D  1.083007e-002 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:12]  2/10 | Batch  81/124 | D  5.075417e-003 [↓▼] | Valid D  9.630994e-003 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:12]  2/10 | Batch  91/124 | D  1.343214e-002 [↑ ] | Valid D  8.666289e-003 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:13]  2/10 | Batch 101/124 | D  6.054885e-003 [↓ ] | Valid D  8.039203e-003 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:13]  2/10 | Batch 111/124 | D  1.964125e-002 [↑ ] | Valid D  7.339509e-003 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:13]  2/10 | Batch 121/124 | D  4.401092e-003 [↓▼] | Valid D  6.376633e-003 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:13]  3/10 | Batch   1/124 | D  7.068173e-003 [↑ ] | Valid D  6.426438e-003 [↑ ] | Stag: 10 Ovfit: 0
[12/11/2015 20:21:13]  3/10 | Batch  11/124 | D  3.763680e-003 [↓▼] | Valid D  6.076077e-003 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:13]  3/10 | Batch  21/124 | D  9.855231e-003 [↑ ] | Valid D  5.091224e-003 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:13]  3/10 | Batch  31/124 | D  1.263964e-002 [↑ ] | Valid D  4.641499e-003 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:13]  3/10 | Batch  41/124 | D  1.205439e-002 [↓ ] | Valid D  4.599225e-003 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:13]  3/10 | Batch  51/124 | D  2.941387e-003 [↓▼] | Valid D  4.381890e-003 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:13]  3/10 | Batch  61/124 | D  2.546543e-002 [↑ ] | Valid D  4.439059e-003 [↑ ] | Stag: 10 Ovfit: 0
[12/11/2015 20:21:13]  3/10 | Batch  71/124 | D  9.878366e-003 [↓ ] | Valid D  4.358966e-003 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:13]  3/10 | Batch  81/124 | D  1.868963e-003 [↓▼] | Valid D  3.960044e-003 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:13]  3/10 | Batch  91/124 | D  7.171181e-003 [↑ ] | Valid D  3.634899e-003 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:13]  3/10 | Batch 101/124 | D  2.681098e-003 [↓ ] | Valid D  3.636524e-003 [↑ ] | Stag: 10 Ovfit: 0
[12/11/2015 20:21:13]  3/10 | Batch 111/124 | D  1.502046e-002 [↑ ] | Valid D  3.393996e-003 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:13]  3/10 | Batch 121/124 | D  2.381395e-003 [↓ ] | Valid D  3.178693e-003 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:13]  4/10 | Batch   1/124 | D  3.185510e-003 [↑ ] | Valid D  3.240891e-003 [↑ ] | Stag: 10 Ovfit: 0
[12/11/2015 20:21:13]  4/10 | Batch  11/124 | D  2.029225e-003 [↓ ] | Valid D  3.163968e-003 [↓ ] | Stag: 20 Ovfit: 0
[12/11/2015 20:21:13]  4/10 | Batch  21/124 | D  6.450378e-003 [↑ ] | Valid D  2.772849e-003 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:13]  4/10 | Batch  31/124 | D  7.448227e-003 [↑ ] | Valid D  2.572560e-003 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:13]  4/10 | Batch  41/124 | D  9.700718e-003 [↑ ] | Valid D  2.693694e-003 [↑ ] | Stag: 10 Ovfit: 0
[12/11/2015 20:21:13]  4/10 | Batch  51/124 | D  1.799919e-003 [↓▼] | Valid D  2.737873e-003 [↑ ] | Stag: 20 Ovfit: 1
[12/11/2015 20:21:13]  4/10 | Batch  61/124 | D  1.919956e-002 [↑ ] | Valid D  2.778393e-003 [↑ ] | Stag: 30 Ovfit: 3
[12/11/2015 20:21:13]  4/10 | Batch  71/124 | D  5.462923e-003 [↓ ] | Valid D  2.870561e-003 [↑ ] | Stag: 40 Ovfit: 3
[12/11/2015 20:21:13]  4/10 | Batch  81/124 | D  1.455469e-003 [↓▼] | Valid D  2.632472e-003 [↓ ] | Stag: 50 Ovfit: 4
[12/11/2015 20:21:14]  4/10 | Batch  91/124 | D  5.270801e-003 [↑ ] | Valid D  2.455564e-003 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:14]  4/10 | Batch 101/124 | D  2.057914e-003 [↓ ] | Valid D  2.511977e-003 [↑ ] | Stag: 10 Ovfit: 0
[12/11/2015 20:21:14]  4/10 | Batch 111/124 | D  1.314815e-002 [↑ ] | Valid D  2.393763e-003 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:14]  4/10 | Batch 121/124 | D  2.033168e-003 [↓ ] | Valid D  2.358985e-003 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:14]  5/10 | Batch   1/124 | D  2.199435e-003 [↑ ] | Valid D  2.389120e-003 [↑ ] | Stag: 10 Ovfit: 0
[12/11/2015 20:21:14]  5/10 | Batch  11/124 | D  1.668178e-003 [↓ ] | Valid D  2.356529e-003 [↓ ] | Stag: 20 Ovfit: 0
[12/11/2015 20:21:14]  5/10 | Batch  21/124 | D  5.649061e-003 [↑ ] | Valid D  2.151499e-003 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:14]  5/10 | Batch  31/124 | D  5.264180e-003 [↓ ] | Valid D  2.038927e-003 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:14]  5/10 | Batch  41/124 | D  8.416546e-003 [↑ ] | Valid D  2.145057e-003 [↑ ] | Stag: 10 Ovfit: 0
[12/11/2015 20:21:14]  5/10 | Batch  51/124 | D  1.564733e-003 [↓ ] | Valid D  2.208556e-003 [↑ ] | Stag: 20 Ovfit: 0
[12/11/2015 20:21:14]  5/10 | Batch  61/124 | D  1.581773e-002 [↑ ] | Valid D  2.233998e-003 [↑ ] | Stag: 30 Ovfit: 0
[12/11/2015 20:21:14]  5/10 | Batch  71/124 | D  3.898179e-003 [↓ ] | Valid D  2.347554e-003 [↑ ] | Stag: 40 Ovfit: 0
[12/11/2015 20:21:14]  5/10 | Batch  81/124 | D  1.395002e-003 [↓▼] | Valid D  2.182974e-003 [↓ ] | Stag: 50 Ovfit: 1
[12/11/2015 20:21:14]  5/10 | Batch  91/124 | D  4.450763e-003 [↑ ] | Valid D  2.069927e-003 [↓ ] | Stag: 60 Ovfit: 1
[12/11/2015 20:21:14]  5/10 | Batch 101/124 | D  1.927794e-003 [↓ ] | Valid D  2.129479e-003 [↑ ] | Stag: 70 Ovfit: 1
[12/11/2015 20:21:14]  5/10 | Batch 111/124 | D  1.238949e-002 [↑ ] | Valid D  2.059099e-003 [↓ ] | Stag: 80 Ovfit: 1
[12/11/2015 20:21:14]  5/10 | Batch 121/124 | D  1.969593e-003 [↓ ] | Valid D  2.072177e-003 [↑ ] | Stag: 90 Ovfit: 1
[12/11/2015 20:21:14]  6/10 | Batch   1/124 | D  1.885590e-003 [↓ ] | Valid D  2.087292e-003 [↑ ] | Stag:100 Ovfit: 1
[12/11/2015 20:21:14]  6/10 | Batch  11/124 | D  1.577425e-003 [↓ ] | Valid D  2.074389e-003 [↓ ] | Stag:110 Ovfit: 1
[12/11/2015 20:21:14]  6/10 | Batch  21/124 | D  5.410788e-003 [↑ ] | Valid D  1.943973e-003 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:14]  6/10 | Batch  31/124 | D  4.188792e-003 [↓ ] | Valid D  1.863442e-003 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:14]  6/10 | Batch  41/124 | D  7.516511e-003 [↑ ] | Valid D  1.951990e-003 [↑ ] | Stag: 10 Ovfit: 0
[12/11/2015 20:21:14]  6/10 | Batch  51/124 | D  1.510475e-003 [↓ ] | Valid D  2.003860e-003 [↑ ] | Stag: 20 Ovfit: 0
[12/11/2015 20:21:14]  6/10 | Batch  61/124 | D  1.375423e-002 [↑ ] | Valid D  2.020531e-003 [↑ ] | Stag: 30 Ovfit: 0
[12/11/2015 20:21:14]  6/10 | Batch  71/124 | D  3.260145e-003 [↓ ] | Valid D  2.129138e-003 [↑ ] | Stag: 40 Ovfit: 0
[12/11/2015 20:21:15]  6/10 | Batch  81/124 | D  1.402565e-003 [↓ ] | Valid D  2.002138e-003 [↓ ] | Stag: 50 Ovfit: 0
[12/11/2015 20:21:15]  6/10 | Batch  91/124 | D  3.999386e-003 [↑ ] | Valid D  1.920336e-003 [↓ ] | Stag: 60 Ovfit: 0
[12/11/2015 20:21:15]  6/10 | Batch 101/124 | D  1.929424e-003 [↓ ] | Valid D  1.976652e-003 [↑ ] | Stag: 70 Ovfit: 0
[12/11/2015 20:21:15]  6/10 | Batch 111/124 | D  1.205915e-002 [↑ ] | Valid D  1.926643e-003 [↓ ] | Stag: 80 Ovfit: 0
[12/11/2015 20:21:15]  6/10 | Batch 121/124 | D  1.978536e-003 [↓ ] | Valid D  1.951888e-003 [↑ ] | Stag: 90 Ovfit: 0
[12/11/2015 20:21:15]  7/10 | Batch   1/124 | D  1.769614e-003 [↓ ] | Valid D  1.959661e-003 [↑ ] | Stag:100 Ovfit: 0
[12/11/2015 20:21:15]  7/10 | Batch  11/124 | D  1.555518e-003 [↓ ] | Valid D  1.955613e-003 [↓ ] | Stag:110 Ovfit: 0
[12/11/2015 20:21:15]  7/10 | Batch  21/124 | D  5.217655e-003 [↑ ] | Valid D  1.861573e-003 [↓ ] | Stag:120 Ovfit: 0
[12/11/2015 20:21:15]  7/10 | Batch  31/124 | D  3.625835e-003 [↓ ] | Valid D  1.796666e-003 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:15]  7/10 | Batch  41/124 | D  6.929778e-003 [↑ ] | Valid D  1.872346e-003 [↑ ] | Stag: 10 Ovfit: 0
[12/11/2015 20:21:15]  7/10 | Batch  51/124 | D  1.502809e-003 [↓ ] | Valid D  1.913079e-003 [↑ ] | Stag: 20 Ovfit: 0
[12/11/2015 20:21:15]  7/10 | Batch  61/124 | D  1.241405e-002 [↑ ] | Valid D  1.924762e-003 [↑ ] | Stag: 30 Ovfit: 0
[12/11/2015 20:21:15]  7/10 | Batch  71/124 | D  2.962820e-003 [↓ ] | Valid D  2.024504e-003 [↑ ] | Stag: 40 Ovfit: 0
[12/11/2015 20:21:15]  7/10 | Batch  81/124 | D  1.421725e-003 [↓ ] | Valid D  1.919308e-003 [↓ ] | Stag: 50 Ovfit: 0
[12/11/2015 20:21:15]  7/10 | Batch  91/124 | D  3.717377e-003 [↑ ] | Valid D  1.854433e-003 [↓ ] | Stag: 60 Ovfit: 0
[12/11/2015 20:21:15]  7/10 | Batch 101/124 | D  1.973184e-003 [↓ ] | Valid D  1.907719e-003 [↑ ] | Stag: 70 Ovfit: 0
[12/11/2015 20:21:15]  7/10 | Batch 111/124 | D  1.190252e-002 [↑ ] | Valid D  1.867085e-003 [↓ ] | Stag: 80 Ovfit: 0
[12/11/2015 20:21:15]  7/10 | Batch 121/124 | D  2.006255e-003 [↓ ] | Valid D  1.894716e-003 [↑ ] | Stag: 90 Ovfit: 0
[12/11/2015 20:21:15]  8/10 | Batch   1/124 | D  1.721533e-003 [↓ ] | Valid D  1.898627e-003 [↑ ] | Stag:100 Ovfit: 0
[12/11/2015 20:21:15]  8/10 | Batch  11/124 | D  1.553262e-003 [↓ ] | Valid D  1.897926e-003 [↓ ] | Stag:110 Ovfit: 0
[12/11/2015 20:21:15]  8/10 | Batch  21/124 | D  5.004487e-003 [↑ ] | Valid D  1.823838e-003 [↓ ] | Stag:120 Ovfit: 0
[12/11/2015 20:21:15]  8/10 | Batch  31/124 | D  3.308986e-003 [↓ ] | Valid D  1.768821e-003 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:15]  8/10 | Batch  41/124 | D  6.563510e-003 [↑ ] | Valid D  1.835302e-003 [↑ ] | Stag: 10 Ovfit: 0
[12/11/2015 20:21:15]  8/10 | Batch  51/124 | D  1.507999e-003 [↓ ] | Valid D  1.868091e-003 [↑ ] | Stag: 20 Ovfit: 0
[12/11/2015 20:21:15]  8/10 | Batch  61/124 | D  1.148601e-002 [↑ ] | Valid D  1.876653e-003 [↑ ] | Stag: 30 Ovfit: 0
[12/11/2015 20:21:16]  8/10 | Batch  71/124 | D  2.807777e-003 [↓ ] | Valid D  1.968064e-003 [↑ ] | Stag: 40 Ovfit: 0
[12/11/2015 20:21:16]  8/10 | Batch  81/124 | D  1.440011e-003 [↓ ] | Valid D  1.876611e-003 [↓ ] | Stag: 50 Ovfit: 0
[12/11/2015 20:21:16]  8/10 | Batch  91/124 | D  3.522004e-003 [↑ ] | Valid D  1.821817e-003 [↓ ] | Stag: 60 Ovfit: 0
[12/11/2015 20:21:16]  8/10 | Batch 101/124 | D  2.031282e-003 [↓ ] | Valid D  1.872902e-003 [↑ ] | Stag: 70 Ovfit: 0
[12/11/2015 20:21:16]  8/10 | Batch 111/124 | D  1.182362e-002 [↑ ] | Valid D  1.836957e-003 [↓ ] | Stag: 80 Ovfit: 0
[12/11/2015 20:21:16]  8/10 | Batch 121/124 | D  2.035742e-003 [↓ ] | Valid D  1.864137e-003 [↑ ] | Stag: 90 Ovfit: 0
[12/11/2015 20:21:16]  9/10 | Batch   1/124 | D  1.699795e-003 [↓ ] | Valid D  1.865989e-003 [↑ ] | Stag:100 Ovfit: 0
[12/11/2015 20:21:16]  9/10 | Batch  11/124 | D  1.556397e-003 [↓ ] | Valid D  1.866347e-003 [↑ ] | Stag:110 Ovfit: 0
[12/11/2015 20:21:16]  9/10 | Batch  21/124 | D  4.788828e-003 [↑ ] | Valid D  1.804229e-003 [↓ ] | Stag:120 Ovfit: 0
[12/11/2015 20:21:16]  9/10 | Batch  31/124 | D  3.119682e-003 [↓ ] | Valid D  1.756223e-003 [↓▼] | Stag:  0 Ovfit: 0
[12/11/2015 20:21:16]  9/10 | Batch  41/124 | D  6.336636e-003 [↑ ] | Valid D  1.816257e-003 [↑ ] | Stag: 10 Ovfit: 0
[12/11/2015 20:21:16]  9/10 | Batch  51/124 | D  1.516153e-003 [↓ ] | Valid D  1.843593e-003 [↑ ] | Stag: 20 Ovfit: 0
[12/11/2015 20:21:16]  9/10 | Batch  61/124 | D  1.080968e-002 [↑ ] | Valid D  1.850113e-003 [↑ ] | Stag: 30 Ovfit: 0
[12/11/2015 20:21:16]  9/10 | Batch  71/124 | D  2.720124e-003 [↓ ] | Valid D  1.934669e-003 [↑ ] | Stag: 40 Ovfit: 0
[12/11/2015 20:21:16]  9/10 | Batch  81/124 | D  1.455176e-003 [↓ ] | Valid D  1.852409e-003 [↓ ] | Stag: 50 Ovfit: 0
[12/11/2015 20:21:16]  9/10 | Batch  91/124 | D  3.375944e-003 [↑ ] | Valid D  1.804057e-003 [↓ ] | Stag: 60 Ovfit: 0
[12/11/2015 20:21:16]  9/10 | Batch 101/124 | D  2.093168e-003 [↓ ] | Valid D  1.853583e-003 [↑ ] | Stag: 70 Ovfit: 0
[12/11/2015 20:21:16]  9/10 | Batch 111/124 | D  1.178356e-002 [↑ ] | Valid D  1.820183e-003 [↓ ] | Stag: 80 Ovfit: 0
[12/11/2015 20:21:16]  9/10 | Batch 121/124 | D  2.061530e-003 [↓ ] | Valid D  1.846045e-003 [↑ ] | Stag: 90 Ovfit: 0
[12/11/2015 20:21:16] 10/10 | Batch   1/124 | D  1.689459e-003 [↓ ] | Valid D  1.846794e-003 [↑ ] | Stag:100 Ovfit: 0
[12/11/2015 20:21:16] 10/10 | Batch  11/124 | D  1.560583e-003 [↓ ] | Valid D  1.847311e-003 [↑ ] | Stag:110 Ovfit: 0
[12/11/2015 20:21:16] 10/10 | Batch  21/124 | D  4.588457e-003 [↑ ] | Valid D  1.792883e-003 [↓ ] | Stag:120 Ovfit: 0
[12/11/2015 20:21:16] 10/10 | Batch  31/124 | D  3.001853e-003 [↓ ] | Valid D  1.750141e-003 [↓ ] | Stag:130 Ovfit: 0
[12/11/2015 20:21:16] 10/10 | Batch  41/124 | D  6.195725e-003 [↑ ] | Valid D  1.805622e-003 [↑ ] | Stag:140 Ovfit: 0
[12/11/2015 20:21:16] 10/10 | Batch  51/124 | D  1.524289e-003 [↓ ] | Valid D  1.829196e-003 [↑ ] | Stag:150 Ovfit: 0
[12/11/2015 20:21:17] 10/10 | Batch  61/124 | D  1.029841e-002 [↑ ] | Valid D  1.834366e-003 [↑ ] | Stag:160 Ovfit: 0
[12/11/2015 20:21:17] 10/10 | Batch  71/124 | D  2.667856e-003 [↓ ] | Valid D  1.913492e-003 [↑ ] | Stag:170 Ovfit: 0
[12/11/2015 20:21:17] 10/10 | Batch  81/124 | D  1.467351e-003 [↓ ] | Valid D  1.837669e-003 [↓ ] | Stag:180 Ovfit: 0
[12/11/2015 20:21:17] 10/10 | Batch  91/124 | D  3.261143e-003 [↑ ] | Valid D  1.793646e-003 [↓ ] | Stag:190 Ovfit: 0
[12/11/2015 20:21:17] 10/10 | Batch 101/124 | D  2.153974e-003 [↓ ] | Valid D  1.842048e-003 [↑ ] | Stag:200 Ovfit: 0
[12/11/2015 20:21:17] 10/10 | Batch 111/124 | D  1.176465e-002 [↑ ] | Valid D  1.810117e-003 [↓ ] | Stag:210 Ovfit: 0
[12/11/2015 20:21:17] 10/10 | Batch 121/124 | D  2.082179e-003 [↓ ] | Valid D  1.834467e-003 [↑ ] | Stag:220 Ovfit: 0
[12/11/2015 20:21:17] Duration       : 00:00:05.2093910
[12/11/2015 20:21:17] Loss initial   : D  4.748471e-001
[12/11/2015 20:21:17] Loss final     : D  1.395002e-003 (Best)
[12/11/2015 20:21:17] Loss change    : D -4.734521e-001 (-99.71 %)
[12/11/2015 20:21:17] Loss chg. / s  : D -9.088434e-002
[12/11/2015 20:21:17] Epochs / s     : 1.919610181
[12/11/2015 20:21:17] Epochs / min   : 115.1766109
[12/11/2015 20:21:17] --- Training finished

After a 5-second training, we can see that the characteristics of the problem domain (distinguishing between the digits of 0 and 1) is captured in the model weights.

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let l = (n.[0] :?> Linear)
l.VisualizeWRowsAsImageGrid(28) |> printfn "%s"

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Hype.Neural.Linear
   784 -> 1
   Learnable parameters: 785
   Init: Standard
   W's rows reshaped to (28 x 28), presented in a (1 x 1) grid:
DM : 28 x 28
----------------------------
----------------------------
------------▴▴▴▴▴-----------
---------▴--▴▴▴▴▴▴-▴--------
--------▴▴▪▴▪▪▪▴-▴▴▴▪▪▪▴----
------▴-▴▴▴▴▪▪▴▴-·-▴▪▪▪▪▴---
------▴--▴▴-▴▴--···▴▪▴▴▴▴---
----▴---------▴▴-· ---------
---------··---▴▪--·-·····---
-------······▴▪▪▪▴-······---
------·····  ▴●●●▴·     ·---
-----·· ·    ▪♦■♦▪      ·---
-----· ·     ●■■♦▴      ·---
-----·      ·♦██♦·      ·---
-----·      ▴■██●       ·---
----·       ▪██■▪       ·---
----·      -●█■♦-       ·---
----·      ▴♦█■●·     ···---
----·     ·▴♦♦♦●·   ····----
----·    ·▴▪●●●▪·· ····--▴--
----······-▴▪▪▪▴--------▴---
-----▴▴----·--▴▴-▴▴-▴▴------
-----▴▪▪▴-· ··--▴▴▪▴▴▴▴-----
----▴▪▪▪▪▴-· ·-▴▴▪▴▴▴▴------
-----▴▪▴▴▴▴·---▴▴▴▴▴--------
------------▴▴▴▴------------
----------------------------
----------------------------

   b:
DV : 1

Classifier

You can create classifiers by instantiating types such as LogisticClassifier or SoftmaxClassifier, and passing a classification function of the form DM->DMin the constructor. Alternatively, you can directly pass the model we have just trained.

Please see the API reference and the source code for a better understanding of how classifiers are implemented.

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let cc = LogisticClassifier(n)

Let's test the class predictions for 10 random elements from the MNIST test set, which, if you remember, we've filtered to have only 0s and 1s.

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let pred = cc.Classify(MNISTtest01.X.[*,0..9]);;
let real = MNISTtest01.Y.[*, 0..9] |> DM.toDV |> DV.toArray |> Array.map (float32>>int)

val pred : int [] = [|1; 0; 1; 0; 1; 0; 0; 1; 1; 1|]
val real : int [] = [|1; 0; 1; 0; 1; 0; 0; 1; 1; 1|]

The classifier seems to be working well. We can compute the classification error for a given dataset.

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let error = cc.ClassificationError(MNISTtest01);;

val error : float32 = 0.000472813234f

The classification error is 0.047%.

Finally, this is how you would classify single digits.

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let cls = cc.Classify(MNISTtest01.X.[*,0]);;
MNISTtest01.X.[*,0] |> DV.visualizeAsDM 28 |> printfn "%s"

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val cls : int = 1

DM : 28 x 28




            ♦               
            ●♦              
             █              
             ■·             
            ▪█-             
            ▴█-             
             ■♦             
             ♦█·            
             -█▪            
              █▪            
              ●▪            
              ▪█            
              ▪█-           
              ▪█▴           
              ▪█■           
               █■           
               ██           
               ▪█           
                █▴          
                █●

And this is how you would classify many digits efficiently at the same time, by running them through the model together as the columns of an input matrix.

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let clss = cc.Classify(MNISTtest01.X.[*,5..9]);;
MNISTtest01.[5..9].VisualizeXColsAsImageGrid(28) |> printfn "%s"

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val clss : int [] = [|0; 0; 1; 1; 1|]

Hype.Dataset
   X: 784 x 5
   Y: 1 x 5
X's columns reshaped to (28 x 28), presented in a (2 x 3) grid:
DM : 56 x 84




             ██·                                                                    
            ●███♦-                        ·████♦·                   -█▴             
            ██████■-                     ♦███████-                  ▪██·            
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val fsi : Compiler.Interactive.InteractiveSession

Full name: Microsoft.FSharp.Compiler.Interactive.Settings.fsi
property Compiler.Interactive.InteractiveSession.ShowDeclarationValues: bool
namespace Hype
namespace Hype.Neural
namespace DiffSharp
namespace DiffSharp.AD
module Float32

from DiffSharp.AD
module Util

from DiffSharp
val MNIST : Dataset

Full name: Regression.MNIST
Multiple items
type Dataset =
  new : s:seq<DV * DV> -> Dataset
  new : xi:seq<int> * y:DM -> Dataset
  new : x:DM * yi:seq<int> -> Dataset
  new : xi:seq<int> * yi:seq<int> -> Dataset
  new : x:DM * y:DM -> Dataset
  new : xi:seq<int> * onehotdimsx:int * y:DM -> Dataset
  new : x:DM * yi:seq<int> * onehotdimsy:int -> Dataset
  new : xi:seq<int> * onehotdimsx:int * yi:seq<int> * onehotdimsy:int -> Dataset
  private new : x:DM * y:DM * xi:seq<int> * yi:seq<int> -> Dataset
  member AppendBiasRowX : unit -> Dataset
  ...

Full name: Hype.Dataset

--------------------
new : s:seq<DV * DV> -> Dataset
new : x:DM * y:DM -> Dataset
new : xi:seq<int> * yi:seq<int> -> Dataset
new : x:DM * yi:seq<int> -> Dataset
new : xi:seq<int> * y:DM -> Dataset
new : x:DM * yi:seq<int> * onehotdimsy:int -> Dataset
new : xi:seq<int> * onehotdimsx:int * y:DM -> Dataset
new : xi:seq<int> * onehotdimsx:int * yi:seq<int> * onehotdimsy:int -> Dataset
type Util =
  static member LoadDelimited : filename:string -> DM
  static member LoadDelimited : filename:string * separators:char [] -> DM
  static member LoadImage : filename:string -> DM
  static member LoadMNISTLabels : filename:string -> int []
  static member LoadMNISTLabels : filename:string * n:int -> int []
  static member LoadMNISTPixels : filename:string -> DM
  static member LoadMNISTPixels : filename:string * n:int -> DM
  static member VisualizeDMRowsAsImageGrid : w:DM * imagerows:int -> string
  static member printLog : s:string -> unit
  static member printModel : f:(DV -> DV) -> d:Dataset -> unit

Full name: Hype.Util
static member Util.LoadMNISTPixels : filename:string -> DM
static member Util.LoadMNISTPixels : filename:string * n:int -> DM
static member Util.LoadMNISTLabels : filename:string -> int []
static member Util.LoadMNISTLabels : filename:string * n:int -> int []
val toDV : v:seq<'a> -> DV (requires member op_Explicit)

Full name: DiffSharp.AD.Float32.DOps.toDV
Multiple items
union case DM.DM: float32 [,] -> DM

--------------------
module DM

from DiffSharp.AD.Float32

--------------------
type DM =
  | DM of float32 [,]
  | DMF of DM * DM * uint32
  | DMR of DM * DM ref * TraceOp * uint32 ref * uint32
  member Copy : unit -> DM
  member GetCols : unit -> seq<DV>
  member GetForward : t:DM * i:uint32 -> DM
  member GetReverse : i:uint32 -> DM
  member GetRows : unit -> seq<DV>
  member GetSlice : rowStart:int option * rowFinish:int option * col:int -> DV
  member GetSlice : row:int * colStart:int option * colFinish:int option -> DV
  member GetSlice : rowStart:int option * rowFinish:int option * colStart:int option * colFinish:int option -> DM
  member ToMathematicaString : unit -> string
  member ToMatlabString : unit -> string
  override ToString : unit -> string
  member Visualize : unit -> string
  member A : DM
  member Cols : int
  member F : uint32
  member Item : i:int * j:int -> D with get
  member Length : int
  member P : DM
  member PD : DM
  member Rows : int
  member T : DM
  member A : DM with set
  member F : uint32 with set
  static member Abs : a:DM -> DM
  static member Acos : a:DM -> DM
  static member AddDiagonal : a:DM * b:DV -> DM
  static member AddItem : a:DM * i:int * j:int * b:D -> DM
  static member AddSubMatrix : a:DM * i:int * j:int * b:DM -> DM
  static member Asin : a:DM -> DM
  static member Atan : a:DM -> DM
  static member Atan2 : a:int * b:DM -> DM
  static member Atan2 : a:DM * b:int -> DM
  static member Atan2 : a:float32 * b:DM -> DM
  static member Atan2 : a:DM * b:float32 -> DM
  static member Atan2 : a:D * b:DM -> DM
  static member Atan2 : a:DM * b:D -> DM
  static member Atan2 : a:DM * b:DM -> DM
  static member Ceiling : a:DM -> DM
  static member Cos : a:DM -> DM
  static member Cosh : a:DM -> DM
  static member Det : a:DM -> D
  static member Diagonal : a:DM -> DV
  static member Exp : a:DM -> DM
  static member Floor : a:DM -> DM
  static member Inverse : a:DM -> DM
  static member Log : a:DM -> DM
  static member Log10 : a:DM -> DM
  static member Max : a:DM -> D
  static member Max : a:D * b:DM -> DM
  static member Max : a:DM * b:D -> DM
  static member Max : a:DM * b:DM -> DM
  static member MaxIndex : a:DM -> int * int
  static member Mean : a:DM -> D
  static member Min : a:DM -> D
  static member Min : a:D * b:DM -> DM
  static member Min : a:DM * b:D -> DM
  static member Min : a:DM * b:DM -> DM
  static member MinIndex : a:DM -> int * int
  static member Normalize : a:DM -> DM
  static member OfArray : m:int * a:D [] -> DM
  static member OfArray2D : a:D [,] -> DM
  static member OfCols : n:int * a:DV -> DM
  static member OfRows : s:seq<DV> -> DM
  static member OfRows : m:int * a:DV -> DM
  static member Op_DM_D : a:DM * ff:(float32 [,] -> float32) * fd:(DM -> D) * df:(D * DM * DM -> D) * r:(DM -> TraceOp) -> D
  static member Op_DM_DM : a:DM * ff:(float32 [,] -> float32 [,]) * fd:(DM -> DM) * df:(DM * DM * DM -> DM) * r:(DM -> TraceOp) -> DM
  static member Op_DM_DM_DM : a:DM * b:DM * ff:(float32 [,] * float32 [,] -> float32 [,]) * fd:(DM * DM -> DM) * df_da:(DM * DM * DM -> DM) * df_db:(DM * DM * DM -> DM) * df_dab:(DM * DM * DM * DM * DM -> DM) * r_d_d:(DM * DM -> TraceOp) * r_d_c:(DM * DM -> TraceOp) * r_c_d:(DM * DM -> TraceOp) -> DM
  static member Op_DM_DV : a:DM * ff:(float32 [,] -> float32 []) * fd:(DM -> DV) * df:(DV * DM * DM -> DV) * r:(DM -> TraceOp) -> DV
  static member Op_DM_DV_DM : a:DM * b:DV * ff:(float32 [,] * float32 [] -> float32 [,]) * fd:(DM * DV -> DM) * df_da:(DM * DM * DM -> DM) * df_db:(DM * DV * DV -> DM) * df_dab:(DM * DM * DM * DV * DV -> DM) * r_d_d:(DM * DV -> TraceOp) * r_d_c:(DM * DV -> TraceOp) * r_c_d:(DM * DV -> TraceOp) -> DM
  static member Op_DM_DV_DV : a:DM * b:DV * ff:(float32 [,] * float32 [] -> float32 []) * fd:(DM * DV -> DV) * df_da:(DV * DM * DM -> DV) * df_db:(DV * DV * DV -> DV) * df_dab:(DV * DM * DM * DV * DV -> DV) * r_d_d:(DM * DV -> TraceOp) * r_d_c:(DM * DV -> TraceOp) * r_c_d:(DM * DV -> TraceOp) -> DV
  static member Op_DM_D_DM : a:DM * b:D * ff:(float32 [,] * float32 -> float32 [,]) * fd:(DM * D -> DM) * df_da:(DM * DM * DM -> DM) * df_db:(DM * D * D -> DM) * df_dab:(DM * DM * DM * D * D -> DM) * r_d_d:(DM * D -> TraceOp) * r_d_c:(DM * D -> TraceOp) * r_c_d:(DM * D -> TraceOp) -> DM
  static member Op_DV_DM_DM : a:DV * b:DM * ff:(float32 [] * float32 [,] -> float32 [,]) * fd:(DV * DM -> DM) * df_da:(DM * DV * DV -> DM) * df_db:(DM * DM * DM -> DM) * df_dab:(DM * DV * DV * DM * DM -> DM) * r_d_d:(DV * DM -> TraceOp) * r_d_c:(DV * DM -> TraceOp) * r_c_d:(DV * DM -> TraceOp) -> DM
  static member Op_DV_DM_DV : a:DV * b:DM * ff:(float32 [] * float32 [,] -> float32 []) * fd:(DV * DM -> DV) * df_da:(DV * DV * DV -> DV) * df_db:(DV * DM * DM -> DV) * df_dab:(DV * DV * DV * DM * DM -> DV) * r_d_d:(DV * DM -> TraceOp) * r_d_c:(DV * DM -> TraceOp) * r_c_d:(DV * DM -> TraceOp) -> DV
  static member Op_D_DM_DM : a:D * b:DM * ff:(float32 * float32 [,] -> float32 [,]) * fd:(D * DM -> DM) * df_da:(DM * D * D -> DM) * df_db:(DM * DM * DM -> DM) * df_dab:(DM * D * D * DM * DM -> DM) * r_d_d:(D * DM -> TraceOp) * r_d_c:(D * DM -> TraceOp) * r_c_d:(D * DM -> TraceOp) -> DM
  static member Pow : a:int * b:DM -> DM
  static member Pow : a:DM * b:int -> DM
  static member Pow : a:float32 * b:DM -> DM
  static member Pow : a:DM * b:float32 -> DM
  static member Pow : a:D * b:DM -> DM
  static member Pow : a:DM * b:D -> DM
  static member Pow : a:DM * b:DM -> DM
  static member ReLU : a:DM -> DM
  static member ReshapeToDV : a:DM -> DV
  static member Round : a:DM -> DM
  static member Sigmoid : a:DM -> DM
  static member Sign : a:DM -> DM
  static member Sin : a:DM -> DM
  static member Sinh : a:DM -> DM
  static member SoftPlus : a:DM -> DM
  static member SoftSign : a:DM -> DM
  static member Solve : a:DM * b:DV -> DV
  static member SolveSymmetric : a:DM * b:DV -> DV
  static member Sqrt : a:DM -> DM
  static member StandardDev : a:DM -> D
  static member Standardize : a:DM -> DM
  static member Sum : a:DM -> D
  static member Tan : a:DM -> DM
  static member Tanh : a:DM -> DM
  static member Trace : a:DM -> D
  static member Transpose : a:DM -> DM
  static member Variance : a:DM -> D
  static member ZeroMN : m:int -> n:int -> DM
  static member Zero : DM
  static member ( + ) : a:int * b:DM -> DM
  static member ( + ) : a:DM * b:int -> DM
  static member ( + ) : a:float32 * b:DM -> DM
  static member ( + ) : a:DM * b:float32 -> DM
  static member ( + ) : a:DM * b:DV -> DM
  static member ( + ) : a:DV * b:DM -> DM
  static member ( + ) : a:D * b:DM -> DM
  static member ( + ) : a:DM * b:D -> DM
  static member ( + ) : a:DM * b:DM -> DM
  static member ( / ) : a:int * b:DM -> DM
  static member ( / ) : a:DM * b:int -> DM
  static member ( / ) : a:float32 * b:DM -> DM
  static member ( / ) : a:DM * b:float32 -> DM
  static member ( / ) : a:D * b:DM -> DM
  static member ( / ) : a:DM * b:D -> DM
  static member ( ./ ) : a:DM * b:DM -> DM
  static member ( .* ) : a:DM * b:DM -> DM
  static member op_Explicit : d:float32 [,] -> DM
  static member op_Explicit : d:DM -> float32 [,]
  static member ( * ) : a:int * b:DM -> DM
  static member ( * ) : a:DM * b:int -> DM
  static member ( * ) : a:float32 * b:DM -> DM
  static member ( * ) : a:DM * b:float32 -> DM
  static member ( * ) : a:D * b:DM -> DM
  static member ( * ) : a:DM * b:D -> DM
  static member ( * ) : a:DV * b:DM -> DV
  static member ( * ) : a:DM * b:DV -> DV
  static member ( * ) : a:DM * b:DM -> DM
  static member ( - ) : a:int * b:DM -> DM
  static member ( - ) : a:DM * b:int -> DM
  static member ( - ) : a:float32 * b:DM -> DM
  static member ( - ) : a:DM * b:float32 -> DM
  static member ( - ) : a:D * b:DM -> DM
  static member ( - ) : a:DM * b:D -> DM
  static member ( - ) : a:DM * b:DM -> DM
  static member ( ~- ) : a:DM -> DM

Full name: DiffSharp.AD.Float32.DM
val ofDV : m:int -> v:DV -> DM

Full name: DiffSharp.AD.Float32.DM.ofDV
val MNISTtrain : Dataset

Full name: Regression.MNISTtrain
val MNISTvalid : Dataset

Full name: Regression.MNISTvalid
val MNISTtest : Dataset

Full name: Regression.MNISTtest
val MNISTtrain01 : Dataset

Full name: Regression.MNISTtrain01
member Dataset.Shuffle : unit -> Dataset
val x : DV
val y : DV
union case D.D: float32 -> D
val MNISTvalid01 : Dataset

Full name: Regression.MNISTvalid01
val MNISTtest01 : Dataset

Full name: Regression.MNISTtest01
property Dataset.X: DM
Multiple items
union case DV.DV: float32 [] -> DV

--------------------
module DV

from DiffSharp.AD.Float32

--------------------
type DV =
  | DV of float32 []
  | DVF of DV * DV * uint32
  | DVR of DV * DV ref * TraceOp * uint32 ref * uint32
  member Copy : unit -> DV
  member GetForward : t:DV * i:uint32 -> DV
  member GetReverse : i:uint32 -> DV
  member GetSlice : lower:int option * upper:int option -> DV
  member ToArray : unit -> D []
  member ToColDM : unit -> DM
  member ToMathematicaString : unit -> string
  member ToMatlabString : unit -> string
  member ToRowDM : unit -> DM
  override ToString : unit -> string
  member Visualize : unit -> string
  member A : DV
  member F : uint32
  member Item : i:int -> D with get
  member Length : int
  member P : DV
  member PD : DV
  member T : DV
  member A : DV with set
  member F : uint32 with set
  static member Abs : a:DV -> DV
  static member Acos : a:DV -> DV
  static member AddItem : a:DV * i:int * b:D -> DV
  static member AddSubVector : a:DV * i:int * b:DV -> DV
  static member Append : a:DV * b:DV -> DV
  static member Asin : a:DV -> DV
  static member Atan : a:DV -> DV
  static member Atan2 : a:int * b:DV -> DV
  static member Atan2 : a:DV * b:int -> DV
  static member Atan2 : a:float32 * b:DV -> DV
  static member Atan2 : a:DV * b:float32 -> DV
  static member Atan2 : a:D * b:DV -> DV
  static member Atan2 : a:DV * b:D -> DV
  static member Atan2 : a:DV * b:DV -> DV
  static member Ceiling : a:DV -> DV
  static member Cos : a:DV -> DV
  static member Cosh : a:DV -> DV
  static member Exp : a:DV -> DV
  static member Floor : a:DV -> DV
  static member L1Norm : a:DV -> D
  static member L2Norm : a:DV -> D
  static member L2NormSq : a:DV -> D
  static member Log : a:DV -> DV
  static member Log10 : a:DV -> DV
  static member LogSumExp : a:DV -> D
  static member Max : a:DV -> D
  static member Max : a:D * b:DV -> DV
  static member Max : a:DV * b:D -> DV
  static member Max : a:DV * b:DV -> DV
  static member MaxIndex : a:DV -> int
  static member Mean : a:DV -> D
  static member Min : a:DV -> D
  static member Min : a:D * b:DV -> DV
  static member Min : a:DV * b:D -> DV
  static member Min : a:DV * b:DV -> DV
  static member MinIndex : a:DV -> int
  static member Normalize : a:DV -> DV
  static member OfArray : a:D [] -> DV
  static member Op_DV_D : a:DV * ff:(float32 [] -> float32) * fd:(DV -> D) * df:(D * DV * DV -> D) * r:(DV -> TraceOp) -> D
  static member Op_DV_DM : a:DV * ff:(float32 [] -> float32 [,]) * fd:(DV -> DM) * df:(DM * DV * DV -> DM) * r:(DV -> TraceOp) -> DM
  static member Op_DV_DV : a:DV * ff:(float32 [] -> float32 []) * fd:(DV -> DV) * df:(DV * DV * DV -> DV) * r:(DV -> TraceOp) -> DV
  static member Op_DV_DV_D : a:DV * b:DV * ff:(float32 [] * float32 [] -> float32) * fd:(DV * DV -> D) * df_da:(D * DV * DV -> D) * df_db:(D * DV * DV -> D) * df_dab:(D * DV * DV * DV * DV -> D) * r_d_d:(DV * DV -> TraceOp) * r_d_c:(DV * DV -> TraceOp) * r_c_d:(DV * DV -> TraceOp) -> D
  static member Op_DV_DV_DM : a:DV * b:DV * ff:(float32 [] * float32 [] -> float32 [,]) * fd:(DV * DV -> DM) * df_da:(DM * DV * DV -> DM) * df_db:(DM * DV * DV -> DM) * df_dab:(DM * DV * DV * DV * DV -> DM) * r_d_d:(DV * DV -> TraceOp) * r_d_c:(DV * DV -> TraceOp) * r_c_d:(DV * DV -> TraceOp) -> DM
  static member Op_DV_DV_DV : a:DV * b:DV * ff:(float32 [] * float32 [] -> float32 []) * fd:(DV * DV -> DV) * df_da:(DV * DV * DV -> DV) * df_db:(DV * DV * DV -> DV) * df_dab:(DV * DV * DV * DV * DV -> DV) * r_d_d:(DV * DV -> TraceOp) * r_d_c:(DV * DV -> TraceOp) * r_c_d:(DV * DV -> TraceOp) -> DV
  static member Op_DV_D_DV : a:DV * b:D * ff:(float32 [] * float32 -> float32 []) * fd:(DV * D -> DV) * df_da:(DV * DV * DV -> DV) * df_db:(DV * D * D -> DV) * df_dab:(DV * DV * DV * D * D -> DV) * r_d_d:(DV * D -> TraceOp) * r_d_c:(DV * D -> TraceOp) * r_c_d:(DV * D -> TraceOp) -> DV
  static member Op_D_DV_DV : a:D * b:DV * ff:(float32 * float32 [] -> float32 []) * fd:(D * DV -> DV) * df_da:(DV * D * D -> DV) * df_db:(DV * DV * DV -> DV) * df_dab:(DV * D * D * DV * DV -> DV) * r_d_d:(D * DV -> TraceOp) * r_d_c:(D * DV -> TraceOp) * r_c_d:(D * DV -> TraceOp) -> DV
  static member Pow : a:int * b:DV -> DV
  static member Pow : a:DV * b:int -> DV
  static member Pow : a:float32 * b:DV -> DV
  static member Pow : a:DV * b:float32 -> DV
  static member Pow : a:D * b:DV -> DV
  static member Pow : a:DV * b:D -> DV
  static member Pow : a:DV * b:DV -> DV
  static member ReLU : a:DV -> DV
  static member ReshapeToDM : m:int * a:DV -> DM
  static member Round : a:DV -> DV
  static member Sigmoid : a:DV -> DV
  static member Sign : a:DV -> DV
  static member Sin : a:DV -> DV
  static member Sinh : a:DV -> DV
  static member SoftMax : a:DV -> DV
  static member SoftPlus : a:DV -> DV
  static member SoftSign : a:DV -> DV
  static member Split : d:DV * n:seq<int> -> seq<DV>
  static member Sqrt : a:DV -> DV
  static member StandardDev : a:DV -> D
  static member Standardize : a:DV -> DV
  static member Sum : a:DV -> D
  static member Tan : a:DV -> DV
  static member Tanh : a:DV -> DV
  static member Variance : a:DV -> D
  static member ZeroN : n:int -> DV
  static member Zero : DV
  static member ( + ) : a:int * b:DV -> DV
  static member ( + ) : a:DV * b:int -> DV
  static member ( + ) : a:float32 * b:DV -> DV
  static member ( + ) : a:DV * b:float32 -> DV
  static member ( + ) : a:D * b:DV -> DV
  static member ( + ) : a:DV * b:D -> DV
  static member ( + ) : a:DV * b:DV -> DV
  static member ( &* ) : a:DV * b:DV -> DM
  static member ( / ) : a:int * b:DV -> DV
  static member ( / ) : a:DV * b:int -> DV
  static member ( / ) : a:float32 * b:DV -> DV
  static member ( / ) : a:DV * b:float32 -> DV
  static member ( / ) : a:D * b:DV -> DV
  static member ( / ) : a:DV * b:D -> DV
  static member ( ./ ) : a:DV * b:DV -> DV
  static member ( .* ) : a:DV * b:DV -> DV
  static member op_Explicit : d:float32 [] -> DV
  static member op_Explicit : d:DV -> float32 []
  static member ( * ) : a:int * b:DV -> DV
  static member ( * ) : a:DV * b:int -> DV
  static member ( * ) : a:float32 * b:DV -> DV
  static member ( * ) : a:DV * b:float32 -> DV
  static member ( * ) : a:D * b:DV -> DV
  static member ( * ) : a:DV * b:D -> DV
  static member ( * ) : a:DV * b:DV -> D
  static member ( - ) : a:int * b:DV -> DV
  static member ( - ) : a:DV * b:int -> DV
  static member ( - ) : a:float32 * b:DV -> DV
  static member ( - ) : a:DV * b:float32 -> DV
  static member ( - ) : a:D * b:DV -> DV
  static member ( - ) : a:DV * b:D -> DV
  static member ( - ) : a:DV * b:DV -> DV
  static member ( ~- ) : a:DV -> DV

Full name: DiffSharp.AD.Float32.DV
val visualizeAsDM : m:int -> v:DV -> string

Full name: DiffSharp.AD.Float32.DV.visualizeAsDM
val printfn : format:Printf.TextWriterFormat<'T> -> 'T

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.printfn
property Dataset.Y: DM
val n : FeedForward

Full name: Regression.n
Multiple items
type FeedForward =
  inherit Layer
  new : unit -> FeedForward
  member Add : f:(DM -> DM) -> unit
  member Add : l:Layer -> unit
  override Decode : w:DV -> unit
  override Encode : unit -> DV
  override Init : unit -> unit
  member Insert : i:int * f:(DM -> DM) -> unit
  member Insert : i:int * l:Layer -> unit
  member Remove : i:int -> unit
  ...

Full name: Hype.Neural.FeedForward

--------------------
new : unit -> FeedForward
member FeedForward.Add : f:(DM -> DM) -> unit
member FeedForward.Add : l:Layer -> unit
Multiple items
type Linear =
  inherit Layer
  new : inputs:int * outputs:int -> Linear
  new : inputs:int * outputs:int * initializer:Initializer -> Linear
  override Decode : w:DV -> unit
  override Encode : unit -> DV
  override Init : unit -> unit
  override Reset : unit -> unit
  override Run : x:DM -> DM
  override ToString : unit -> string
  override ToStringFull : unit -> string
  ...

Full name: Hype.Neural.Linear

--------------------
new : inputs:int * outputs:int -> Linear
new : inputs:int * outputs:int * initializer:Initializer -> Linear
val sigmoid : x:'a -> 'a (requires member Sigmoid)

Full name: DiffSharp.Util.sigmoid
val l : Linear

Full name: Regression.l
member Linear.VisualizeWRowsAsImageGrid : imagerows:int -> string
val p : Params

Full name: Regression.p
Multiple items
module Params

from Hype

--------------------
type Params =
  {Epochs: int;
   Method: Method;
   LearningRate: LearningRate;
   Momentum: Momentum;
   Loss: Loss;
   Regularization: Regularization;
   GradientClipping: GradientClipping;
   Batch: Batch;
   EarlyStopping: EarlyStopping;
   ImprovementThreshold: D;
   ...}

Full name: Hype.Params
val Default : Params

Full name: Hype.Params.Default
type Batch =
  | Full
  | Minibatch of int
  | Stochastic
  override ToString : unit -> string
  member Func : (Dataset -> int -> Dataset)

Full name: Hype.Batch
union case Batch.Minibatch: int -> Batch
type EarlyStopping =
  | Early of int * int
  | NoEarly
  override ToString : unit -> string
  static member DefaultEarly : EarlyStopping

Full name: Hype.EarlyStopping
property EarlyStopping.DefaultEarly: EarlyStopping
member Layer.Train : d:Dataset -> D * D []
member Layer.Train : d:Dataset * par:Params -> D * D []
member Layer.Train : d:Dataset * v:Dataset -> D * D []
member Layer.Train : d:Dataset * v:Dataset * par:Params -> D * D []
val cc : LogisticClassifier

Full name: Regression.cc
Multiple items
type LogisticClassifier =
  inherit Classifier
  new : l:Layer -> LogisticClassifier
  new : f:(DM -> DM) -> LogisticClassifier
  override Classify : x:DV -> int
  override Classify : x:DM -> int []

Full name: Hype.LogisticClassifier

--------------------
new : f:(DM -> DM) -> LogisticClassifier
new : l:Layer -> LogisticClassifier
val pred : int []

Full name: Regression.pred
override LogisticClassifier.Classify : x:DV -> int
override LogisticClassifier.Classify : x:DM -> int []
val real : int []

Full name: Regression.real
val toDV : m:DM -> DV

Full name: DiffSharp.AD.Float32.DM.toDV
val toArray : v:DV -> D []

Full name: DiffSharp.AD.Float32.DV.toArray
Multiple items
module Array

from DiffSharp.Util

--------------------
module Array

from Microsoft.FSharp.Collections
val map : mapping:('T -> 'U) -> array:'T [] -> 'U []

Full name: Microsoft.FSharp.Collections.Array.map
Multiple items
val float32 : value:'T -> float32 (requires member op_Explicit)

Full name: Microsoft.FSharp.Core.Operators.float32

--------------------
type float32 = System.Single

Full name: Microsoft.FSharp.Core.float32

--------------------
type float32<'Measure> = float32

Full name: Microsoft.FSharp.Core.float32<_>
Multiple items
val int : value:'T -> int (requires member op_Explicit)

Full name: Microsoft.FSharp.Core.Operators.int

--------------------
type int = int32

Full name: Microsoft.FSharp.Core.int

--------------------
type int<'Measure> = int

Full name: Microsoft.FSharp.Core.int<_>
val error : float32

Full name: Regression.error
member Classifier.ClassificationError : d:Dataset -> float32
member Classifier.ClassificationError : x:DM * y:int [] -> float32
val cls : int

Full name: Regression.cls
val clss : int []

Full name: Regression.clss

Basics
Examples