From 632df3c34214bc102adb76948a33a449a7e1ed6a Mon Sep 17 00:00:00 2001 From: autodocs Date: Thu, 28 Sep 2017 10:32:09 +0000 Subject: [PATCH] build based on d3419c9 --- release-0.3/contributing.html | 2 +- release-0.3/data/onehot.html | 4 +- release-0.3/gpu.html | 25 ++ release-0.3/index.html | 2 +- release-0.3/models/basics.html | 2 +- release-0.3/models/layers.html | 4 +- release-0.3/models/recurrence.html | 2 +- release-0.3/search.html | 2 +- release-0.3/search_index.js | 20 +- release-0.3/training/optimisers.html | 2 +- release-0.3/training/training.html | 3 +- stable/contributing.html | 2 +- stable/data/onehot.html | 4 +- stable/gpu.html | 25 ++ stable/index.html | 2 +- stable/models/basics.html | 2 +- stable/models/layers.html | 4 +- stable/models/recurrence.html | 2 +- stable/search.html | 2 +- stable/search_index.js | 20 +- stable/training/optimisers.html | 2 +- stable/training/training.html | 3 +- v0.3.2/assets/arrow.svg | 63 ++++ v0.3.2/assets/documenter.css | 541 +++++++++++++++++++++++++++ v0.3.2/assets/documenter.js | 129 +++++++ v0.3.2/assets/search.js | 91 +++++ v0.3.2/contributing.html | 9 + v0.3.2/data/onehot.html | 40 ++ v0.3.2/gpu.html | 25 ++ v0.3.2/index.html | 10 + v0.3.2/models/basics.html | 78 ++++ v0.3.2/models/layers.html | 14 + v0.3.2/models/recurrence.html | 42 +++ v0.3.2/search.html | 9 + v0.3.2/search_index.js | 251 +++++++++++++ v0.3.2/siteinfo.js | 1 + v0.3.2/training/optimisers.html | 30 ++ v0.3.2/training/training.html | 18 + versions.js | 1 + 39 files changed, 1462 insertions(+), 26 deletions(-) create mode 100644 release-0.3/gpu.html create mode 100644 stable/gpu.html create mode 100644 v0.3.2/assets/arrow.svg create mode 100644 v0.3.2/assets/documenter.css create mode 100644 v0.3.2/assets/documenter.js create mode 100644 v0.3.2/assets/search.js create mode 100644 v0.3.2/contributing.html create mode 100644 v0.3.2/data/onehot.html create mode 100644 v0.3.2/gpu.html create mode 100644 v0.3.2/index.html create mode 100644 v0.3.2/models/basics.html create mode 100644 v0.3.2/models/layers.html create mode 100644 v0.3.2/models/recurrence.html create mode 100644 v0.3.2/search.html create mode 100644 v0.3.2/search_index.js create mode 100644 v0.3.2/siteinfo.js create mode 100644 v0.3.2/training/optimisers.html create mode 100644 v0.3.2/training/training.html diff --git a/release-0.3/contributing.html b/release-0.3/contributing.html index 698722ce..21a65472 100644 --- a/release-0.3/contributing.html +++ b/release-0.3/contributing.html @@ -6,4 +6,4 @@ m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m) ga('create', 'UA-36890222-9', 'auto'); ga('send', 'pageview'); -

Contributing & Help

Contributing & Help

If you need help, please ask on the Julia forum, the slack (channel #machine-learning), or Flux's Gitter.

Right now, the best way to help out is to try out the examples and report any issues or missing features as you find them. The second best way is to help us spread the word, perhaps by starring the repo.

If you're interested in hacking on Flux, most of the code is pretty straightforward. Adding new layer definitions or cost functions is simple using the Flux DSL itself, and things like data utilities and training processes are all plain Julia code.

If you get stuck or need anything, let us know!

+

Contributing & Help

Contributing & Help

If you need help, please ask on the Julia forum, the slack (channel #machine-learning), or Flux's Gitter.

Right now, the best way to help out is to try out the examples and report any issues or missing features as you find them. The second best way is to help us spread the word, perhaps by starring the repo.

If you're interested in hacking on Flux, most of the code is pretty straightforward. Adding new layer definitions or cost functions is simple using the Flux DSL itself, and things like data utilities and training processes are all plain Julia code.

If you get stuck or need anything, let us know!

diff --git a/release-0.3/data/onehot.html b/release-0.3/data/onehot.html index 4e840987..041bf1b1 100644 --- a/release-0.3/data/onehot.html +++ b/release-0.3/data/onehot.html @@ -6,7 +6,7 @@ m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m) ga('create', 'UA-36890222-9', 'auto'); ga('send', 'pageview'); -

One-Hot Encoding

One-Hot Encoding

It's common to encode categorical variables (like true, false or cat, dog) in "one-of-k" or "one-hot" form. Flux provides the onehot function to make this easy.

julia> using Flux: onehot
+

One-Hot Encoding

One-Hot Encoding

It's common to encode categorical variables (like true, false or cat, dog) in "one-of-k" or "one-hot" form. Flux provides the onehot function to make this easy.

julia> using Flux: onehot
 
 julia> onehot(:b, [:a, :b, :c])
 3-element Flux.OneHotVector:
@@ -37,4 +37,4 @@ julia> onecold(ans, [:a, :b, :c])
 3-element Array{Symbol,1}:
   :b
   :a
-  :b

Note that these operations returned OneHotVector and OneHotMatrix rather than Arrays. OneHotVectors behave like normal vectors but avoid any unnecessary cost compared to using an integer index directly. For example, multiplying a matrix with a one-hot vector simply slices out the relevant row of the matrix under the hood.

+ :b

Note that these operations returned OneHotVector and OneHotMatrix rather than Arrays. OneHotVectors behave like normal vectors but avoid any unnecessary cost compared to using an integer index directly. For example, multiplying a matrix with a one-hot vector simply slices out the relevant row of the matrix under the hood.

diff --git a/release-0.3/gpu.html b/release-0.3/gpu.html new file mode 100644 index 00000000..08872a41 --- /dev/null +++ b/release-0.3/gpu.html @@ -0,0 +1,25 @@ + +GPU Support · Flux

GPU Support

GPU Support

Support for array operations on other hardware backends, like GPUs, is provided by external packages like CuArrays and CLArrays. Flux doesn't care what array type you use, so we can just plug these in without any other changes.

For example, we can use CuArrays (with the cu converter) to run our basic example on an NVIDIA GPU.

using CuArrays
+
+W = cu(rand(2, 5)) # a 2×5 CuArray
+b = cu(rand(2))
+
+predict(x) = W*x .+ b
+loss(x, y) = sum((predict(x) .- y).^2)
+
+x, y = cu(rand(5)), cu(rand(2)) # Dummy data
+loss(x, y) # ~ 3

Note that we convert both the parameters (W, b) and the data set (x, y) to cuda arrays. Taking derivatives and training works exactly as before.

If you define a structured model, like a Dense layer or Chain, you just need to convert the internal parameters. Flux provides mapparams, which allows you to alter all parameters of a model at once.

d = Dense(10, 5, σ)
+d = mapparams(cu, d)
+d.W # Tracked CuArray
+d(cu(rand(10))) # CuArray output
+
+m = Chain(Dense(10, 5, σ), Dense(5, 2), softmax)
+m = mapparams(cu, m)
+d(cu(rand(10)))

The mnist example contains the code needed to run the model on the GPU; just uncomment the lines after using CuArrays.

diff --git a/release-0.3/index.html b/release-0.3/index.html index b3fb6887..391847f7 100644 --- a/release-0.3/index.html +++ b/release-0.3/index.html @@ -6,5 +6,5 @@ m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m) ga('create', 'UA-36890222-9', 'auto'); ga('send', 'pageview'); -

Home

Flux: The Julia Machine Learning Library

Flux is a library for machine learning. It comes "batteries-included" with many useful tools built in, but also lets you use the full power of the Julia language where you need it. The whole stack is implemented in clean Julia code (right down to the GPU kernels) and any part can be tweaked to your liking.

Installation

Install Julia 0.6.0 or later, if you haven't already.

Pkg.add("Flux")
+

Home

Flux: The Julia Machine Learning Library

Flux is a library for machine learning. It comes "batteries-included" with many useful tools built in, but also lets you use the full power of the Julia language where you need it. The whole stack is implemented in clean Julia code (right down to the GPU kernels) and any part can be tweaked to your liking.

Installation

Install Julia 0.6.0 or later, if you haven't already.

Pkg.add("Flux")
 Pkg.test("Flux") # Check things installed correctly

Start with the basics. The model zoo is also a good starting point for many common kinds of models.

diff --git a/release-0.3/models/basics.html b/release-0.3/models/basics.html index b6b34a4a..69192b8b 100644 --- a/release-0.3/models/basics.html +++ b/release-0.3/models/basics.html @@ -6,7 +6,7 @@ m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m) ga('create', 'UA-36890222-9', 'auto'); ga('send', 'pageview'); -

Basics

Model-Building Basics

Taking Gradients

Consider a simple linear regression, which tries to predict an output array y from an input x. (It's a good idea to follow this example in the Julia repl.)

W = rand(2, 5)
+

Basics

Model-Building Basics

Taking Gradients

Consider a simple linear regression, which tries to predict an output array y from an input x. (It's a good idea to follow this example in the Julia repl.)

W = rand(2, 5)
 b = rand(2)
 
 predict(x) = W*x .+ b
diff --git a/release-0.3/models/layers.html b/release-0.3/models/layers.html
index 01f8e87b..c689b6d5 100644
--- a/release-0.3/models/layers.html
+++ b/release-0.3/models/layers.html
@@ -6,9 +6,9 @@ m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
 
 ga('create', 'UA-36890222-9', 'auto');
 ga('send', 'pageview');
-

Layer Reference

Model Layers

Flux.ChainType.
Chain(layers...)

Chain multiple layers / functions together, so that they are called in sequence on a given input.

m = Chain(x -> x^2, x -> x+1)
+

Layer Reference

Model Layers

Flux.ChainType.
Chain(layers...)

Chain multiple layers / functions together, so that they are called in sequence on a given input.

m = Chain(x -> x^2, x -> x+1)
 m(5) == 26
 
 m = Chain(Dense(10, 5), Dense(5, 2))
 x = rand(10)
-m(x) == m[2](m[1](x))

Chain also supports indexing and slicing, e.g. m[2] or m[1:end-1]. m[1:3](x) will calculate the output of the first three layers.

source
Flux.DenseType.
Dense(in::Integer, out::Integer, σ = identity)

Creates a traditional Dense layer with parameters W and b.

y = σ.(W * x .+ b)

The input x must be a vector of length in, or a batch of vectors represented as an in × N matrix. The out y will be a vector or batch of length in.

source
+m(x) == m[2](m[1](x))

Chain also supports indexing and slicing, e.g. m[2] or m[1:end-1]. m[1:3](x) will calculate the output of the first three layers.

source
Flux.DenseType.
Dense(in::Integer, out::Integer, σ = identity)

Creates a traditional Dense layer with parameters W and b.

y = σ.(W * x .+ b)

The input x must be a vector of length in, or a batch of vectors represented as an in × N matrix. The out y will be a vector or batch of length in.

source
diff --git a/release-0.3/models/recurrence.html b/release-0.3/models/recurrence.html index 17e8abc2..ee30fa89 100644 --- a/release-0.3/models/recurrence.html +++ b/release-0.3/models/recurrence.html @@ -6,7 +6,7 @@ m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m) ga('create', 'UA-36890222-9', 'auto'); ga('send', 'pageview'); -

Recurrence

Recurrent Models

Recurrent Cells

In the simple feedforward case, our model m is a simple function from various inputs xᵢ to predictions yᵢ. (For example, each x might be an MNIST digit and each y a digit label.) Each prediction is completely independent of any others, and using the same x will always produce the same y.

y₁ = f(x₁)
+

Recurrence

Recurrent Models

Recurrent Cells

In the simple feedforward case, our model m is a simple function from various inputs xᵢ to predictions yᵢ. (For example, each x might be an MNIST digit and each y a digit label.) Each prediction is completely independent of any others, and using the same x will always produce the same y.

y₁ = f(x₁)
 y₂ = f(x₂)
 y₃ = f(x₃)
 # ...

Recurrent networks introduce a hidden state that gets carried over each time we run the model. The model now takes the old h as an input, and produces a new h as output, each time we run it.

h = # ... initial state ...
diff --git a/release-0.3/search.html b/release-0.3/search.html
index 86fc913d..d94fbbc3 100644
--- a/release-0.3/search.html
+++ b/release-0.3/search.html
@@ -6,4 +6,4 @@ m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
 
 ga('create', 'UA-36890222-9', 'auto');
 ga('send', 'pageview');
-

Search

Search

Number of results: loading...

    +

    Search

    Search

    Number of results: loading...

      diff --git a/release-0.3/search_index.js b/release-0.3/search_index.js index ac4ef48e..9b0f0acc 100644 --- a/release-0.3/search_index.js +++ b/release-0.3/search_index.js @@ -173,7 +173,7 @@ var documenterSearchIndex = {"docs": [ "page": "Training", "title": "Training", "category": "section", - "text": "To actually train a model we need three things:A loss function, that evaluates how well a model is doing given some input data.\nA collection of data points that will be provided to the loss function.\nAn optimiser that will update the model parameters appropriately.With these we can call Flux.train!:Flux.train!(loss, data, opt)There are plenty of examples in the model zoo." + "text": "To actually train a model we need three things:A model loss function, that evaluates how well a model is doing given some input data.\nA collection of data points that will be provided to the loss function.\nAn optimiser that will update the model parameters appropriately.With these we can call Flux.train!:Flux.train!(modelLoss, data, opt)There are plenty of examples in the model zoo." }, { @@ -181,7 +181,7 @@ var documenterSearchIndex = {"docs": [ "page": "Training", "title": "Loss Functions", "category": "section", - "text": "The loss that we defined in basics is completely valid for training. We can also define a loss in terms of some model:m = Chain(\n Dense(784, 32, σ),\n Dense(32, 10), softmax)\n\nloss(x, y) = Flux.mse(m(x), y)The loss will almost always be defined in terms of some cost function that measures the distance of the prediction m(x) from the target y. Flux has several of these built in, like mse for mean squared error or logloss for cross entropy loss, but you can calculate it however you want." + "text": "The loss that we defined in basics is completely valid for training. We can also define a loss in terms of some model:m = Chain(\n Dense(784, 32, σ),\n Dense(32, 10), softmax)\n\n# Model loss function\nloss(x, y) = Flux.mse(m(x), y)The loss will almost always be defined in terms of some cost function that measures the distance of the prediction m(x) from the target y. Flux has several of these built in, like mse for mean squared error or logloss for cross entropy loss, but you can calculate it however you want." }, { @@ -216,6 +216,22 @@ var documenterSearchIndex = {"docs": [ "text": "onehotbatch creates a batch (matrix) of one-hot vectors, and argmax treats matrices as batches.julia> using Flux: onehotbatch\n\njulia> onehotbatch([:b, :a, :b], [:a, :b, :c])\n3×3 Flux.OneHotMatrix:\n false true false\n true false true\n false false false\n\njulia> onecold(ans, [:a, :b, :c])\n3-element Array{Symbol,1}:\n :b\n :a\n :bNote that these operations returned OneHotVector and OneHotMatrix rather than Arrays. OneHotVectors behave like normal vectors but avoid any unnecessary cost compared to using an integer index directly. For example, multiplying a matrix with a one-hot vector simply slices out the relevant row of the matrix under the hood." }, +{ + "location": "gpu.html#", + "page": "GPU Support", + "title": "GPU Support", + "category": "page", + "text": "" +}, + +{ + "location": "gpu.html#GPU-Support-1", + "page": "GPU Support", + "title": "GPU Support", + "category": "section", + "text": "Support for array operations on other hardware backends, like GPUs, is provided by external packages like CuArrays and CLArrays. Flux doesn't care what array type you use, so we can just plug these in without any other changes.For example, we can use CuArrays (with the cu converter) to run our basic example on an NVIDIA GPU.using CuArrays\n\nW = cu(rand(2, 5)) # a 2×5 CuArray\nb = cu(rand(2))\n\npredict(x) = W*x .+ b\nloss(x, y) = sum((predict(x) .- y).^2)\n\nx, y = cu(rand(5)), cu(rand(2)) # Dummy data\nloss(x, y) # ~ 3Note that we convert both the parameters (W, b) and the data set (x, y) to cuda arrays. Taking derivatives and training works exactly as before.If you define a structured model, like a Dense layer or Chain, you just need to convert the internal parameters. Flux provides mapparams, which allows you to alter all parameters of a model at once.d = Dense(10, 5, σ)\nd = mapparams(cu, d)\nd.W # Tracked CuArray\nd(cu(rand(10))) # CuArray output\n\nm = Chain(Dense(10, 5, σ), Dense(5, 2), softmax)\nm = mapparams(cu, m)\nd(cu(rand(10)))The mnist example contains the code needed to run the model on the GPU; just uncomment the lines after using CuArrays." +}, + { "location": "contributing.html#", "page": "Contributing & Help", diff --git a/release-0.3/training/optimisers.html b/release-0.3/training/optimisers.html index 93615408..c6ad6fb2 100644 --- a/release-0.3/training/optimisers.html +++ b/release-0.3/training/optimisers.html @@ -6,7 +6,7 @@ m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m) ga('create', 'UA-36890222-9', 'auto'); ga('send', 'pageview'); -

      Optimisers

      Optimisers

      Consider a simple linear regression. We create some dummy data, calculate a loss, and backpropagate to calculate gradients for the parameters W and b.

      W = param(rand(2, 5))
      +

      Optimisers

      Optimisers

      Consider a simple linear regression. We create some dummy data, calculate a loss, and backpropagate to calculate gradients for the parameters W and b.

      W = param(rand(2, 5))
       b = param(rand(2))
       
       predict(x) = W*x .+ b
      diff --git a/release-0.3/training/training.html b/release-0.3/training/training.html
      index 252ce1bf..db7baac2 100644
      --- a/release-0.3/training/training.html
      +++ b/release-0.3/training/training.html
      @@ -6,10 +6,11 @@ m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
       
       ga('create', 'UA-36890222-9', 'auto');
       ga('send', 'pageview');
      -

      Training

      Training

      To actually train a model we need three things:

      • A loss function, that evaluates how well a model is doing given some input data.

      • A collection of data points that will be provided to the loss function.

      • An optimiser that will update the model parameters appropriately.

      With these we can call Flux.train!:

      Flux.train!(loss, data, opt)

      There are plenty of examples in the model zoo.

      Loss Functions

      The loss that we defined in basics is completely valid for training. We can also define a loss in terms of some model:

      m = Chain(
      +

      Training

      Training

      To actually train a model we need three things:

      • A model loss function, that evaluates how well a model is doing given some input data.

      • A collection of data points that will be provided to the loss function.

      • An optimiser that will update the model parameters appropriately.

      With these we can call Flux.train!:

      Flux.train!(modelLoss, data, opt)

      There are plenty of examples in the model zoo.

      Loss Functions

      The loss that we defined in basics is completely valid for training. We can also define a loss in terms of some model:

      m = Chain(
         Dense(784, 32, σ),
         Dense(32, 10), softmax)
       
      +# Model loss function
       loss(x, y) = Flux.mse(m(x), y)

      The loss will almost always be defined in terms of some cost function that measures the distance of the prediction m(x) from the target y. Flux has several of these built in, like mse for mean squared error or logloss for cross entropy loss, but you can calculate it however you want.

      Callbacks

      train! takes an additional argument, cb, that's used for callbacks so that you can observe the training process. For example:

      train!(loss, data, opt, cb = () -> println("training"))

      Callbacks are called for every batch of training data. You can slow this down using Flux.throttle(f, timeout) which prevents f from being called more than once every timeout seconds.

      A more typical callback might look like this:

      test_x, test_y = # ... create single batch of test data ...
       evalcb() = @show(loss(test_x, test_y))
       
      diff --git a/stable/contributing.html b/stable/contributing.html
      index 698722ce..21a65472 100644
      --- a/stable/contributing.html
      +++ b/stable/contributing.html
      @@ -6,4 +6,4 @@ m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
       
       ga('create', 'UA-36890222-9', 'auto');
       ga('send', 'pageview');
      -

      Contributing & Help

      Contributing & Help

      If you need help, please ask on the Julia forum, the slack (channel #machine-learning), or Flux's Gitter.

      Right now, the best way to help out is to try out the examples and report any issues or missing features as you find them. The second best way is to help us spread the word, perhaps by starring the repo.

      If you're interested in hacking on Flux, most of the code is pretty straightforward. Adding new layer definitions or cost functions is simple using the Flux DSL itself, and things like data utilities and training processes are all plain Julia code.

      If you get stuck or need anything, let us know!

      +

      Contributing & Help

      Contributing & Help

      If you need help, please ask on the Julia forum, the slack (channel #machine-learning), or Flux's Gitter.

      Right now, the best way to help out is to try out the examples and report any issues or missing features as you find them. The second best way is to help us spread the word, perhaps by starring the repo.

      If you're interested in hacking on Flux, most of the code is pretty straightforward. Adding new layer definitions or cost functions is simple using the Flux DSL itself, and things like data utilities and training processes are all plain Julia code.

      If you get stuck or need anything, let us know!

      diff --git a/stable/data/onehot.html b/stable/data/onehot.html index 4e840987..041bf1b1 100644 --- a/stable/data/onehot.html +++ b/stable/data/onehot.html @@ -6,7 +6,7 @@ m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m) ga('create', 'UA-36890222-9', 'auto'); ga('send', 'pageview'); -

      One-Hot Encoding

      One-Hot Encoding

      It's common to encode categorical variables (like true, false or cat, dog) in "one-of-k" or "one-hot" form. Flux provides the onehot function to make this easy.

      julia> using Flux: onehot
      +

      One-Hot Encoding

      One-Hot Encoding

      It's common to encode categorical variables (like true, false or cat, dog) in "one-of-k" or "one-hot" form. Flux provides the onehot function to make this easy.

      julia> using Flux: onehot
       
       julia> onehot(:b, [:a, :b, :c])
       3-element Flux.OneHotVector:
      @@ -37,4 +37,4 @@ julia> onecold(ans, [:a, :b, :c])
       3-element Array{Symbol,1}:
         :b
         :a
      -  :b

      Note that these operations returned OneHotVector and OneHotMatrix rather than Arrays. OneHotVectors behave like normal vectors but avoid any unnecessary cost compared to using an integer index directly. For example, multiplying a matrix with a one-hot vector simply slices out the relevant row of the matrix under the hood.

      + :b

      Note that these operations returned OneHotVector and OneHotMatrix rather than Arrays. OneHotVectors behave like normal vectors but avoid any unnecessary cost compared to using an integer index directly. For example, multiplying a matrix with a one-hot vector simply slices out the relevant row of the matrix under the hood.

      diff --git a/stable/gpu.html b/stable/gpu.html new file mode 100644 index 00000000..08872a41 --- /dev/null +++ b/stable/gpu.html @@ -0,0 +1,25 @@ + +GPU Support · Flux

      GPU Support

      GPU Support

      Support for array operations on other hardware backends, like GPUs, is provided by external packages like CuArrays and CLArrays. Flux doesn't care what array type you use, so we can just plug these in without any other changes.

      For example, we can use CuArrays (with the cu converter) to run our basic example on an NVIDIA GPU.

      using CuArrays
      +
      +W = cu(rand(2, 5)) # a 2×5 CuArray
      +b = cu(rand(2))
      +
      +predict(x) = W*x .+ b
      +loss(x, y) = sum((predict(x) .- y).^2)
      +
      +x, y = cu(rand(5)), cu(rand(2)) # Dummy data
      +loss(x, y) # ~ 3

      Note that we convert both the parameters (W, b) and the data set (x, y) to cuda arrays. Taking derivatives and training works exactly as before.

      If you define a structured model, like a Dense layer or Chain, you just need to convert the internal parameters. Flux provides mapparams, which allows you to alter all parameters of a model at once.

      d = Dense(10, 5, σ)
      +d = mapparams(cu, d)
      +d.W # Tracked CuArray
      +d(cu(rand(10))) # CuArray output
      +
      +m = Chain(Dense(10, 5, σ), Dense(5, 2), softmax)
      +m = mapparams(cu, m)
      +d(cu(rand(10)))

      The mnist example contains the code needed to run the model on the GPU; just uncomment the lines after using CuArrays.

      diff --git a/stable/index.html b/stable/index.html index b3fb6887..391847f7 100644 --- a/stable/index.html +++ b/stable/index.html @@ -6,5 +6,5 @@ m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m) ga('create', 'UA-36890222-9', 'auto'); ga('send', 'pageview'); -

      Home

      Flux: The Julia Machine Learning Library

      Flux is a library for machine learning. It comes "batteries-included" with many useful tools built in, but also lets you use the full power of the Julia language where you need it. The whole stack is implemented in clean Julia code (right down to the GPU kernels) and any part can be tweaked to your liking.

      Installation

      Install Julia 0.6.0 or later, if you haven't already.

      Pkg.add("Flux")
      +

      Home

      Flux: The Julia Machine Learning Library

      Flux is a library for machine learning. It comes "batteries-included" with many useful tools built in, but also lets you use the full power of the Julia language where you need it. The whole stack is implemented in clean Julia code (right down to the GPU kernels) and any part can be tweaked to your liking.

      Installation

      Install Julia 0.6.0 or later, if you haven't already.

      Pkg.add("Flux")
       Pkg.test("Flux") # Check things installed correctly

      Start with the basics. The model zoo is also a good starting point for many common kinds of models.

      diff --git a/stable/models/basics.html b/stable/models/basics.html index b6b34a4a..69192b8b 100644 --- a/stable/models/basics.html +++ b/stable/models/basics.html @@ -6,7 +6,7 @@ m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m) ga('create', 'UA-36890222-9', 'auto'); ga('send', 'pageview'); -

      Basics

      Model-Building Basics

      Taking Gradients

      Consider a simple linear regression, which tries to predict an output array y from an input x. (It's a good idea to follow this example in the Julia repl.)

      W = rand(2, 5)
      +

      Basics

      Model-Building Basics

      Taking Gradients

      Consider a simple linear regression, which tries to predict an output array y from an input x. (It's a good idea to follow this example in the Julia repl.)

      W = rand(2, 5)
       b = rand(2)
       
       predict(x) = W*x .+ b
      diff --git a/stable/models/layers.html b/stable/models/layers.html
      index 01f8e87b..c689b6d5 100644
      --- a/stable/models/layers.html
      +++ b/stable/models/layers.html
      @@ -6,9 +6,9 @@ m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
       
       ga('create', 'UA-36890222-9', 'auto');
       ga('send', 'pageview');
      -

      Layer Reference

      Model Layers

      Flux.ChainType.
      Chain(layers...)

      Chain multiple layers / functions together, so that they are called in sequence on a given input.

      m = Chain(x -> x^2, x -> x+1)
      +

      Layer Reference

      Model Layers

      Flux.ChainType.
      Chain(layers...)

      Chain multiple layers / functions together, so that they are called in sequence on a given input.

      m = Chain(x -> x^2, x -> x+1)
       m(5) == 26
       
       m = Chain(Dense(10, 5), Dense(5, 2))
       x = rand(10)
      -m(x) == m[2](m[1](x))

      Chain also supports indexing and slicing, e.g. m[2] or m[1:end-1]. m[1:3](x) will calculate the output of the first three layers.

      source
      Flux.DenseType.
      Dense(in::Integer, out::Integer, σ = identity)

      Creates a traditional Dense layer with parameters W and b.

      y = σ.(W * x .+ b)

      The input x must be a vector of length in, or a batch of vectors represented as an in × N matrix. The out y will be a vector or batch of length in.

      source
      +m(x) == m[2](m[1](x))

      Chain also supports indexing and slicing, e.g. m[2] or m[1:end-1]. m[1:3](x) will calculate the output of the first three layers.

      source
      Flux.DenseType.
      Dense(in::Integer, out::Integer, σ = identity)

      Creates a traditional Dense layer with parameters W and b.

      y = σ.(W * x .+ b)

      The input x must be a vector of length in, or a batch of vectors represented as an in × N matrix. The out y will be a vector or batch of length in.

      source
      diff --git a/stable/models/recurrence.html b/stable/models/recurrence.html index 17e8abc2..ee30fa89 100644 --- a/stable/models/recurrence.html +++ b/stable/models/recurrence.html @@ -6,7 +6,7 @@ m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m) ga('create', 'UA-36890222-9', 'auto'); ga('send', 'pageview'); -

      Recurrence

      Recurrent Models

      Recurrent Cells

      In the simple feedforward case, our model m is a simple function from various inputs xᵢ to predictions yᵢ. (For example, each x might be an MNIST digit and each y a digit label.) Each prediction is completely independent of any others, and using the same x will always produce the same y.

      y₁ = f(x₁)
      +

      Recurrence

      Recurrent Models

      Recurrent Cells

      In the simple feedforward case, our model m is a simple function from various inputs xᵢ to predictions yᵢ. (For example, each x might be an MNIST digit and each y a digit label.) Each prediction is completely independent of any others, and using the same x will always produce the same y.

      y₁ = f(x₁)
       y₂ = f(x₂)
       y₃ = f(x₃)
       # ...

      Recurrent networks introduce a hidden state that gets carried over each time we run the model. The model now takes the old h as an input, and produces a new h as output, each time we run it.

      h = # ... initial state ...
      diff --git a/stable/search.html b/stable/search.html
      index 86fc913d..d94fbbc3 100644
      --- a/stable/search.html
      +++ b/stable/search.html
      @@ -6,4 +6,4 @@ m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
       
       ga('create', 'UA-36890222-9', 'auto');
       ga('send', 'pageview');
      -

      Search

      Search

      Number of results: loading...

        +

        Search

        Search

        Number of results: loading...

          diff --git a/stable/search_index.js b/stable/search_index.js index ac4ef48e..9b0f0acc 100644 --- a/stable/search_index.js +++ b/stable/search_index.js @@ -173,7 +173,7 @@ var documenterSearchIndex = {"docs": [ "page": "Training", "title": "Training", "category": "section", - "text": "To actually train a model we need three things:A loss function, that evaluates how well a model is doing given some input data.\nA collection of data points that will be provided to the loss function.\nAn optimiser that will update the model parameters appropriately.With these we can call Flux.train!:Flux.train!(loss, data, opt)There are plenty of examples in the model zoo." + "text": "To actually train a model we need three things:A model loss function, that evaluates how well a model is doing given some input data.\nA collection of data points that will be provided to the loss function.\nAn optimiser that will update the model parameters appropriately.With these we can call Flux.train!:Flux.train!(modelLoss, data, opt)There are plenty of examples in the model zoo." }, { @@ -181,7 +181,7 @@ var documenterSearchIndex = {"docs": [ "page": "Training", "title": "Loss Functions", "category": "section", - "text": "The loss that we defined in basics is completely valid for training. We can also define a loss in terms of some model:m = Chain(\n Dense(784, 32, σ),\n Dense(32, 10), softmax)\n\nloss(x, y) = Flux.mse(m(x), y)The loss will almost always be defined in terms of some cost function that measures the distance of the prediction m(x) from the target y. Flux has several of these built in, like mse for mean squared error or logloss for cross entropy loss, but you can calculate it however you want." + "text": "The loss that we defined in basics is completely valid for training. We can also define a loss in terms of some model:m = Chain(\n Dense(784, 32, σ),\n Dense(32, 10), softmax)\n\n# Model loss function\nloss(x, y) = Flux.mse(m(x), y)The loss will almost always be defined in terms of some cost function that measures the distance of the prediction m(x) from the target y. Flux has several of these built in, like mse for mean squared error or logloss for cross entropy loss, but you can calculate it however you want." }, { @@ -216,6 +216,22 @@ var documenterSearchIndex = {"docs": [ "text": "onehotbatch creates a batch (matrix) of one-hot vectors, and argmax treats matrices as batches.julia> using Flux: onehotbatch\n\njulia> onehotbatch([:b, :a, :b], [:a, :b, :c])\n3×3 Flux.OneHotMatrix:\n false true false\n true false true\n false false false\n\njulia> onecold(ans, [:a, :b, :c])\n3-element Array{Symbol,1}:\n :b\n :a\n :bNote that these operations returned OneHotVector and OneHotMatrix rather than Arrays. OneHotVectors behave like normal vectors but avoid any unnecessary cost compared to using an integer index directly. For example, multiplying a matrix with a one-hot vector simply slices out the relevant row of the matrix under the hood." }, +{ + "location": "gpu.html#", + "page": "GPU Support", + "title": "GPU Support", + "category": "page", + "text": "" +}, + +{ + "location": "gpu.html#GPU-Support-1", + "page": "GPU Support", + "title": "GPU Support", + "category": "section", + "text": "Support for array operations on other hardware backends, like GPUs, is provided by external packages like CuArrays and CLArrays. Flux doesn't care what array type you use, so we can just plug these in without any other changes.For example, we can use CuArrays (with the cu converter) to run our basic example on an NVIDIA GPU.using CuArrays\n\nW = cu(rand(2, 5)) # a 2×5 CuArray\nb = cu(rand(2))\n\npredict(x) = W*x .+ b\nloss(x, y) = sum((predict(x) .- y).^2)\n\nx, y = cu(rand(5)), cu(rand(2)) # Dummy data\nloss(x, y) # ~ 3Note that we convert both the parameters (W, b) and the data set (x, y) to cuda arrays. Taking derivatives and training works exactly as before.If you define a structured model, like a Dense layer or Chain, you just need to convert the internal parameters. Flux provides mapparams, which allows you to alter all parameters of a model at once.d = Dense(10, 5, σ)\nd = mapparams(cu, d)\nd.W # Tracked CuArray\nd(cu(rand(10))) # CuArray output\n\nm = Chain(Dense(10, 5, σ), Dense(5, 2), softmax)\nm = mapparams(cu, m)\nd(cu(rand(10)))The mnist example contains the code needed to run the model on the GPU; just uncomment the lines after using CuArrays." +}, + { "location": "contributing.html#", "page": "Contributing & Help", diff --git a/stable/training/optimisers.html b/stable/training/optimisers.html index 93615408..c6ad6fb2 100644 --- a/stable/training/optimisers.html +++ b/stable/training/optimisers.html @@ -6,7 +6,7 @@ m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m) ga('create', 'UA-36890222-9', 'auto'); ga('send', 'pageview'); -

          Optimisers

          Optimisers

          Consider a simple linear regression. We create some dummy data, calculate a loss, and backpropagate to calculate gradients for the parameters W and b.

          W = param(rand(2, 5))
          +

          Optimisers

          Optimisers

          Consider a simple linear regression. We create some dummy data, calculate a loss, and backpropagate to calculate gradients for the parameters W and b.

          W = param(rand(2, 5))
           b = param(rand(2))
           
           predict(x) = W*x .+ b
          diff --git a/stable/training/training.html b/stable/training/training.html
          index 252ce1bf..db7baac2 100644
          --- a/stable/training/training.html
          +++ b/stable/training/training.html
          @@ -6,10 +6,11 @@ m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
           
           ga('create', 'UA-36890222-9', 'auto');
           ga('send', 'pageview');
          -

          Training

          Training

          To actually train a model we need three things:

          • A loss function, that evaluates how well a model is doing given some input data.

          • A collection of data points that will be provided to the loss function.

          • An optimiser that will update the model parameters appropriately.

          With these we can call Flux.train!:

          Flux.train!(loss, data, opt)

          There are plenty of examples in the model zoo.

          Loss Functions

          The loss that we defined in basics is completely valid for training. We can also define a loss in terms of some model:

          m = Chain(
          +

          Training

          Training

          To actually train a model we need three things:

          • A model loss function, that evaluates how well a model is doing given some input data.

          • A collection of data points that will be provided to the loss function.

          • An optimiser that will update the model parameters appropriately.

          With these we can call Flux.train!:

          Flux.train!(modelLoss, data, opt)

          There are plenty of examples in the model zoo.

          Loss Functions

          The loss that we defined in basics is completely valid for training. We can also define a loss in terms of some model:

          m = Chain(
             Dense(784, 32, σ),
             Dense(32, 10), softmax)
           
          +# Model loss function
           loss(x, y) = Flux.mse(m(x), y)

          The loss will almost always be defined in terms of some cost function that measures the distance of the prediction m(x) from the target y. Flux has several of these built in, like mse for mean squared error or logloss for cross entropy loss, but you can calculate it however you want.

          Callbacks

          train! takes an additional argument, cb, that's used for callbacks so that you can observe the training process. For example:

          train!(loss, data, opt, cb = () -> println("training"))

          Callbacks are called for every batch of training data. You can slow this down using Flux.throttle(f, timeout) which prevents f from being called more than once every timeout seconds.

          A more typical callback might look like this:

          test_x, test_y = # ... create single batch of test data ...
           evalcb() = @show(loss(test_x, test_y))
           
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          +    background-color: #eeeeee;
          +}
          +
          +.admonition-title {
          +    border-radius: 3px 3px 0 0;
          +    background-color: #9b9b9b;
          +    padding: 0.15em 0.5em;
          +}
          +
          +.admonition-text {
          +    padding: 0.5em;
          +}
          +
          +.admonition-text > :first-child {
          +    margin-top: 0;
          +}
          +
          +.admonition-text > :last-child {
          +    margin-bottom: 0;
          +}
          +
          +.admonition > .admonition-title:before {
          +    font-family: "FontAwesome";
          +    margin-right: 5px;
          +    content: "\f06a";
          +}
          +
          +.admonition.warning > .admonition-title {
          +    background-color: #f0b37e;
          +}
          +
          +.admonition.warning {
          +    background-color: #ffedcc;
          +}
          +
          +.admonition.note > .admonition-title {
          +    background-color: #6ab0de;
          +}
          +
          +.admonition.note {
          +    background-color: #e7f2fa;
          +}
          +
          +.admonition.tip > .admonition-title {
          +    background-color: #1abc9c;
          +}
          +
          +.admonition.tip {
          +    background-color: #dbfaf4;
          +}
          +
          +
          +/* footnotes */
          +.footnote {
          +    padding-left: 0.8em;
          +    border-left: 2px solid #ccc;
          +}
          +
          +/* Search page */
          +#search-results .category {
          +    font-size: smaller;
          +}
          +
          +#search-results .category:before {
          +    content: " ";
          +}
          +
          +/* Overriding the  block style of highligh.js.
          + * We have to override the padding and the background-color, since we style this
          + * part ourselves. Specifically, we style the 
           surrounding the , while
          + * highlight.js applies the .hljs style directly to the  tag.
          + */
          +.hljs {
          +    background-color: transparent;
          +    padding: 0;
          +}
          +
          +@media only screen and (max-width: 768px) {
          +    nav.toc {
          +        position: fixed;
          +        overflow-y: scroll;
          +        width: 16em;
          +        left: -16em;
          +        -webkit-overflow-scrolling: touch;
          +        -webkit-transition-property: left; /* Safari */
          +        -webkit-transition-duration: 0.3s; /* Safari */
          +        transition-property: left;
          +        transition-duration: 0.3s;
          +        -webkit-transition-timing-function: ease-out; /* Safari */
          +        transition-timing-function: ease-out;
          +        z-index: 2;
          +    }
          +
          +    nav.toc.show {
          +        left: 0;
          +    }
          +
          +    article {
          +        margin-left: 0;
          +        padding: 3em 0.9em 0 0.9em; /* top right bottom left */
          +        overflow-wrap: break-word;
          +    }
          +
          +    article > header {
          +        position: fixed;
          +        left: 0;
          +        z-index: 1;
          +    }
          +
          +    article > header nav, hr {
          +        display: none;
          +    }
          +
          +    article > header div#topbar {
          +        display: block; /* is mobile */
          +        position: fixed;
          +        width: 100%;
          +        height: 1.5em;
          +        padding-top: 1em;
          +        padding-bottom: 1em;
          +        background-color: #fcfcfc;
          +        box-shadow: 0 1px 3px rgba(0,0,0,.26);
          +        top: 0;
          +        -webkit-transition-property: top; /* Safari */
          +        -webkit-transition-duration: 0.3s; /* Safari */
          +        transition-property: top;
          +        transition-duration: 0.3s;
          +    }
          +
          +    article > header div#topbar.headroom--unpinned.headroom--not-top.headroom--not-bottom {
          +        top: -4em;
          +        -webkit-transition-property: top; /* Safari */
          +        -webkit-transition-duration: 0.7s; /* Safari */
          +        transition-property: top;
          +        transition-duration: 0.7s;
          +    }
          +
          +    article > header div#topbar span {
          +        position: fixed;
          +        width: 80%;
          +        height: 1.5em;
          +        margin-top: -0.1em;
          +        margin-left: 0.9em;
          +        font-size: 1.2em;
          +        overflow: hidden;
          +    }
          +
          +    article > header div#topbar a.fa-bars {
          +        float: right;
          +        padding: 0.6em;
          +        margin-top: -0.6em;
          +        margin-right: 0.3em;
          +        font-size: 1.5em;
          +    }
          +
          +    article > header div#topbar a.fa-bars:visited {
          +        color: #3091d1;
          +    }
          +
          +    article table {
          +        overflow-x: auto;
          +        display: block;
          +    }
          +
          +    article div.MathJax_Display {
          +        overflow: scroll;
          +    }
          +
          +    article span.MathJax {
          +        overflow: hidden;
          +    }
          +}
          +
          +@media only screen and (max-width: 320px) {
          +    body {
          +        font-size: 15px;
          +    }
          +}
          diff --git a/v0.3.2/assets/documenter.js b/v0.3.2/assets/documenter.js
          new file mode 100644
          index 00000000..5d31622f
          --- /dev/null
          +++ b/v0.3.2/assets/documenter.js
          @@ -0,0 +1,129 @@
          +/*
          + * Part of Documenter.jl
          + *     https://github.com/JuliaDocs/Documenter.jl
          + *
          + * License: MIT
          + */
          +
          +requirejs.config({
          +    paths: {
          +        'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.1.1/jquery.min',
          +        'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.12.0/jquery-ui.min',
          +        'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.9.3/headroom.min',
          +        'mathjax': 'https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS_HTML',
          +        'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/9.12.0/highlight.min',
          +        'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/9.12.0/languages/julia.min',
          +        'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/9.12.0/languages/julia-repl.min',
          +    },
          +    shim: {
          +        'mathjax' : {
          +            exports: "MathJax"
          +        },
          +        'highlight-julia': ['highlight'],
          +        'highlight-julia-repl': ['highlight'],
          +    }
          +});
          +
          +// Load MathJax
          +require(['mathjax'], function(MathJax) {
          +    MathJax.Hub.Config({
          +      "tex2jax": {
          +        inlineMath: [['$','$'], ['\\(','\\)']],
          +        processEscapes: true
          +      }
          +    });
          +    MathJax.Hub.Config({
          +      config: ["MMLorHTML.js"],
          +      jax: [
          +        "input/TeX",
          +        "output/HTML-CSS",
          +        "output/NativeMML"
          +      ],
          +      extensions: [
          +        "MathMenu.js",
          +        "MathZoom.js",
          +        "TeX/AMSmath.js",
          +        "TeX/AMSsymbols.js",
          +        "TeX/autobold.js",
          +        "TeX/autoload-all.js"
          +      ]
          +    });
          +    MathJax.Hub.Config({
          +      TeX: { equationNumbers: { autoNumber: "AMS" } }
          +    });
          +})
          +
          +require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($, hljs) {
          +    $(document).ready(function() {
          +        hljs.initHighlighting();
          +    })
          +
          +})
          +
          +// update the version selector with info from the siteinfo.js and ../versions.js files
          +require(['jquery'], function($) {
          +    $(document).ready(function() {
          +        var version_selector = $("#version-selector");
          +
          +        // add the current version to the selector based on siteinfo.js, but only if the selector is empty
          +        if (typeof DOCUMENTER_CURRENT_VERSION !== 'undefined' && $('#version-selector > option').length == 0) {
          +            var option = $("");
          +            version_selector.append(option);
          +        }
          +
          +        if (typeof DOC_VERSIONS !== 'undefined') {
          +            var existing_versions = $('#version-selector > option');
          +            var existing_versions_texts = existing_versions.map(function(i,x){return x.text});
          +            DOC_VERSIONS.forEach(function(each) {
          +                var version_url = documenterBaseURL + "/../" + each;
          +                var existing_id = $.inArray(each, existing_versions_texts);
          +                // if not already in the version selector, add it as a new option,
          +                // otherwise update the old option with the URL and enable it
          +                if (existing_id == -1) {
          +                    var option = $("");
          +                    version_selector.append(option);
          +                } else {
          +                    var option = existing_versions[existing_id];
          +                    option.value = version_url;
          +                    option.disabled = false;
          +                }
          +            });
          +        }
          +
          +        // only show the version selector if the selector has been populated
          +        if ($('#version-selector > option').length > 0) {
          +            version_selector.css("visibility", "visible");
          +        }
          +    })
          +
          +})
          +
          +// mobile
          +require(['jquery', 'headroom'], function($, Headroom) {
          +    $(document).ready(function() {
          +        var navtoc = $("nav.toc");
          +        $("nav.toc li.current a.toctext").click(function() {
          +            navtoc.toggleClass('show');
          +        });
          +        $("article > header div#topbar a.fa-bars").click(function(ev) {
          +            ev.preventDefault();
          +            navtoc.toggleClass('show');
          +            if (navtoc.hasClass('show')) {
          +                var title = $("article > header div#topbar span").text();
          +                $("nav.toc ul li a:contains('" + title + "')").focus();
          +            }
          +        });
          +        $("article#docs").bind('click', function(ev) {
          +            if ($(ev.target).is('div#topbar a.fa-bars')) {
          +                return;
          +            }
          +            if (navtoc.hasClass('show')) {
          +                navtoc.removeClass('show');
          +            }
          +        });
          +        if ($("article > header div#topbar").css('display') == 'block') {
          +            var headroom = new Headroom(document.querySelector("article > header div#topbar"), {"tolerance": {"up": 10, "down": 10}});
          +            headroom.init();
          +        }
          +    })
          +})
          diff --git a/v0.3.2/assets/search.js b/v0.3.2/assets/search.js
          new file mode 100644
          index 00000000..4e3e9a4a
          --- /dev/null
          +++ b/v0.3.2/assets/search.js
          @@ -0,0 +1,91 @@
          +/*
          + * Part of Documenter.jl
          + *     https://github.com/JuliaDocs/Documenter.jl
          + *
          + * License: MIT
          + */
          +
          +// parseUri 1.2.2
          +// (c) Steven Levithan 
          +// MIT License
          +function parseUri (str) {
          +	var	o   = parseUri.options,
          +		m   = o.parser[o.strictMode ? "strict" : "loose"].exec(str),
          +		uri = {},
          +		i   = 14;
          +
          +	while (i--) uri[o.key[i]] = m[i] || "";
          +
          +	uri[o.q.name] = {};
          +	uri[o.key[12]].replace(o.q.parser, function ($0, $1, $2) {
          +		if ($1) uri[o.q.name][$1] = $2;
          +	});
          +
          +	return uri;
          +};
          +parseUri.options = {
          +	strictMode: false,
          +	key: ["source","protocol","authority","userInfo","user","password","host","port","relative","path","directory","file","query","anchor"],
          +	q:   {
          +		name:   "queryKey",
          +		parser: /(?:^|&)([^&=]*)=?([^&]*)/g
          +	},
          +	parser: {
          +		strict: /^(?:([^:\/?#]+):)?(?:\/\/((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?))?((((?:[^?#\/]*\/)*)([^?#]*))(?:\?([^#]*))?(?:#(.*))?)/,
          +		loose:  /^(?:(?![^:@]+:[^:@\/]*@)([^:\/?#.]+):)?(?:\/\/)?((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?)(((\/(?:[^?#](?![^?#\/]*\.[^?#\/.]+(?:[?#]|$)))*\/?)?([^?#\/]*))(?:\?([^#]*))?(?:#(.*))?)/
          +	}
          +};
          +
          +requirejs.config({
          +    paths: {
          +        'jquery': 'https://code.jquery.com/jquery-3.1.0.js?',
          +        'lunr': 'https://cdnjs.cloudflare.com/ajax/libs/lunr.js/0.7.1/lunr.min',
          +    }
          +});
          +
          +var currentScript = document.currentScript;
          +
          +require(["jquery", "lunr"], function($, lunr) {
          +    var index = lunr(function () {
          +        this.ref('location')
          +        this.field('title', {boost: 10})
          +        this.field('text')
          +    })
          +    var store = {}
          +
          +    documenterSearchIndex['docs'].forEach(function(e) {
          +        index.add(e)
          +        store[e.location] = e
          +    })
          +
          +    $(function(){
          +        function update_search(query) {
          +            results = index.search(query)
          +            $('#search-info').text("Number of results: " + results.length)
          +            $('#search-results').empty()
          +            results.forEach(function(result) {
          +                data = store[result.ref]
          +                link = $('')
          +                link.text(data.title)
          +                link.attr('href', documenterBaseURL+'/'+result.ref)
          +                cat = $('('+data.category+')')
          +                li = $('
        • ').append(link).append(cat) + $('#search-results').append(li) + }) + } + + function update_search_box() { + query = $('#search-query').val() + update_search(query) + } + + $('#search-query').keyup(update_search_box) + $('#search-query').change(update_search_box) + + search_query = parseUri(window.location).queryKey["q"] + if(search_query !== undefined) { + $("#search-query").val(search_query) + } + update_search_box(); + }) +}) diff --git a/v0.3.2/contributing.html b/v0.3.2/contributing.html new file mode 100644 index 00000000..21a65472 --- /dev/null +++ b/v0.3.2/contributing.html @@ -0,0 +1,9 @@ + +Contributing & Help · Flux

          Contributing & Help

          Contributing & Help

          If you need help, please ask on the Julia forum, the slack (channel #machine-learning), or Flux's Gitter.

          Right now, the best way to help out is to try out the examples and report any issues or missing features as you find them. The second best way is to help us spread the word, perhaps by starring the repo.

          If you're interested in hacking on Flux, most of the code is pretty straightforward. Adding new layer definitions or cost functions is simple using the Flux DSL itself, and things like data utilities and training processes are all plain Julia code.

          If you get stuck or need anything, let us know!

          diff --git a/v0.3.2/data/onehot.html b/v0.3.2/data/onehot.html new file mode 100644 index 00000000..041bf1b1 --- /dev/null +++ b/v0.3.2/data/onehot.html @@ -0,0 +1,40 @@ + +One-Hot Encoding · Flux

          One-Hot Encoding

          One-Hot Encoding

          It's common to encode categorical variables (like true, false or cat, dog) in "one-of-k" or "one-hot" form. Flux provides the onehot function to make this easy.

          julia> using Flux: onehot
          +
          +julia> onehot(:b, [:a, :b, :c])
          +3-element Flux.OneHotVector:
          + false
          +  true
          + false
          +
          +julia> onehot(:c, [:a, :b, :c])
          +3-element Flux.OneHotVector:
          + false
          + false
          +  true

          The inverse is argmax (which can take a general probability distribution, as well as just booleans).

          julia> argmax(ans, [:a, :b, :c])
          +:c
          +
          +julia> argmax([true, false, false], [:a, :b, :c])
          +:a
          +
          +julia> argmax([0.3, 0.2, 0.5], [:a, :b, :c])
          +:c

          Batches

          onehotbatch creates a batch (matrix) of one-hot vectors, and argmax treats matrices as batches.

          julia> using Flux: onehotbatch
          +
          +julia> onehotbatch([:b, :a, :b], [:a, :b, :c])
          +3×3 Flux.OneHotMatrix:
          + false   true  false
          +  true  false   true
          + false  false  false
          +
          +julia> onecold(ans, [:a, :b, :c])
          +3-element Array{Symbol,1}:
          +  :b
          +  :a
          +  :b

          Note that these operations returned OneHotVector and OneHotMatrix rather than Arrays. OneHotVectors behave like normal vectors but avoid any unnecessary cost compared to using an integer index directly. For example, multiplying a matrix with a one-hot vector simply slices out the relevant row of the matrix under the hood.

          diff --git a/v0.3.2/gpu.html b/v0.3.2/gpu.html new file mode 100644 index 00000000..08872a41 --- /dev/null +++ b/v0.3.2/gpu.html @@ -0,0 +1,25 @@ + +GPU Support · Flux

          GPU Support

          GPU Support

          Support for array operations on other hardware backends, like GPUs, is provided by external packages like CuArrays and CLArrays. Flux doesn't care what array type you use, so we can just plug these in without any other changes.

          For example, we can use CuArrays (with the cu converter) to run our basic example on an NVIDIA GPU.

          using CuArrays
          +
          +W = cu(rand(2, 5)) # a 2×5 CuArray
          +b = cu(rand(2))
          +
          +predict(x) = W*x .+ b
          +loss(x, y) = sum((predict(x) .- y).^2)
          +
          +x, y = cu(rand(5)), cu(rand(2)) # Dummy data
          +loss(x, y) # ~ 3

          Note that we convert both the parameters (W, b) and the data set (x, y) to cuda arrays. Taking derivatives and training works exactly as before.

          If you define a structured model, like a Dense layer or Chain, you just need to convert the internal parameters. Flux provides mapparams, which allows you to alter all parameters of a model at once.

          d = Dense(10, 5, σ)
          +d = mapparams(cu, d)
          +d.W # Tracked CuArray
          +d(cu(rand(10))) # CuArray output
          +
          +m = Chain(Dense(10, 5, σ), Dense(5, 2), softmax)
          +m = mapparams(cu, m)
          +d(cu(rand(10)))

          The mnist example contains the code needed to run the model on the GPU; just uncomment the lines after using CuArrays.

          diff --git a/v0.3.2/index.html b/v0.3.2/index.html new file mode 100644 index 00000000..391847f7 --- /dev/null +++ b/v0.3.2/index.html @@ -0,0 +1,10 @@ + +Home · Flux

          Home

          Flux: The Julia Machine Learning Library

          Flux is a library for machine learning. It comes "batteries-included" with many useful tools built in, but also lets you use the full power of the Julia language where you need it. The whole stack is implemented in clean Julia code (right down to the GPU kernels) and any part can be tweaked to your liking.

          Installation

          Install Julia 0.6.0 or later, if you haven't already.

          Pkg.add("Flux")
          +Pkg.test("Flux") # Check things installed correctly

          Start with the basics. The model zoo is also a good starting point for many common kinds of models.

          diff --git a/v0.3.2/models/basics.html b/v0.3.2/models/basics.html new file mode 100644 index 00000000..69192b8b --- /dev/null +++ b/v0.3.2/models/basics.html @@ -0,0 +1,78 @@ + +Basics · Flux

          Basics

          Model-Building Basics

          Taking Gradients

          Consider a simple linear regression, which tries to predict an output array y from an input x. (It's a good idea to follow this example in the Julia repl.)

          W = rand(2, 5)
          +b = rand(2)
          +
          +predict(x) = W*x .+ b
          +loss(x, y) = sum((predict(x) .- y).^2)
          +
          +x, y = rand(5), rand(2) # Dummy data
          +loss(x, y) # ~ 3

          To improve the prediction we can take the gradients of W and b with respect to the loss function and perform gradient descent. We could calculate gradients by hand, but Flux will do it for us if we tell it that W and b are trainable parameters.

          using Flux.Tracker: param, back!, data, grad
          +
          +W = param(W)
          +b = param(b)
          +
          +l = loss(x, y)
          +
          +back!(l)

          loss(x, y) returns the same number, but it's now a tracked value that records gradients as it goes along. Calling back! then calculates the gradient of W and b. We can see what this gradient is, and modify W to train the model.

          grad(W)
          +
          +W.data .-= 0.1grad(W)
          +
          +loss(x, y) # ~ 2.5

          The loss has decreased a little, meaning that our prediction x is closer to the target y. If we have some data we can already try training the model.

          All deep learning in Flux, however complex, is a simple generalisation of this example. Of course, models can look very different – they might have millions of parameters or complex control flow, and there are ways to manage this complexity. Let's see what that looks like.

          Building Layers

          It's common to create more complex models than the linear regression above. For example, we might want to have two linear layers with a nonlinearity like sigmoid (σ) in between them. In the above style we could write this as:

          W1 = param(rand(3, 5))
          +b1 = param(rand(3))
          +layer1(x) = W1 * x .+ b1
          +
          +W2 = param(rand(2, 3))
          +b2 = param(rand(2))
          +layer2(x) = W2 * x .+ b2
          +
          +model(x) = layer2(σ.(layer1(x)))
          +
          +model(rand(5)) # => 2-element vector

          This works but is fairly unwieldy, with a lot of repetition – especially as we add more layers. One way to factor this out is to create a function that returns linear layers.

          function linear(in, out)
          +  W = param(randn(out, in))
          +  b = param(randn(out))
          +  x -> W * x .+ b
          +end
          +
          +linear1 = linear(5, 3) # we can access linear1.W etc
          +linear2 = linear(3, 2)
          +
          +model(x) = linear2(σ.(linear1(x)))
          +
          +model(x) # => 2-element vector

          Another (equivalent) way is to create a struct that explicitly represents the affine layer.

          struct Affine
          +  W
          +  b
          +end
          +
          +Affine(in::Integer, out::Integer) =
          +  Affine(param(randn(out, in)), param(randn(out)))
          +
          +# Overload call, so the object can be used as a function
          +(m::Affine)(x) = m.W * x .+ m.b
          +
          +a = Affine(10, 5)
          +
          +a(rand(10)) # => 5-element vector

          Congratulations! You just built the Dense layer that comes with Flux. Flux has many interesting layers available, but they're all things you could have built yourself very easily.

          (There is one small difference with Dense – for convenience it also takes an activation function, like Dense(10, 5, σ).)

          Stacking It Up

          It's pretty common to write models that look something like:

          layer1 = Dense(10, 5, σ)
          +# ...
          +model(x) = layer3(layer2(layer1(x)))

          For long chains, it might be a bit more intuitive to have a list of layers, like this:

          using Flux
          +
          +layers = [Dense(10, 5, σ), Dense(5, 2), softmax]
          +
          +model(x) = foldl((x, m) -> m(x), x, layers)
          +
          +model(rand(10)) # => 2-element vector

          Handily, this is also provided for in Flux:

          model2 = Chain(
          +  Dense(10, 5, σ),
          +  Dense(5, 2),
          +  softmax)
          +
          +model2(rand(10)) # => 2-element vector

          This quickly starts to look like a high-level deep learning library; yet you can see how it falls out of simple abstractions, and we lose none of the power of Julia code.

          A nice property of this approach is that because "models" are just functions (possibly with trainable parameters), you can also see this as simple function composition.

          m = Dense(5, 2) ∘ Dense(10, 5, σ)
          +
          +m(rand(10))

          Likewise, Chain will happily work with any Julia function.

          m = Chain(x -> x^2, x -> x+1)
          +
          +m(5) # => 26
          diff --git a/v0.3.2/models/layers.html b/v0.3.2/models/layers.html new file mode 100644 index 00000000..c689b6d5 --- /dev/null +++ b/v0.3.2/models/layers.html @@ -0,0 +1,14 @@ + +Layer Reference · Flux

          Layer Reference

          Model Layers

          Flux.ChainType.
          Chain(layers...)

          Chain multiple layers / functions together, so that they are called in sequence on a given input.

          m = Chain(x -> x^2, x -> x+1)
          +m(5) == 26
          +
          +m = Chain(Dense(10, 5), Dense(5, 2))
          +x = rand(10)
          +m(x) == m[2](m[1](x))

          Chain also supports indexing and slicing, e.g. m[2] or m[1:end-1]. m[1:3](x) will calculate the output of the first three layers.

          source
          Flux.DenseType.
          Dense(in::Integer, out::Integer, σ = identity)

          Creates a traditional Dense layer with parameters W and b.

          y = σ.(W * x .+ b)

          The input x must be a vector of length in, or a batch of vectors represented as an in × N matrix. The out y will be a vector or batch of length in.

          source
          diff --git a/v0.3.2/models/recurrence.html b/v0.3.2/models/recurrence.html new file mode 100644 index 00000000..ee30fa89 --- /dev/null +++ b/v0.3.2/models/recurrence.html @@ -0,0 +1,42 @@ + +Recurrence · Flux

          Recurrence

          Recurrent Models

          Recurrent Cells

          In the simple feedforward case, our model m is a simple function from various inputs xᵢ to predictions yᵢ. (For example, each x might be an MNIST digit and each y a digit label.) Each prediction is completely independent of any others, and using the same x will always produce the same y.

          y₁ = f(x₁)
          +y₂ = f(x₂)
          +y₃ = f(x₃)
          +# ...

          Recurrent networks introduce a hidden state that gets carried over each time we run the model. The model now takes the old h as an input, and produces a new h as output, each time we run it.

          h = # ... initial state ...
          +y₁, h = f(x₁, h)
          +y₂, h = f(x₂, h)
          +y₃, h = f(x₃, h)
          +# ...

          Information stored in h is preserved for the next prediction, allowing it to function as a kind of memory. This also means that the prediction made for a given x depends on all the inputs previously fed into the model.

          (This might be important if, for example, each x represents one word of a sentence; the model's interpretation of the word "bank" should change if the previous input was "river" rather than "investment".)

          Flux's RNN support closely follows this mathematical perspective. The most basic RNN is as close as possible to a standard Dense layer, and the output and hidden state are the same. By convention, the hidden state is the first input and output.

          Wxh = randn(5, 10)
          +Whh = randn(5, 5)
          +b   = randn(5)
          +
          +function rnn(h, x)
          +  h = tanh.(Wxh * x .+ Whh * h .+ b)
          +  return h, h
          +end
          +
          +x = rand(10) # dummy data
          +h = rand(5)  # initial hidden state
          +
          +h, y = rnn(h, x)

          If you run the last line a few times, you'll notice the output y changing slightly even though the input x is the same.

          We sometimes refer to functions like rnn above, which explicitly manage state, as recurrent cells. There are various recurrent cells available, which are documented in the layer reference. The hand-written example above can be replaced with:

          using Flux
          +
          +rnn2 = Flux.RNNCell(10, 5)
          +
          +x = rand(10) # dummy data
          +h = rand(5)  # initial hidden state
          +
          +h, y = rnn2(h, x)

          Stateful Models

          For the most part, we don't want to manage hidden states ourselves, but to treat our models as being stateful. Flux provides the Recur wrapper to do this.

          x = rand(10)
          +h = rand(5)
          +
          +m = Flux.Recur(rnn, h)
          +
          +y = m(x)

          The Recur wrapper stores the state between runs in the m.state field.

          If you use the RNN(10, 5) constructor – as opposed to RNNCell – you'll see that it's simply a wrapped cell.

          julia> RNN(10, 5)
          +Recur(RNNCell(Dense(15, 5)))

          Sequences

          Often we want to work with sequences of inputs, rather than individual xs.

          seq = [rand(10) for i = 1:10]

          With Recur, applying our model to each element of a sequence is trivial:

          m.(seq) # returns a list of 5-element vectors

          This works even when we've chain recurrent layers into a larger model.

          m = Chain(LSTM(10, 15), Dense(15, 5))
          +m.(seq)

          Truncating Gradients

          By default, calculating the gradients in a recurrent layer involves the entire history. For example, if we call the model on 100 inputs, calling back! will calculate the gradient for those 100 calls. If we then calculate another 10 inputs we have to calculate 110 gradients – this accumulates and quickly becomes expensive.

          To avoid this we can truncate the gradient calculation, forgetting the history.

          truncate!(m)

          Calling truncate! wipes the slate clean, so we can call the model with more inputs without building up an expensive gradient computation.

          diff --git a/v0.3.2/search.html b/v0.3.2/search.html new file mode 100644 index 00000000..d94fbbc3 --- /dev/null +++ b/v0.3.2/search.html @@ -0,0 +1,9 @@ + +Search · Flux

          Search

          Search

          Number of results: loading...

            diff --git a/v0.3.2/search_index.js b/v0.3.2/search_index.js new file mode 100644 index 00000000..9b0f0acc --- /dev/null +++ b/v0.3.2/search_index.js @@ -0,0 +1,251 @@ +var documenterSearchIndex = {"docs": [ + +{ + "location": "index.html#", + "page": "Home", + "title": "Home", + "category": "page", + "text": "" +}, + +{ + "location": "index.html#Flux:-The-Julia-Machine-Learning-Library-1", + "page": "Home", + "title": "Flux: The Julia Machine Learning Library", + "category": "section", + "text": "Flux is a library for machine learning. It comes \"batteries-included\" with many useful tools built in, but also lets you use the full power of the Julia language where you need it. The whole stack is implemented in clean Julia code (right down to the GPU kernels) and any part can be tweaked to your liking." +}, + +{ + "location": "index.html#Installation-1", + "page": "Home", + "title": "Installation", + "category": "section", + "text": "Install Julia 0.6.0 or later, if you haven't already.Pkg.add(\"Flux\")\nPkg.test(\"Flux\") # Check things installed correctlyStart with the basics. The model zoo is also a good starting point for many common kinds of models." +}, + +{ + "location": "models/basics.html#", + "page": "Basics", + "title": "Basics", + "category": "page", + "text": "" +}, + +{ + "location": "models/basics.html#Model-Building-Basics-1", + "page": "Basics", + "title": "Model-Building Basics", + "category": "section", + "text": "" +}, + +{ + "location": "models/basics.html#Taking-Gradients-1", + "page": "Basics", + "title": "Taking Gradients", + "category": "section", + "text": "Consider a simple linear regression, which tries to predict an output array y from an input x. (It's a good idea to follow this example in the Julia repl.)W = rand(2, 5)\nb = rand(2)\n\npredict(x) = W*x .+ b\nloss(x, y) = sum((predict(x) .- y).^2)\n\nx, y = rand(5), rand(2) # Dummy data\nloss(x, y) # ~ 3To improve the prediction we can take the gradients of W and b with respect to the loss function and perform gradient descent. We could calculate gradients by hand, but Flux will do it for us if we tell it that W and b are trainable parameters.using Flux.Tracker: param, back!, data, grad\n\nW = param(W)\nb = param(b)\n\nl = loss(x, y)\n\nback!(l)loss(x, y) returns the same number, but it's now a tracked value that records gradients as it goes along. Calling back! then calculates the gradient of W and b. We can see what this gradient is, and modify W to train the model.grad(W)\n\nW.data .-= 0.1grad(W)\n\nloss(x, y) # ~ 2.5The loss has decreased a little, meaning that our prediction x is closer to the target y. If we have some data we can already try training the model.All deep learning in Flux, however complex, is a simple generalisation of this example. Of course, models can look very different – they might have millions of parameters or complex control flow, and there are ways to manage this complexity. Let's see what that looks like." +}, + +{ + "location": "models/basics.html#Building-Layers-1", + "page": "Basics", + "title": "Building Layers", + "category": "section", + "text": "It's common to create more complex models than the linear regression above. For example, we might want to have two linear layers with a nonlinearity like sigmoid (σ) in between them. In the above style we could write this as:W1 = param(rand(3, 5))\nb1 = param(rand(3))\nlayer1(x) = W1 * x .+ b1\n\nW2 = param(rand(2, 3))\nb2 = param(rand(2))\nlayer2(x) = W2 * x .+ b2\n\nmodel(x) = layer2(σ.(layer1(x)))\n\nmodel(rand(5)) # => 2-element vectorThis works but is fairly unwieldy, with a lot of repetition – especially as we add more layers. One way to factor this out is to create a function that returns linear layers.function linear(in, out)\n W = param(randn(out, in))\n b = param(randn(out))\n x -> W * x .+ b\nend\n\nlinear1 = linear(5, 3) # we can access linear1.W etc\nlinear2 = linear(3, 2)\n\nmodel(x) = linear2(σ.(linear1(x)))\n\nmodel(x) # => 2-element vectorAnother (equivalent) way is to create a struct that explicitly represents the affine layer.struct Affine\n W\n b\nend\n\nAffine(in::Integer, out::Integer) =\n Affine(param(randn(out, in)), param(randn(out)))\n\n# Overload call, so the object can be used as a function\n(m::Affine)(x) = m.W * x .+ m.b\n\na = Affine(10, 5)\n\na(rand(10)) # => 5-element vectorCongratulations! You just built the Dense layer that comes with Flux. Flux has many interesting layers available, but they're all things you could have built yourself very easily.(There is one small difference with Dense – for convenience it also takes an activation function, like Dense(10, 5, σ).)" +}, + +{ + "location": "models/basics.html#Stacking-It-Up-1", + "page": "Basics", + "title": "Stacking It Up", + "category": "section", + "text": "It's pretty common to write models that look something like:layer1 = Dense(10, 5, σ)\n# ...\nmodel(x) = layer3(layer2(layer1(x)))For long chains, it might be a bit more intuitive to have a list of layers, like this:using Flux\n\nlayers = [Dense(10, 5, σ), Dense(5, 2), softmax]\n\nmodel(x) = foldl((x, m) -> m(x), x, layers)\n\nmodel(rand(10)) # => 2-element vectorHandily, this is also provided for in Flux:model2 = Chain(\n Dense(10, 5, σ),\n Dense(5, 2),\n softmax)\n\nmodel2(rand(10)) # => 2-element vectorThis quickly starts to look like a high-level deep learning library; yet you can see how it falls out of simple abstractions, and we lose none of the power of Julia code.A nice property of this approach is that because \"models\" are just functions (possibly with trainable parameters), you can also see this as simple function composition.m = Dense(5, 2) ∘ Dense(10, 5, σ)\n\nm(rand(10))Likewise, Chain will happily work with any Julia function.m = Chain(x -> x^2, x -> x+1)\n\nm(5) # => 26" +}, + +{ + "location": "models/recurrence.html#", + "page": "Recurrence", + "title": "Recurrence", + "category": "page", + "text": "" +}, + +{ + "location": "models/recurrence.html#Recurrent-Models-1", + "page": "Recurrence", + "title": "Recurrent Models", + "category": "section", + "text": "" +}, + +{ + "location": "models/recurrence.html#Recurrent-Cells-1", + "page": "Recurrence", + "title": "Recurrent Cells", + "category": "section", + "text": "In the simple feedforward case, our model m is a simple function from various inputs xᵢ to predictions yᵢ. (For example, each x might be an MNIST digit and each y a digit label.) Each prediction is completely independent of any others, and using the same x will always produce the same y.y₁ = f(x₁)\ny₂ = f(x₂)\ny₃ = f(x₃)\n# ...Recurrent networks introduce a hidden state that gets carried over each time we run the model. The model now takes the old h as an input, and produces a new h as output, each time we run it.h = # ... initial state ...\ny₁, h = f(x₁, h)\ny₂, h = f(x₂, h)\ny₃, h = f(x₃, h)\n# ...Information stored in h is preserved for the next prediction, allowing it to function as a kind of memory. This also means that the prediction made for a given x depends on all the inputs previously fed into the model.(This might be important if, for example, each x represents one word of a sentence; the model's interpretation of the word \"bank\" should change if the previous input was \"river\" rather than \"investment\".)Flux's RNN support closely follows this mathematical perspective. The most basic RNN is as close as possible to a standard Dense layer, and the output and hidden state are the same. By convention, the hidden state is the first input and output.Wxh = randn(5, 10)\nWhh = randn(5, 5)\nb = randn(5)\n\nfunction rnn(h, x)\n h = tanh.(Wxh * x .+ Whh * h .+ b)\n return h, h\nend\n\nx = rand(10) # dummy data\nh = rand(5) # initial hidden state\n\nh, y = rnn(h, x)If you run the last line a few times, you'll notice the output y changing slightly even though the input x is the same.We sometimes refer to functions like rnn above, which explicitly manage state, as recurrent cells. There are various recurrent cells available, which are documented in the layer reference. The hand-written example above can be replaced with:using Flux\n\nrnn2 = Flux.RNNCell(10, 5)\n\nx = rand(10) # dummy data\nh = rand(5) # initial hidden state\n\nh, y = rnn2(h, x)" +}, + +{ + "location": "models/recurrence.html#Stateful-Models-1", + "page": "Recurrence", + "title": "Stateful Models", + "category": "section", + "text": "For the most part, we don't want to manage hidden states ourselves, but to treat our models as being stateful. Flux provides the Recur wrapper to do this.x = rand(10)\nh = rand(5)\n\nm = Flux.Recur(rnn, h)\n\ny = m(x)The Recur wrapper stores the state between runs in the m.state field.If you use the RNN(10, 5) constructor – as opposed to RNNCell – you'll see that it's simply a wrapped cell.julia> RNN(10, 5)\nRecur(RNNCell(Dense(15, 5)))" +}, + +{ + "location": "models/recurrence.html#Sequences-1", + "page": "Recurrence", + "title": "Sequences", + "category": "section", + "text": "Often we want to work with sequences of inputs, rather than individual xs.seq = [rand(10) for i = 1:10]With Recur, applying our model to each element of a sequence is trivial:m.(seq) # returns a list of 5-element vectorsThis works even when we've chain recurrent layers into a larger model.m = Chain(LSTM(10, 15), Dense(15, 5))\nm.(seq)" +}, + +{ + "location": "models/recurrence.html#Truncating-Gradients-1", + "page": "Recurrence", + "title": "Truncating Gradients", + "category": "section", + "text": "By default, calculating the gradients in a recurrent layer involves the entire history. For example, if we call the model on 100 inputs, calling back! will calculate the gradient for those 100 calls. If we then calculate another 10 inputs we have to calculate 110 gradients – this accumulates and quickly becomes expensive.To avoid this we can truncate the gradient calculation, forgetting the history.truncate!(m)Calling truncate! wipes the slate clean, so we can call the model with more inputs without building up an expensive gradient computation." +}, + +{ + "location": "models/layers.html#", + "page": "Layer Reference", + "title": "Layer Reference", + "category": "page", + "text": "" +}, + +{ + "location": "models/layers.html#Flux.Chain", + "page": "Layer Reference", + "title": "Flux.Chain", + "category": "Type", + "text": "Chain(layers...)\n\nChain multiple layers / functions together, so that they are called in sequence on a given input.\n\nm = Chain(x -> x^2, x -> x+1)\nm(5) == 26\n\nm = Chain(Dense(10, 5), Dense(5, 2))\nx = rand(10)\nm(x) == m[2](m[1](x))\n\nChain also supports indexing and slicing, e.g. m[2] or m[1:end-1]. m[1:3](x) will calculate the output of the first three layers.\n\n\n\n" +}, + +{ + "location": "models/layers.html#Flux.Dense", + "page": "Layer Reference", + "title": "Flux.Dense", + "category": "Type", + "text": "Dense(in::Integer, out::Integer, σ = identity)\n\nCreates a traditional Dense layer with parameters W and b.\n\ny = σ.(W * x .+ b)\n\nThe input x must be a vector of length in, or a batch of vectors represented as an in × N matrix. The out y will be a vector or batch of length in.\n\n\n\n" +}, + +{ + "location": "models/layers.html#Model-Layers-1", + "page": "Layer Reference", + "title": "Model Layers", + "category": "section", + "text": "Chain\nDense" +}, + +{ + "location": "training/optimisers.html#", + "page": "Optimisers", + "title": "Optimisers", + "category": "page", + "text": "" +}, + +{ + "location": "training/optimisers.html#Optimisers-1", + "page": "Optimisers", + "title": "Optimisers", + "category": "section", + "text": "Consider a simple linear regression. We create some dummy data, calculate a loss, and backpropagate to calculate gradients for the parameters W and b.W = param(rand(2, 5))\nb = param(rand(2))\n\npredict(x) = W*x .+ b\nloss(x, y) = sum((predict(x) .- y).^2)\n\nx, y = rand(5), rand(2) # Dummy data\nl = loss(x, y) # ~ 3\nback!(l)We want to update each parameter, using the gradient, in order to improve (reduce) the loss. Here's one way to do that:using Flux.Tracker: data, grad\n\nfunction update()\n η = 0.1 # Learning Rate\n for p in (W, b)\n x, Δ = data(p), grad(p)\n x .-= η .* Δ # Apply the update\n Δ .= 0 # Clear the gradient\n end\nendIf we call update, the parameters W and b will change and our loss should go down.There are two pieces here: one is that we need a list of trainable parameters for the model ([W, b] in this case), and the other is the update step. In this case the update is simply gradient descent (x .-= η .* Δ), but we might choose to do something more advanced, like adding momentum.In this case, getting the variables is trivial, but you can imagine it'd be more of a pain with some complex stack of layers.m = Chain(\n Dense(10, 5, σ),\n Dense(5, 2), softmax)Instead of having to write [m[1].W, m[1].b, ...], Flux provides a params function params(m) that returns a list of all parameters in the model for you.For the update step, there's nothing whatsoever wrong with writing the loop above – it'll work just fine – but Flux provides various optimisers that make it more convenient.opt = SGD([W, b], 0.1) # Gradient descent with learning rate 0.1\n\nopt()An optimiser takes a parameter list and returns a function that does the same thing as update above. We can pass either opt or update to our training loop, which will then run the optimiser after every mini-batch of data." +}, + +{ + "location": "training/training.html#", + "page": "Training", + "title": "Training", + "category": "page", + "text": "" +}, + +{ + "location": "training/training.html#Training-1", + "page": "Training", + "title": "Training", + "category": "section", + "text": "To actually train a model we need three things:A model loss function, that evaluates how well a model is doing given some input data.\nA collection of data points that will be provided to the loss function.\nAn optimiser that will update the model parameters appropriately.With these we can call Flux.train!:Flux.train!(modelLoss, data, opt)There are plenty of examples in the model zoo." +}, + +{ + "location": "training/training.html#Loss-Functions-1", + "page": "Training", + "title": "Loss Functions", + "category": "section", + "text": "The loss that we defined in basics is completely valid for training. We can also define a loss in terms of some model:m = Chain(\n Dense(784, 32, σ),\n Dense(32, 10), softmax)\n\n# Model loss function\nloss(x, y) = Flux.mse(m(x), y)The loss will almost always be defined in terms of some cost function that measures the distance of the prediction m(x) from the target y. Flux has several of these built in, like mse for mean squared error or logloss for cross entropy loss, but you can calculate it however you want." +}, + +{ + "location": "training/training.html#Callbacks-1", + "page": "Training", + "title": "Callbacks", + "category": "section", + "text": "train! takes an additional argument, cb, that's used for callbacks so that you can observe the training process. For example:train!(loss, data, opt, cb = () -> println(\"training\"))Callbacks are called for every batch of training data. You can slow this down using Flux.throttle(f, timeout) which prevents f from being called more than once every timeout seconds.A more typical callback might look like this:test_x, test_y = # ... create single batch of test data ...\nevalcb() = @show(loss(test_x, test_y))\n\nFlux.train!(loss, data, opt,\n cb = throttle(evalcb, 5))" +}, + +{ + "location": "data/onehot.html#", + "page": "One-Hot Encoding", + "title": "One-Hot Encoding", + "category": "page", + "text": "" +}, + +{ + "location": "data/onehot.html#One-Hot-Encoding-1", + "page": "One-Hot Encoding", + "title": "One-Hot Encoding", + "category": "section", + "text": "It's common to encode categorical variables (like true, false or cat, dog) in \"one-of-k\" or \"one-hot\" form. Flux provides the onehot function to make this easy.julia> using Flux: onehot\n\njulia> onehot(:b, [:a, :b, :c])\n3-element Flux.OneHotVector:\n false\n true\n false\n\njulia> onehot(:c, [:a, :b, :c])\n3-element Flux.OneHotVector:\n false\n false\n trueThe inverse is argmax (which can take a general probability distribution, as well as just booleans).julia> argmax(ans, [:a, :b, :c])\n:c\n\njulia> argmax([true, false, false], [:a, :b, :c])\n:a\n\njulia> argmax([0.3, 0.2, 0.5], [:a, :b, :c])\n:c" +}, + +{ + "location": "data/onehot.html#Batches-1", + "page": "One-Hot Encoding", + "title": "Batches", + "category": "section", + "text": "onehotbatch creates a batch (matrix) of one-hot vectors, and argmax treats matrices as batches.julia> using Flux: onehotbatch\n\njulia> onehotbatch([:b, :a, :b], [:a, :b, :c])\n3×3 Flux.OneHotMatrix:\n false true false\n true false true\n false false false\n\njulia> onecold(ans, [:a, :b, :c])\n3-element Array{Symbol,1}:\n :b\n :a\n :bNote that these operations returned OneHotVector and OneHotMatrix rather than Arrays. OneHotVectors behave like normal vectors but avoid any unnecessary cost compared to using an integer index directly. For example, multiplying a matrix with a one-hot vector simply slices out the relevant row of the matrix under the hood." +}, + +{ + "location": "gpu.html#", + "page": "GPU Support", + "title": "GPU Support", + "category": "page", + "text": "" +}, + +{ + "location": "gpu.html#GPU-Support-1", + "page": "GPU Support", + "title": "GPU Support", + "category": "section", + "text": "Support for array operations on other hardware backends, like GPUs, is provided by external packages like CuArrays and CLArrays. Flux doesn't care what array type you use, so we can just plug these in without any other changes.For example, we can use CuArrays (with the cu converter) to run our basic example on an NVIDIA GPU.using CuArrays\n\nW = cu(rand(2, 5)) # a 2×5 CuArray\nb = cu(rand(2))\n\npredict(x) = W*x .+ b\nloss(x, y) = sum((predict(x) .- y).^2)\n\nx, y = cu(rand(5)), cu(rand(2)) # Dummy data\nloss(x, y) # ~ 3Note that we convert both the parameters (W, b) and the data set (x, y) to cuda arrays. Taking derivatives and training works exactly as before.If you define a structured model, like a Dense layer or Chain, you just need to convert the internal parameters. Flux provides mapparams, which allows you to alter all parameters of a model at once.d = Dense(10, 5, σ)\nd = mapparams(cu, d)\nd.W # Tracked CuArray\nd(cu(rand(10))) # CuArray output\n\nm = Chain(Dense(10, 5, σ), Dense(5, 2), softmax)\nm = mapparams(cu, m)\nd(cu(rand(10)))The mnist example contains the code needed to run the model on the GPU; just uncomment the lines after using CuArrays." +}, + +{ + "location": "contributing.html#", + "page": "Contributing & Help", + "title": "Contributing & Help", + "category": "page", + "text": "" +}, + +{ + "location": "contributing.html#Contributing-and-Help-1", + "page": "Contributing & Help", + "title": "Contributing & Help", + "category": "section", + "text": "If you need help, please ask on the Julia forum, the slack (channel #machine-learning), or Flux's Gitter.Right now, the best way to help out is to try out the examples and report any issues or missing features as you find them. The second best way is to help us spread the word, perhaps by starring the repo.If you're interested in hacking on Flux, most of the code is pretty straightforward. Adding new layer definitions or cost functions is simple using the Flux DSL itself, and things like data utilities and training processes are all plain Julia code.If you get stuck or need anything, let us know!" +}, + +]} diff --git a/v0.3.2/siteinfo.js b/v0.3.2/siteinfo.js new file mode 100644 index 00000000..b2defe14 --- /dev/null +++ b/v0.3.2/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "v0.3.2"; diff --git a/v0.3.2/training/optimisers.html b/v0.3.2/training/optimisers.html new file mode 100644 index 00000000..c6ad6fb2 --- /dev/null +++ b/v0.3.2/training/optimisers.html @@ -0,0 +1,30 @@ + +Optimisers · Flux

            Optimisers

            Optimisers

            Consider a simple linear regression. We create some dummy data, calculate a loss, and backpropagate to calculate gradients for the parameters W and b.

            W = param(rand(2, 5))
            +b = param(rand(2))
            +
            +predict(x) = W*x .+ b
            +loss(x, y) = sum((predict(x) .- y).^2)
            +
            +x, y = rand(5), rand(2) # Dummy data
            +l = loss(x, y) # ~ 3
            +back!(l)

            We want to update each parameter, using the gradient, in order to improve (reduce) the loss. Here's one way to do that:

            using Flux.Tracker: data, grad
            +
            +function update()
            +  η = 0.1 # Learning Rate
            +  for p in (W, b)
            +    x, Δ = data(p), grad(p)
            +    x .-= η .* Δ # Apply the update
            +    Δ .= 0       # Clear the gradient
            +  end
            +end

            If we call update, the parameters W and b will change and our loss should go down.

            There are two pieces here: one is that we need a list of trainable parameters for the model ([W, b] in this case), and the other is the update step. In this case the update is simply gradient descent (x .-= η .* Δ), but we might choose to do something more advanced, like adding momentum.

            In this case, getting the variables is trivial, but you can imagine it'd be more of a pain with some complex stack of layers.

            m = Chain(
            +  Dense(10, 5, σ),
            +  Dense(5, 2), softmax)

            Instead of having to write [m[1].W, m[1].b, ...], Flux provides a params function params(m) that returns a list of all parameters in the model for you.

            For the update step, there's nothing whatsoever wrong with writing the loop above – it'll work just fine – but Flux provides various optimisers that make it more convenient.

            opt = SGD([W, b], 0.1) # Gradient descent with learning rate 0.1
            +
            +opt()

            An optimiser takes a parameter list and returns a function that does the same thing as update above. We can pass either opt or update to our training loop, which will then run the optimiser after every mini-batch of data.

            diff --git a/v0.3.2/training/training.html b/v0.3.2/training/training.html new file mode 100644 index 00000000..db7baac2 --- /dev/null +++ b/v0.3.2/training/training.html @@ -0,0 +1,18 @@ + +Training · Flux

            Training

            Training

            To actually train a model we need three things:

            • A model loss function, that evaluates how well a model is doing given some input data.

            • A collection of data points that will be provided to the loss function.

            • An optimiser that will update the model parameters appropriately.

            With these we can call Flux.train!:

            Flux.train!(modelLoss, data, opt)

            There are plenty of examples in the model zoo.

            Loss Functions

            The loss that we defined in basics is completely valid for training. We can also define a loss in terms of some model:

            m = Chain(
            +  Dense(784, 32, σ),
            +  Dense(32, 10), softmax)
            +
            +# Model loss function
            +loss(x, y) = Flux.mse(m(x), y)

            The loss will almost always be defined in terms of some cost function that measures the distance of the prediction m(x) from the target y. Flux has several of these built in, like mse for mean squared error or logloss for cross entropy loss, but you can calculate it however you want.

            Callbacks

            train! takes an additional argument, cb, that's used for callbacks so that you can observe the training process. For example:

            train!(loss, data, opt, cb = () -> println("training"))

            Callbacks are called for every batch of training data. You can slow this down using Flux.throttle(f, timeout) which prevents f from being called more than once every timeout seconds.

            A more typical callback might look like this:

            test_x, test_y = # ... create single batch of test data ...
            +evalcb() = @show(loss(test_x, test_y))
            +
            +Flux.train!(loss, data, opt,
            +            cb = throttle(evalcb, 5))
            diff --git a/versions.js b/versions.js index 3eaff596..ba692fa4 100644 --- a/versions.js +++ b/versions.js @@ -4,6 +4,7 @@ var DOC_VERSIONS = [ "release-0.3", "release-0.2", "release-0.1", + "v0.3.2", "v0.3.1", "v0.3.0", "v0.2.1",