diff --git a/latest/models/layers.html b/latest/models/layers.html index 25d64dfb..64141f9e 100644 --- a/latest/models/layers.html +++ b/latest/models/layers.html @@ -11,20 +11,20 @@ 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.

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Flux.Dense — Type.
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 out.

julia> d = Dense(5, 2)
+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.

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Flux.Dense — Type.
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 out.

julia> d = Dense(5, 2)
 Dense(5, 2)
 
 julia> d(rand(5))
 Tracked 2-element Array{Float64,1}:
   0.00257447
-  -0.00449443
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Flux.Conv2D — Type.
Conv2D(size, in=>out)
-Conv2d(size, in=>out, relu)

Standard convolutional layer. size should be a tuple like (2, 2). in and out specify the number of input and output channels respectively.

Data should be stored in WHCN order. In other words, a 100×100 RGB image would be a 100×100×3 array, and a batch of 50 would be a 100×100×3×50 array.

Takes the keyword arguments pad and stride.

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Recurrent Layers

Much like the core layers above, but can be used to process sequence data (as well as other kinds of structured data).

Flux.RNN — Function.
RNN(in::Integer, out::Integer, σ = tanh)

The most basic recurrent layer; essentially acts as a Dense layer, but with the output fed back into the input each time step.

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Flux.LSTM — Function.
LSTM(in::Integer, out::Integer, σ = tanh)

Long Short Term Memory recurrent layer. Behaves like an RNN but generally exhibits a longer memory span over sequences.

See this article for a good overview of the internals.

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Flux.Recur — Type.
Recur(cell)

Recur takes a recurrent cell and makes it stateful, managing the hidden state in the background. cell should be a model of the form:

h, y = cell(h, x...)

For example, here's a recurrent network that keeps a running total of its inputs.

accum(h, x) = (h+x, x)
+  -0.00449443
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Flux.Conv2D — Type.
Conv2D(size, in=>out)
+Conv2d(size, in=>out, relu)

Standard convolutional layer. size should be a tuple like (2, 2). in and out specify the number of input and output channels respectively.

Data should be stored in WHCN order. In other words, a 100×100 RGB image would be a 100×100×3 array, and a batch of 50 would be a 100×100×3×50 array.

Takes the keyword arguments pad and stride.

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Recurrent Layers

Much like the core layers above, but can be used to process sequence data (as well as other kinds of structured data).

Flux.RNN — Function.
RNN(in::Integer, out::Integer, σ = tanh)

The most basic recurrent layer; essentially acts as a Dense layer, but with the output fed back into the input each time step.

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Flux.LSTM — Function.
LSTM(in::Integer, out::Integer, σ = tanh)

Long Short Term Memory recurrent layer. Behaves like an RNN but generally exhibits a longer memory span over sequences.

See this article for a good overview of the internals.

source
Flux.Recur — Type.
Recur(cell)

Recur takes a recurrent cell and makes it stateful, managing the hidden state in the background. cell should be a model of the form:

h, y = cell(h, x...)

For example, here's a recurrent network that keeps a running total of its inputs.

accum(h, x) = (h+x, x)
 rnn = Flux.Recur(accum, 0)
 rnn(2) # 2
 rnn(3) # 3
 rnn.state # 5
 rnn.(1:10) # apply to a sequence
-rnn.state # 60
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Activation Functions

Non-linearities that go between layers of your model. Most of these functions are defined in NNlib but are available by default in Flux.

Note that, unless otherwise stated, activation functions operate on scalars. To apply them to an array you can call σ.(xs), relu.(xs) and so on.

NNlib.σ — Function.
σ(x) = 1 / (1 + exp(-x))

Classic sigmoid activation function.

1 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀│
+rnn.state # 60
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Activation Functions

Non-linearities that go between layers of your model. Most of these functions are defined in NNlib but are available by default in Flux.

Note that, unless otherwise stated, activation functions operate on scalars. To apply them to an array you can call σ.(xs), relu.(xs) and so on.

NNlib.σ — Function.
σ(x) = 1 / (1 + exp(-x))

Classic sigmoid activation function.

1 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀│
   │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠉⠀⠀│
   │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀│
   │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
@@ -99,10 +99,10 @@ rnn.state # 60
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Normalisation & Regularisation

These layers don't affect the structure of the network but may improve training times or reduce overfitting.

Flux.testmode! — Function.
testmode!(m)
-testmode!(m, false)

Put layers like Dropout and BatchNorm into testing mode (or back to training mode with false).

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Flux.BatchNorm — Type.
BatchNorm(dims...; λ = identity,
+testmode!(m, false)

Put layers like Dropout and BatchNorm into testing mode (or back to training mode with false).

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Flux.BatchNorm — Type.
BatchNorm(dims...; λ = identity,
           initβ = zeros, initγ = ones, ϵ = 1e-8, momentum = .1)

Batch Normalization Layer for Dense layer.

See Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift

In the example of MNIST, in order to normalize the input of other layer, put the BatchNorm layer before activation function.

m = Chain(
   Dense(28^2, 64),
   BatchNorm(64, λ = relu),
   Dense(64, 10),
   BatchNorm(10),
-  softmax)
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Flux.Dropout — Type.
Dropout(p)

A Dropout layer. For each input, either sets that input to 0 (with probability p) or scales it by 1/(1-p). This is used as a regularisation, i.e. it reduces overfitting during training.

Does nothing to the input once in testmode!.

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Flux.LayerNorm — Type.
LayerNorm(h::Integer)

A normalisation layer designed to be used with recurrent hidden states of size h. Normalises the mean/stddev of each input before applying a per-neuron gain/bias.

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+ softmax)source
Flux.Dropout — Type.
Dropout(p)

A Dropout layer. For each input, either sets that input to 0 (with probability p) or scales it by 1/(1-p). This is used as a regularisation, i.e. it reduces overfitting during training.

Does nothing to the input once in testmode!.

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Flux.LayerNorm — Type.
LayerNorm(h::Integer)

A normalisation layer designed to be used with recurrent hidden states of size h. Normalises the mean/stddev of each input before applying a per-neuron gain/bias.

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diff --git a/latest/models/regularisation.html b/latest/models/regularisation.html index 5f9a4f06..d85a8b62 100644 --- a/latest/models/regularisation.html +++ b/latest/models/regularisation.html @@ -19,8 +19,6 @@ julia> sum(norm, params(m)) Dense(128, 32, relu), Dense(32, 10), softmax) -ps = params(m) - -loss(x, y) = crossentropy(m(x), y) + sum(norm, ps) +loss(x, y) = crossentropy(m(x), y) + sum(norm, params(m)) loss(rand(28^2), rand(10)) diff --git a/latest/search_index.js b/latest/search_index.js index 1247919c..775b6db7 100644 --- a/latest/search_index.js +++ b/latest/search_index.js @@ -133,7 +133,7 @@ var documenterSearchIndex = {"docs": [ "page": "Regularisation", "title": "Regularisation", "category": "section", - "text": "Applying regularisation to model parameters is straightforward. We just need to apply an appropriate regulariser, such as norm, to each model parameter and add the result to the overall loss.For example, say we have a simple regression.m = Dense(10, 5)\nloss(x, y) = crossentropy(softmax(m(x)), y)We can regularise this by taking the (L2) norm of the parameters, m.W and m.b.penalty() = norm(m.W) + norm(m.b)\nloss(x, y) = crossentropy(softmax(m(x)), y) + penalty()When working with layers, Flux provides the params function to grab all parameters at once. We can easily penalise everything with sum(norm, params).julia> params(m)\n2-element Array{Any,1}:\n param([0.355408 0.533092; … 0.430459 0.171498])\n param([0.0, 0.0, 0.0, 0.0, 0.0])\n\njulia> sum(norm, params(m))\n26.01749952921026 (tracked)Here's a larger example with a multi-layer perceptron.m = Chain(\n Dense(28^2, 128, relu),\n Dense(128, 32, relu),\n Dense(32, 10), softmax)\n\nps = params(m)\n\nloss(x, y) = crossentropy(m(x), y) + sum(norm, ps)\n\nloss(rand(28^2), rand(10))" + "text": "Applying regularisation to model parameters is straightforward. We just need to apply an appropriate regulariser, such as norm, to each model parameter and add the result to the overall loss.For example, say we have a simple regression.m = Dense(10, 5)\nloss(x, y) = crossentropy(softmax(m(x)), y)We can regularise this by taking the (L2) norm of the parameters, m.W and m.b.penalty() = norm(m.W) + norm(m.b)\nloss(x, y) = crossentropy(softmax(m(x)), y) + penalty()When working with layers, Flux provides the params function to grab all parameters at once. We can easily penalise everything with sum(norm, params).julia> params(m)\n2-element Array{Any,1}:\n param([0.355408 0.533092; … 0.430459 0.171498])\n param([0.0, 0.0, 0.0, 0.0, 0.0])\n\njulia> sum(norm, params(m))\n26.01749952921026 (tracked)Here's a larger example with a multi-layer perceptron.m = Chain(\n Dense(28^2, 128, relu),\n Dense(128, 32, relu),\n Dense(32, 10), softmax)\n\nloss(x, y) = crossentropy(m(x), y) + sum(norm, params(m))\n\nloss(rand(28^2), rand(10))" }, { diff --git a/latest/training/optimisers.html b/latest/training/optimisers.html index 2eaf0592..a4ebcd1f 100644 --- a/latest/training/optimisers.html +++ b/latest/training/optimisers.html @@ -24,4 +24,4 @@ end

If we call update, the parameters W 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() # Carry out the update, modifying `W` and `b`.

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.

Optimiser Reference

All optimisers return a function that, when called, will update the parameters passed to it.

Flux.Optimise.SGD — Function.
SGD(params, η = 0.1; decay = 0)

Classic gradient descent optimiser with learning rate η. For each parameter p and its gradient δp, this runs p -= η*δp.

Supports inverse decaying learning rate if the decay argument is provided.

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Flux.Optimise.Momentum — Function.
Momentum(params, η = 0.01; ρ = 0.9, decay = 0)

SGD with learning rate η, momentum ρ and optional learning rate inverse decay.

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Flux.Optimise.Nesterov — Function.
Nesterov(params, η = 0.01; ρ = 0.9, decay = 0)

SGD with learning rate η, Nesterov momentum ρ and optional learning rate inverse decay.

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Flux.Optimise.ADAM — Function.
ADAM(params, η = 0.001; β1 = 0.9, β2 = 0.999, ϵ = 1e-08, decay = 0)

ADAM optimiser.

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+opt() # Carry out the update, modifying `W` and `b`.

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.

Optimiser Reference

All optimisers return a function that, when called, will update the parameters passed to it.

Flux.Optimise.SGD — Function.
SGD(params, η = 0.1; decay = 0)

Classic gradient descent optimiser with learning rate η. For each parameter p and its gradient δp, this runs p -= η*δp.

Supports inverse decaying learning rate if the decay argument is provided.

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Flux.Optimise.Momentum — Function.
Momentum(params, η = 0.01; ρ = 0.9, decay = 0)

SGD with learning rate η, momentum ρ and optional learning rate inverse decay.

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Flux.Optimise.Nesterov — Function.
Nesterov(params, η = 0.01; ρ = 0.9, decay = 0)

SGD with learning rate η, Nesterov momentum ρ and optional learning rate inverse decay.

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Flux.Optimise.ADAM — Function.
ADAM(params, η = 0.001; β1 = 0.9, β2 = 0.999, ϵ = 1e-08, decay = 0)

ADAM optimiser.

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