diff --git a/latest/models/layers.html b/latest/models/layers.html index 934fe185..79da5315 100644 --- a/latest/models/layers.html +++ b/latest/models/layers.html @@ -11,15 +11,10 @@ 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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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.

σ
-relu
-leakyrelu
-elu
-swish
-softmax
+ -0.00449443source

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.

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NNlib.relu — Function.
relu(x) = max(0, x)

Rectified Linear Unit activation function.

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NNlib.leakyrelu — Function.
leakyrelu(x) = max(0.01x, x)

Leaky Rectified Linear Unit activation function.

You can also specify the coefficient explicitly, e.g. leakyrelu(x, 0.01).

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NNlib.elu — Function.
elu(x; α = 1) = x > 0 ? x : α * (exp(x) - one(x)

Exponential Linear Unit activation function. See Fast and Accurate Deep Network Learning by Exponential Linear Units

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NNlib.swish — Function.
swish(x) = x * σ(x)

Self-gated actvation function.

See Swish: a Self-Gated Activation Function.

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diff --git a/latest/search_index.js b/latest/search_index.js index b1a56ec4..1c9b6a26 100644 --- a/latest/search_index.js +++ b/latest/search_index.js @@ -144,12 +144,52 @@ var documenterSearchIndex = {"docs": [ "text": "These core layers form the foundation of almost all neural networks.Chain\nDense" }, +{ + "location": "models/layers.html#NNlib.σ", + "page": "Layer Reference", + "title": "NNlib.σ", + "category": "Function", + "text": "σ(x) = 1 / (1 + exp(-x))\n\nClassic sigmoid activation function.\n\n\n\n" +}, + +{ + "location": "models/layers.html#NNlib.relu", + "page": "Layer Reference", + "title": "NNlib.relu", + "category": "Function", + "text": "relu(x) = max(0, x)\n\nRectified Linear Unit activation function.\n\n\n\n" +}, + +{ + "location": "models/layers.html#NNlib.leakyrelu", + "page": "Layer Reference", + "title": "NNlib.leakyrelu", + "category": "Function", + "text": "leakyrelu(x) = max(0.01x, x)\n\nLeaky Rectified Linear Unit activation function.\n\nYou can also specify the coefficient explicitly, e.g. leakyrelu(x, 0.01).\n\n\n\n" +}, + +{ + "location": "models/layers.html#NNlib.elu", + "page": "Layer Reference", + "title": "NNlib.elu", + "category": "Function", + "text": "elu(x; α = 1) = x > 0 ? x : α * (exp(x) - one(x)\n\nExponential Linear Unit activation function. See Fast and Accurate Deep Network Learning by Exponential Linear Units\n\n\n\n" +}, + +{ + "location": "models/layers.html#NNlib.swish", + "page": "Layer Reference", + "title": "NNlib.swish", + "category": "Function", + "text": "swish(x) = x * σ(x)\n\nSelf-gated actvation function.\n\nSee Swish: a Self-Gated Activation Function.\n\n\n\n" +}, + { "location": "models/layers.html#Activation-Functions-1", "page": "Layer Reference", "title": "Activation Functions", "category": "section", - "text": "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.σ\nrelu\nleakyrelu\nelu\nswish\nsoftmax" + "text": "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.σ\nrelu\nleakyrelu\nelu\nswish" }, { diff --git a/latest/training/optimisers.html b/latest/training/optimisers.html index 0c7b1dc9..239b3f62 100644 --- a/latest/training/optimisers.html +++ b/latest/training/optimisers.html @@ -27,4 +27,4 @@ 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 = 1; decay = 0)

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

Supports decayed learning rate decay if the decay argument is provided.

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Flux.Optimise.Momentum — Function.
Momentum(params, ρ, decay = 0)

SGD with momentum ρ and optional learning rate decay.

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Flux.Optimise.Nesterov — Function.
Nesterov(params, ρ, decay = 0)

SGD with Nesterov momentum ρ and optional learning rate decay.

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Flux.Optimise.RMSProp — Function.
RMSProp(params; η = 0.001, ρ = 0.9, ϵ = 1e-8, decay = 0)

RMSProp optimiser. Parameters other than learning rate don't need tuning. Often a good choice for recurrent networks.

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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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Flux.Optimise.ADAGrad — Function.
ADAGrad(params; η = 0.01, ϵ = 1e-8, decay = 0)

ADAGrad optimiser. Parameters don't need tuning.

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Flux.Optimise.ADADelta — Function.
ADADelta(params; η = 0.01, ρ = 0.95, ϵ = 1e-8, decay = 0)

ADADelta optimiser. Parameters don't need tuning.

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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 = 1; decay = 0)

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

Supports decayed learning rate decay if the decay argument is provided.

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Flux.Optimise.Momentum — Function.
Momentum(params, ρ, decay = 0)

SGD with momentum ρ and optional learning rate decay.

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Flux.Optimise.Nesterov — Function.
Nesterov(params, ρ, decay = 0)

SGD with Nesterov momentum ρ and optional learning rate decay.

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Flux.Optimise.RMSProp — Function.
RMSProp(params; η = 0.001, ρ = 0.9, ϵ = 1e-8, decay = 0)

RMSProp optimiser. Parameters other than learning rate don't need tuning. Often a good choice for recurrent networks.

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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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Flux.Optimise.ADAGrad — Function.
ADAGrad(params; η = 0.01, ϵ = 1e-8, decay = 0)

ADAGrad optimiser. Parameters don't need tuning.

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Flux.Optimise.ADADelta — Function.
ADADelta(params; η = 0.01, ρ = 0.95, ϵ = 1e-8, decay = 0)

ADADelta optimiser. Parameters don't need tuning.

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