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.

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))
Array{Float64,1}:
  0.00257447
  -0.00449443

Conv(size, in=>out)
Conv(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.

Example: Applying Conv layer to a 1-channel input using a 2x2 window size, giving us a 16-channel output. Output is activated with ReLU.

size = (2,2)
in = 1
out = 16
Conv((2, 2), 1=>16, relu)

Data should be stored in WHCN order (width, height, # channels, batch size). In other words, a 100×100 RGB image would be a 100×100×3×1 array, and a batch of 50 would be a 100×100×3×50 array.

Takes the keyword arguments pad, stride and dilation.

MaxPool(k)

Max pooling layer. k stands for the size of the window for each dimension of the input.

Takes the keyword arguments pad and stride.

GlobalMaxPool()

Global max pooling layer.

Transforms (w,h,c,b)-shaped input into (1,1,c,b)-shaped output, by performing max pooling on the complete (w,h)-shaped feature maps.

MeanPool(k)

Mean pooling layer. k stands for the size of the window for each dimension of the input.

Takes the keyword arguments pad and stride.

GlobalMeanPool()

Global mean pooling layer.

Transforms (w,h,c,b)-shaped input into (1,1,c,b)-shaped output, by performing mean pooling on the complete (w,h)-shaped feature maps.

DepthwiseConv(size, in=>out)
DepthwiseConv(size, in=>out, relu)

Depthwise convolutional layer. size should be a tuple like (2, 2). in and out specify the number of input and output channels respectively. Note that out must be an integer multiple of in.

Data should be stored in WHCN order (width, height, # channels, # batches). In other words, a 100×100 RGB image would be a 100×100×3×1 array, and a batch of 50 would be a 100×100×3×50 array.

Takes the keyword arguments pad, stride and dilation.

ConvTranspose(size, in=>out)
ConvTranspose(size, in=>out, relu)

Standard convolutional transpose 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 (width, height, # channels, # batches). In other words, a 100×100 RGB image would be a 100×100×3×1 array, and a batch of 50 would be a 100×100×3×50 array.

Takes the keyword arguments pad, stride and dilation.

CrossCor(size, in=>out)
CrossCor(size, in=>out, relu)

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

Example: Applying CrossCor layer to a 1-channel input using a 2x2 window size, giving us a 16-channel output. Output is activated with ReLU.

size = (2,2)
in = 1
out = 16
CrossCor((2, 2), 1=>16, relu)

Data should be stored in WHCN order (width, height, # channels, # batches). In other words, a 100×100 RGB image would be a 100×100×3×1 array, and a batch of 50 would be a 100×100×3×50 array.

Takes the keyword arguments pad, stride and dilation.

flatten(x::AbstractArray)

Transforms (w,h,c,b)-shaped input into (w x h x c,b)-shaped output, by linearizing all values for each element in the batch.

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.

LSTM(in::Integer, out::Integer)

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.

GRU(in::Integer, out::Integer)

Gated Recurrent Unit layer. Behaves like an RNN but generally exhibits a longer memory span over sequences.

See this article for a good overview of the internals.

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

Maxout(over)

Maxout is a neural network layer, which has a number of internal layers, which all have the same input, and the maxout returns the elementwise maximium of the internal layers' outputs.

Maxout over linear dense layers satisfies the univeral approximation theorem.

Reference: Ian J. Goodfellow, David Warde-Farley, Mehdi Mirza, Aaron Courville, and Yoshua Bengio.

1. Maxout networks.

In Proceedings of the 30th International Conference on International Conference on Machine Learning - Volume 28 (ICML'13), Sanjoy Dasgupta and David McAllester (Eds.), Vol. 28. JMLR.org III-1319-III-1327. https://arxiv.org/pdf/1302.4389.pdf

SkipConnection(layers, connection)

Creates a Skip Connection, of a layer or Chain of consecutive layers plus a shortcut connection. The connection function will combine the result of the layers with the original input, to give the final output.

The simplest 'ResNet'-type connection is just SkipConnection(layer, +), and requires the output of the layers to be the same shape as the input. Here is a more complicated example:

m = Conv((3,3), 4=>7, pad=(1,1))
x = ones(5,5,4,10);
size(m(x)) == (5, 5, 7, 10)

sm = SkipConnection(m, (mx, x) -> cat(mx, x, dims=3))
size(sm(x)) == (5, 5, 11, 10)

BatchNorm(channels::Integer, σ = identity;
          initβ = zeros, initγ = ones,
          ϵ = 1e-8, momentum = .1)

Batch Normalization layer. The channels input should be the size of the channel dimension in your data (see below).

Given an array with N dimensions, call the N-1th the channel dimension. (For a batch of feature vectors this is just the data dimension, for WHCN images it's the usual channel dimension.)

BatchNorm computes the mean and variance for each each W×H×1×N slice and shifts them to have a new mean and variance (corresponding to the learnable, per-channel bias and scale parameters).

Use testmode! during inference.

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

Example:

m = Chain(
  Dense(28^2, 64),
  BatchNorm(64, relu),
  Dense(64, 10),
  BatchNorm(10),
  softmax)

Dropout(p, dims = :)

A Dropout layer. In the forward pass, applies the dropout function on the input.

Does nothing to the input once testmode! is true.

dropout(p, dims = :)

Dropout function. For each input, either sets that input to 0 (with probability p) or scales it by 1/(1-p). The dims argument is to specify the unbroadcasted dimensions, i.e. dims=1 does dropout along columns and dims=2 along rows. This is used as a regularisation, i.e. it reduces overfitting during training.

See also Dropout.

AlphaDropout(p)

A dropout layer. It is used in Self-Normalizing Neural Networks. (https://papers.nips.cc/paper/6698-self-normalizing-neural-networks.pdf) The AlphaDropout layer ensures that mean and variance of activations remains the same as before.

Does nothing to the input once testmode! is false.

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.

Group Normalization. This layer can outperform Batch-Normalization and Instance-Normalization.

GroupNorm(chs::Integer, G::Integer, λ = identity;
          initβ = (i) -> zeros(Float32, i), initγ = (i) -> ones(Float32, i),
          ϵ = 1f-5, momentum = 0.1f0)

$chs$ is the number of channels, the channel dimension of your input. For an array of N dimensions, the (N-1)th index is the channel dimension.

$G$ is the number of groups along which the statistics would be computed. The number of channels must be an integer multiple of the number of groups.

Use testmode! during inference.

Example:

m = Chain(Conv((3,3), 1=>32, leakyrelu;pad = 1),
          GroupNorm(32,16)) # 32 channels, 16 groups (G = 16), thus 2 channels per group used

Link : https://arxiv.org/pdf/1803.08494.pdf

testmode!(m, mode = true)

Set a layer or model's test mode (see below). Using :auto mode will treat any gradient computation as training.

Note: if you manually set a model into test mode, you need to manually place it back into train mode during training phase.

Possible values include:

• false for training
• true for testing
• :auto or nothing for Flux to detect the mode automatically

trainmode!(m, mode = true)

Set a layer of model's train mode (see below). Symmetric to testmode! (i.e. `trainmode!(m, mode) == testmode!(m, !mode)).

Note: if you manually set a model into train mode, you need to manually place it into test mode during testing phase.

Possible values include:

• true for training
• false for testing
• :auto or nothing for Flux to detect the mode automatically

mae(ŷ, y)

Return the mean of absolute error sum(abs.(ŷ .- y)) / length(y)

mse(ŷ, y)

Return the mean squared error sum((ŷ .- y).^2) / length(y).

msle(ŷ, y; ϵ=eps(eltype(ŷ)))

Returns the mean of the squared logarithmic errors sum((log.(ŷ .+ ϵ) .- log.(y .+ ϵ)).^2) / length(y). The ϵ term provides numerical stability.

This error penalizes an under-predicted estimate greater than an over-predicted estimate.

huber_loss(ŷ, y; δ=1.0)

Computes the mean of the Huber loss given the prediction ŷ and true values y. By default, δ is set to 1.0.

                | 0.5*|ŷ - y|,   for |ŷ - y| <= δ
  Hubber loss = |
                |  δ*(|ŷ - y| - 0.5*δ),  otherwise

Huber Loss.

crossentropy(ŷ, y; weight=1)

Return the crossentropy computed as -sum(y .* log.(ŷ) .* weight) / size(y, 2).

See also logitcrossentropy, binarycrossentropy.

logitcrossentropy(ŷ, y; weight=1)

Return the crossentropy computed after a softmax operation:

-sum(y .* logsoftmax(ŷ) .* weight) / size(y, 2)

See also crossentropy, binarycrossentropy.

binarycrossentropy(ŷ, y; ϵ=eps(ŷ))

Return -y*log(ŷ + ϵ) - (1-y)*log(1-ŷ + ϵ). The ϵ term provides numerical stability.

Typically, the prediction ŷ is given by the output of a sigmoid activation.

logitbinarycrossentropy(ŷ, y)

logitbinarycrossentropy(ŷ, y) is mathematically equivalent to binarycrossentropy(σ(ŷ), y) but it is more numerically stable.

See also binarycrossentropy, sigmoid, logsigmoid.

kldivergence(ŷ, y)

KLDivergence is a measure of how much one probability distribution is different from the other. It is always non-negative and zero only when both the distributions are equal everywhere.

KL Divergence.

poisson(ŷ, y)

Poisson loss function is a measure of how the predicted distribution diverges from the expected distribution. Returns sum(ŷ .- y .* log.(ŷ)) / size(y, 2)

Poisson Loss.

hinge(ŷ, y)

Measures the loss given the prediction ŷ and true labels y (containing 1 or -1). Returns sum((max.(0, 1 .- ŷ .* y))) / size(y, 2)

Hinge Loss See also squared_hinge.

squared_hinge(ŷ, y)

Computes squared hinge loss given the prediction ŷ and true labels y (conatining 1 or -1). Returns sum((max.(0, 1 .- ŷ .* y)).^2) / size(y, 2)

See also hinge.

dice_coeff_loss(ŷ, y; smooth=1)

Loss function used in Image Segmentation. Calculates loss based on dice coefficient. Similar to F1_score. Returns 1 - 2*sum(|ŷ .* y| + smooth) / (sum(ŷ.^2) + sum(y.^2) + smooth)

V-Net: Fully Convolutional Neural Networks forVolumetric Medical Image Segmentation

tversky_loss(ŷ, y; β=0.7)

Used with imbalanced data to give more weightage to False negatives. Larger β weigh recall higher than precision (by placing more emphasis on false negatives) Returns 1 - sum(|y .* ŷ| + 1) / (sum(y .* ŷ + β*(1 .- y) .* ŷ + (1 - β)*y .* (1 .- ŷ)) + 1)

Tversky loss function for image segmentation using 3D fully convolutional deep networks