Merge branch 'master' into batchnorm

docs/src/models/basics.md

@@ -151,3 +151,13 @@ m = Chain(x -> x^2, x -> x+1)
 
 m(5) # => 26
 ```
+
+## Layer helpers
+
+Flux provides a set of helpers for custom layers, which you can enable by calling
+
+```julia
+Flux.treelike(Affine)
+```
+
+This enables a useful extra set of functionality for our `Affine` layer, such as [collecting its parameters](../training/optimisers.md) or [moving it to the GPU](../gpu.md).

docs/src/models/layers.md

@@ -36,6 +36,8 @@ swish
 These layers don't affect the structure of the network but may improve training times or reduce overfitting.
 
 ```@docs
+Flux.testmode!
 BatchNorm
 Dropout
+LayerNorm
 ```

docs/src/training/optimisers.md

@@ -58,8 +58,5 @@ All optimisers return a function that, when called, will update the parameters p
 SGD
 Momentum
 Nesterov
-RMSProp
 ADAM
-ADAGrad
-ADADelta
 ```

src/Flux.jl

@@ -7,12 +7,13 @@ module Flux
 using Juno, Requires
 using Lazy: @forward
 
-export BatchNorm, Chain, Dense, RNN, LSTM, Dropout,
+export Chain, Dense, RNN, LSTM,
-  SGD, ADAM, Momentum, Nesterov,
+  Dropout, LayerNorm, BatchNorm,
+  SGD, ADAM, Momentum, Nesterov, AMSGrad,
   param, params, mapleaves
 
 using NNlib
-export σ, relu, leakyrelu, elu, swish, softmax
+export σ, sigmoid, relu, leakyrelu, elu, swish, softmax
 
 include("tracker/Tracker.jl")
 using .Tracker
@@ -22,7 +23,7 @@ using .Optimise
 
 include("utils.jl")
 include("onehot.jl")
-include("tree.jl")
+include("treelike.jl")
 
 include("layers/stateless.jl")
 include("layers/basic.jl")
@@ -31,4 +32,6 @@ include("layers/normalisation.jl")
 
 include("data/Data.jl")
 
+include("batches/Batches.jl")
+
 end # module

src/batches/Batches.jl

@@ -0,0 +1,7 @@
+module Batches
+
+import ..Flux
+
+include("batch.jl")
+
+end

src/batches/batch.jl

@@ -0,0 +1,8 @@
+struct Batch{T,A,M}
+  data::A
+  mask::M
+end
+
+Batch{T}(data, mask) where T = Batch{T,typeof(data),typeof(mask)}(data, mask)
+
+Batch(xs) = Batch{typeof(first(xs))}(Flux.batch(xs),trues(length(xs)))

src/data/cmudict.jl

@@ -33,7 +33,7 @@ function rawdict()
        filter(!isempty, split.(split(readstring(deps("CMUDict", "cmudict")), "\n"))))
 end
 
-validword(s) = ismatch(r"^[\w-\.]+$", s)
+validword(s) = ismatch(r"^[\w\-\.]+$", s)
 
 cmudict() = filter((s, ps) -> validword(s), rawdict())
 

src/layers/basic.jl

@@ -78,3 +78,32 @@ function Base.show(io::IO, l::Dense)
   l.σ == identity || print(io, ", ", l.σ)
   print(io, ")")
 end
+
+"""
+    Diagonal(in::Integer)
+
+Creates an element-wise linear transformation layer with learnable
+vectors `α` and `β`:
+
+    y = α .* x .+ β
+
+The input `x` must be a array where `size(x, 1) == in`.
+"""
+struct Diagonal{T}
+  α::T
+  β::T
+end
+
+Diagonal(in::Integer; initα = ones, initβ = zeros) =
+  Diagonal(param(initα(in)), param(initβ(in)))
+
+treelike(Diagonal)
+
+function (a::Diagonal)(x)
+  α, β = a.α, a.β
+  α.*x .+ β
+end
+
+function Base.show(io::IO, l::Diagonal)
+  print(io, "Diagonal(", length(l.α), ")")
+end

src/layers/normalisation.jl

@@ -44,6 +44,29 @@ end
 
 _testmode!(a::Dropout, test) = (a.active = !test)
 
+"""
+
+    LayerNorm(h::Integer)
+
+A [normalisation layer](https://arxiv.org/pdf/1607.06450.pdf) 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.
+"""
+struct LayerNorm{T}
+  diag::Diagonal{T}
+end
+
+LayerNorm(h::Integer) =
+  LayerNorm(Diagonal(h))
+
+treelike(LayerNorm)
+
+(a::LayerNorm)(x) = a.diag(normalise(x))
+
+function Base.show(io::IO, l::LayerNorm)
+  print(io, "LayerNorm(", length(l.diag.α), ")")
+end
+
 """
     BatchNorm(dims...; λ = identity,
               initβ = zeros, initγ = ones, ϵ = 1e-8, momentum = .1)
@@ -65,8 +88,6 @@ julia> m = Chain(
   BatchNorm(10),
   softmax)
 Chain(Dense(784, 64), BatchNorm(64, λ = NNlib.relu), Dense(64, 10), BatchNorm(10), NNlib.softmax)
-
-julia> opt = SGD(params(m), 10, decay = .1)  # a crazy learning rate
 ```
 """
 mutable struct BatchNorm{F,V,N}

src/layers/stateless.jl

@@ -1,14 +1,27 @@
+using NNlib: log_fast
+
 # Cost functions
 
 mse(ŷ, y) = sum((ŷ .- y).^2)/length(y)
 
 crossentropy(ŷ::AbstractVecOrMat, y::AbstractVecOrMat) =
-  -sum(y .* log.(ŷ)) / size(y, 2)
+  -sum(y .* log_fast.(ŷ)) / size(y, 2)
 
 @deprecate logloss(x, y) crossentropy(x, y)
 
 function logitcrossentropy(logŷ::AbstractVecOrMat, y::AbstractVecOrMat)
   logŷ = logŷ .- maximum(logŷ, 1)
-  ypred = logŷ .- log.(sum(exp.(logŷ), 1))
+  ypred = logŷ .- log_fast.(sum(exp.(logŷ), 1))
   -sum(y .* ypred) / size(y, 2)
 end
+
+"""
+    normalise(x::AbstractVecOrMat)
+
+Normalise each column of `x` to mean 0 and standard deviation 1.
+"""
+function normalise(x::AbstractVecOrMat)
+  μ′ = mean(x, 1)
+  σ′ = std(x, 1, mean = μ′)
+  return (x .- μ′) ./ σ′
+end

src/onehot.jl

@@ -1,3 +1,5 @@
+import Base: *
+
 struct OneHotVector <: AbstractVector{Bool}
   ix::UInt32
   of::UInt32
@@ -7,7 +9,7 @@ Base.size(xs::OneHotVector) = (Int64(xs.of),)
 
 Base.getindex(xs::OneHotVector, i::Integer) = i == xs.ix
 
-Base.:*(A::AbstractMatrix, b::OneHotVector) = A[:, b.ix]
+A::AbstractMatrix * b::OneHotVector = A[:, b.ix]
 
 struct OneHotMatrix{A<:AbstractVector{OneHotVector}} <: AbstractMatrix{Bool}
   height::Int
@@ -18,7 +20,7 @@ Base.size(xs::OneHotMatrix) = (Int64(xs.height),length(xs.data))
 
 Base.getindex(xs::OneHotMatrix, i::Int, j::Int) = xs.data[j][i]
 
-Base.:*(A::AbstractMatrix, B::OneHotMatrix) = A[:, map(x->x.ix, B.data)]
+A::AbstractMatrix * B::OneHotMatrix = A[:, map(x->x.ix, B.data)]
 
 Base.hcat(x::OneHotVector, xs::OneHotVector...) = OneHotMatrix(length(x), [x, xs...])
 
@@ -40,10 +42,22 @@ function onehot(l, labels)
   OneHotVector(i, length(labels))
 end
 
-onehotbatch(ls, labels) = OneHotMatrix(length(labels), [onehot(l, labels) for l in ls])
+function onehot(l, labels, unk)
+  i = findfirst(labels, l)
+  i > 0 || return onehot(unk, labels)
+  OneHotVector(i, length(labels))
+end
+
+onehotbatch(ls, labels, unk...) =
+  OneHotMatrix(length(labels), [onehot(l, labels, unk...) for l in ls])
 
 argmax(y::AbstractVector, labels = 1:length(y)) =
   labels[findfirst(y, maximum(y))]
 
 argmax(y::AbstractMatrix, l...) =
   squeeze(mapslices(y -> argmax(y, l...), y, 1), 1)
+
+# Ambiguity hack
+
+a::TrackedMatrix * b::OneHotVector = TrackedArray(Tracker.Call(*, a, b))
+a::TrackedMatrix * b::OneHotMatrix = TrackedArray(Tracker.Call(*, a, b))

src/optimise/Optimise.jl

@@ -1,7 +1,7 @@
 module Optimise
 
 export update!, params, train!,
-  SGD, ADAM, Momentum, Nesterov, RMSProp, ADAGrad, ADADelta
+  SGD, ADAM, Momentum, Nesterov, RMSProp, ADAGrad, ADADelta, AMSGrad
 
 struct Param{T}
   x::T

src/optimise/interface.jl

@@ -1,5 +1,7 @@
 call(f, xs...) = f(xs...)
 
+# note for optimisers: set to zero
+# p.Δ at the end of the weigths update
 function optimiser(ps, fs...)
   ps = [Param(p) for p in ps]
   fs = map(ps) do p
@@ -10,64 +12,73 @@ function optimiser(ps, fs...)
 end
 
 """
-    SGD(params, η = 1; decay = 0)
+    SGD(params, η = 0.1; decay = 0)
 
-Classic gradient descent optimiser. For each parameter `p` and its
+Classic gradient descent optimiser with learning rate `η`.
-gradient `δp`, this runs `p -= η*δp`.
+For each parameter `p` and its gradient `δp`, this runs `p -= η*δp`.
 
-Supports decayed learning rate decay if the `decay` argument is provided.
+Supports inverse decaying learning rate if the `decay` argument is provided.
 """
-SGD(ps, η = 1; decay = 0) =
+SGD(ps, η = 0.1; decay = 0) =
-  optimiser(ps, p -> invdecay(p, decay), p -> descent(p, η))
+  optimiser(ps, p -> invdecay(p, decay), p -> descent(p,η))
 
 """
-    Momentum(params, ρ, decay = 0)
+    Momentum(params, η = 0.01; ρ = 0.9, decay = 0)
 
-SGD with momentum `ρ` and optional learning rate decay.
+SGD with learning rate  `η`, momentum `ρ` and optional learning rate inverse decay.
 """
-Momentum(ps, ρ; decay = 0) =
+Momentum(ps, η = 0.01; ρ = 0.9, decay = 0) =
-  optimiser(ps, p -> momentum(p, ρ), p -> invdecay(p, decay), p -> descent(p, 1))
+  optimiser(ps, p->invdecay(p,decay), p->momentum(p, ρ, η), p->descent(p,1))
 
 """
-    Nesterov(params, ρ, decay = 0)
+    Nesterov(params, η = 0.01; ρ = 0.9, decay = 0)
 
-SGD with Nesterov momentum `ρ` and optional learning rate decay.
+SGD with learning rate  `η`, Nesterov momentum `ρ` and optional learning rate inverse decay.
 """
-Nesterov(ps, ρ; decay = 0) =
+Nesterov(ps, η = 0.01; ρ = 0.9, decay = 0) =
-  optimiser(ps, p -> nesterov(p, ρ), p -> invdecay(p, decay), p -> descent(p, 1))
+  optimiser(ps, p->invdecay(p,decay), p->nesterov(p, ρ, η), p->descent(p,1))
 
 """
-    RMSProp(params; η = 0.001, ρ = 0.9, ϵ = 1e-8, decay = 0)
+    RMSProp(params, η = 0.001; ρ = 0.9, ϵ = 1e-8, decay = 0)
 
 [RMSProp](http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf)
 optimiser. Parameters other than learning rate don't need tuning. Often a good
 choice for recurrent networks.
 """
 RMSProp(ps, η = 0.001; ρ = 0.9, ϵ = 1e-8, decay = 0) =
-  optimiser(ps, p -> rmsprop(p; η = η, ρ = ρ, ϵ = ϵ), p -> invdecay(p, decay), p -> descent(p, 1))
+  optimiser(ps, p->rmsprop(p; η=η, ρ=ρ, ϵ=ϵ), p->invdecay(p,decay), p->descent(p,1))
 
 """
-    ADAM(params; η = 0.001, β1 = 0.9, β2 = 0.999, ϵ = 1e-08, decay = 0)
+    ADAM(params, η = 0.001; β1 = 0.9, β2 = 0.999, ϵ = 1e-08, decay = 0)
 
 [ADAM](https://arxiv.org/abs/1412.6980v8) optimiser.
 """
 ADAM(ps, η = 0.001; β1 = 0.9, β2 = 0.999, ϵ = 1e-08, decay = 0) =
-  optimiser(ps, p -> adam(p; η = η, β1 = β1, β2 = β2, ϵ = ϵ), p -> invdecay(p, decay), p -> descent(p, 1))
+  optimiser(ps, p->adam(p; η=η, β1=β1, β2=β2, ϵ=ϵ), p->invdecay(p,decay), p->descent(p,1))
 
 """
-    ADAGrad(params; η = 0.01, ϵ = 1e-8, decay = 0)
+    ADAGrad(params, η = 0.01; ϵ = 1e-8, decay = 0)
 
 [ADAGrad](http://www.jmlr.org/papers/volume12/duchi11a/duchi11a.pdf) optimiser.
 Parameters don't need tuning.
 """
-ADAGrad(ps; η = 0.01, ϵ = 1e-8, decay = 0) =
+ADAGrad(ps, η = 0.01; ϵ = 1e-8, decay = 0) =
-  optimiser(ps, p -> adagrad(p; η = η, ϵ = ϵ), p -> invdecay(p, decay), p -> descent(p, 1))
+  optimiser(ps, p->adagrad(p; η=η, ϵ=ϵ), p->invdecay(p,decay), p->descent(p,1))
 
 """
-    ADADelta(params; η = 0.01, ρ = 0.95, ϵ = 1e-8, decay = 0)
+    ADADelta(params; ρ = 0.9, ϵ = 1e-8, decay = 0)
 
 [ADADelta](http://arxiv.org/abs/1212.5701) optimiser. Parameters don't need
 tuning.
 """
-ADADelta(ps; η = 0.01, ρ = 0.95, ϵ = 1e-8, decay = 0) =
+ADADelta(ps; ρ = 0.9, ϵ = 1e-8, decay = 0) =
-  optimiser(ps, p -> adadelta(p; ρ = ρ, ϵ = ϵ), p -> invdecay(p, decay), p -> descent(p, 1))
+  optimiser(ps, p->adadelta(p; ρ=ρ, ϵ=ϵ), p->descent(p,1))
+
+"""
+    AMSGrad(params; η = 0.001, β1 = 0.9, β2 = 0.999, ϵ = 1e-08, decay = 0)
+
+[AMSGrad](https://openreview.net/forum?id=ryQu7f-RZ) optimiser. Parameters don't need
+tuning.
+"""
+AMSGrad(ps, η = 0.001; β1 = 0.9, β2 = 0.999, ϵ = 1e-08, decay = 0) =
+  optimiser(ps, p -> amsgrad(p; η = η, β1 = β1, β2 = β2, ϵ = ϵ), p -> invdecay(p, decay), p -> descent(p, 1))

src/optimise/optimisers.jl

@@ -1,74 +1,97 @@
 function descent(p::Param, η::Real)
   function ()
-    p.x .-= p.Δ .* η
+    @. p.x -= η * p.Δ
-    p.Δ .= 0
+    @. p.Δ = 0
   end
 end
 
-function momentum(p::Param, ρ::Real)
+function momentum(p::Param, ρ, η)
-  mo = zeros(p.x)
+  v = zeros(p.x)
-  () -> p.Δ .= mo .= ρ .* mo .+ p.Δ
-end
-
-function nesterov(p::Param, ρ::Real)
-  mo = zeros(p.x)
   function ()
-    mo  .= ρ .* mo .+ p.Δ
+    @. v = ρ * v - η * p.Δ
-    p.Δ .= ρ .* mo .+ p.Δ
+    @. p.Δ = -v
   end
 end
 
-function clip(p::Param, thresh::Real)
+# Ref. https://arxiv.org/pdf/1212.0901.pdf
-  () -> clamp!(p.Δ, -thresh, thresh)
+function nesterov(p::Param, ρ, η)
-end
+  v = zeros(p.x)
-
-function weightdecay(p::Param, γ::Real)
-  () -> p.Δ .+= γ .* p.x
-end
-
-function invdecay(p::Param, γ::Real)
-  n = 0
   function ()
-    p.Δ .*= 1 / (1 + γ * n)
+    d = @. ρ^2 * v - (1+ρ) * η * p.Δ
-    n += 1
+    @. v = ρ*v - η*p.Δ
+    @. p.Δ = -d
   end
 end
 
 function rmsprop(p::Param; η::Real = 0.001, ρ::Real = 0.9, ϵ::Real = 1e-8)
-  acc  = zeros(p.x) .+ ϵ
+  acc  = zeros(p.x)
   function ()
-    @. acc = ρ * acc + (1 - ρ) * p.Δ ^ 2
+    @. acc = ρ * acc + (1 - ρ) * p.Δ^2
-    @. p.Δ /= √acc * η
+    @. p.Δ *= η / (√acc + ϵ)
   end
 end
 
 function adagrad(p::Param; η::Real = 0.01, ϵ::Real = 1e-8)
   acc = zeros(p.x) .+ ϵ
   function ()
-    @. acc += p.Δ ^ 2
+    @. acc += p.Δ^2
-    @. p.Δ /= √acc * η
+    @. p.Δ *= η / √acc
   end
 end
 
-function adadelta(p::Param; ρ::Real = 0.95, ϵ::Real = 1e-8)
+function adadelta(p::Param; ρ::Real = 0.9, ϵ::Real = 1e-8)
-  acc = zeros(p.x) .+ ϵ
+  acc = zeros(p.x)
-  Δacc = zeros(p.x) .+ ϵ
+  Δacc = zeros(p.x)
   function ()
-    @. acc = ρ * acc + (1 - ρ) * p.Δ ^ 2
+    @. acc = ρ * acc + (1 - ρ) * p.Δ^2
-    @. p.Δ *= √Δacc / √acc
+    @. p.Δ *= √(Δacc + ϵ) / √(acc + ϵ)
-    @. Δacc = ρ * Δacc + (1 - ρ) * p.Δ ^ 2
+    @. Δacc = ρ * Δacc + (1 - ρ) * p.Δ^2
-  end
+   end
 end
 
 function adam(p::Param; η::Real = 0.001, β1::Real = 0.9, β2::Real = 0.999, ϵ::Real = 1e-8)
   mt = zeros(p.x)
-  vt = zeros(p.x) .+ ϵ
+  vt = zeros(p.x)
   β1p, β2p = β1, β2
   function ()
     @. mt = β1 * mt + (1 - β1) * p.Δ
-    @. vt = β2 * vt + (1 - β2) * p.Δ ^ 2
+    @. vt = β2 * vt + (1 - β2) * p.Δ^2
-    @. p.Δ = √(1 - β2p) / √(1 - β1p) * mt / √vt * η
+    @. p.Δ =  mt / (1 - β1p) / (√(vt / (1 - β2p)) + ϵ) * η
     β1p *= β1
     β2p *= β2
   end
 end
+
+function amsgrad(p::Param; η::Real = 0.001, β1::Real = 0.9, β2::Real = 0.999, ϵ::Real = 1e-8)
+  mt = zeros(p.x)
+  vt = zeros(p.x) .+ ϵ
+  v̂t = zeros(p.x) .+ ϵ
+  function ()
+    @. mt = β1 * mt + (1 - β1) * p.Δ
+    @. vt = β2 * vt + (1 - β2) * p.Δ ^ 2
+    @. v̂t = max.(v̂t, vt)
+    @. p.Δ = η * mt / √v̂t
+  end
+end
+
+clip(p::Param, thresh::Real) = () -> clamp!(p.Δ, -thresh, thresh)
+
+function expdecay(p::Param, γ::Real)
+  if γ != 0
+    return () -> p.Δ .+= γ .* p.x
+  else
+    return () -> nothing
+  end
+end
+
+function invdecay(p::Param, γ::Real)
+  if γ != 0
+    n = 0
+    return () -> begin
+      p.Δ .*= 1 / (1 + γ * n)
+      n += 1
+    end
+  else
+    return () -> nothing
+  end
+end

src/optimise/train.jl

@@ -1,8 +1,8 @@
 using Juno
 using Flux.Tracker: back!
 
-tocb(f) = f
+runall(f) = f
-tocb(fs::AbstractVector) = () -> foreach(call, fs)
+runall(fs::AbstractVector) = () -> foreach(call, fs)
 
 """
     train!(loss, data, opt; cb = () -> ())
@@ -11,10 +11,11 @@ For each datapoint `d` in `data` computes the gradient of `loss(d...)` through
 backpropagation and calls the optimizer `opt` and the callback `cb`
 (i.e. `opt()` and `cb()`).
 
-Multiple callbacks can be passed to `cb` as an array.
+Multiple optimisers and callbacks can be passed to `opt` and `cb` as arrays.
 """
 function train!(loss, data, opt; cb = () -> ())
-  cb = tocb(cb)
+  cb = runall(cb)
+  opt = runall(opt)
   @progress for d in data
     l = loss(d...)
     isinf(l.data[]) && error("Loss is Inf")

src/tracker/Tracker.jl

@@ -1,6 +1,6 @@
 module Tracker
 
-export TrackedArray, param, back!
+export TrackedArray, TrackedVector, TrackedMatrix, param, back!
 
 data(x) = x
 istracked(x) = false
@@ -38,7 +38,9 @@ TrackedArray(c::Call) = TrackedArray(c, c())
 
 TrackedArray(x::AbstractArray) = TrackedArray(Call(nothing), x, zeros(x))
 
-param(xs) = TrackedArray(AbstractFloat.(xs))
+isleaf(x::TrackedArray) = x.f == Call(nothing)
+
+param(xs) = TrackedArray(map(x -> AbstractFloat(x), xs))
 param(xs::Real) = param(fill(xs))
 
 istracked(x::TrackedArray) = true
@@ -56,6 +58,7 @@ Base.similar(x::TrackedArray, dims::Union{AbstractUnitRange,Integer}...) =
 
 Base.similar(x::TrackedArray, T::Type) = similar(data(x), T)
 
+# TODO decide if keeping both data and value. The problem is TrackedScalar
 value(x) = x
 value(x::TrackedArray) = data(x)
 value(x::TrackedScalar) = data(x)[]
@@ -67,6 +70,7 @@ Base.:(==)(x::TrackedArray, y::TrackedArray) = value(x) == value(x)
 Base.isless(x::TrackedScalar, y) = isless(value(x), y)
 Base.isless(x, y::TrackedScalar) = isless(x, value(y))
 Base.isless(x::TrackedScalar, y::TrackedScalar) = isless(value(x), value(y))
+Base.isapprox(x::TrackedScalar, y; kws...) = isapprox(x.data[], y; kws...)
 
 Base.show(io::IO, ::Type{TrackedArray{T,N,A}}) where {T,N,A<:AbstractArray{T,N}} =
   print(io, "TrackedArray{…,$A}")

src/tracker/lib.jl

@@ -1,5 +1,3 @@
-import Base: *
-
 toarray(xs::AbstractArray, ys::AbstractArray) = ys
 toarray(xs::AbstractArray, y) = similar(xs, typeof(y), ()) .= y
 
@@ -60,25 +58,55 @@ Base.findfirst(xs::TrackedArray, args...) = findfirst(xs.data, args...)
 Base.mean(xs::TrackedArray) = TrackedArray(Call(mean, xs), toarray(xs.data, mean(xs.data)))
 Base.mean(xs::TrackedArray, region) = TrackedArray(Call(mean, xs, region))
 
+# Hacks to get std working
+Base.std(x::TrackedArray; mean = Base.mean(x)) =
+  sqrt.(sum((x .- mean).^2) ./ (length(x)-1))
+Base.std(x::TrackedArray, dim; mean = Base.mean(x, dim)) =
+  sqrt.(sum((x .- mean).^2, dim) ./ (size(x, dim)-1))
+
 back(::typeof(mean), Δ, xs::TrackedArray) = back(xs, similar(xs.data) .= Δ ./ length(xs.data))
 back(::typeof(mean), Δ, xs::TrackedArray, region) =
   back(xs, similar(xs.data) .= Δ ./ prod(size(xs.data, region...)))
 
 # BLAS
 
-a::TrackedMatrix * b::TrackedMatrix  = TrackedArray(Call(*, a, b))
+for f in :[*, Ac_mul_B].args
-a::TrackedMatrix * b::AbstractMatrix = TrackedArray(Call(*, a, b))
+  @eval begin
-a::AbstractMatrix * b::TrackedMatrix = TrackedArray(Call(*, a, b))
+    import Base.$f
+    $f(a::TrackedMatrix, b::TrackedMatrix)  = TrackedArray(Call($f, a, b))
+    $f(a::TrackedMatrix, b::AbstractMatrix) = TrackedArray(Call($f, a, b))
+    $f(a::AbstractMatrix, b::TrackedMatrix) = TrackedArray(Call($f, a, b))
 
-a::TrackedMatrix * b::TrackedVector  = TrackedArray(Call(*, a, b))
+    $f(a::TrackedMatrix, b::TrackedVector)  = TrackedArray(Call($f, a, b))
-a::TrackedMatrix * b::AbstractVector = TrackedArray(Call(*, a, b))
+    $f(a::TrackedMatrix, b::AbstractVector) = TrackedArray(Call($f, a, b))
-a::AbstractMatrix * b::TrackedVector = TrackedArray(Call(*, a, b))
+    $f(a::AbstractMatrix, b::TrackedVector) = TrackedArray(Call($f, a, b))
+
+    $f(a::TrackedVector, b::TrackedVector)  = TrackedArray(Call($f, a, b))
+    $f(a::TrackedVector, b::AbstractVector) = TrackedArray(Call($f, a, b))
+    $f(a::AbstractVector, b::TrackedVector) = TrackedArray(Call($f, a, b))
+  end
+end
 
 function back(::typeof(*), Δ, a::AbstractMatrix, b::AbstractVecOrMat)
   @back(a, A_mul_Bt(Δ, data(b)))
   @back(b, At_mul_B(data(a), Δ))
 end
 
+function back(::typeof(Ac_mul_B), Δ, a::AbstractVecOrMat{<:Real}, b::AbstractVecOrMat{<:Real})
+  @back(a, A_mul_Bt(Δ, data(b))')
+  @back(b, *(data(a), Δ))
+end
+
+# Fast path for matrix-vector
+function back(::typeof(*), Δ::AbstractVector, W::TrackedMatrix, x::AbstractVector)
+  if isleaf(W)
+    W.grad .+= Δ .* data(x).'
+  else
+    back(W, A_mul_Bt(Δ, data(x)))
+  end
+  @back(x, At_mul_B(data(W), Δ))
+end
+
 # NNlib
 
 import NNlib: softmax, ∇softmax

src/treelike.jl

@@ -35,3 +35,5 @@ function params(m)
   prefor(p -> p isa TrackedArray && push!(ps, p), m)
   return ps
 end
+
+params(m...) = params(m)

test/optimise.jl

@@ -0,0 +1,17 @@
+using Flux.Optimise
+using Flux.Tracker
+
+@testset "Optimise" begin
+  w = randn(10, 10)
+  for Opt in [SGD, Nesterov, Momentum, ADAM, RMSProp, ps -> ADAGrad(ps, 0.1), ADADelta, AMSGrad]
+    w′ = param(randn(10, 10))
+    loss(x) = Flux.mse(w*x, w′*x)
+    opt = Opt([w′])
+    for t=1:10^5
+      l = loss(rand(10))
+      back!(l)
+      opt()
+    end
+    @test Flux.mse(w, w′) < 0.01
+  end
+end

test/runtests.jl

@@ -5,5 +5,6 @@ using Flux, Base.Test
 include("utils.jl")
 include("tracker.jl")
 include("layers/normalisation.jl")
+include("optimise.jl")
 
 end

test/tracker.jl

@@ -9,6 +9,8 @@ gradtest(f, dims...) = gradtest(f, rand.(dims)...)
 @test gradtest((x, W, b) -> σ.(W*x .+ b), 5, (2,5), 2)
 @test gradtest((x, W, b) -> σ.(W*x .+ b), (5,3), (2,5), 2)
 
+@test gradtest((w, x) -> w'*x, randn(10, 2), randn(10))
+
 @test gradtest(x -> sin.(sum(x, (2, 3))), (3,4,5))
 
 @test gradtest(x -> softmax(x).*(1:3), 3)
@@ -32,23 +34,12 @@ gradtest(f, dims...) = gradtest(f, rand.(dims)...)
   @test gradtest(x -> mean(x, [1, 2]), rand(2, 3, 4))
 end
 
+@test gradtest(x -> std(x), rand(5,5))
+@test gradtest(x -> std(x, 1), rand(5,5))
+
 @test gradtest(rand(5)) do x
   y = x.^2
   2y + x
 end
 
-for T in [Float32, Float64]
-    @test isa(param(T(1)), TrackedArray{T, 0})
-    @test isa(param(rand(T, 2)), TrackedArray{T, 1})
-    @test isa(param(rand(T, 2,2)), TrackedArray{T, 2})
-end
-
-# TODO: do we wand this behaviour ??
-F = typeof(AbstractFloat(1))
-for T in [Int32, Int64]
-    @test isa(param(T(1)), TrackedArray{F, 0})
-    @test isa(param(rand(T, 2)), TrackedArray{F, 1})
-    @test isa(param(rand(T, 2,2)), TrackedArray{F, 2})
-end
-
 end #testset