initial sketch

src/Flux.jl

@@ -22,7 +22,7 @@ export Tracker, TrackedArray, TrackedVector, TrackedMatrix, param
 include("optimise/Optimise.jl")
 using .Optimise
 using .Optimise: @epochs
-export SGD, ADAM, AdaMax, Momentum, Nesterov,
+export SGD, Descent, ADAM, AdaMax, Momentum, Nesterov,
        RMSProp, ADAGrad, ADADelta, AMSGrad
 
 include("utils.jl")

src/optimise/Optimise.jl

@@ -1,21 +1,9 @@
 module Optimise
 
 export train!,
-  SGD, ADAM, AdaMax, Momentum, Nesterov, RMSProp, ADAGrad, ADADelta, AMSGrad
-
-struct Param{T}
-  x::T
-  Δ::T
-end
-
-Base.convert(::Type{Param}, x::AbstractArray) = Param(x, zeros(x))
+  SGD, Descent, ADAM, AdaMax, Momentum, Nesterov, RMSProp, ADAGrad, ADADelta, AMSGrad
 
 include("optimisers.jl")
-include("interface.jl")
 include("train.jl")
 
-using Flux.Tracker: TrackedArray
-
-Base.convert(::Type{Param}, x::TrackedArray) = Param(x.data, x.grad)
-
 end

src/optimise/interface.jl

@@ -1,93 +0,0 @@
-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
-    os = map(f -> f(p), fs)
-    () -> foreach(call, os)
-  end
-  () -> foreach(call, fs)
-end
-
-"""
-    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.
-"""
-SGD(ps, η = 0.1; decay = 0) =
-  optimiser(ps, p -> invdecay(p, decay), p -> descent(p,η))
-
-"""
-    Momentum(params, η = 0.01; ρ = 0.9, decay = 0)
-
-SGD with learning rate  `η`, momentum `ρ` and optional learning rate inverse decay.
-"""
-Momentum(ps, η = 0.01; ρ = 0.9, decay = 0) =
-  optimiser(ps, p->invdecay(p,decay), p->momentum(p, ρ, η), p->descent(p,1))
-
-"""
-    Nesterov(params, η = 0.01; ρ = 0.9, decay = 0)
-
-SGD with learning rate  `η`, Nesterov momentum `ρ` and optional learning rate inverse decay.
-"""
-Nesterov(ps, η = 0.01; ρ = 0.9, decay = 0) =
-  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](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))
-
-"""
-    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))
-
-"""
-    AdaMax(params, η = 0.001; β1 = 0.9, β2 = 0.999, ϵ = 1e-08, decay = 0)
-
-[AdaMax](https://arxiv.org/abs/1412.6980v9) optimiser. Variant of ADAM based on
-the ∞-norm.
-"""
-AdaMax(ps, η = 0.002; β1 = 0.9, β2 = 0.999, ϵ = 1e-08, decay = 0) =
-  optimiser(ps, p->adamax(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](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) =
-  optimiser(ps, p->adagrad(p; η=η, ϵ=ϵ), p->invdecay(p,decay), p->descent(p,1))
-
-"""
-    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; ρ = 0.9, ϵ = 1e-8, decay = 0) =
-  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

@@ -1,109 +1,139 @@
-function descent(p::Param, η::Real)
-  function ()
-    @. p.x -= η * p.Δ
-    @. p.Δ = 0
-  end
+using Flux
+using Base: @get!
+
+const ϵ = 1e-8
+
+# TODO: should use weak refs
+
+"""
+    Descent(η)
+
+Classic gradient descent optimiser with learning rate `η`.
+For each parameter `p` and its gradient `δp`, this runs `p -= η*δp`.
+"""
+mutable struct Descent
+  eta::Float64
 end
 
-function momentum(p::Param, ρ, η)
-  v = zeros(p.x)
-  function ()
-    @. v = ρ * v - η * p.Δ
-    @. p.Δ = -v
-  end
+function update!(o::Descent, x, Δ)
+  Δ .*= o.eta
 end
 
-# Ref. https://arxiv.org/pdf/1212.0901.pdf
-function nesterov(p::Param, ρ, η)
-  v = zeros(p.x)
-  function ()
-    d = @. ρ^2 * v - (1+ρ) * η * p.Δ
-    @. v = ρ*v - η*p.Δ
-    @. p.Δ = -d
-  end
+"""
+    Momentum(params, η = 0.01; ρ = 0.9, decay = 0)
+
+Gradient descent with learning rate `η` and momentum `ρ`.
+"""
+mutable struct Momentum
+  eta::Float64
+  rho::Float64
+  velocity::ObjectIdDict
 end
 
-function rmsprop(p::Param; η::Real = 0.001, ρ::Real = 0.9, ϵ::Real = 1e-8)
-  acc  = zeros(p.x)
-  function ()
-    @. acc = ρ * acc + (1 - ρ) * p.Δ^2
-    @. p.Δ *= η / (√acc + ϵ)
-  end
+Momentum(η, ρ = 0.9) = Momentum(η, ρ, ObjectIdDict())
+
+function update!(o::Momentum, x, Δ)
+  η, ρ = o.eta, o.rho
+  v = @get!(o.velocity, x, zero(x))::typeof(x)
+  @. v = ρ * v - η * Δ
+  @. Δ = -v
 end
 
-function adagrad(p::Param; η::Real = 0.01, ϵ::Real = 1e-8)
-  acc = zeros(p.x) .+ ϵ
-  function ()
-    @. acc += p.Δ^2
-    @. p.Δ *= η / √acc
-  end
+"""
+    Nesterov(eta, ρ = 0.9)
+
+Gradient descent with learning rate  `η` and Nesterov momentum `ρ`.
+"""
+mutable struct Nesterov
+  eta::Float64
+  rho::Float64
+  velocity::ObjectIdDict
 end
 
-function adadelta(p::Param; ρ::Real = 0.9, ϵ::Real = 1e-8)
-  acc = zeros(p.x)
-  Δacc = zeros(p.x)
-  function ()
-    @. acc = ρ * acc + (1 - ρ) * p.Δ^2
-    @. p.Δ *= √(Δacc + ϵ) / √(acc + ϵ)
-    @. Δacc = ρ * Δacc + (1 - ρ) * p.Δ^2
-   end
+Nesterov(η, ρ = 0.9) = Nesterov(η, ρ, ObjectIdDict())
+
+function update!(o::Nesterov, x, Δ)
+  η, ρ = o.eta, o.rho
+  v = @get!(o.velocity, x, zero(x))::typeof(x)
+  d = @. ρ^2 * v - (1+ρ) * η * Δ
+  @. v = ρ*v - η*Δ
+  @. Δ = -d
 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)
-  β1p, β2p = β1, β2
-  function ()
-    @. mt = β1 * mt + (1 - β1) * p.Δ
-    @. vt = β2 * vt + (1 - β2) * p.Δ^2
-    @. p.Δ =  mt / (1 - β1p) / (√(vt / (1 - β2p)) + ϵ) * η
-    β1p *= β1
-    β2p *= β2
-  end
+"""
+    RMSProp(η = 0.001, ρ = 0.9)
+
+[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.
+"""
+mutable struct RMSProp
+  eta::Float64
+  rho::Float64
+  acc::ObjectIdDict
 end
 
-function adamax(p::Param; η::Real = 0.002, β1::Real = 0.9, β2::Real = 0.999, ϵ::Real = 1e-8)
-  mt = zeros(p.x)
-  ut = zeros(p.x)
-  β1p = β1
-  function ()
-    @. mt = β1 * mt + (1 - β1) * p.Δ
-    @. ut = max(β2 * ut, abs(p.Δ))
-    @. p.Δ = (η/(1 - β1p)) * mt/(ut + ϵ)
-    β1p *= β1
-  end
+RMSProp(η = 0.001, ρ = 0.9) = RMSProp(η, ρ, ObjectIdDict())
+
+function update!(o::RMSProp, x, Δ)
+  η, ρ = o.eta, o.rho
+  acc = @get!(o.acc, x, zero(x))::typeof(x)
+  @. acc = ρ * acc + (1 - ρ) * Δ^2
+  @. Δ *= η / (√acc + ϵ)
 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
+"""
+    ADAM(params, η = 0.001; β1 = 0.9, β2 = 0.999, ϵ = 1e-08, decay = 0)
+
+[ADAM](https://arxiv.org/abs/1412.6980v8) optimiser.
+"""
+mutable struct ADAM
+  eta::Float64
+  beta::Tuple{Float64,Float64}
+  state::ObjectIdDict
 end
 
-clip(p::Param, thresh::Real) = () -> clamp!(p.Δ, -thresh, thresh)
+ADAM(η = 0.001, β = (0.9, 0.999)) = ADAM(η, β, ObjectIdDict())
 
-function expdecay(p::Param, γ::Real)
-  if γ != 0
-    return () -> p.Δ .+= γ .* p.x
-  else
-    return () -> nothing
-  end
+function update!(o::ADAM, x, Δ)
+  η, β = o.eta, o.beta
+  mt, vt, βp = @get!(o.state, x, (zero(x), zero(x), β))
+  @. mt = β[1] * mt + (1 - β[1]) * Δ
+  @. vt = β[2] * vt + (1 - β[2]) * Δ^2
+  @. Δ =  mt / (1 - βp[1]) / (√(vt / (1 - βp[2])) + ϵ) * η
+  o.state[x] = (mt, vt, βp .* β)
 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
+# """
+#     AdaMax(params, η = 0.001; β1 = 0.9, β2 = 0.999, ϵ = 1e-08, decay = 0)
+#
+# [AdaMax](https://arxiv.org/abs/1412.6980v9) optimiser. Variant of ADAM based on
+# the ∞-norm.
+# """
+
+# """
+#     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.
+# """
+
+# """
+#     ADADelta(params; ρ = 0.9, ϵ = 1e-8, decay = 0)
+#
+# [ADADelta](http://arxiv.org/abs/1212.5701) optimiser. Parameters don't need
+# tuning.
+# """
+
+# """
+#     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.
+# """
+
+# struct Optimiser
+#   os::Vector{Any}
+# end
+
+# TODO: decay

src/optimise/train.jl

@@ -1,6 +1,16 @@
 using Juno
-using Flux.Tracker: back!
+using Flux.Tracker: data, grad, back!
 
+function update!(opt, xs)
+  for x in xs
+    x, Δ = data(x), grad(x)
+    update!(opt, x, Δ)
+    x .-= Δ
+    Δ .= 0
+  end
+end
+
+# Callback niceties
 runall(f) = f
 runall(fs::AbstractVector) = () -> foreach(call, fs)
 

src/tracker/Tracker.jl

@@ -10,6 +10,7 @@ istracked(x) = tracker(x) ≠ nothing
 isleaf(x) = !istracked(x) || isleaf(tracker(x))
 data(x) = istracked(x) ? data(tracker(x)) : x
 grad(x) = grad(tracker(x))
+grad(::Void) = nothing
 
 struct Call{F,As<:Tuple}
   func::F