Add glorot (Xavier) initialization

Set default `Dense` and `RNN` inits to `glorot_uniform()` for `W`, `zeros` for `b`.

src/layers/basic.jl

@@ -63,8 +63,10 @@ struct Dense{F,S,T}
   b::T
 end
 
-Dense(in::Integer, out::Integer, σ = identity; init = initn) =
-  Dense(σ, param(init(out, in)), param(init(out)))
+function Dense(in::Integer, out::Integer, σ = identity;
+               initW = glorot_uniform, initb = zeros)
+  return Dense(σ, param(initW(out, in)), param(initb(out)))
+end
 
 treelike(Dense)
 

src/layers/recurrent.jl

@@ -79,8 +79,8 @@ struct RNNCell{D,V}
   h::V
 end
 
-RNNCell(in::Integer, out::Integer, σ = tanh; init = initn) =
-  RNNCell(Dense(in+out, out, σ, init = init), param(init(out)))
+RNNCell(in::Integer, out::Integer, σ = tanh; initW = glorot_uniform, initb = zeros) =
+  RNNCell(Dense(in+out, out, σ, initW = initW, initb = initb), param(initW(out)))
 
 function (m::RNNCell)(h, x)
   h = m.d(combine(x, h))
@@ -113,10 +113,10 @@ struct LSTMCell{D1,D2,V}
   h::V; c::V
 end
 
-function LSTMCell(in, out; init = initn)
-  cell = LSTMCell([Dense(in+out, out, σ, init = init) for _ = 1:3]...,
-                  Dense(in+out, out, tanh, init = init),
-                  param(init(out)), param(init(out)))
+function LSTMCell(in, out; initW = glorot_uniform, initb = zeros)
+  cell = LSTMCell([Dense(in+out, out, σ, initW = initW, initb = initb) for _ = 1:3]...,
+                  Dense(in+out, out, tanh, initW = initW, initb = initb),
+                  param(initW(out)), param(initW(out)))
   cell.forget.b.data .= 1
   return cell
 end

src/utils.jl

@@ -1,6 +1,8 @@
 # Arrays
 
 initn(dims...) = randn(dims...)/100
+glorot_uniform(dims...) = (rand(dims...) - 0.5)*sqrt(24.0/(sum(dims)))
+glorot_normal(dims...) = (randn(dims...)*sqrt(2.0/sum(dims)))
 
 flatten(xs) = reshape(xs, size(xs, 1), :)
 

test/utils.jl

@@ -1,4 +1,4 @@
-using Flux: throttle
+using Flux: throttle, initn, glorot_uniform, glorot_normal
 
 @testset "Throttle" begin
   @testset "default behaviour" begin
@@ -47,3 +47,26 @@ using Flux: throttle
     @test a == [1, 3]
   end
 end
+
+@testset "Initialization" begin
+  # Set random seed so that these tests don't fail randomly
+  srand(0)
+  # initn() should yield a kernel with stddev ~= 1e-2
+  v = initn(10, 10)
+  @test std(v) > 0.9*1e-2
+  @test std(v) < 1.1*1e-2
+
+  # glorot_uniform should yield a kernel with stddev ~= sqrt(6/(n_in + n_out)),
+  # and glorot_normal should yield a kernel with stddev != 2/(n_in _ n_out)
+  for (n_in, n_out) in [(100, 100), (100, 400)]
+    v = glorot_uniform(n_in, n_out)
+    @test minimum(v) > -1.1*sqrt(6/(n_in + n_out))
+    @test minimum(v) < -0.9*sqrt(6/(n_in + n_out))
+    @test maximum(v) >  0.9*sqrt(6/(n_in + n_out))
+    @test maximum(v) <  1.1*sqrt(6/(n_in + n_out))
+
+    v = glorot_normal(n_in, n_out)
+    @test std(v) > 0.9*sqrt(2/(n_in + n_out))
+    @test std(v) < 1.1*sqrt(2/(n_in + n_out))
+  end
+end