Support for lecun normal weight initialization (#2311)

* Support for lecun normal weight initialization

* add test

* add to docs

* Update utils.jl

* fixup

* fix rtol

* doctests

---------

Co-authored-by: Michael Abbott <32575566+mcabbott@users.noreply.github.com>

Author: RohitRathore1

docs/src/reference/utilities.md

@@ -35,6 +35,7 @@ Flux.glorot_normal
 Flux.kaiming_uniform
 Flux.kaiming_normal
 Flux.truncated_normal
+Flux.lecun_normal
 Flux.orthogonal
 Flux.sparse_init
 Flux.identity_init

src/Flux.jl

@@ -119,6 +119,7 @@ export MPIBackend, NCCLBackend, DistributedUtils
   kaiming_uniform,
   kaiming_normal,
   truncated_normal,
+  lecun_normal,
   orthogonal,
   sparse_init,
   identity_init,

src/utils.jl

@@ -248,6 +248,48 @@ truncated_normal(rng::AbstractRNG=default_rng(); init_kwargs...) = (dims...; kwa
 
 ChainRulesCore.@non_differentiable truncated_normal(::Any...)
 
+"""
+    lecun_normal([rng], size...) -> Array
+    lecun_normal([rng]; kw...) -> Function
+
+Return an `Array{Float32}` of the given `size` containing random numbers drawn from a truncated normal
+distribution centered on 0 with stddev `sqrt(1 / fan_in)`, where `fan_in` is the number of input units 
+in the weight tensor.
+
+# Examples
+```jldoctest; setup = :(using Random; Random.seed!(0))
+julia> using Statistics
+
+julia> round(std(Flux.lecun_normal(10, 1000)), digits=3)
+0.032f0
+
+julia> round(std(Flux.lecun_normal(1000, 10)), digits=3)
+0.32f0
+
+julia> round(std(Flux.lecun_normal(1000, 1000)), digits=3)
+0.032f0
+
+julia> Dense(10 => 1000, selu; init = Flux.lecun_normal())
+Dense(10 => 1000, selu)  # 11_000 parameters
+
+julia> round(std(ans.weight), digits=3)
+0.313f0
+```
+
+# References
+
+[1] Lecun, Yann, et al. "Efficient backprop." Neural networks: Tricks of the trade. Springer, Berlin, Heidelberg, 2012. 9-48.
+"""
+function lecun_normal(rng::AbstractRNG, dims::Integer...; gain::Real=1)
+  std = Float32(gain)*sqrt(1.0f0 / first(nfan(dims...))) # calculates the standard deviation based on the `fan_in` value
+  return truncated_normal(rng, dims...; mean=0, std=std)
+end
+
+lecun_normal(dims::Integer...; kwargs...) = lecun_normal(default_rng(), dims...; kwargs...)
+lecun_normal(rng::AbstractRNG=default_rng(); init_kwargs...) = (dims...; kwargs...) -> lecun_normal(rng, dims...; init_kwargs..., kwargs...)
+
+ChainRulesCore.@non_differentiable lecun_normal(::Any...)
+
 """
     orthogonal([rng], size...; gain = 1) -> Array
     orthogonal([rng]; kw...) -> Function

test/utils.jl

@@ -1,6 +1,6 @@
 using Flux
 using Flux: throttle, nfan, glorot_uniform, glorot_normal,
-             kaiming_normal, kaiming_uniform, orthogonal, truncated_normal,
+             kaiming_normal, kaiming_uniform, orthogonal, truncated_normal, lecun_normal,
              sparse_init, identity_init, unstack, batch, unbatch,
              unsqueeze, params, loadmodel!
 using MLUtils
@@ -75,7 +75,7 @@ end
       kaiming_uniform, kaiming_normal, 
       orthogonal, 
       sparse_init,
-      truncated_normal,
+      truncated_normal, lecun_normal,
       identity_init,
       Flux.rand32,
       Flux.randn32,
@@ -192,6 +192,11 @@ end
     end
   end
 
+  @testset "lecun_normal" begin
+    @test std(Flux.lecun_normal(10, 1000)) ≈ 0.032f0 rtol=0.1
+    @test std(Flux.lecun_normal(1000, 10)) ≈ 0.317f0 rtol=0.1
+  end
+
   @testset "Partial application" begin
     partial_ku = kaiming_uniform(gain=1e9)
     @test maximum(partial_ku(8, 8)) > 1e9 / 2