diff --git a/src/Flux.jl b/src/Flux.jl
index 8ad4d1f9..88b2108e 100644
--- a/src/Flux.jl
+++ b/src/Flux.jl
@@ -13,7 +13,7 @@ export Chain, Dense, RNN, LSTM, GRU, Conv2D,
   param, params, mapleaves
 
 using NNlib
-export σ, sigmoid, relu, leakyrelu, elu, swish, softmax, logsoftmax,
+export σ, sigmoid, logσ, logsigmoid, relu, leakyrelu, elu, swish, softmax, logsoftmax,
   conv2d, maxpool2d, avgpool2d
 
 include("tracker/Tracker.jl")
diff --git a/src/layers/stateless.jl b/src/layers/stateless.jl
index 63c40cb8..34683fbf 100644
--- a/src/layers/stateless.jl
+++ b/src/layers/stateless.jl
@@ -1,4 +1,4 @@
-using NNlib: log_fast
+using NNlib: log_fast, logsoftmax, logσ
 
 # Cost functions
 
@@ -10,12 +10,37 @@ end
 
 @deprecate logloss(x, y) crossentropy(x, y)
 
-function logitcrossentropy(logŷ::AbstractVecOrMat, y::AbstractVecOrMat)
-  logŷ = logŷ .- maximum(logŷ, 1)
-  ypred = logŷ .- log_fast.(sum(exp.(logŷ), 1))
-  -sum(y .* ypred) / size(y, 2)
+function logitcrossentropy(logŷ::AbstractVecOrMat, y::AbstractVecOrMat; weight = 1)
+  return -sum(y .* logsoftmax(logŷ) .* weight) / size(y, 2)
 end
 
+"""
+    binarycrossentropy(ŷ, y)
+
+Return `-y*log(ŷ) - (1-y)*log(1-ŷ)`.
+
+    julia> binarycrossentropy.(σ.([-1.1491, 0.8619, 0.3127]), [1, 1, 0.])
+    3-element Array{Float64,1}:
+    1.4244
+    0.352317
+    0.86167
+"""
+binarycrossentropy(ŷ, y) = -y*log_fast(ŷ) - (1 - y)*log_fast(1 - ŷ)
+
+"""
+    logitbinarycrossentropy(logŷ, y)
+
+`logitbinarycrossentropy(logŷ, y)` is mathematically equivalent to `binarycrossentropy(σ(logŷ), y)`
+but it is more numerically stable.
+
+    julia> logitbinarycrossentropy.([-1.1491, 0.8619, 0.3127], [1, 1, 0.])
+    3-element Array{Float64,1}:
+     1.4244
+     0.352317
+     0.86167
+"""
+logitbinarycrossentropy(logŷ, y) = (1 - y)*logŷ - logσ(logŷ)
+
 """
     normalise(x::AbstractVecOrMat)
 
diff --git a/test/layers/stateless.jl b/test/layers/stateless.jl
index 23304eb1..ecfa7014 100644
--- a/test/layers/stateless.jl
+++ b/test/layers/stateless.jl
@@ -1,26 +1,49 @@
-using Flux: onehotbatch, mse, crossentropy
+using Base.Test
+using Flux: onehotbatch, mse, crossentropy, logitcrossentropy, 
+            σ, binarycrossentropy, logitbinarycrossentropy
 
 @testset "losses" begin
   # First, regression-style y's
   y = [1, 1, 0, 0]
-  y_hat = [.9, .1, .1, .9]
+  ŷ = [.9, .1, .1, .9]
 
   @testset "mse" begin
-    @test mse(y_hat, y) ≈ (.1^2 + .9^2)/2
+    @test mse(ŷ, y) ≈ (.1^2 + .9^2)/2
   end
 
   # Now onehot y's
   y = onehotbatch([1, 1, 0, 0], 0:1)
-  y_hat = [.1 .9; .9 .1; .9 .1; .1 .9]'
-  y_logloss = 1.203972804325936
+  ŷ = [.1 .9; .9 .1; .9 .1; .1 .9]'
+  v = log(.1 / .9)
+  logŷ = [v 0.0; 0.0 v; 0.0 v; v 0.0]'
+  lossvalue = 1.203972804325936
 
   @testset "crossentropy" begin
-    @test crossentropy(y_hat, y) ≈ y_logloss
+    @test crossentropy(ŷ, y) ≈ lossvalue
+  end
+
+  @testset "logitcrossentropy" begin
+    @test logitcrossentropy(logŷ, y) ≈ lossvalue
   end
 
   @testset "weighted_crossentropy" begin
-    @test crossentropy(y_hat, y, weight = ones(2)) ≈ y_logloss
-    @test crossentropy(y_hat, y, weight = [.5, .5]) ≈ y_logloss/2
-    @test crossentropy(y_hat, y, weight = [2, .5]) ≈ 1.5049660054074199
+    @test crossentropy(ŷ, y, weight = ones(2)) ≈ lossvalue
+    @test crossentropy(ŷ, y, weight = [.5, .5]) ≈ lossvalue/2
+    @test crossentropy(ŷ, y, weight = [2, .5]) ≈ 1.5049660054074199
+  end
+
+  @testset "weighted_logitcrossentropy" begin
+    @test logitcrossentropy(logŷ, y, weight = ones(2)) ≈ lossvalue
+    @test logitcrossentropy(logŷ, y, weight = [.5, .5]) ≈ lossvalue/2
+    @test logitcrossentropy(logŷ, y, weight = [2, .5]) ≈ 1.5049660054074199
+  end
+
+  logŷ, y = randn(3), rand(3)
+  @testset "binarycrossentropy" begin
+    @test binarycrossentropy.(σ.(logŷ), y) ≈ -y.*log.(σ.(logŷ)) - (1 - y).*log.(1 - σ.(logŷ))
+  end
+  
+  @testset "logitbinarycrossentropy" begin
+    @test logitbinarycrossentropy.(logŷ, y) ≈ binarycrossentropy.(σ.(logŷ), y)
   end
 end
diff --git a/test/tracker.jl b/test/tracker.jl
index 36b0fad1..12d018e1 100644
--- a/test/tracker.jl
+++ b/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((x, W, b) -> logσ.(W*x .+ b), 5, (2,5), 2)
+@test gradtest((x, W, b) -> logσ.(W*x .+ b), (5,3), (2,5), 2)
 
 @test gradtest((w, x) -> w'*x, randn(10, 2), randn(10))
 @test gradtest((w, x) -> w*x', randn(5,5), randn(5,5))