Getting Started

Installation

Install Julia v1.10 or above. Lux.jl is available through the Julia package manager. You can enter it by pressing ] in the REPL and then typing add Lux. Alternatively, you can also do

julia

import Pkg
Pkg.add("Lux")

Update to v1

If you are using a pre-v1 version of Lux.jl, please see the Updating to v1 section for instructions on how to update.

Quickstart

Pre-Requisites

You need to install Optimisers and Zygote if not done already. Pkg.add(["Optimisers", "Zygote"])

julia

using Lux, Random, Optimisers, Zygote
# using LuxCUDA, AMDGPU, Metal, oneAPI # Optional packages for GPU support

We take randomness very seriously

julia

# Seeding
rng = Random.default_rng()
Random.seed!(rng, 0)

Random.TaskLocalRNG()

Build the model

julia

# Construct the layer
model = Chain(Dense(128, 256, tanh), Chain(Dense(256, 1, tanh), Dense(1, 10)))

Chain(
    layer_1 = Dense(128 => 256, tanh),  # 33_024 parameters
    layer_2 = Chain(
        layer_1 = Dense(256 => 1, tanh),  # 257 parameters
        layer_2 = Dense(1 => 10),       # 20 parameters
    ),
)         # Total: 33_301 parameters,
          #        plus 0 states.

Models don't hold parameters and states so initialize them. From there on, we can just use our standard AD and Optimisers API. However, here we will show how to use Lux's Training API that provides an uniform API over all supported AD systems.

julia

# Get the device determined by Lux
dev = gpu_device()

# Parameter and State Variables
ps, st = Lux.setup(rng, model) |> dev

# Dummy Input
x = rand(rng, Float32, 128, 2) |> dev

# Run the model
y, st = Lux.apply(model, x, ps, st)

# Gradients
## First construct a TrainState
train_state = Lux.Training.TrainState(model, ps, st, Adam(0.0001f0))

## We can compute the gradients using Training.compute_gradients
gs, loss, stats, train_state = Lux.Training.compute_gradients(
    AutoZygote(), MSELoss(),
    (x, dev(rand(rng, Float32, 10, 2))), train_state
)

## Optimization
train_state = Training.apply_gradients!(train_state, gs) # or Training.apply_gradients (no `!` at the end)

# Both these steps can be combined into a single call
gs, loss, stats, train_state = Training.single_train_step!(
    AutoZygote(), MSELoss(),
    (x, dev(rand(rng, Float32, 10, 2))), train_state
)

((layer_1 = (weight = Float32[0.0017983615 0.006062332 … 0.0053392933 0.0056276177; 0.0011292367 0.0041270256 … 0.003585879 0.0038155357; … ; -0.0008762945 -0.0031371699 … -0.0027350332 -0.0029033197; 0.0011154839 0.002197485 … 0.0021741025 0.0021157824], bias = Float32[0.006656272, 0.004425203, 0.0028994146, -0.0116051175, 0.0031301186, 0.0037318026, 0.0136483535, 0.013969757, -0.015173428, -0.005173992  …  -0.0018621369, -0.0015270555, -0.007873881, -0.0076395273, -0.0022123815, 0.0039605754, 0.0034407252, -0.0045406874, -0.003383829, 0.0029306945]), layer_2 = (layer_1 = (weight = Float32[0.04993449 0.03202845 … -0.059382 0.07701616], bias = Float32[0.08797912]), layer_2 = (weight = Float32[-0.094527975; -0.11476975; … ; -0.016841749; -0.0698748;;], bias = Float32[-0.21608135, -0.26255828, -0.23534852, -0.21524015, -0.055711076, -0.20314303, -0.1895644, 0.03666526, -0.03937737, -0.15905891]))), 0.8455785f0, NamedTuple(), Lux.Training.TrainState{Nothing, Nothing, Chain{@NamedTuple{layer_1::Dense{typeof(tanh), Int64, Int64, Nothing, Nothing, Static.True}, layer_2::Chain{@NamedTuple{layer_1::Dense{typeof(tanh), Int64, Int64, Nothing, Nothing, Static.True}, layer_2::Dense{typeof(identity), Int64, Int64, Nothing, Nothing, Static.True}}, Nothing}}, Nothing}, @NamedTuple{layer_1::@NamedTuple{weight::Matrix{Float32}, bias::Vector{Float32}}, layer_2::@NamedTuple{layer_1::@NamedTuple{weight::Matrix{Float32}, bias::Vector{Float32}}, layer_2::@NamedTuple{weight::Matrix{Float32}, bias::Vector{Float32}}}}, @NamedTuple{layer_1::@NamedTuple{}, layer_2::@NamedTuple{layer_1::@NamedTuple{}, layer_2::@NamedTuple{}}}, Adam{Float32, Tuple{Float64, Float64}, Float64}, @NamedTuple{layer_1::@NamedTuple{weight::Optimisers.Leaf{Adam{Float32, Tuple{Float64, Float64}, Float64}, Tuple{Matrix{Float32}, Matrix{Float32}, Tuple{Float32, Float32}}}, bias::Optimisers.Leaf{Adam{Float32, Tuple{Float64, Float64}, Float64}, Tuple{Vector{Float32}, Vector{Float32}, Tuple{Float32, Float32}}}}, layer_2::@NamedTuple{layer_1::@NamedTuple{weight::Optimisers.Leaf{Adam{Float32, Tuple{Float64, Float64}, Float64}, Tuple{Matrix{Float32}, Matrix{Float32}, Tuple{Float32, Float32}}}, bias::Optimisers.Leaf{Adam{Float32, Tuple{Float64, Float64}, Float64}, Tuple{Vector{Float32}, Vector{Float32}, Tuple{Float32, Float32}}}}, layer_2::@NamedTuple{weight::Optimisers.Leaf{Adam{Float32, Tuple{Float64, Float64}, Float64}, Tuple{Matrix{Float32}, Matrix{Float32}, Tuple{Float32, Float32}}}, bias::Optimisers.Leaf{Adam{Float32, Tuple{Float64, Float64}, Float64}, Tuple{Vector{Float32}, Vector{Float32}, Tuple{Float32, Float32}}}}}}}(nothing, nothing, Chain{@NamedTuple{layer_1::Dense{typeof(tanh), Int64, Int64, Nothing, Nothing, Static.True}, layer_2::Chain{@NamedTuple{layer_1::Dense{typeof(tanh), Int64, Int64, Nothing, Nothing, Static.True}, layer_2::Dense{typeof(identity), Int64, Int64, Nothing, Nothing, Static.True}}, Nothing}}, Nothing}((layer_1 = Dense(128 => 256, tanh), layer_2 = Chain{@NamedTuple{layer_1::Dense{typeof(tanh), Int64, Int64, Nothing, Nothing, Static.True}, layer_2::Dense{typeof(identity), Int64, Int64, Nothing, Nothing, Static.True}}, Nothing}((layer_1 = Dense(256 => 1, tanh), layer_2 = Dense(1 => 10)), nothing)), nothing), (layer_1 = (weight = Float32[-0.22542597 0.22379348 … 0.1997513 -0.018708104; -0.023026714 0.15451026 … -0.065325744 0.18120264; … ; 0.038037397 -0.07125516 … -0.03306083 0.039138064; -0.18810266 -0.09693537 … -0.18102062 0.019230088], bias = Float32[0.030937059, -0.060276944, 0.084569596, 0.00040024254, -0.065509446, -0.08527214, -0.026523968, 0.06347208, 0.042247728, 0.027705256  …  -0.06052852, 0.03504307, -0.028244259, 0.06788022, 0.0027464977, -0.06942153, 0.0064240773, 0.0141069945, -0.029283267, 0.01174226]), layer_2 = (layer_1 = (weight = Float32[0.12008221 0.06026435 … -0.070576 0.1577647], bias = Float32[0.026844418]), layer_2 = (weight = Float32[0.5345728; -0.28288874; … ; -0.32983455; -0.45298168;;], bias = Float32[-0.59751064, -0.7033041, -0.8457602, -0.53789175, -0.31473723, 0.17461234, -0.82945836, 0.67841595, 0.35837248, -0.14941788]))), (layer_1 = NamedTuple(), layer_2 = (layer_1 = NamedTuple(), layer_2 = NamedTuple())), Adam(eta=0.0001, beta=(0.9, 0.999), epsilon=1.0e-8), (layer_1 = (weight = Leaf(Adam(eta=0.0001, beta=(0.9, 0.999), epsilon=1.0e-8), (Float32[0.000926728 0.000860063 … 0.00110328 0.000908301; 0.000480834 0.000574605 … 0.000665883 0.000584197; … ; -0.000391039 -0.000438617 … -0.000520651 -0.000449867; 0.00106235 0.000365587 … 0.000813131 0.000495484], Float32[7.20343f-8 4.46976f-8 … 6.84867f-8 4.63952f-8; 1.79691f-8 2.02649f-8 … 2.45046f-8 1.96227f-8; … ; 1.21215f-8 1.17657f-8 … 1.50136f-8 1.15681f-8; 1.12738f-7 7.45199f-9 … 4.8495f-8 1.44173f-8], (0.729, 0.997003))), bias = Leaf(Adam(eta=0.0001, beta=(0.9, 0.999), epsilon=1.0e-8), (Float32[0.00169459, 0.000977637, 0.00103866, -0.00234933, 0.000659175, 0.000868318, 0.00303222, 0.00271383, -0.00326585, -0.0014993  …  -0.000480712, -0.000501535, -0.00174489, -0.00160158, -0.000470662, 0.00127967, 0.000618911, -0.00103705, -0.000773079, 0.00146704], Float32[1.74884f-7, 5.48983f-8, 7.75433f-8, 3.08981f-7, 2.45763f-8, 4.41623f-8, 5.29156f-7, 4.09021f-7, 6.07287f-7, 1.45678f-7  …  1.4164f-8, 1.73391f-8, 1.7507f-7, 1.44894f-7, 1.25673f-8, 1.1198f-7, 2.11545f-8, 6.25338f-8, 3.4755f-8, 1.78565f-7], (0.729, 0.997003)))), layer_2 = (layer_1 = (weight = Leaf(Adam(eta=0.0001, beta=(0.9, 0.999), epsilon=1.0e-8), (Float32[0.00443555 0.00163654 … -0.0124978 0.0123434], Float32[2.53181f-6 1.32838f-6 … 8.83289f-6 8.58873f-6], (0.729, 0.997003))), bias = Leaf(Adam(eta=0.0001, beta=(0.9, 0.999), epsilon=1.0e-8), (Float32[0.0191175], Float32[2.08743f-5], (0.729, 0.997003)))), layer_2 = (weight = Leaf(Adam(eta=0.0001, beta=(0.9, 0.999), epsilon=1.0e-8), (Float32[-0.0172084; -0.0213176; … ; -0.00376332; -0.0116419;;], Float32[1.63537f-5; 2.51152f-5; … ; 8.16783f-7; 7.55419f-6;;], (0.729, 0.997003))), bias = Leaf(Adam(eta=0.0001, beta=(0.9, 0.999), epsilon=1.0e-8), (Float32[-0.0365001, -0.045083, -0.0507623, -0.0390298, -0.0242259, -0.0404982, -0.0358925, 0.0114351, -0.00803444, -0.0248332], Float32[7.40417f-5, 0.000112652, 0.000146818, 8.41229f-5, 4.60234f-5, 9.15105f-5, 7.13093f-5, 8.78741f-6, 3.62043f-6, 3.51285f-5], (0.729, 0.997003)))))), 2))

Defining Custom Layers

We can train our model using the above code, but let's go ahead and see how to use Reactant. Reactant is a julia frontend that generates MLIR and then compiles it using XLA (after running fancy optimizations). It is the current recommended way to train large models in Lux. For more details on using Reactant, see the manual.

julia

using Lux, Random, Optimisers, Reactant, Enzyme
using Printf # For pretty printing

dev = reactant_device()

(::ReactantDevice{Missing, Missing, Missing}) (generic function with 1 method)

We will define a custom MLP using the @compact macro. The macro takes in a list of parameters, layers and states, and a function defining the forward pass of the neural network.

julia

n_in = 1
n_out = 1
nlayers = 3

model = @compact(
    w1=Dense(n_in => 32),
    w2=[Dense(32 => 32) for i in 1:nlayers],
    w3=Dense(32 => n_out),
    act=relu
) do x
    embed = act(w1(x))
    for w in w2
        embed = act(w(embed))
    end
    out = w3(embed)
    @return out
end

@compact(
    w1 = Dense(1 => 32),                # 64 parameters
    w2 = NamedTuple(
        1 = Dense(32 => 32),            # 1_056 parameters
        2 = Dense(32 => 32),            # 1_056 parameters
        3 = Dense(32 => 32),            # 1_056 parameters
    ),
    w3 = Dense(32 => 1),                # 33 parameters
    act = relu,
) do x 
    embed = act(w1(x))
    for w = w2
        embed = act(w(embed))
    end
    out = w3(embed)
    return out
end       # Total: 3_265 parameters,
          #        plus 1 states.

We can initialize the model and train it with the same code as before!

julia

rng = Random.default_rng()
Random.seed!(rng, 0)

ps, st = Lux.setup(rng, model) |> dev

x = rand(rng, Float32, n_in, 32) |> dev

@jit model(x, ps, st)  # 1×32 Matrix and updated state as output.

x_data = reshape(collect(-2.0f0:0.1f0:2.0f0), 1, :)
y_data = 2 .* x_data .- x_data .^ 3
x_data, y_data = dev(x_data), dev(y_data)

function train_model!(model, ps, st, x_data, y_data)
    train_state = Lux.Training.TrainState(model, ps, st, Adam(0.001f0))

    for iter in 1:1000
        _, loss, _, train_state = Lux.Training.single_train_step!(
            AutoEnzyme(), MSELoss(),
            (x_data, y_data), train_state
        )
        if iter % 100 == 1 || iter == 1000
            @printf "Iteration: %04d \t Loss: %10.9g\n" iter loss
        end
    end

    return model, ps, st
end

train_model!(model, ps, st, x_data, y_data)

2025-05-23 23:12:44.284262: I external/xla/xla/service/service.cc:152] XLA service 0x120acae0 initialized for platform CUDA (this does not guarantee that XLA will be used). Devices:
2025-05-23 23:12:44.284466: I external/xla/xla/service/service.cc:160]   StreamExecutor device (0): NVIDIA A100-PCIE-40GB MIG 1g.5gb, Compute Capability 8.0
WARNING: All log messages before absl::InitializeLog() is called are written to STDERR
I0000 00:00:1748041964.285263  847441 se_gpu_pjrt_client.cc:1026] Using BFC allocator.
I0000 00:00:1748041964.285346  847441 gpu_helpers.cc:136] XLA backend allocating 3825205248 bytes on device 0 for BFCAllocator.
I0000 00:00:1748041964.285375  847441 gpu_helpers.cc:177] XLA backend will use up to 1275068416 bytes on device 0 for CollectiveBFCAllocator.
I0000 00:00:1748041964.299179  847441 cuda_dnn.cc:529] Loaded cuDNN version 90400
E0000 00:00:1748042237.836396  847441 buffer_comparator.cc:145] Difference at 16: 0, expected 18.4532
E0000 00:00:1748042237.836446  847441 buffer_comparator.cc:145] Difference at 17: 0, expected 16.1701
E0000 00:00:1748042237.836457  847441 buffer_comparator.cc:145] Difference at 18: 0, expected 18.5372
E0000 00:00:1748042237.836461  847441 buffer_comparator.cc:145] Difference at 19: 0, expected 17.7684
E0000 00:00:1748042237.836464  847441 buffer_comparator.cc:145] Difference at 20: 0, expected 17.8078
E0000 00:00:1748042237.836467  847441 buffer_comparator.cc:145] Difference at 21: 0, expected 17.412
E0000 00:00:1748042237.836470  847441 buffer_comparator.cc:145] Difference at 22: 0, expected 18.0425
E0000 00:00:1748042237.836474  847441 buffer_comparator.cc:145] Difference at 23: 0, expected 17.7822
E0000 00:00:1748042237.836477  847441 buffer_comparator.cc:145] Difference at 24: 0, expected 16.8692
E0000 00:00:1748042237.836480  847441 buffer_comparator.cc:145] Difference at 25: 0, expected 19.6248
2025-05-23 23:17:17.836490: E external/xla/xla/service/gpu/autotuning/gemm_fusion_autotuner.cc:1179] Results do not match the reference. This is likely a bug/unexpected loss of precision.
E0000 00:00:1748042237.839380  847441 buffer_comparator.cc:145] Difference at 16: 0, expected 18.4532
E0000 00:00:1748042237.839394  847441 buffer_comparator.cc:145] Difference at 17: 0, expected 16.1701
E0000 00:00:1748042237.839399  847441 buffer_comparator.cc:145] Difference at 18: 0, expected 18.5372
E0000 00:00:1748042237.839402  847441 buffer_comparator.cc:145] Difference at 19: 0, expected 17.7684
E0000 00:00:1748042237.839405  847441 buffer_comparator.cc:145] Difference at 20: 0, expected 17.8078
E0000 00:00:1748042237.839408  847441 buffer_comparator.cc:145] Difference at 21: 0, expected 17.412
E0000 00:00:1748042237.839411  847441 buffer_comparator.cc:145] Difference at 22: 0, expected 18.0425
E0000 00:00:1748042237.839414  847441 buffer_comparator.cc:145] Difference at 23: 0, expected 17.7822
E0000 00:00:1748042237.839417  847441 buffer_comparator.cc:145] Difference at 24: 0, expected 16.8692
E0000 00:00:1748042237.839420  847441 buffer_comparator.cc:145] Difference at 25: 0, expected 19.6248
2025-05-23 23:17:17.839426: E external/xla/xla/service/gpu/autotuning/gemm_fusion_autotuner.cc:1179] Results do not match the reference. This is likely a bug/unexpected loss of precision.
E0000 00:00:1748042237.842302  847441 buffer_comparator.cc:145] Difference at 656: 0, expected 15.8892
E0000 00:00:1748042237.842316  847441 buffer_comparator.cc:145] Difference at 657: 0, expected 15.1292
E0000 00:00:1748042237.842321  847441 buffer_comparator.cc:145] Difference at 658: 0, expected 14.0499
E0000 00:00:1748042237.842324  847441 buffer_comparator.cc:145] Difference at 659: 0, expected 13.8377
E0000 00:00:1748042237.842327  847441 buffer_comparator.cc:145] Difference at 660: 0, expected 13.7353
E0000 00:00:1748042237.842330  847441 buffer_comparator.cc:145] Difference at 661: 0, expected 15.7468
E0000 00:00:1748042237.842333  847441 buffer_comparator.cc:145] Difference at 662: 0, expected 14.9101
E0000 00:00:1748042237.842336  847441 buffer_comparator.cc:145] Difference at 663: 0, expected 14.8135
E0000 00:00:1748042237.842339  847441 buffer_comparator.cc:145] Difference at 664: 0, expected 13.6403
E0000 00:00:1748042237.842342  847441 buffer_comparator.cc:145] Difference at 665: 0, expected 15.8348
2025-05-23 23:17:17.842347: E external/xla/xla/service/gpu/autotuning/gemm_fusion_autotuner.cc:1179] Results do not match the reference. This is likely a bug/unexpected loss of precision.
E0000 00:00:1748042237.845220  847441 buffer_comparator.cc:145] Difference at 672: 0, expected 16.0696
E0000 00:00:1748042237.845232  847441 buffer_comparator.cc:145] Difference at 673: 0, expected 14.3019
E0000 00:00:1748042237.845237  847441 buffer_comparator.cc:145] Difference at 674: 0, expected 15.5573
E0000 00:00:1748042237.845240  847441 buffer_comparator.cc:145] Difference at 675: 0, expected 14.6242
E0000 00:00:1748042237.845243  847441 buffer_comparator.cc:145] Difference at 676: 0, expected 14.8486
E0000 00:00:1748042237.845248  847441 buffer_comparator.cc:145] Difference at 677: 0, expected 14.7699
E0000 00:00:1748042237.845251  847441 buffer_comparator.cc:145] Difference at 678: 0, expected 15.1617
E0000 00:00:1748042237.845254  847441 buffer_comparator.cc:145] Difference at 679: 0, expected 14.9394
E0000 00:00:1748042237.845257  847441 buffer_comparator.cc:145] Difference at 680: 0, expected 13.4678
E0000 00:00:1748042237.845260  847441 buffer_comparator.cc:145] Difference at 681: 0, expected 16.1851
2025-05-23 23:17:17.845265: E external/xla/xla/service/gpu/autotuning/gemm_fusion_autotuner.cc:1179] Results do not match the reference. This is likely a bug/unexpected loss of precision.
E0000 00:00:1748042237.848159  847441 buffer_comparator.cc:145] Difference at 672: 0, expected 16.0696
E0000 00:00:1748042237.848171  847441 buffer_comparator.cc:145] Difference at 673: 0, expected 14.3019
E0000 00:00:1748042237.848176  847441 buffer_comparator.cc:145] Difference at 674: 0, expected 15.5573
E0000 00:00:1748042237.848179  847441 buffer_comparator.cc:145] Difference at 675: 0, expected 14.6242
E0000 00:00:1748042237.848182  847441 buffer_comparator.cc:145] Difference at 676: 0, expected 14.8486
E0000 00:00:1748042237.848185  847441 buffer_comparator.cc:145] Difference at 677: 0, expected 14.7699
E0000 00:00:1748042237.848188  847441 buffer_comparator.cc:145] Difference at 678: 0, expected 15.1617
E0000 00:00:1748042237.848191  847441 buffer_comparator.cc:145] Difference at 679: 0, expected 14.9394
E0000 00:00:1748042237.848194  847441 buffer_comparator.cc:145] Difference at 680: 0, expected 13.4678
E0000 00:00:1748042237.848197  847441 buffer_comparator.cc:145] Difference at 681: 0, expected 16.1851
2025-05-23 23:17:17.848203: E external/xla/xla/service/gpu/autotuning/gemm_fusion_autotuner.cc:1179] Results do not match the reference. This is likely a bug/unexpected loss of precision.
E0000 00:00:1748042237.851079  847441 buffer_comparator.cc:145] Difference at 688: 0, expected 15.1187
E0000 00:00:1748042237.851091  847441 buffer_comparator.cc:145] Difference at 689: 0, expected 14.6251
E0000 00:00:1748042237.851096  847441 buffer_comparator.cc:145] Difference at 690: 0, expected 14.2005
E0000 00:00:1748042237.851099  847441 buffer_comparator.cc:145] Difference at 691: 0, expected 15.1561
E0000 00:00:1748042237.851102  847441 buffer_comparator.cc:145] Difference at 692: 0, expected 15.4235
E0000 00:00:1748042237.851105  847441 buffer_comparator.cc:145] Difference at 693: 0, expected 14.1331
E0000 00:00:1748042237.851108  847441 buffer_comparator.cc:145] Difference at 694: 0, expected 14.4063
E0000 00:00:1748042237.851112  847441 buffer_comparator.cc:145] Difference at 695: 0, expected 14.0259
E0000 00:00:1748042237.851115  847441 buffer_comparator.cc:145] Difference at 696: 0, expected 15.0279
E0000 00:00:1748042237.851118  847441 buffer_comparator.cc:145] Difference at 729: 0, expected 14.5946
2025-05-23 23:17:17.851123: E external/xla/xla/service/gpu/autotuning/gemm_fusion_autotuner.cc:1179] Results do not match the reference. This is likely a bug/unexpected loss of precision.
E0000 00:00:1748042237.854005  847441 buffer_comparator.cc:145] Difference at 688: 0, expected 15.1187
E0000 00:00:1748042237.854017  847441 buffer_comparator.cc:145] Difference at 689: 0, expected 14.6251
E0000 00:00:1748042237.854021  847441 buffer_comparator.cc:145] Difference at 690: 0, expected 14.2005
E0000 00:00:1748042237.854025  847441 buffer_comparator.cc:145] Difference at 691: 0, expected 15.1561
E0000 00:00:1748042237.854028  847441 buffer_comparator.cc:145] Difference at 692: 0, expected 15.4235
E0000 00:00:1748042237.854031  847441 buffer_comparator.cc:145] Difference at 693: 0, expected 14.1331
E0000 00:00:1748042237.854034  847441 buffer_comparator.cc:145] Difference at 694: 0, expected 14.4063
E0000 00:00:1748042237.854037  847441 buffer_comparator.cc:145] Difference at 695: 0, expected 14.0259
E0000 00:00:1748042237.854040  847441 buffer_comparator.cc:145] Difference at 696: 0, expected 15.0279
E0000 00:00:1748042237.854045  847441 buffer_comparator.cc:145] Difference at 729: 0, expected 14.5946
2025-05-23 23:17:17.854050: E external/xla/xla/service/gpu/autotuning/gemm_fusion_autotuner.cc:1179] Results do not match the reference. This is likely a bug/unexpected loss of precision.
E0000 00:00:1748042237.869436  847441 buffer_comparator.cc:145] Difference at 16: -nan, expected 29.4863
E0000 00:00:1748042237.869474  847441 buffer_comparator.cc:145] Difference at 17: -nan, expected 25.4275
E0000 00:00:1748042237.869481  847441 buffer_comparator.cc:145] Difference at 18: -nan, expected 29.498
E0000 00:00:1748042237.869485  847441 buffer_comparator.cc:145] Difference at 19: -nan, expected 24.9024
E0000 00:00:1748042237.869488  847441 buffer_comparator.cc:145] Difference at 20: -nan, expected 31.8883
E0000 00:00:1748042237.869491  847441 buffer_comparator.cc:145] Difference at 21: -nan, expected 30.5795
E0000 00:00:1748042237.869494  847441 buffer_comparator.cc:145] Difference at 22: -nan, expected 26.1755
E0000 00:00:1748042237.869497  847441 buffer_comparator.cc:145] Difference at 23: -nan, expected 30.0282
E0000 00:00:1748042237.869500  847441 buffer_comparator.cc:145] Difference at 24: -nan, expected 25.7237
E0000 00:00:1748042237.869503  847441 buffer_comparator.cc:145] Difference at 25: -nan, expected 25.7191
2025-05-23 23:17:17.869511: E external/xla/xla/service/gpu/autotuning/gemm_fusion_autotuner.cc:1179] Results do not match the reference. This is likely a bug/unexpected loss of precision.
E0000 00:00:1748042237.872418  847441 buffer_comparator.cc:145] Difference at 16: -nan, expected 29.4863
E0000 00:00:1748042237.872434  847441 buffer_comparator.cc:145] Difference at 17: -nan, expected 25.4275
E0000 00:00:1748042237.872439  847441 buffer_comparator.cc:145] Difference at 18: -nan, expected 29.498
E0000 00:00:1748042237.872442  847441 buffer_comparator.cc:145] Difference at 19: -nan, expected 24.9024
E0000 00:00:1748042237.872445  847441 buffer_comparator.cc:145] Difference at 20: -nan, expected 31.8883
E0000 00:00:1748042237.872448  847441 buffer_comparator.cc:145] Difference at 21: -nan, expected 30.5795
E0000 00:00:1748042237.872451  847441 buffer_comparator.cc:145] Difference at 22: -nan, expected 26.1755
E0000 00:00:1748042237.872454  847441 buffer_comparator.cc:145] Difference at 23: -nan, expected 30.0282
E0000 00:00:1748042237.872457  847441 buffer_comparator.cc:145] Difference at 24: -nan, expected 25.7237
E0000 00:00:1748042237.872460  847441 buffer_comparator.cc:145] Difference at 25: -nan, expected 25.7191
2025-05-23 23:17:17.872466: E external/xla/xla/service/gpu/autotuning/gemm_fusion_autotuner.cc:1179] Results do not match the reference. This is likely a bug/unexpected loss of precision.
E0000 00:00:1748042237.875352  847441 buffer_comparator.cc:145] Difference at 512: -nan, expected 13.9275
E0000 00:00:1748042237.875367  847441 buffer_comparator.cc:145] Difference at 513: -nan, expected 12.9447
E0000 00:00:1748042237.875372  847441 buffer_comparator.cc:145] Difference at 514: -nan, expected 13.899
E0000 00:00:1748042237.875375  847441 buffer_comparator.cc:145] Difference at 515: -nan, expected 14.1578
E0000 00:00:1748042237.875378  847441 buffer_comparator.cc:145] Difference at 516: -nan, expected 15.4892
E0000 00:00:1748042237.875381  847441 buffer_comparator.cc:145] Difference at 517: -nan, expected 16.545
E0000 00:00:1748042237.875384  847441 buffer_comparator.cc:145] Difference at 518: -nan, expected 17.8581
E0000 00:00:1748042237.875387  847441 buffer_comparator.cc:145] Difference at 519: -nan, expected 13.0536
E0000 00:00:1748042237.875390  847441 buffer_comparator.cc:145] Difference at 520: -nan, expected 16.1329
E0000 00:00:1748042237.875393  847441 buffer_comparator.cc:145] Difference at 521: -nan, expected 14.5245
2025-05-23 23:17:17.875398: E external/xla/xla/service/gpu/autotuning/gemm_fusion_autotuner.cc:1179] Results do not match the reference. This is likely a bug/unexpected loss of precision.
E0000 00:00:1748042237.878310  847441 buffer_comparator.cc:145] Difference at 528: -nan, expected 17.5032
E0000 00:00:1748042237.878323  847441 buffer_comparator.cc:145] Difference at 529: -nan, expected 15.1785
E0000 00:00:1748042237.878327  847441 buffer_comparator.cc:145] Difference at 530: -nan, expected 15.9473
E0000 00:00:1748042237.878330  847441 buffer_comparator.cc:145] Difference at 531: -nan, expected 14.437
E0000 00:00:1748042237.878333  847441 buffer_comparator.cc:145] Difference at 532: -nan, expected 17.9637
E0000 00:00:1748042237.878336  847441 buffer_comparator.cc:145] Difference at 533: -nan, expected 17.3157
E0000 00:00:1748042237.878339  847441 buffer_comparator.cc:145] Difference at 534: -nan, expected 15.7802
E0000 00:00:1748042237.878342  847441 buffer_comparator.cc:145] Difference at 535: -nan, expected 17.6887
E0000 00:00:1748042237.878345  847441 buffer_comparator.cc:145] Difference at 536: -nan, expected 15.1881
E0000 00:00:1748042237.878348  847441 buffer_comparator.cc:145] Difference at 537: -nan, expected 14.4224
2025-05-23 23:17:17.878352: E external/xla/xla/service/gpu/autotuning/gemm_fusion_autotuner.cc:1179] Results do not match the reference. This is likely a bug/unexpected loss of precision.
E0000 00:00:1748042237.881221  847441 buffer_comparator.cc:145] Difference at 528: -nan, expected 17.5032
E0000 00:00:1748042237.881233  847441 buffer_comparator.cc:145] Difference at 529: -nan, expected 15.1785
E0000 00:00:1748042237.881238  847441 buffer_comparator.cc:145] Difference at 530: -nan, expected 15.9473
E0000 00:00:1748042237.881241  847441 buffer_comparator.cc:145] Difference at 531: -nan, expected 14.437
E0000 00:00:1748042237.881244  847441 buffer_comparator.cc:145] Difference at 532: -nan, expected 17.9637
E0000 00:00:1748042237.881247  847441 buffer_comparator.cc:145] Difference at 533: -nan, expected 17.3157
E0000 00:00:1748042237.881250  847441 buffer_comparator.cc:145] Difference at 534: -nan, expected 15.7802
E0000 00:00:1748042237.881253  847441 buffer_comparator.cc:145] Difference at 535: -nan, expected 17.6887
E0000 00:00:1748042237.881256  847441 buffer_comparator.cc:145] Difference at 536: -nan, expected 15.1881
E0000 00:00:1748042237.881259  847441 buffer_comparator.cc:145] Difference at 537: -nan, expected 14.4224
2025-05-23 23:17:17.881263: E external/xla/xla/service/gpu/autotuning/gemm_fusion_autotuner.cc:1179] Results do not match the reference. This is likely a bug/unexpected loss of precision.
E0000 00:00:1748042237.884152  847441 buffer_comparator.cc:145] Difference at 528: -nan, expected 17.5032
E0000 00:00:1748042237.884164  847441 buffer_comparator.cc:145] Difference at 529: -nan, expected 15.1785
E0000 00:00:1748042237.884168  847441 buffer_comparator.cc:145] Difference at 530: -nan, expected 15.9473
E0000 00:00:1748042237.884171  847441 buffer_comparator.cc:145] Difference at 531: -nan, expected 14.437
E0000 00:00:1748042237.884174  847441 buffer_comparator.cc:145] Difference at 532: -nan, expected 17.9637
E0000 00:00:1748042237.884177  847441 buffer_comparator.cc:145] Difference at 533: -nan, expected 17.3157
E0000 00:00:1748042237.884180  847441 buffer_comparator.cc:145] Difference at 534: -nan, expected 15.7802
E0000 00:00:1748042237.884183  847441 buffer_comparator.cc:145] Difference at 535: -nan, expected 17.6887
E0000 00:00:1748042237.884186  847441 buffer_comparator.cc:145] Difference at 536: -nan, expected 15.1881
E0000 00:00:1748042237.884189  847441 buffer_comparator.cc:145] Difference at 537: -nan, expected 14.4224
2025-05-23 23:17:17.884194: E external/xla/xla/service/gpu/autotuning/gemm_fusion_autotuner.cc:1179] Results do not match the reference. This is likely a bug/unexpected loss of precision.
E0000 00:00:1748042237.910001  847441 buffer_comparator.cc:145] Difference at 16: -nan, expected 11.328
E0000 00:00:1748042237.910045  847441 buffer_comparator.cc:145] Difference at 17: -nan, expected 8.55983
E0000 00:00:1748042237.910056  847441 buffer_comparator.cc:145] Difference at 18: -nan, expected 10.4588
E0000 00:00:1748042237.910059  847441 buffer_comparator.cc:145] Difference at 19: -nan, expected 8.81169
E0000 00:00:1748042237.910062  847441 buffer_comparator.cc:145] Difference at 20: -nan, expected 8.98138
E0000 00:00:1748042237.910065  847441 buffer_comparator.cc:145] Difference at 21: -nan, expected 9.49466
E0000 00:00:1748042237.910068  847441 buffer_comparator.cc:145] Difference at 22: -nan, expected 8.4604
E0000 00:00:1748042237.910071  847441 buffer_comparator.cc:145] Difference at 23: -nan, expected 9.78691
E0000 00:00:1748042237.910073  847441 buffer_comparator.cc:145] Difference at 24: -nan, expected 8.15491
E0000 00:00:1748042237.910076  847441 buffer_comparator.cc:145] Difference at 25: -nan, expected 13.0125
2025-05-23 23:17:17.910086: E external/xla/xla/service/gpu/autotuning/gemm_fusion_autotuner.cc:1179] Results do not match the reference. This is likely a bug/unexpected loss of precision.
E0000 00:00:1748042237.912374  847441 buffer_comparator.cc:145] Difference at 16: -nan, expected 11.328
E0000 00:00:1748042237.912391  847441 buffer_comparator.cc:145] Difference at 17: -nan, expected 8.55983
E0000 00:00:1748042237.912395  847441 buffer_comparator.cc:145] Difference at 18: -nan, expected 10.4588
E0000 00:00:1748042237.912398  847441 buffer_comparator.cc:145] Difference at 19: -nan, expected 8.81169
E0000 00:00:1748042237.912401  847441 buffer_comparator.cc:145] Difference at 20: -nan, expected 8.98138
E0000 00:00:1748042237.912404  847441 buffer_comparator.cc:145] Difference at 21: -nan, expected 9.49466
E0000 00:00:1748042237.912407  847441 buffer_comparator.cc:145] Difference at 22: -nan, expected 8.4604
E0000 00:00:1748042237.912410  847441 buffer_comparator.cc:145] Difference at 23: -nan, expected 9.78691
E0000 00:00:1748042237.912412  847441 buffer_comparator.cc:145] Difference at 24: -nan, expected 8.15491
E0000 00:00:1748042237.912415  847441 buffer_comparator.cc:145] Difference at 25: -nan, expected 13.0125
2025-05-23 23:17:17.912420: E external/xla/xla/service/gpu/autotuning/gemm_fusion_autotuner.cc:1179] Results do not match the reference. This is likely a bug/unexpected loss of precision.
E0000 00:00:1748042237.914516  847441 buffer_comparator.cc:145] Difference at 656: -nan, expected 8.69665
E0000 00:00:1748042237.914528  847441 buffer_comparator.cc:145] Difference at 657: -nan, expected 7.68202
E0000 00:00:1748042237.914532  847441 buffer_comparator.cc:145] Difference at 658: -nan, expected 7.88703
E0000 00:00:1748042237.914535  847441 buffer_comparator.cc:145] Difference at 659: -nan, expected 7.16689
E0000 00:00:1748042237.914538  847441 buffer_comparator.cc:145] Difference at 660: -nan, expected 6.63868
E0000 00:00:1748042237.914541  847441 buffer_comparator.cc:145] Difference at 661: -nan, expected 8.39542
E0000 00:00:1748042237.914544  847441 buffer_comparator.cc:145] Difference at 662: -nan, expected 7.00635
E0000 00:00:1748042237.914547  847441 buffer_comparator.cc:145] Difference at 663: -nan, expected 7.06674
E0000 00:00:1748042237.914549  847441 buffer_comparator.cc:145] Difference at 664: -nan, expected 6.11613
E0000 00:00:1748042237.914552  847441 buffer_comparator.cc:145] Difference at 665: -nan, expected 8.63651
2025-05-23 23:17:17.914557: E external/xla/xla/service/gpu/autotuning/gemm_fusion_autotuner.cc:1179] Results do not match the reference. This is likely a bug/unexpected loss of precision.
E0000 00:00:1748042237.916639  847441 buffer_comparator.cc:145] Difference at 672: -nan, expected 8.61244
E0000 00:00:1748042237.916651  847441 buffer_comparator.cc:145] Difference at 673: -nan, expected 6.1493
E0000 00:00:1748042237.916655  847441 buffer_comparator.cc:145] Difference at 674: -nan, expected 8.90756
E0000 00:00:1748042237.916658  847441 buffer_comparator.cc:145] Difference at 675: -nan, expected 7.1184
E0000 00:00:1748042237.916661  847441 buffer_comparator.cc:145] Difference at 676: -nan, expected 8.03527
E0000 00:00:1748042237.916665  847441 buffer_comparator.cc:145] Difference at 677: -nan, expected 7.44864
E0000 00:00:1748042237.916668  847441 buffer_comparator.cc:145] Difference at 678: -nan, expected 7.35203
E0000 00:00:1748042237.916671  847441 buffer_comparator.cc:145] Difference at 679: -nan, expected 7.89603
E0000 00:00:1748042237.916674  847441 buffer_comparator.cc:145] Difference at 680: -nan, expected 7.3266
E0000 00:00:1748042237.916676  847441 buffer_comparator.cc:145] Difference at 681: -nan, expected 9.7807
2025-05-23 23:17:17.916681: E external/xla/xla/service/gpu/autotuning/gemm_fusion_autotuner.cc:1179] Results do not match the reference. This is likely a bug/unexpected loss of precision.
E0000 00:00:1748042237.918767  847441 buffer_comparator.cc:145] Difference at 672: -nan, expected 8.61244
E0000 00:00:1748042237.918780  847441 buffer_comparator.cc:145] Difference at 673: -nan, expected 6.1493
E0000 00:00:1748042237.918784  847441 buffer_comparator.cc:145] Difference at 674: -nan, expected 8.90756
E0000 00:00:1748042237.918787  847441 buffer_comparator.cc:145] Difference at 675: -nan, expected 7.1184
E0000 00:00:1748042237.918789  847441 buffer_comparator.cc:145] Difference at 676: -nan, expected 8.03527
E0000 00:00:1748042237.918792  847441 buffer_comparator.cc:145] Difference at 677: -nan, expected 7.44864
E0000 00:00:1748042237.918795  847441 buffer_comparator.cc:145] Difference at 678: -nan, expected 7.35203
E0000 00:00:1748042237.918798  847441 buffer_comparator.cc:145] Difference at 679: -nan, expected 7.89603
E0000 00:00:1748042237.918801  847441 buffer_comparator.cc:145] Difference at 680: -nan, expected 7.3266
E0000 00:00:1748042237.918803  847441 buffer_comparator.cc:145] Difference at 681: -nan, expected 9.7807
2025-05-23 23:17:17.918808: E external/xla/xla/service/gpu/autotuning/gemm_fusion_autotuner.cc:1179] Results do not match the reference. This is likely a bug/unexpected loss of precision.
E0000 00:00:1748042237.920906  847441 buffer_comparator.cc:145] Difference at 688: -nan, expected 7.86868
E0000 00:00:1748042237.920918  847441 buffer_comparator.cc:145] Difference at 689: -nan, expected 7.33715
E0000 00:00:1748042237.920922  847441 buffer_comparator.cc:145] Difference at 690: -nan, expected 6.05665
E0000 00:00:1748042237.920925  847441 buffer_comparator.cc:145] Difference at 691: -nan, expected 7.16547
E0000 00:00:1748042237.920928  847441 buffer_comparator.cc:145] Difference at 692: -nan, expected 8.27916
E0000 00:00:1748042237.920931  847441 buffer_comparator.cc:145] Difference at 693: -nan, expected 5.80258
E0000 00:00:1748042237.920934  847441 buffer_comparator.cc:145] Difference at 694: -nan, expected 6.06621
E0000 00:00:1748042237.920936  847441 buffer_comparator.cc:145] Difference at 695: -nan, expected 7.00273
E0000 00:00:1748042237.920939  847441 buffer_comparator.cc:145] Difference at 696: -nan, expected 7.92525
E0000 00:00:1748042237.920942  847441 buffer_comparator.cc:145] Difference at 729: -nan, expected 7.66068
2025-05-23 23:17:17.920947: E external/xla/xla/service/gpu/autotuning/gemm_fusion_autotuner.cc:1179] Results do not match the reference. This is likely a bug/unexpected loss of precision.
E0000 00:00:1748042237.923032  847441 buffer_comparator.cc:145] Difference at 688: -nan, expected 7.86868
E0000 00:00:1748042237.923044  847441 buffer_comparator.cc:145] Difference at 689: -nan, expected 7.33715
E0000 00:00:1748042237.923048  847441 buffer_comparator.cc:145] Difference at 690: -nan, expected 6.05665
E0000 00:00:1748042237.923051  847441 buffer_comparator.cc:145] Difference at 691: -nan, expected 7.16547
E0000 00:00:1748042237.923054  847441 buffer_comparator.cc:145] Difference at 692: -nan, expected 8.27916
E0000 00:00:1748042237.923057  847441 buffer_comparator.cc:145] Difference at 693: -nan, expected 5.80258
E0000 00:00:1748042237.923060  847441 buffer_comparator.cc:145] Difference at 694: -nan, expected 6.06621
E0000 00:00:1748042237.923063  847441 buffer_comparator.cc:145] Difference at 695: -nan, expected 7.00273
E0000 00:00:1748042237.923067  847441 buffer_comparator.cc:145] Difference at 696: -nan, expected 7.92525
E0000 00:00:1748042237.923070  847441 buffer_comparator.cc:145] Difference at 729: -nan, expected 7.66068
2025-05-23 23:17:17.923074: E external/xla/xla/service/gpu/autotuning/gemm_fusion_autotuner.cc:1179] Results do not match the reference. This is likely a bug/unexpected loss of precision.
Iteration: 0001 	 Loss: 2.08073235
Iteration: 0101 	 Loss: 0.142443746
Iteration: 0201 	 Loss: 0.00498719513
Iteration: 0301 	 Loss: 0.00116170431
Iteration: 0401 	 Loss: 0.000497820089
Iteration: 0501 	 Loss: 0.00027494994
Iteration: 0601 	 Loss: 0.000180605697
Iteration: 0701 	 Loss: 0.000201430521
Iteration: 0801 	 Loss: 0.000379697973
Iteration: 0901 	 Loss: 0.000106757798
Iteration: 1000 	 Loss: 0.000231371887

Training with Optimization.jl

If you are coming from the SciML ecosystem and want to use Optimization.jl, please refer to the Optimization.jl Tutorial.

Additional Packages

LuxDL hosts various packages that provide additional functionality for Lux.jl. All packages mentioned in this documentation are available via the Julia General Registry.

You can install all those packages via import Pkg; Pkg.add(<package name>).

XLA (CPU/GPU/TPU) Support

Lux.jl supports XLA compilation for CPU, GPU, and TPU using Reactant.jl.

GPU Support

GPU Support for Lux.jl requires loading additional packages:

LuxCUDA.jl for CUDA support.
AMDGPU.jl for AMDGPU support.
Metal.jl for Apple Metal support.
oneAPI.jl for oneAPI support.

Trusted by

Getting Started ​

Installation ​

Quickstart ​

Defining Custom Layers ​

Additional Packages ​

XLA (CPU/GPU/TPU) Support ​

GPU Support ​

Getting Started

Installation

Quickstart

Defining Custom Layers

Additional Packages

XLA (CPU/GPU/TPU) Support

GPU Support