Convolutional VAE for MNIST
Convolutional variational autoencoder (CVAE) implementation in MLX using MNIST. This is based on the CVAE implementation in MLX.
julia
using Lux,
Reactant,
MLDatasets,
Random,
Statistics,
Enzyme,
MLUtils,
DataAugmentation,
ConcreteStructs,
OneHotArrays,
ImageShow,
Images,
Printf,
Optimisers
const xdev = reactant_device(; force=true)
const cdev = cpu_device()
const IN_VSCODE = isdefined(Main, :VSCodeServer)falseModel Definition
First we will define the encoder.It maps the input to a normal distribution in latent space and sample a latent vector from that distribution.
julia
function cvae_encoder(
rng=Random.default_rng();
num_latent_dims::Int,
image_shape::Dims{3},
max_num_filters::Int,
)
flattened_dim = prod(image_shape[1:2] .÷ 8) * max_num_filters
return @compact(;
embed=Chain(
Chain(
Conv((3, 3), image_shape[3] => max_num_filters ÷ 4; stride=2, pad=1),
BatchNorm(max_num_filters ÷ 4, leakyrelu),
),
Chain(
Conv((3, 3), max_num_filters ÷ 4 => max_num_filters ÷ 2; stride=2, pad=1),
BatchNorm(max_num_filters ÷ 2, leakyrelu),
),
Chain(
Conv((3, 3), max_num_filters ÷ 2 => max_num_filters; stride=2, pad=1),
BatchNorm(max_num_filters, leakyrelu),
),
FlattenLayer(),
),
proj_mu=Dense(flattened_dim, num_latent_dims; init_bias=zeros32),
proj_log_var=Dense(flattened_dim, num_latent_dims; init_bias=zeros32),
rng
) do x
y = embed(x)
μ = proj_mu(y)
logσ² = proj_log_var(y)
T = eltype(logσ²)
logσ² = clamp.(logσ², -T(20.0f0), T(10.0f0))
σ = exp.(logσ² .* T(0.5))
# Generate a tensor of random values from a normal distribution
ϵ = randn_like(Lux.replicate(rng), σ)
# Reparameterization trick to backpropagate through sampling
z = ϵ .* σ .+ μ
@return z, μ, logσ²
end
endSimilarly we define the decoder.
julia
function cvae_decoder(; num_latent_dims::Int, image_shape::Dims{3}, max_num_filters::Int)
flattened_dim = prod(image_shape[1:2] .÷ 8) * max_num_filters
return @compact(;
linear=Dense(num_latent_dims, flattened_dim),
upchain=Chain(
Chain(
Upsample(2),
Conv((3, 3), max_num_filters => max_num_filters ÷ 2; stride=1, pad=1),
BatchNorm(max_num_filters ÷ 2, leakyrelu),
),
Chain(
Upsample(2),
Conv((3, 3), max_num_filters ÷ 2 => max_num_filters ÷ 4; stride=1, pad=1),
BatchNorm(max_num_filters ÷ 4, leakyrelu),
),
Chain(
Upsample(2),
Conv(
(3, 3), max_num_filters ÷ 4 => image_shape[3], sigmoid; stride=1, pad=1
),
),
),
max_num_filters
) do x
y = linear(x)
img = reshape(y, image_shape[1] ÷ 8, image_shape[2] ÷ 8, max_num_filters, :)
@return upchain(img)
end
end
@concrete struct CVAE <: AbstractLuxContainerLayer{(:encoder, :decoder)}
encoder <: AbstractLuxLayer
decoder <: AbstractLuxLayer
end
function CVAE(
rng=Random.default_rng();
num_latent_dims::Int,
image_shape::Dims{3},
max_num_filters::Int,
)
decoder = cvae_decoder(; num_latent_dims, image_shape, max_num_filters)
encoder = cvae_encoder(rng; num_latent_dims, image_shape, max_num_filters)
return CVAE(encoder, decoder)
end
function (cvae::CVAE)(x, ps, st)
(z, μ, logσ²), st_enc = cvae.encoder(x, ps.encoder, st.encoder)
x_rec, st_dec = cvae.decoder(z, ps.decoder, st.decoder)
return (x_rec, μ, logσ²), (; encoder=st_enc, decoder=st_dec)
end
function encode(cvae::CVAE, x, ps, st)
(z, _, _), st_enc = cvae.encoder(x, ps.encoder, st.encoder)
return z, (; encoder=st_enc, st.decoder)
end
function decode(cvae::CVAE, z, ps, st)
x_rec, st_dec = cvae.decoder(z, ps.decoder, st.decoder)
return x_rec, (; decoder=st_dec, st.encoder)
endLoading MNIST
julia
@concrete struct TensorDataset
dataset
transform
total_samples::Int
end
Base.length(ds::TensorDataset) = ds.total_samples
function Base.getindex(ds::TensorDataset, idxs::Union{Vector{<:Integer},AbstractRange})
img = Image.(eachslice(convert2image(ds.dataset, idxs); dims=3))
return stack(parent ∘ itemdata ∘ Base.Fix1(apply, ds.transform), img)
end
function loadmnist(batchsize, image_size::Dims{2})
# Load MNIST: Only 1500 for demonstration purposes on CI
train_dataset = MNIST(; split=:train)
N = parse(Bool, get(ENV, "CI", "false")) ? 5000 : length(train_dataset)
train_transform = ScaleKeepAspect(image_size) |> ImageToTensor()
trainset = TensorDataset(train_dataset, train_transform, N)
trainloader = DataLoader(trainset; batchsize, shuffle=true, partial=false)
return trainloader
endHelper Functions
Generate an Image Grid from a list of images
julia
function create_image_grid(imgs::AbstractArray, grid_rows::Int, grid_cols::Int)
total_images = grid_rows * grid_cols
imgs = map(eachslice(imgs[:, :, :, 1:total_images]; dims=4)) do img
cimg = if size(img, 3) == 1
colorview(Gray, view(img, :, :, 1))
else
colorview(RGB, permutedims(img, (3, 1, 2)))
end
return cimg'
end
return create_image_grid(imgs, grid_rows, grid_cols)
end
function create_image_grid(images::Vector, grid_rows::Int, grid_cols::Int)
# Check if the number of images matches the grid
total_images = grid_rows * grid_cols
@assert length(images) == total_images
# Get the size of a single image (assuming all images are the same size)
img_height, img_width = size(images[1])
# Create a blank grid canvas
grid_height = img_height * grid_rows
grid_width = img_width * grid_cols
grid_canvas = similar(images[1], grid_height, grid_width)
# Place each image in the correct position on the canvas
for idx in 1:total_images
row = div(idx - 1, grid_cols) + 1
col = mod(idx - 1, grid_cols) + 1
start_row = (row - 1) * img_height + 1
start_col = (col - 1) * img_width + 1
grid_canvas[start_row:(start_row + img_height - 1), start_col:(start_col + img_width - 1)] .= images[idx]
end
return grid_canvas
end
function loss_function(model, ps, st, X)
(y, μ, logσ²), st = model(X, ps, st)
reconstruction_loss = MSELoss(; agg=sum)(y, X)
kldiv_loss = -sum(1 .+ logσ² .- μ .^ 2 .- exp.(logσ²)) / 2
loss = reconstruction_loss + kldiv_loss
return loss, st, (; y, μ, logσ², reconstruction_loss, kldiv_loss)
end
function generate_images(
model, ps, st; num_samples::Int=128, num_latent_dims::Int, decode_compiled=nothing
)
z = get_device((ps, st))(randn(Float32, num_latent_dims, num_samples))
if decode_compiled === nothing
images, _ = decode(model, z, ps, Lux.testmode(st))
else
images, _ = decode_compiled(model, z, ps, Lux.testmode(st))
images = cpu_device()(images)
end
return create_image_grid(images, 8, num_samples ÷ 8)
end
function reconstruct_images(model, ps, st, X)
(recon, _, _), _ = model(X, ps, Lux.testmode(st))
recon = cpu_device()(recon)
return create_image_grid(recon, 8, size(X, ndims(X)) ÷ 8)
endreconstruct_images (generic function with 1 method)Training the Model
julia
function main(;
batchsize=128,
image_size=(64, 64),
num_latent_dims=8,
max_num_filters=64,
seed=0,
epochs=50,
weight_decay=1.0e-5,
learning_rate=1.0e-3,
num_samples=batchsize,
)
rng = Xoshiro()
Random.seed!(rng, seed)
cvae = CVAE(rng; num_latent_dims, image_shape=(image_size..., 1), max_num_filters)
ps, st = Lux.setup(rng, cvae) |> xdev
z = xdev(randn(Float32, num_latent_dims, num_samples))
decode_compiled = @compile decode(cvae, z, ps, Lux.testmode(st))
x = randn(Float32, image_size..., 1, batchsize) |> xdev
cvae_compiled = @compile cvae(x, ps, Lux.testmode(st))
train_dataloader = loadmnist(batchsize, image_size) |> xdev
opt = AdamW(; eta=learning_rate, lambda=weight_decay)
train_state = Training.TrainState(cvae, ps, st, opt)
@printf "Total Trainable Parameters: %0.4f M\n" (Lux.parameterlength(ps) / 1.0e6)
empty_row, model_img_full = nothing, nothing
for epoch in 1:epochs
loss_total = 0.0f0
total_samples = 0
start_time = time()
for (i, X) in enumerate(train_dataloader)
(_, loss, _, train_state) = Training.single_train_step!(
AutoEnzyme(), loss_function, X, train_state; return_gradients=Val(false)
)
loss_total += loss
total_samples += size(X, ndims(X))
if i % 250 == 0 || i == length(train_dataloader)
throughput = total_samples / (time() - start_time)
@printf "Epoch %d, Iter %d, Loss: %.7f, Throughput: %.6f im/s\n" epoch i loss throughput
end
end
total_time = time() - start_time
train_loss = loss_total / length(train_dataloader)
throughput = total_samples / total_time
@printf "Epoch %d, Train Loss: %.7f, Time: %.4fs, Throughput: %.6f im/s\n" epoch train_loss total_time throughput
if IN_VSCODE || epoch == epochs
recon_images = reconstruct_images(
cvae_compiled,
train_state.parameters,
train_state.states,
first(train_dataloader),
)
gen_images = generate_images(
cvae,
train_state.parameters,
train_state.states;
num_samples,
num_latent_dims,
decode_compiled,
)
if empty_row === nothing
empty_row = similar(gen_images, image_size[1], size(gen_images, 2))
fill!(empty_row, 0)
end
model_img_full = vcat(recon_images, empty_row, gen_images)
IN_VSCODE && display(model_img_full)
end
end
return model_img_full
end
img = main()Total Trainable Parameters: 0.1493 M
Epoch 1, Iter 39, Loss: 23709.7363281, Throughput: 4.784546 im/s
Epoch 1, Train Loss: 39612.0546875, Time: 1043.6660s, Throughput: 4.783139 im/s
Epoch 2, Iter 39, Loss: 17915.8554688, Throughput: 72.694600 im/s
Epoch 2, Train Loss: 20221.9160156, Time: 68.6710s, Throughput: 72.694431 im/s
Epoch 3, Iter 39, Loss: 15977.2890625, Throughput: 73.156202 im/s
Epoch 3, Train Loss: 16558.5039062, Time: 68.2377s, Throughput: 73.156022 im/s
Epoch 4, Iter 39, Loss: 14957.2451172, Throughput: 73.299175 im/s
Epoch 4, Train Loss: 15081.5156250, Time: 68.1046s, Throughput: 73.299002 im/s
Epoch 5, Iter 39, Loss: 14716.1982422, Throughput: 73.253993 im/s
Epoch 5, Train Loss: 14144.2275391, Time: 68.1466s, Throughput: 73.253814 im/s
Epoch 6, Iter 39, Loss: 13682.9921875, Throughput: 72.784752 im/s
Epoch 6, Train Loss: 13422.0468750, Time: 68.5860s, Throughput: 72.784561 im/s
Epoch 7, Iter 39, Loss: 13254.1308594, Throughput: 73.010247 im/s
Epoch 7, Train Loss: 12926.5566406, Time: 68.3741s, Throughput: 73.010074 im/s
Epoch 8, Iter 39, Loss: 12135.5410156, Throughput: 73.290202 im/s
Epoch 8, Train Loss: 12712.0839844, Time: 68.1129s, Throughput: 73.290029 im/s
Epoch 9, Iter 39, Loss: 11748.8076172, Throughput: 73.324228 im/s
Epoch 9, Train Loss: 12273.1484375, Time: 68.0813s, Throughput: 73.324054 im/s
Epoch 10, Iter 39, Loss: 12347.8359375, Throughput: 72.959865 im/s
Epoch 10, Train Loss: 12006.8642578, Time: 68.4213s, Throughput: 72.959702 im/s
Epoch 11, Iter 39, Loss: 12061.1171875, Throughput: 72.755392 im/s
Epoch 11, Train Loss: 11914.9843750, Time: 68.6136s, Throughput: 72.755224 im/s
Epoch 12, Iter 39, Loss: 11044.7832031, Throughput: 73.321919 im/s
Epoch 12, Train Loss: 11757.7968750, Time: 68.0835s, Throughput: 73.321749 im/s
Epoch 13, Iter 39, Loss: 11601.7451172, Throughput: 73.178894 im/s
Epoch 13, Train Loss: 11543.7744141, Time: 68.2165s, Throughput: 73.178728 im/s
Epoch 14, Iter 39, Loss: 11414.5185547, Throughput: 73.162515 im/s
Epoch 14, Train Loss: 11364.8916016, Time: 68.2318s, Throughput: 73.162341 im/s
Epoch 15, Iter 39, Loss: 11854.3183594, Throughput: 72.732060 im/s
Epoch 15, Train Loss: 11315.4755859, Time: 68.6357s, Throughput: 72.731865 im/s
Epoch 16, Iter 39, Loss: 10780.8847656, Throughput: 72.819364 im/s
Epoch 16, Train Loss: 11122.2490234, Time: 68.5533s, Throughput: 72.819199 im/s
Epoch 17, Iter 39, Loss: 11141.4804688, Throughput: 72.884859 im/s
Epoch 17, Train Loss: 11098.9814453, Time: 68.4918s, Throughput: 72.884678 im/s
Epoch 18, Iter 39, Loss: 11228.5107422, Throughput: 73.187646 im/s
Epoch 18, Train Loss: 10955.6142578, Time: 68.2084s, Throughput: 73.187469 im/s
Epoch 19, Iter 39, Loss: 10776.5146484, Throughput: 72.834019 im/s
Epoch 19, Train Loss: 10839.1357422, Time: 68.5396s, Throughput: 72.833846 im/s
Epoch 20, Iter 39, Loss: 11239.9755859, Throughput: 73.278053 im/s
Epoch 20, Train Loss: 10718.1621094, Time: 68.1243s, Throughput: 73.277843 im/s
Epoch 21, Iter 39, Loss: 10491.0517578, Throughput: 72.986327 im/s
Epoch 21, Train Loss: 10681.5498047, Time: 68.3965s, Throughput: 72.986180 im/s
Epoch 22, Iter 39, Loss: 10995.9570312, Throughput: 73.135147 im/s
Epoch 22, Train Loss: 10568.6777344, Time: 68.2574s, Throughput: 73.134969 im/s
Epoch 23, Iter 39, Loss: 10259.7753906, Throughput: 72.818659 im/s
Epoch 23, Train Loss: 10513.3105469, Time: 68.5540s, Throughput: 72.818487 im/s
Epoch 24, Iter 39, Loss: 10564.4990234, Throughput: 72.435619 im/s
Epoch 24, Train Loss: 10460.9570312, Time: 68.9166s, Throughput: 72.435422 im/s
Epoch 25, Iter 39, Loss: 10099.8417969, Throughput: 72.762994 im/s
Epoch 25, Train Loss: 10417.5673828, Time: 68.6065s, Throughput: 72.762815 im/s
Epoch 26, Iter 39, Loss: 10421.3701172, Throughput: 71.920607 im/s
Epoch 26, Train Loss: 10291.8417969, Time: 69.4100s, Throughput: 71.920439 im/s
Epoch 27, Iter 39, Loss: 10332.1542969, Throughput: 72.470533 im/s
Epoch 27, Train Loss: 10170.1171875, Time: 68.8833s, Throughput: 72.470354 im/s
Epoch 28, Iter 39, Loss: 10414.2109375, Throughput: 72.731638 im/s
Epoch 28, Train Loss: 10211.5253906, Time: 68.6360s, Throughput: 72.731469 im/s
Epoch 29, Iter 39, Loss: 10229.8828125, Throughput: 74.036006 im/s
Epoch 29, Train Loss: 10152.9482422, Time: 67.4268s, Throughput: 74.035829 im/s
Epoch 30, Iter 39, Loss: 10022.5488281, Throughput: 73.097046 im/s
Epoch 30, Train Loss: 10097.3505859, Time: 68.2929s, Throughput: 73.096862 im/s
Epoch 31, Iter 39, Loss: 9969.2412109, Throughput: 72.781774 im/s
Epoch 31, Train Loss: 10056.9335938, Time: 68.5888s, Throughput: 72.781610 im/s
Epoch 32, Iter 39, Loss: 10402.6640625, Throughput: 72.072708 im/s
Epoch 32, Train Loss: 10062.1181641, Time: 69.2636s, Throughput: 72.072508 im/s
Epoch 33, Iter 39, Loss: 9348.0927734, Throughput: 71.845979 im/s
Epoch 33, Train Loss: 9980.1611328, Time: 69.4821s, Throughput: 71.845825 im/s
Epoch 34, Iter 39, Loss: 9740.7460938, Throughput: 71.732123 im/s
Epoch 34, Train Loss: 9976.4326172, Time: 69.5924s, Throughput: 71.731937 im/s
Epoch 35, Iter 39, Loss: 9620.7666016, Throughput: 72.315286 im/s
Epoch 35, Train Loss: 9798.8115234, Time: 69.0312s, Throughput: 72.315108 im/s
Epoch 36, Iter 39, Loss: 9560.7773438, Throughput: 71.943058 im/s
Epoch 36, Train Loss: 9873.7714844, Time: 69.3884s, Throughput: 71.942894 im/s
Epoch 37, Iter 39, Loss: 9822.9902344, Throughput: 72.016072 im/s
Epoch 37, Train Loss: 9857.9287109, Time: 69.3180s, Throughput: 72.015885 im/s
Epoch 38, Iter 39, Loss: 9548.0537109, Throughput: 71.546794 im/s
Epoch 38, Train Loss: 9770.3623047, Time: 69.7727s, Throughput: 71.546624 im/s
Epoch 39, Iter 39, Loss: 9796.1806641, Throughput: 71.392936 im/s
Epoch 39, Train Loss: 9713.8828125, Time: 69.9231s, Throughput: 71.392767 im/s
Epoch 40, Iter 39, Loss: 9592.5605469, Throughput: 71.806915 im/s
Epoch 40, Train Loss: 9722.4042969, Time: 69.5199s, Throughput: 71.806730 im/s
Epoch 41, Iter 39, Loss: 9478.2275391, Throughput: 72.201927 im/s
Epoch 41, Train Loss: 9667.8232422, Time: 69.1396s, Throughput: 72.201768 im/s
Epoch 42, Iter 39, Loss: 9511.6093750, Throughput: 71.040978 im/s
Epoch 42, Train Loss: 9615.7431641, Time: 70.2695s, Throughput: 71.040803 im/s
Epoch 43, Iter 39, Loss: 9742.1542969, Throughput: 71.666278 im/s
Epoch 43, Train Loss: 9601.1406250, Time: 69.6563s, Throughput: 71.666124 im/s
Epoch 44, Iter 39, Loss: 9178.7187500, Throughput: 71.784041 im/s
Epoch 44, Train Loss: 9542.4140625, Time: 69.5421s, Throughput: 71.783869 im/s
Epoch 45, Iter 39, Loss: 9261.2695312, Throughput: 71.665436 im/s
Epoch 45, Train Loss: 9483.0966797, Time: 69.6572s, Throughput: 71.665259 im/s
Epoch 46, Iter 39, Loss: 9509.0468750, Throughput: 72.450102 im/s
Epoch 46, Train Loss: 9492.9472656, Time: 68.9028s, Throughput: 72.449932 im/s
Epoch 47, Iter 39, Loss: 9463.7167969, Throughput: 71.688638 im/s
Epoch 47, Train Loss: 9455.3935547, Time: 69.6346s, Throughput: 71.688471 im/s
Epoch 48, Iter 39, Loss: 9721.0019531, Throughput: 71.675526 im/s
Epoch 48, Train Loss: 9439.2080078, Time: 69.6474s, Throughput: 71.675340 im/s
Epoch 49, Iter 39, Loss: 9172.4648438, Throughput: 71.591071 im/s
Epoch 49, Train Loss: 9463.2919922, Time: 69.7295s, Throughput: 71.590903 im/s
Epoch 50, Iter 39, Loss: 9742.7382812, Throughput: 72.821963 im/s
Epoch 50, Train Loss: 9415.4208984, Time: 68.5509s, Throughput: 72.821821 im/s
Appendix
julia
using InteractiveUtils
InteractiveUtils.versioninfo()
if @isdefined(MLDataDevices)
if @isdefined(CUDA) && MLDataDevices.functional(CUDADevice)
println()
CUDA.versioninfo()
end
if @isdefined(AMDGPU) && MLDataDevices.functional(AMDGPUDevice)
println()
AMDGPU.versioninfo()
end
endJulia Version 1.12.5
Commit 5fe89b8ddc1 (2026-02-09 16:05 UTC)
Build Info:
Official https://julialang.org release
Platform Info:
OS: Linux (x86_64-linux-gnu)
CPU: 4 × AMD EPYC 7763 64-Core Processor
WORD_SIZE: 64
LLVM: libLLVM-18.1.7 (ORCJIT, znver3)
GC: Built with stock GC
Threads: 4 default, 1 interactive, 4 GC (on 4 virtual cores)
Environment:
JULIA_DEBUG = Literate
LD_LIBRARY_PATH =
JULIA_NUM_THREADS = 4
JULIA_CPU_HARD_MEMORY_LIMIT = 100%
JULIA_PKG_PRECOMPILE_AUTO = 0This page was generated using Literate.jl.