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: 24105.8164062, Throughput: 10.947930 im/s
Epoch 1, Train Loss: 39585.2773438, Time: 456.2995s, Throughput: 10.940183 im/s
Epoch 2, Iter 39, Loss: 18082.8984375, Throughput: 82.699545 im/s
Epoch 2, Train Loss: 19946.3476562, Time: 60.3633s, Throughput: 82.699215 im/s
Epoch 3, Iter 39, Loss: 16205.8867188, Throughput: 83.697036 im/s
Epoch 3, Train Loss: 16594.6230469, Time: 59.6439s, Throughput: 83.696743 im/s
Epoch 4, Iter 39, Loss: 13799.1894531, Throughput: 83.340001 im/s
Epoch 4, Train Loss: 14959.5156250, Time: 59.8994s, Throughput: 83.339727 im/s
Epoch 5, Iter 39, Loss: 13042.5048828, Throughput: 83.343608 im/s
Epoch 5, Train Loss: 13971.4453125, Time: 59.8968s, Throughput: 83.343307 im/s
Epoch 6, Iter 39, Loss: 13434.6757812, Throughput: 83.392634 im/s
Epoch 6, Train Loss: 13391.5322266, Time: 59.8616s, Throughput: 83.392350 im/s
Epoch 7, Iter 39, Loss: 13281.9423828, Throughput: 83.710461 im/s
Epoch 7, Train Loss: 12897.3857422, Time: 59.6343s, Throughput: 83.710174 im/s
Epoch 8, Iter 39, Loss: 12624.3105469, Throughput: 83.215725 im/s
Epoch 8, Train Loss: 12468.8955078, Time: 59.9889s, Throughput: 83.215414 im/s
Epoch 9, Iter 39, Loss: 11300.0849609, Throughput: 84.182756 im/s
Epoch 9, Train Loss: 12245.2744141, Time: 59.2998s, Throughput: 84.182452 im/s
Epoch 10, Iter 39, Loss: 11744.6611328, Throughput: 84.161659 im/s
Epoch 10, Train Loss: 11921.1289062, Time: 59.3146s, Throughput: 84.161341 im/s
Epoch 11, Iter 39, Loss: 12131.6542969, Throughput: 84.036918 im/s
Epoch 11, Train Loss: 11754.1982422, Time: 59.4027s, Throughput: 84.036584 im/s
Epoch 12, Iter 39, Loss: 12180.2539062, Throughput: 84.175795 im/s
Epoch 12, Train Loss: 11537.8730469, Time: 59.3047s, Throughput: 84.175517 im/s
Epoch 13, Iter 39, Loss: 11230.5830078, Throughput: 83.175038 im/s
Epoch 13, Train Loss: 11379.1650391, Time: 60.0182s, Throughput: 83.174747 im/s
Epoch 14, Iter 39, Loss: 11113.9189453, Throughput: 84.212608 im/s
Epoch 14, Train Loss: 11245.1806641, Time: 59.2787s, Throughput: 84.212326 im/s
Epoch 15, Iter 39, Loss: 11493.0937500, Throughput: 82.897810 im/s
Epoch 15, Train Loss: 11049.4423828, Time: 60.2189s, Throughput: 82.897557 im/s
Epoch 16, Iter 39, Loss: 10461.7949219, Throughput: 83.179371 im/s
Epoch 16, Train Loss: 10952.6123047, Time: 60.0151s, Throughput: 83.179112 im/s
Epoch 17, Iter 39, Loss: 10596.8808594, Throughput: 83.552799 im/s
Epoch 17, Train Loss: 10895.8955078, Time: 59.7468s, Throughput: 83.552524 im/s
Epoch 18, Iter 39, Loss: 10986.5703125, Throughput: 83.687990 im/s
Epoch 18, Train Loss: 10750.9443359, Time: 59.6503s, Throughput: 83.687718 im/s
Epoch 19, Iter 39, Loss: 11365.5644531, Throughput: 84.614118 im/s
Epoch 19, Train Loss: 10620.9716797, Time: 58.9975s, Throughput: 84.613822 im/s
Epoch 20, Iter 39, Loss: 10621.5156250, Throughput: 84.023237 im/s
Epoch 20, Train Loss: 10588.4931641, Time: 59.4123s, Throughput: 84.022939 im/s
Epoch 21, Iter 39, Loss: 10053.2148438, Throughput: 84.009482 im/s
Epoch 21, Train Loss: 10514.9443359, Time: 59.4221s, Throughput: 84.009214 im/s
Epoch 22, Iter 39, Loss: 11073.2080078, Throughput: 83.754702 im/s
Epoch 22, Train Loss: 10348.8457031, Time: 59.6028s, Throughput: 83.754435 im/s
Epoch 23, Iter 39, Loss: 10746.5048828, Throughput: 84.155900 im/s
Epoch 23, Train Loss: 10399.0927734, Time: 59.3187s, Throughput: 84.155611 im/s
Epoch 24, Iter 39, Loss: 10436.0722656, Throughput: 84.115622 im/s
Epoch 24, Train Loss: 10359.7294922, Time: 59.3471s, Throughput: 84.115363 im/s
Epoch 25, Iter 39, Loss: 10074.0253906, Throughput: 83.670800 im/s
Epoch 25, Train Loss: 10224.0654297, Time: 59.6626s, Throughput: 83.670511 im/s
Epoch 26, Iter 39, Loss: 10053.7216797, Throughput: 83.492469 im/s
Epoch 26, Train Loss: 10237.4326172, Time: 59.7900s, Throughput: 83.492191 im/s
Epoch 27, Iter 39, Loss: 9544.2988281, Throughput: 83.161632 im/s
Epoch 27, Train Loss: 10128.0371094, Time: 60.0279s, Throughput: 83.161366 im/s
Epoch 28, Iter 39, Loss: 10489.5205078, Throughput: 84.420658 im/s
Epoch 28, Train Loss: 10047.3681641, Time: 59.1326s, Throughput: 84.420377 im/s
Epoch 29, Iter 39, Loss: 9825.6474609, Throughput: 83.812599 im/s
Epoch 29, Train Loss: 9980.2558594, Time: 59.5617s, Throughput: 83.812302 im/s
Epoch 30, Iter 39, Loss: 10163.9335938, Throughput: 84.210254 im/s
Epoch 30, Train Loss: 9913.6513672, Time: 59.2804s, Throughput: 84.209981 im/s
Epoch 31, Iter 39, Loss: 9916.3896484, Throughput: 83.599623 im/s
Epoch 31, Train Loss: 9884.8046875, Time: 59.7134s, Throughput: 83.599321 im/s
Epoch 32, Iter 39, Loss: 10366.9843750, Throughput: 84.053914 im/s
Epoch 32, Train Loss: 9981.4052734, Time: 59.3906s, Throughput: 84.053652 im/s
Epoch 33, Iter 39, Loss: 9639.4033203, Throughput: 84.143229 im/s
Epoch 33, Train Loss: 9911.8398438, Time: 59.3276s, Throughput: 84.142947 im/s
Epoch 34, Iter 39, Loss: 10117.0937500, Throughput: 83.955970 im/s
Epoch 34, Train Loss: 9795.6005859, Time: 59.4599s, Throughput: 83.955698 im/s
Epoch 35, Iter 39, Loss: 9432.5830078, Throughput: 83.825127 im/s
Epoch 35, Train Loss: 9750.6513672, Time: 59.5528s, Throughput: 83.824834 im/s
Epoch 36, Iter 39, Loss: 9656.9707031, Throughput: 84.082213 im/s
Epoch 36, Train Loss: 9660.9453125, Time: 59.3707s, Throughput: 84.081947 im/s
Epoch 37, Iter 39, Loss: 9775.6044922, Throughput: 83.959628 im/s
Epoch 37, Train Loss: 9630.8847656, Time: 59.4574s, Throughput: 83.959328 im/s
Epoch 38, Iter 39, Loss: 9403.2109375, Throughput: 84.447016 im/s
Epoch 38, Train Loss: 9559.5263672, Time: 59.1142s, Throughput: 84.446731 im/s
Epoch 39, Iter 39, Loss: 9224.4062500, Throughput: 83.456223 im/s
Epoch 39, Train Loss: 9587.6054688, Time: 59.8160s, Throughput: 83.455942 im/s
Epoch 40, Iter 39, Loss: 9445.1494141, Throughput: 83.128617 im/s
Epoch 40, Train Loss: 9504.6992188, Time: 60.0517s, Throughput: 83.128338 im/s
Epoch 41, Iter 39, Loss: 9564.5390625, Throughput: 84.193341 im/s
Epoch 41, Train Loss: 9532.4023438, Time: 59.2923s, Throughput: 84.193064 im/s
Epoch 42, Iter 39, Loss: 10397.0917969, Throughput: 83.808953 im/s
Epoch 42, Train Loss: 9438.7724609, Time: 59.5642s, Throughput: 83.808660 im/s
Epoch 43, Iter 39, Loss: 9463.2236328, Throughput: 83.642170 im/s
Epoch 43, Train Loss: 9509.8417969, Time: 59.6830s, Throughput: 83.641921 im/s
Epoch 44, Iter 39, Loss: 9551.9033203, Throughput: 83.469967 im/s
Epoch 44, Train Loss: 9449.2031250, Time: 59.8061s, Throughput: 83.469710 im/s
Epoch 45, Iter 39, Loss: 9370.0664062, Throughput: 83.927592 im/s
Epoch 45, Train Loss: 9478.2968750, Time: 59.4801s, Throughput: 83.927287 im/s
Epoch 46, Iter 39, Loss: 9151.3007812, Throughput: 83.916633 im/s
Epoch 46, Train Loss: 9341.2294922, Time: 59.4878s, Throughput: 83.916363 im/s
Epoch 47, Iter 39, Loss: 9743.4619141, Throughput: 83.751321 im/s
Epoch 47, Train Loss: 9344.9501953, Time: 59.6052s, Throughput: 83.751031 im/s
Epoch 48, Iter 39, Loss: 9034.9531250, Throughput: 83.750784 im/s
Epoch 48, Train Loss: 9364.2724609, Time: 59.6056s, Throughput: 83.750527 im/s
Epoch 49, Iter 39, Loss: 9649.0898438, Throughput: 83.689692 im/s
Epoch 49, Train Loss: 9380.2255859, Time: 59.6491s, Throughput: 83.689399 im/s
Epoch 50, Iter 39, Loss: 9853.7412109, Throughput: 84.015573 im/s
Epoch 50, Train Loss: 9368.7773438, Time: 59.4177s, Throughput: 84.015320 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 1.12.6
Commit 15346901f00 (2026-04-09 19:20 UTC)
Build Info:
Official https://julialang.org release
Platform Info:
OS: Linux (x86_64-linux-gnu)
CPU: 4 × AMD EPYC 9V74 80-Core Processor
WORD_SIZE: 64
LLVM: libLLVM-18.1.7 (ORCJIT, znver4)
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.