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: 24103.2246094, Throughput: 4.256182 im/s
Epoch 1, Train Loss: 39669.5820312, Time: 1173.1682s, Throughput: 4.255144 im/s
Epoch 2, Iter 39, Loss: 17992.7597656, Throughput: 70.610926 im/s
Epoch 2, Train Loss: 20113.4687500, Time: 70.6975s, Throughput: 70.610694 im/s
Epoch 3, Iter 39, Loss: 17049.8847656, Throughput: 70.390551 im/s
Epoch 3, Train Loss: 16843.8632812, Time: 70.9188s, Throughput: 70.390352 im/s
Epoch 4, Iter 39, Loss: 15357.3564453, Throughput: 70.546175 im/s
Epoch 4, Train Loss: 15247.3330078, Time: 70.7624s, Throughput: 70.545984 im/s
Epoch 5, Iter 39, Loss: 14778.0947266, Throughput: 70.381460 im/s
Epoch 5, Train Loss: 14302.2373047, Time: 70.9279s, Throughput: 70.381282 im/s
Epoch 6, Iter 39, Loss: 13817.2998047, Throughput: 70.710553 im/s
Epoch 6, Train Loss: 13646.4453125, Time: 70.5979s, Throughput: 70.710357 im/s
Epoch 7, Iter 39, Loss: 13233.8574219, Throughput: 70.273477 im/s
Epoch 7, Train Loss: 13053.5761719, Time: 71.0370s, Throughput: 70.273266 im/s
Epoch 8, Iter 39, Loss: 12012.6992188, Throughput: 70.409789 im/s
Epoch 8, Train Loss: 12668.7714844, Time: 70.8994s, Throughput: 70.409619 im/s
Epoch 9, Iter 39, Loss: 11801.4785156, Throughput: 70.193224 im/s
Epoch 9, Train Loss: 12324.0761719, Time: 71.1182s, Throughput: 70.193045 im/s
Epoch 10, Iter 39, Loss: 11626.4316406, Throughput: 70.482906 im/s
Epoch 10, Train Loss: 12034.8144531, Time: 70.8259s, Throughput: 70.482716 im/s
Epoch 11, Iter 39, Loss: 11972.6298828, Throughput: 70.172560 im/s
Epoch 11, Train Loss: 11832.1582031, Time: 71.1391s, Throughput: 70.172385 im/s
Epoch 12, Iter 39, Loss: 11322.0195312, Throughput: 70.225251 im/s
Epoch 12, Train Loss: 11712.0419922, Time: 71.0857s, Throughput: 70.225064 im/s
Epoch 13, Iter 39, Loss: 11445.9140625, Throughput: 70.384589 im/s
Epoch 13, Train Loss: 11552.6660156, Time: 70.9248s, Throughput: 70.384414 im/s
Epoch 14, Iter 39, Loss: 11222.8554688, Throughput: 70.557438 im/s
Epoch 14, Train Loss: 11358.8320312, Time: 70.7510s, Throughput: 70.557269 im/s
Epoch 15, Iter 39, Loss: 10535.9882812, Throughput: 70.444420 im/s
Epoch 15, Train Loss: 11192.4101562, Time: 70.8645s, Throughput: 70.444250 im/s
Epoch 16, Iter 39, Loss: 11169.4785156, Throughput: 70.639672 im/s
Epoch 16, Train Loss: 11089.0039062, Time: 70.6687s, Throughput: 70.639487 im/s
Epoch 17, Iter 39, Loss: 10504.7373047, Throughput: 70.567541 im/s
Epoch 17, Train Loss: 10940.9794922, Time: 70.7409s, Throughput: 70.567378 im/s
Epoch 18, Iter 39, Loss: 11127.7392578, Throughput: 70.371274 im/s
Epoch 18, Train Loss: 10797.5068359, Time: 70.9382s, Throughput: 70.371120 im/s
Epoch 19, Iter 39, Loss: 10484.2802734, Throughput: 70.070207 im/s
Epoch 19, Train Loss: 10758.7529297, Time: 71.2430s, Throughput: 70.070040 im/s
Epoch 20, Iter 39, Loss: 10749.1435547, Throughput: 70.292152 im/s
Epoch 20, Train Loss: 10640.7226562, Time: 71.0180s, Throughput: 70.291996 im/s
Epoch 21, Iter 39, Loss: 11088.7988281, Throughput: 70.792346 im/s
Epoch 21, Train Loss: 10686.0205078, Time: 70.5163s, Throughput: 70.792179 im/s
Epoch 22, Iter 39, Loss: 11372.0517578, Throughput: 70.544159 im/s
Epoch 22, Train Loss: 10509.5781250, Time: 70.7644s, Throughput: 70.543987 im/s
Epoch 23, Iter 39, Loss: 9910.3281250, Throughput: 70.634507 im/s
Epoch 23, Train Loss: 10446.5654297, Time: 70.6738s, Throughput: 70.634332 im/s
Epoch 24, Iter 39, Loss: 10622.8222656, Throughput: 70.614602 im/s
Epoch 24, Train Loss: 10393.3789062, Time: 70.6938s, Throughput: 70.614443 im/s
Epoch 25, Iter 39, Loss: 10515.2597656, Throughput: 70.677372 im/s
Epoch 25, Train Loss: 10300.9619141, Time: 70.6310s, Throughput: 70.677195 im/s
Epoch 26, Iter 39, Loss: 10333.3652344, Throughput: 70.580372 im/s
Epoch 26, Train Loss: 10322.0048828, Time: 70.7280s, Throughput: 70.580202 im/s
Epoch 27, Iter 39, Loss: 10259.3408203, Throughput: 70.491554 im/s
Epoch 27, Train Loss: 10225.8173828, Time: 70.8172s, Throughput: 70.491384 im/s
Epoch 28, Iter 39, Loss: 9915.3710938, Throughput: 70.640358 im/s
Epoch 28, Train Loss: 10126.9326172, Time: 70.6680s, Throughput: 70.640164 im/s
Epoch 29, Iter 39, Loss: 9643.7441406, Throughput: 69.679248 im/s
Epoch 29, Train Loss: 10150.8955078, Time: 71.6427s, Throughput: 69.679078 im/s
Epoch 30, Iter 39, Loss: 10249.1406250, Throughput: 69.758139 im/s
Epoch 30, Train Loss: 10141.6298828, Time: 71.5617s, Throughput: 69.757956 im/s
Epoch 31, Iter 39, Loss: 10328.5605469, Throughput: 70.017735 im/s
Epoch 31, Train Loss: 10008.3974609, Time: 71.2964s, Throughput: 70.017542 im/s
Epoch 32, Iter 39, Loss: 10493.3261719, Throughput: 70.319464 im/s
Epoch 32, Train Loss: 9955.7968750, Time: 70.9905s, Throughput: 70.319279 im/s
Epoch 33, Iter 39, Loss: 10159.3525391, Throughput: 70.623498 im/s
Epoch 33, Train Loss: 9992.3769531, Time: 70.6849s, Throughput: 70.623326 im/s
Epoch 34, Iter 39, Loss: 10598.3896484, Throughput: 70.386652 im/s
Epoch 34, Train Loss: 9853.7080078, Time: 70.9227s, Throughput: 70.386478 im/s
Epoch 35, Iter 39, Loss: 9924.6357422, Throughput: 70.345673 im/s
Epoch 35, Train Loss: 9818.8955078, Time: 70.9640s, Throughput: 70.345507 im/s
Epoch 36, Iter 39, Loss: 9567.5712891, Throughput: 70.399828 im/s
Epoch 36, Train Loss: 9835.0371094, Time: 70.9094s, Throughput: 70.399659 im/s
Epoch 37, Iter 39, Loss: 10216.3789062, Throughput: 70.481635 im/s
Epoch 37, Train Loss: 9797.8857422, Time: 70.8271s, Throughput: 70.481460 im/s
Epoch 38, Iter 39, Loss: 9814.8027344, Throughput: 70.500596 im/s
Epoch 38, Train Loss: 9747.6289062, Time: 70.8081s, Throughput: 70.500428 im/s
Epoch 39, Iter 39, Loss: 9174.5478516, Throughput: 70.230434 im/s
Epoch 39, Train Loss: 9700.7470703, Time: 71.0805s, Throughput: 70.230244 im/s
Epoch 40, Iter 39, Loss: 9148.4550781, Throughput: 70.767968 im/s
Epoch 40, Train Loss: 9661.7841797, Time: 70.5406s, Throughput: 70.767793 im/s
Epoch 41, Iter 39, Loss: 9324.3789062, Throughput: 70.247796 im/s
Epoch 41, Train Loss: 9605.0195312, Time: 71.0629s, Throughput: 70.247624 im/s
Epoch 42, Iter 39, Loss: 9687.5000000, Throughput: 70.646067 im/s
Epoch 42, Train Loss: 9606.8154297, Time: 70.6623s, Throughput: 70.645903 im/s
Epoch 43, Iter 39, Loss: 9596.2822266, Throughput: 70.617417 im/s
Epoch 43, Train Loss: 9616.5888672, Time: 70.6909s, Throughput: 70.617243 im/s
Epoch 44, Iter 39, Loss: 9995.4726562, Throughput: 70.290561 im/s
Epoch 44, Train Loss: 9624.6884766, Time: 71.0197s, Throughput: 70.290393 im/s
Epoch 45, Iter 39, Loss: 9040.1591797, Throughput: 70.316502 im/s
Epoch 45, Train Loss: 9469.7207031, Time: 70.9935s, Throughput: 70.316305 im/s
Epoch 46, Iter 39, Loss: 9227.1953125, Throughput: 70.404540 im/s
Epoch 46, Train Loss: 9469.8623047, Time: 70.9047s, Throughput: 70.404368 im/s
Epoch 47, Iter 39, Loss: 9623.4433594, Throughput: 70.428206 im/s
Epoch 47, Train Loss: 9490.9804688, Time: 70.8809s, Throughput: 70.428031 im/s
Epoch 48, Iter 39, Loss: 10132.0742188, Throughput: 70.465284 im/s
Epoch 48, Train Loss: 9429.9433594, Time: 70.8436s, Throughput: 70.465103 im/s
Epoch 49, Iter 39, Loss: 8938.2421875, Throughput: 70.525546 im/s
Epoch 49, Train Loss: 9408.6425781, Time: 70.7830s, Throughput: 70.525369 im/s
Epoch 50, Iter 39, Loss: 9478.2519531, Throughput: 70.642495 im/s
Epoch 50, Train Loss: 9351.7119141, Time: 70.6659s, Throughput: 70.642324 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 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.