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: 23669.0214844, Throughput: 10.124549 im/s
Epoch 1, Train Loss: 39975.1601562, Time: 493.3634s, Throughput: 10.118301 im/s
Epoch 2, Iter 39, Loss: 18302.7792969, Throughput: 68.049236 im/s
Epoch 2, Train Loss: 20375.8925781, Time: 73.3589s, Throughput: 68.049023 im/s
Epoch 3, Iter 39, Loss: 16283.4511719, Throughput: 68.054038 im/s
Epoch 3, Train Loss: 16709.9121094, Time: 73.3537s, Throughput: 68.053838 im/s
Epoch 4, Iter 39, Loss: 13466.8798828, Throughput: 68.032190 im/s
Epoch 4, Train Loss: 15122.2822266, Time: 73.3772s, Throughput: 68.032016 im/s
Epoch 5, Iter 39, Loss: 14304.7539062, Throughput: 68.043028 im/s
Epoch 5, Train Loss: 14137.8144531, Time: 73.3655s, Throughput: 68.042864 im/s
Epoch 6, Iter 39, Loss: 12600.3085938, Throughput: 68.001696 im/s
Epoch 6, Train Loss: 13351.3906250, Time: 73.4102s, Throughput: 68.001472 im/s
Epoch 7, Iter 39, Loss: 12405.7949219, Throughput: 69.244548 im/s
Epoch 7, Train Loss: 12894.4794922, Time: 72.0925s, Throughput: 69.244354 im/s
Epoch 8, Iter 39, Loss: 12413.3720703, Throughput: 68.602105 im/s
Epoch 8, Train Loss: 12526.3232422, Time: 72.7676s, Throughput: 68.601936 im/s
Epoch 9, Iter 39, Loss: 11890.4316406, Throughput: 68.033301 im/s
Epoch 9, Train Loss: 12207.2285156, Time: 73.3760s, Throughput: 68.033115 im/s
Epoch 10, Iter 39, Loss: 12109.4013672, Throughput: 67.690280 im/s
Epoch 10, Train Loss: 11937.8769531, Time: 73.7479s, Throughput: 67.690100 im/s
Epoch 11, Iter 39, Loss: 11775.3535156, Throughput: 68.061594 im/s
Epoch 11, Train Loss: 11712.8369141, Time: 73.3455s, Throughput: 68.061436 im/s
Epoch 12, Iter 39, Loss: 11403.8300781, Throughput: 68.355921 im/s
Epoch 12, Train Loss: 11601.0283203, Time: 73.0297s, Throughput: 68.355734 im/s
Epoch 13, Iter 39, Loss: 11250.1308594, Throughput: 68.534802 im/s
Epoch 13, Train Loss: 11406.9287109, Time: 72.8391s, Throughput: 68.534622 im/s
Epoch 14, Iter 39, Loss: 11398.3183594, Throughput: 68.165342 im/s
Epoch 14, Train Loss: 11303.6406250, Time: 73.2339s, Throughput: 68.165161 im/s
Epoch 15, Iter 39, Loss: 11767.1406250, Throughput: 68.562296 im/s
Epoch 15, Train Loss: 11192.1826172, Time: 72.8099s, Throughput: 68.562135 im/s
Epoch 16, Iter 39, Loss: 10836.2226562, Throughput: 69.231020 im/s
Epoch 16, Train Loss: 10999.6738281, Time: 72.1066s, Throughput: 69.230829 im/s
Epoch 17, Iter 39, Loss: 10251.7041016, Throughput: 69.279984 im/s
Epoch 17, Train Loss: 10919.7597656, Time: 72.0556s, Throughput: 69.279818 im/s
Epoch 18, Iter 39, Loss: 10644.7070312, Throughput: 69.279546 im/s
Epoch 18, Train Loss: 10823.3603516, Time: 72.0561s, Throughput: 69.279341 im/s
Epoch 19, Iter 39, Loss: 11289.3828125, Throughput: 68.848847 im/s
Epoch 19, Train Loss: 10718.5107422, Time: 72.5068s, Throughput: 68.848679 im/s
Epoch 20, Iter 39, Loss: 10420.6542969, Throughput: 68.845076 im/s
Epoch 20, Train Loss: 10539.7568359, Time: 72.5108s, Throughput: 68.844940 im/s
Epoch 21, Iter 39, Loss: 10542.1757812, Throughput: 68.777805 im/s
Epoch 21, Train Loss: 10445.1005859, Time: 72.5817s, Throughput: 68.777634 im/s
Epoch 22, Iter 39, Loss: 10361.1679688, Throughput: 68.743540 im/s
Epoch 22, Train Loss: 10374.2812500, Time: 72.6179s, Throughput: 68.743382 im/s
Epoch 23, Iter 39, Loss: 10557.1943359, Throughput: 68.776692 im/s
Epoch 23, Train Loss: 10406.1728516, Time: 72.5829s, Throughput: 68.776532 im/s
Epoch 24, Iter 39, Loss: 10106.6113281, Throughput: 68.653364 im/s
Epoch 24, Train Loss: 10377.8544922, Time: 72.7133s, Throughput: 68.653187 im/s
Epoch 25, Iter 39, Loss: 10092.6054688, Throughput: 68.915060 im/s
Epoch 25, Train Loss: 10258.3574219, Time: 72.4372s, Throughput: 68.914895 im/s
Epoch 26, Iter 39, Loss: 10645.6298828, Throughput: 68.927061 im/s
Epoch 26, Train Loss: 10262.6572266, Time: 72.4246s, Throughput: 68.926895 im/s
Epoch 27, Iter 39, Loss: 10337.3339844, Throughput: 68.412689 im/s
Epoch 27, Train Loss: 10140.3837891, Time: 72.9691s, Throughput: 68.412527 im/s
Epoch 28, Iter 39, Loss: 10293.0546875, Throughput: 68.378347 im/s
Epoch 28, Train Loss: 10080.1660156, Time: 73.0057s, Throughput: 68.378184 im/s
Epoch 29, Iter 39, Loss: 10612.8369141, Throughput: 68.715038 im/s
Epoch 29, Train Loss: 10073.8808594, Time: 72.6480s, Throughput: 68.714876 im/s
Epoch 30, Iter 39, Loss: 10239.8535156, Throughput: 68.469637 im/s
Epoch 30, Train Loss: 9966.2177734, Time: 72.9084s, Throughput: 68.469470 im/s
Epoch 31, Iter 39, Loss: 10710.3222656, Throughput: 68.559571 im/s
Epoch 31, Train Loss: 10012.6406250, Time: 72.8128s, Throughput: 68.559358 im/s
Epoch 32, Iter 39, Loss: 9745.9951172, Throughput: 68.676341 im/s
Epoch 32, Train Loss: 9882.7548828, Time: 72.6890s, Throughput: 68.676143 im/s
Epoch 33, Iter 39, Loss: 9787.8847656, Throughput: 69.333868 im/s
Epoch 33, Train Loss: 9899.9130859, Time: 71.9996s, Throughput: 69.333696 im/s
Epoch 34, Iter 39, Loss: 10539.0322266, Throughput: 68.515452 im/s
Epoch 34, Train Loss: 9837.1962891, Time: 72.8597s, Throughput: 68.515289 im/s
Epoch 35, Iter 39, Loss: 9744.6542969, Throughput: 67.934433 im/s
Epoch 35, Train Loss: 9805.7861328, Time: 73.4828s, Throughput: 67.934235 im/s
Epoch 36, Iter 39, Loss: 9546.8281250, Throughput: 67.951674 im/s
Epoch 36, Train Loss: 9718.6044922, Time: 73.4642s, Throughput: 67.951502 im/s
Epoch 37, Iter 39, Loss: 10119.2109375, Throughput: 68.748607 im/s
Epoch 37, Train Loss: 9725.8994141, Time: 72.6126s, Throughput: 68.748417 im/s
Epoch 38, Iter 39, Loss: 9806.8525391, Throughput: 67.718084 im/s
Epoch 38, Train Loss: 9681.8994141, Time: 73.7175s, Throughput: 67.717933 im/s
Epoch 39, Iter 39, Loss: 9570.3046875, Throughput: 67.956688 im/s
Epoch 39, Train Loss: 9612.1855469, Time: 73.4587s, Throughput: 67.956508 im/s
Epoch 40, Iter 39, Loss: 9559.7421875, Throughput: 68.146191 im/s
Epoch 40, Train Loss: 9571.6318359, Time: 73.2545s, Throughput: 68.146002 im/s
Epoch 41, Iter 39, Loss: 9602.0146484, Throughput: 68.271227 im/s
Epoch 41, Train Loss: 9613.8828125, Time: 73.1203s, Throughput: 68.271059 im/s
Epoch 42, Iter 39, Loss: 9778.6142578, Throughput: 67.987427 im/s
Epoch 42, Train Loss: 9565.6318359, Time: 73.4255s, Throughput: 67.987251 im/s
Epoch 43, Iter 39, Loss: 9702.7597656, Throughput: 68.292909 im/s
Epoch 43, Train Loss: 9527.6259766, Time: 73.0971s, Throughput: 68.292736 im/s
Epoch 44, Iter 39, Loss: 9159.7744141, Throughput: 68.161749 im/s
Epoch 44, Train Loss: 9563.1494141, Time: 73.2377s, Throughput: 68.161586 im/s
Epoch 45, Iter 39, Loss: 9218.2128906, Throughput: 68.980294 im/s
Epoch 45, Train Loss: 9473.7011719, Time: 72.3687s, Throughput: 68.980122 im/s
Epoch 46, Iter 39, Loss: 9952.1992188, Throughput: 68.659445 im/s
Epoch 46, Train Loss: 9378.1591797, Time: 72.7069s, Throughput: 68.659256 im/s
Epoch 47, Iter 39, Loss: 9560.0312500, Throughput: 68.670714 im/s
Epoch 47, Train Loss: 9346.6210938, Time: 72.6949s, Throughput: 68.670546 im/s
Epoch 48, Iter 39, Loss: 9305.5390625, Throughput: 68.120295 im/s
Epoch 48, Train Loss: 9318.7275391, Time: 73.2823s, Throughput: 68.120108 im/s
Epoch 49, Iter 39, Loss: 9102.9833984, Throughput: 68.555589 im/s
Epoch 49, Train Loss: 9292.0361328, Time: 72.8170s, Throughput: 68.555394 im/s
Epoch 50, Iter 39, Loss: 9303.9628906, Throughput: 68.402689 im/s
Epoch 50, Train Loss: 9338.2158203, Time: 72.9798s, Throughput: 68.402518 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.