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: 24033.4199219, Throughput: 3.968688 im/s
Epoch 1, Train Loss: 39783.6679688, Time: 1258.1358s, Throughput: 3.967775 im/s
Epoch 2, Iter 39, Loss: 17866.2343750, Throughput: 82.696187 im/s
Epoch 2, Train Loss: 20161.1953125, Time: 60.3657s, Throughput: 82.695906 im/s
Epoch 3, Iter 39, Loss: 16421.8769531, Throughput: 84.241595 im/s
Epoch 3, Train Loss: 16492.4804688, Time: 59.2584s, Throughput: 84.241283 im/s
Epoch 4, Iter 39, Loss: 13964.6171875, Throughput: 83.545357 im/s
Epoch 4, Train Loss: 14918.0703125, Time: 59.7522s, Throughput: 83.545085 im/s
Epoch 5, Iter 39, Loss: 14150.0097656, Throughput: 83.114429 im/s
Epoch 5, Train Loss: 14138.6953125, Time: 60.0620s, Throughput: 83.114144 im/s
Epoch 6, Iter 39, Loss: 13694.8515625, Throughput: 83.794336 im/s
Epoch 6, Train Loss: 13314.6250000, Time: 59.5747s, Throughput: 83.794016 im/s
Epoch 7, Iter 39, Loss: 12338.8457031, Throughput: 84.534896 im/s
Epoch 7, Train Loss: 12816.1406250, Time: 59.0527s, Throughput: 84.534603 im/s
Epoch 8, Iter 39, Loss: 12689.6621094, Throughput: 84.738794 im/s
Epoch 8, Train Loss: 12512.3857422, Time: 58.9106s, Throughput: 84.738508 im/s
Epoch 9, Iter 39, Loss: 11879.7402344, Throughput: 84.410283 im/s
Epoch 9, Train Loss: 12142.3427734, Time: 59.1399s, Throughput: 84.409985 im/s
Epoch 10, Iter 39, Loss: 11897.7636719, Throughput: 84.310030 im/s
Epoch 10, Train Loss: 11958.5195312, Time: 59.2102s, Throughput: 84.309758 im/s
Epoch 11, Iter 39, Loss: 12180.3417969, Throughput: 83.866759 im/s
Epoch 11, Train Loss: 11803.3623047, Time: 59.5232s, Throughput: 83.866495 im/s
Epoch 12, Iter 39, Loss: 11223.1933594, Throughput: 84.758522 im/s
Epoch 12, Train Loss: 11505.2500000, Time: 58.8969s, Throughput: 84.758252 im/s
Epoch 13, Iter 39, Loss: 11612.3525391, Throughput: 85.342592 im/s
Epoch 13, Train Loss: 11385.8037109, Time: 58.4938s, Throughput: 85.342333 im/s
Epoch 14, Iter 39, Loss: 11838.5947266, Throughput: 84.253007 im/s
Epoch 14, Train Loss: 11254.1748047, Time: 59.2503s, Throughput: 84.252708 im/s
Epoch 15, Iter 39, Loss: 10921.6484375, Throughput: 84.681953 im/s
Epoch 15, Train Loss: 11087.0644531, Time: 58.9502s, Throughput: 84.681687 im/s
Epoch 16, Iter 39, Loss: 10993.3300781, Throughput: 84.770938 im/s
Epoch 16, Train Loss: 10984.8271484, Time: 58.8883s, Throughput: 84.770666 im/s
Epoch 17, Iter 39, Loss: 10536.5820312, Throughput: 84.339951 im/s
Epoch 17, Train Loss: 10818.9345703, Time: 59.1892s, Throughput: 84.339666 im/s
Epoch 18, Iter 39, Loss: 10528.5644531, Throughput: 84.535117 im/s
Epoch 18, Train Loss: 10748.1738281, Time: 59.0526s, Throughput: 84.534860 im/s
Epoch 19, Iter 39, Loss: 10833.9960938, Throughput: 85.385654 im/s
Epoch 19, Train Loss: 10644.8544922, Time: 58.4644s, Throughput: 85.385354 im/s
Epoch 20, Iter 39, Loss: 10398.4951172, Throughput: 85.767083 im/s
Epoch 20, Train Loss: 10635.7568359, Time: 58.2044s, Throughput: 85.766782 im/s
Epoch 21, Iter 39, Loss: 10073.4794922, Throughput: 86.487386 im/s
Epoch 21, Train Loss: 10494.4042969, Time: 57.7196s, Throughput: 86.487098 im/s
Epoch 22, Iter 39, Loss: 10364.0820312, Throughput: 85.490929 im/s
Epoch 22, Train Loss: 10444.0791016, Time: 58.3924s, Throughput: 85.490632 im/s
Epoch 23, Iter 39, Loss: 9802.7539062, Throughput: 85.779733 im/s
Epoch 23, Train Loss: 10311.7177734, Time: 58.1958s, Throughput: 85.779404 im/s
Epoch 24, Iter 39, Loss: 10442.4433594, Throughput: 85.977925 im/s
Epoch 24, Train Loss: 10216.1767578, Time: 58.0616s, Throughput: 85.977657 im/s
Epoch 25, Iter 39, Loss: 10356.3974609, Throughput: 85.954751 im/s
Epoch 25, Train Loss: 10225.5312500, Time: 58.0773s, Throughput: 85.954437 im/s
Epoch 26, Iter 39, Loss: 10154.7597656, Throughput: 85.296532 im/s
Epoch 26, Train Loss: 10188.0351562, Time: 58.5254s, Throughput: 85.296251 im/s
Epoch 27, Iter 39, Loss: 9993.8398438, Throughput: 85.160392 im/s
Epoch 27, Train Loss: 10164.6835938, Time: 58.6190s, Throughput: 85.160141 im/s
Epoch 28, Iter 39, Loss: 10103.2714844, Throughput: 84.543930 im/s
Epoch 28, Train Loss: 10039.0605469, Time: 59.0464s, Throughput: 84.543657 im/s
Epoch 29, Iter 39, Loss: 9507.7080078, Throughput: 84.835466 im/s
Epoch 29, Train Loss: 10075.3320312, Time: 58.8435s, Throughput: 84.835178 im/s
Epoch 30, Iter 39, Loss: 10592.9746094, Throughput: 85.387231 im/s
Epoch 30, Train Loss: 9931.8935547, Time: 58.4633s, Throughput: 85.386946 im/s
Epoch 31, Iter 39, Loss: 9433.5312500, Throughput: 85.437751 im/s
Epoch 31, Train Loss: 9944.2460938, Time: 58.4287s, Throughput: 85.437452 im/s
Epoch 32, Iter 39, Loss: 9930.5849609, Throughput: 85.026354 im/s
Epoch 32, Train Loss: 9884.2265625, Time: 58.7114s, Throughput: 85.026067 im/s
Epoch 33, Iter 39, Loss: 8999.9257812, Throughput: 85.467258 im/s
Epoch 33, Train Loss: 9801.2294922, Time: 58.4085s, Throughput: 85.466964 im/s
Epoch 34, Iter 39, Loss: 9563.0107422, Throughput: 85.679159 im/s
Epoch 34, Train Loss: 9774.2304688, Time: 58.2641s, Throughput: 85.678861 im/s
Epoch 35, Iter 39, Loss: 9351.7988281, Throughput: 85.405746 im/s
Epoch 35, Train Loss: 9763.3632812, Time: 58.4506s, Throughput: 85.405467 im/s
Epoch 36, Iter 39, Loss: 9980.6699219, Throughput: 85.677409 im/s
Epoch 36, Train Loss: 9696.9863281, Time: 58.2652s, Throughput: 85.677145 im/s
Epoch 37, Iter 39, Loss: 9642.3837891, Throughput: 85.493597 im/s
Epoch 37, Train Loss: 9674.8955078, Time: 58.3906s, Throughput: 85.493270 im/s
Epoch 38, Iter 39, Loss: 9826.5722656, Throughput: 84.972125 im/s
Epoch 38, Train Loss: 9655.5312500, Time: 58.7489s, Throughput: 84.971856 im/s
Epoch 39, Iter 39, Loss: 9592.7666016, Throughput: 84.651665 im/s
Epoch 39, Train Loss: 9685.4267578, Time: 58.9713s, Throughput: 84.651368 im/s
Epoch 40, Iter 39, Loss: 10690.4326172, Throughput: 85.294159 im/s
Epoch 40, Train Loss: 9610.7226562, Time: 58.5271s, Throughput: 85.293871 im/s
Epoch 41, Iter 39, Loss: 9545.5195312, Throughput: 85.436339 im/s
Epoch 41, Train Loss: 9606.9316406, Time: 58.4296s, Throughput: 85.436082 im/s
Epoch 42, Iter 39, Loss: 10022.4296875, Throughput: 85.131522 im/s
Epoch 42, Train Loss: 9531.6611328, Time: 58.6389s, Throughput: 85.131229 im/s
Epoch 43, Iter 39, Loss: 9605.7910156, Throughput: 85.199023 im/s
Epoch 43, Train Loss: 9458.9716797, Time: 58.5924s, Throughput: 85.198747 im/s
Epoch 44, Iter 39, Loss: 9351.2783203, Throughput: 85.108748 im/s
Epoch 44, Train Loss: 9481.1601562, Time: 58.6546s, Throughput: 85.108454 im/s
Epoch 45, Iter 39, Loss: 8716.9316406, Throughput: 84.909664 im/s
Epoch 45, Train Loss: 9377.9550781, Time: 58.7921s, Throughput: 84.909386 im/s
Epoch 46, Iter 39, Loss: 10351.7861328, Throughput: 85.238331 im/s
Epoch 46, Train Loss: 9371.8535156, Time: 58.5654s, Throughput: 85.238052 im/s
Epoch 47, Iter 39, Loss: 9485.9316406, Throughput: 85.453885 im/s
Epoch 47, Train Loss: 9344.7646484, Time: 58.4177s, Throughput: 85.453602 im/s
Epoch 48, Iter 39, Loss: 9347.0546875, Throughput: 84.863636 im/s
Epoch 48, Train Loss: 9318.9980469, Time: 58.8240s, Throughput: 84.863380 im/s
Epoch 49, Iter 39, Loss: 9231.2763672, Throughput: 85.066592 im/s
Epoch 49, Train Loss: 9287.2138672, Time: 58.6837s, Throughput: 85.066256 im/s
Epoch 50, Iter 39, Loss: 9152.1484375, Throughput: 85.002344 im/s
Epoch 50, Train Loss: 9272.3076172, Time: 58.7280s, Throughput: 85.002064 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.