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: 24372.9042969, Throughput: 11.562854 im/s
Epoch 1, Train Loss: 39714.4960938, Time: 432.0219s, Throughput: 11.554971 im/s
Epoch 2, Iter 39, Loss: 17505.5859375, Throughput: 98.262393 im/s
Epoch 2, Train Loss: 20095.0214844, Time: 50.8030s, Throughput: 98.261993 im/s
Epoch 3, Iter 39, Loss: 16085.7988281, Throughput: 98.417893 im/s
Epoch 3, Train Loss: 16551.1601562, Time: 50.7227s, Throughput: 98.417513 im/s
Epoch 4, Iter 39, Loss: 15223.7001953, Throughput: 97.710641 im/s
Epoch 4, Train Loss: 14971.8896484, Time: 51.0906s, Throughput: 97.708752 im/s
Epoch 5, Iter 39, Loss: 13532.3330078, Throughput: 99.125505 im/s
Epoch 5, Train Loss: 14034.1074219, Time: 50.3606s, Throughput: 99.125116 im/s
Epoch 6, Iter 39, Loss: 13642.3681641, Throughput: 99.182665 im/s
Epoch 6, Train Loss: 13311.8203125, Time: 50.3316s, Throughput: 99.182277 im/s
Epoch 7, Iter 39, Loss: 12322.7324219, Throughput: 99.347516 im/s
Epoch 7, Train Loss: 12947.8750000, Time: 50.2481s, Throughput: 99.347066 im/s
Epoch 8, Iter 39, Loss: 12115.5947266, Throughput: 99.140967 im/s
Epoch 8, Train Loss: 12421.3574219, Time: 50.3528s, Throughput: 99.140513 im/s
Epoch 9, Iter 39, Loss: 12022.9667969, Throughput: 98.573957 im/s
Epoch 9, Train Loss: 12132.7138672, Time: 50.6424s, Throughput: 98.573557 im/s
Epoch 10, Iter 39, Loss: 11882.0517578, Throughput: 98.384739 im/s
Epoch 10, Train Loss: 11943.0673828, Time: 50.7398s, Throughput: 98.384353 im/s
Epoch 11, Iter 39, Loss: 11284.8320312, Throughput: 98.698319 im/s
Epoch 11, Train Loss: 11776.0068359, Time: 50.5786s, Throughput: 98.697890 im/s
Epoch 12, Iter 39, Loss: 11614.9482422, Throughput: 98.238999 im/s
Epoch 12, Train Loss: 11542.2988281, Time: 50.8150s, Throughput: 98.238614 im/s
Epoch 13, Iter 39, Loss: 11185.0458984, Throughput: 97.627580 im/s
Epoch 13, Train Loss: 11396.4052734, Time: 51.1333s, Throughput: 97.627188 im/s
Epoch 14, Iter 39, Loss: 10660.5800781, Throughput: 99.434746 im/s
Epoch 14, Train Loss: 11229.9355469, Time: 50.2040s, Throughput: 99.434291 im/s
Epoch 15, Iter 39, Loss: 10423.9121094, Throughput: 100.276783 im/s
Epoch 15, Train Loss: 11161.9462891, Time: 49.7824s, Throughput: 100.276322 im/s
Epoch 16, Iter 39, Loss: 11370.2812500, Throughput: 100.539319 im/s
Epoch 16, Train Loss: 11015.1582031, Time: 49.6524s, Throughput: 100.538937 im/s
Epoch 17, Iter 39, Loss: 10732.5517578, Throughput: 100.202845 im/s
Epoch 17, Train Loss: 10767.1601562, Time: 49.8192s, Throughput: 100.202412 im/s
Epoch 18, Iter 39, Loss: 10289.4277344, Throughput: 98.215311 im/s
Epoch 18, Train Loss: 10800.5498047, Time: 50.8273s, Throughput: 98.214868 im/s
Epoch 19, Iter 39, Loss: 10597.3017578, Throughput: 98.037911 im/s
Epoch 19, Train Loss: 10661.7753906, Time: 50.9193s, Throughput: 98.037574 im/s
Epoch 20, Iter 39, Loss: 10807.9208984, Throughput: 98.417107 im/s
Epoch 20, Train Loss: 10572.5332031, Time: 50.7231s, Throughput: 98.416665 im/s
Epoch 21, Iter 39, Loss: 10950.4746094, Throughput: 98.288137 im/s
Epoch 21, Train Loss: 10534.0966797, Time: 50.7897s, Throughput: 98.287705 im/s
Epoch 22, Iter 39, Loss: 10375.5830078, Throughput: 98.098435 im/s
Epoch 22, Train Loss: 10363.3974609, Time: 50.8879s, Throughput: 98.098024 im/s
Epoch 23, Iter 39, Loss: 10328.7148438, Throughput: 99.131332 im/s
Epoch 23, Train Loss: 10327.9667969, Time: 50.3576s, Throughput: 99.130928 im/s
Epoch 24, Iter 39, Loss: 10260.6005859, Throughput: 98.374399 im/s
Epoch 24, Train Loss: 10415.9882812, Time: 50.7451s, Throughput: 98.373993 im/s
Epoch 25, Iter 39, Loss: 10527.6386719, Throughput: 98.118756 im/s
Epoch 25, Train Loss: 10280.7255859, Time: 50.8773s, Throughput: 98.118368 im/s
Epoch 26, Iter 39, Loss: 9967.4863281, Throughput: 99.122297 im/s
Epoch 26, Train Loss: 10149.4531250, Time: 50.3622s, Throughput: 99.121937 im/s
Epoch 27, Iter 39, Loss: 10079.5107422, Throughput: 97.536744 im/s
Epoch 27, Train Loss: 10057.7617188, Time: 51.1809s, Throughput: 97.536359 im/s
Epoch 28, Iter 39, Loss: 9764.3027344, Throughput: 98.548598 im/s
Epoch 28, Train Loss: 10055.7343750, Time: 50.6554s, Throughput: 98.548216 im/s
Epoch 29, Iter 39, Loss: 10065.3310547, Throughput: 98.227969 im/s
Epoch 29, Train Loss: 10008.4960938, Time: 50.8208s, Throughput: 98.227544 im/s
Epoch 30, Iter 39, Loss: 9825.8710938, Throughput: 98.482365 im/s
Epoch 30, Train Loss: 9964.5244141, Time: 50.6895s, Throughput: 98.481998 im/s
Epoch 31, Iter 39, Loss: 10178.8222656, Throughput: 99.492219 im/s
Epoch 31, Train Loss: 9878.9287109, Time: 50.1750s, Throughput: 99.491809 im/s
Epoch 32, Iter 39, Loss: 10290.6835938, Throughput: 99.399931 im/s
Epoch 32, Train Loss: 9882.0498047, Time: 50.2215s, Throughput: 99.399562 im/s
Epoch 33, Iter 39, Loss: 9788.9082031, Throughput: 98.464112 im/s
Epoch 33, Train Loss: 9833.0107422, Time: 50.6989s, Throughput: 98.463735 im/s
Epoch 34, Iter 39, Loss: 10246.5039062, Throughput: 97.908051 im/s
Epoch 34, Train Loss: 9862.3105469, Time: 50.9868s, Throughput: 97.907609 im/s
Epoch 35, Iter 39, Loss: 10017.0146484, Throughput: 98.695135 im/s
Epoch 35, Train Loss: 9789.9326172, Time: 50.5802s, Throughput: 98.694743 im/s
Epoch 36, Iter 39, Loss: 9162.5458984, Throughput: 98.335093 im/s
Epoch 36, Train Loss: 9748.3056641, Time: 50.7654s, Throughput: 98.334673 im/s
Epoch 37, Iter 39, Loss: 9377.5224609, Throughput: 99.667468 im/s
Epoch 37, Train Loss: 9675.8486328, Time: 50.0867s, Throughput: 99.667116 im/s
Epoch 38, Iter 39, Loss: 10318.0703125, Throughput: 99.682275 im/s
Epoch 38, Train Loss: 9655.0292969, Time: 50.0793s, Throughput: 99.681893 im/s
Epoch 39, Iter 39, Loss: 10008.7773438, Throughput: 98.342005 im/s
Epoch 39, Train Loss: 9644.2529297, Time: 50.7618s, Throughput: 98.341597 im/s
Epoch 40, Iter 39, Loss: 9559.2480469, Throughput: 98.671594 im/s
Epoch 40, Train Loss: 9644.7216797, Time: 50.5922s, Throughput: 98.671274 im/s
Epoch 41, Iter 39, Loss: 9984.8320312, Throughput: 96.520251 im/s
Epoch 41, Train Loss: 9588.2626953, Time: 51.7199s, Throughput: 96.519859 im/s
Epoch 42, Iter 39, Loss: 10215.9462891, Throughput: 98.068762 im/s
Epoch 42, Train Loss: 9599.9345703, Time: 50.9033s, Throughput: 98.068381 im/s
Epoch 43, Iter 39, Loss: 9374.7685547, Throughput: 97.367939 im/s
Epoch 43, Train Loss: 9488.4794922, Time: 51.2696s, Throughput: 97.367576 im/s
Epoch 44, Iter 39, Loss: 9309.9628906, Throughput: 96.941848 im/s
Epoch 44, Train Loss: 9413.8720703, Time: 51.4950s, Throughput: 96.941524 im/s
Epoch 45, Iter 39, Loss: 9505.3046875, Throughput: 97.262315 im/s
Epoch 45, Train Loss: 9411.3535156, Time: 51.3253s, Throughput: 97.261904 im/s
Epoch 46, Iter 39, Loss: 9341.1953125, Throughput: 97.857660 im/s
Epoch 46, Train Loss: 9332.6464844, Time: 51.0131s, Throughput: 97.857282 im/s
Epoch 47, Iter 39, Loss: 9133.4531250, Throughput: 97.807777 im/s
Epoch 47, Train Loss: 9388.8056641, Time: 51.0391s, Throughput: 97.807423 im/s
Epoch 48, Iter 39, Loss: 9633.8554688, Throughput: 96.775783 im/s
Epoch 48, Train Loss: 9333.2119141, Time: 51.5834s, Throughput: 96.775398 im/s
Epoch 49, Iter 39, Loss: 9336.5371094, Throughput: 98.601933 im/s
Epoch 49, Train Loss: 9314.8300781, Time: 50.6280s, Throughput: 98.601492 im/s
Epoch 50, Iter 39, Loss: 9300.1279297, Throughput: 97.219529 im/s
Epoch 50, Train Loss: 9267.1162109, Time: 51.3479s, Throughput: 97.219120 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 1.12.7
Commit 6d172b025e4 (2026-08-15 08:05 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.