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: 23915.8164062, Throughput: 6.423346 im/s
Epoch 1, Train Loss: 39603.1328125, Time: 777.4522s, Throughput: 6.420974 im/s
Epoch 2, Iter 39, Loss: 17508.2539062, Throughput: 75.412271 im/s
Epoch 2, Train Loss: 20094.4765625, Time: 66.1963s, Throughput: 75.412057 im/s
Epoch 3, Iter 39, Loss: 16239.1308594, Throughput: 75.672143 im/s
Epoch 3, Train Loss: 16609.8183594, Time: 65.9690s, Throughput: 75.671927 im/s
Epoch 4, Iter 39, Loss: 14510.9912109, Throughput: 75.936355 im/s
Epoch 4, Train Loss: 15002.1230469, Time: 65.7394s, Throughput: 75.936191 im/s
Epoch 5, Iter 39, Loss: 14343.4511719, Throughput: 75.650578 im/s
Epoch 5, Train Loss: 14139.9326172, Time: 65.9878s, Throughput: 75.650384 im/s
Epoch 6, Iter 39, Loss: 13489.1269531, Throughput: 74.606870 im/s
Epoch 6, Train Loss: 13443.4482422, Time: 66.9109s, Throughput: 74.606700 im/s
Epoch 7, Iter 39, Loss: 12564.5488281, Throughput: 75.505226 im/s
Epoch 7, Train Loss: 12908.4580078, Time: 66.1148s, Throughput: 75.505037 im/s
Epoch 8, Iter 39, Loss: 12603.5595703, Throughput: 75.361190 im/s
Epoch 8, Train Loss: 12413.1542969, Time: 66.2411s, Throughput: 75.361017 im/s
Epoch 9, Iter 39, Loss: 11651.9199219, Throughput: 75.996799 im/s
Epoch 9, Train Loss: 12277.8593750, Time: 65.6871s, Throughput: 75.996627 im/s
Epoch 10, Iter 39, Loss: 11499.0537109, Throughput: 75.512919 im/s
Epoch 10, Train Loss: 12054.9570312, Time: 66.1080s, Throughput: 75.512762 im/s
Epoch 11, Iter 39, Loss: 11520.0478516, Throughput: 75.518823 im/s
Epoch 11, Train Loss: 11754.0195312, Time: 66.1029s, Throughput: 75.518667 im/s
Epoch 12, Iter 39, Loss: 11007.5078125, Throughput: 75.353280 im/s
Epoch 12, Train Loss: 11571.0244141, Time: 66.2481s, Throughput: 75.353106 im/s
Epoch 13, Iter 39, Loss: 12163.0029297, Throughput: 75.480232 im/s
Epoch 13, Train Loss: 11409.9570312, Time: 66.1367s, Throughput: 75.480053 im/s
Epoch 14, Iter 39, Loss: 11220.5937500, Throughput: 74.620971 im/s
Epoch 14, Train Loss: 11267.3974609, Time: 66.8982s, Throughput: 74.620803 im/s
Epoch 15, Iter 39, Loss: 11488.7021484, Throughput: 73.879172 im/s
Epoch 15, Train Loss: 11070.4531250, Time: 67.5700s, Throughput: 73.878987 im/s
Epoch 16, Iter 39, Loss: 11513.0810547, Throughput: 74.959419 im/s
Epoch 16, Train Loss: 11019.2001953, Time: 66.5962s, Throughput: 74.959276 im/s
Epoch 17, Iter 39, Loss: 11800.4023438, Throughput: 75.090556 im/s
Epoch 17, Train Loss: 10896.1230469, Time: 66.4799s, Throughput: 75.090393 im/s
Epoch 18, Iter 39, Loss: 11083.2714844, Throughput: 75.017883 im/s
Epoch 18, Train Loss: 10691.9580078, Time: 66.5443s, Throughput: 75.017701 im/s
Epoch 19, Iter 39, Loss: 11154.3027344, Throughput: 74.434867 im/s
Epoch 19, Train Loss: 10702.8857422, Time: 67.0655s, Throughput: 74.434708 im/s
Epoch 20, Iter 39, Loss: 10019.4980469, Throughput: 75.761761 im/s
Epoch 20, Train Loss: 10609.5498047, Time: 65.8909s, Throughput: 75.761586 im/s
Epoch 21, Iter 39, Loss: 10308.1904297, Throughput: 74.935574 im/s
Epoch 21, Train Loss: 10560.3281250, Time: 66.6174s, Throughput: 74.935407 im/s
Epoch 22, Iter 39, Loss: 10832.8984375, Throughput: 75.132431 im/s
Epoch 22, Train Loss: 10468.3408203, Time: 66.4428s, Throughput: 75.132277 im/s
Epoch 23, Iter 39, Loss: 10587.5410156, Throughput: 74.990531 im/s
Epoch 23, Train Loss: 10432.0205078, Time: 66.5686s, Throughput: 74.990359 im/s
Epoch 24, Iter 39, Loss: 10358.1757812, Throughput: 75.100278 im/s
Epoch 24, Train Loss: 10257.4941406, Time: 66.4713s, Throughput: 75.100116 im/s
Epoch 25, Iter 39, Loss: 10192.9453125, Throughput: 75.004468 im/s
Epoch 25, Train Loss: 10212.1718750, Time: 66.5562s, Throughput: 75.004301 im/s
Epoch 26, Iter 39, Loss: 10259.2802734, Throughput: 74.782459 im/s
Epoch 26, Train Loss: 10169.6308594, Time: 66.7538s, Throughput: 74.782287 im/s
Epoch 27, Iter 39, Loss: 10411.4218750, Throughput: 75.959679 im/s
Epoch 27, Train Loss: 10144.5527344, Time: 65.7192s, Throughput: 75.959495 im/s
Epoch 28, Iter 39, Loss: 10827.0429688, Throughput: 75.548950 im/s
Epoch 28, Train Loss: 10124.6318359, Time: 66.0765s, Throughput: 75.548772 im/s
Epoch 29, Iter 39, Loss: 9821.9570312, Throughput: 75.202660 im/s
Epoch 29, Train Loss: 10068.1494141, Time: 66.3808s, Throughput: 75.202457 im/s
Epoch 30, Iter 39, Loss: 10508.6406250, Throughput: 75.700592 im/s
Epoch 30, Train Loss: 9981.8505859, Time: 65.9441s, Throughput: 75.700427 im/s
Epoch 31, Iter 39, Loss: 10122.0000000, Throughput: 75.331210 im/s
Epoch 31, Train Loss: 9919.9169922, Time: 66.2675s, Throughput: 75.331037 im/s
Epoch 32, Iter 39, Loss: 9646.8984375, Throughput: 75.653497 im/s
Epoch 32, Train Loss: 10002.9843750, Time: 65.9852s, Throughput: 75.653329 im/s
Epoch 33, Iter 39, Loss: 9515.7236328, Throughput: 75.607101 im/s
Epoch 33, Train Loss: 9819.1259766, Time: 66.0257s, Throughput: 75.606926 im/s
Epoch 34, Iter 39, Loss: 9429.7714844, Throughput: 75.119270 im/s
Epoch 34, Train Loss: 9796.8291016, Time: 66.4545s, Throughput: 75.119096 im/s
Epoch 35, Iter 39, Loss: 9183.0585938, Throughput: 74.870265 im/s
Epoch 35, Train Loss: 9818.5781250, Time: 66.6755s, Throughput: 74.870091 im/s
Epoch 36, Iter 39, Loss: 10291.2578125, Throughput: 74.279414 im/s
Epoch 36, Train Loss: 9804.3779297, Time: 67.2058s, Throughput: 74.279250 im/s
Epoch 37, Iter 39, Loss: 9712.8886719, Throughput: 74.053901 im/s
Epoch 37, Train Loss: 9760.3281250, Time: 67.4105s, Throughput: 74.053729 im/s
Epoch 38, Iter 39, Loss: 9677.8105469, Throughput: 75.191390 im/s
Epoch 38, Train Loss: 9709.6943359, Time: 66.3907s, Throughput: 75.191221 im/s
Epoch 39, Iter 39, Loss: 10413.5732422, Throughput: 75.595445 im/s
Epoch 39, Train Loss: 9636.8349609, Time: 66.0359s, Throughput: 75.595280 im/s
Epoch 40, Iter 39, Loss: 10031.2519531, Throughput: 75.351561 im/s
Epoch 40, Train Loss: 9641.0615234, Time: 66.2496s, Throughput: 75.351377 im/s
Epoch 41, Iter 39, Loss: 9884.7041016, Throughput: 75.499246 im/s
Epoch 41, Train Loss: 9530.4716797, Time: 66.1200s, Throughput: 75.499085 im/s
Epoch 42, Iter 39, Loss: 10032.5234375, Throughput: 75.301079 im/s
Epoch 42, Train Loss: 9480.6718750, Time: 66.2940s, Throughput: 75.300926 im/s
Epoch 43, Iter 39, Loss: 9225.8125000, Throughput: 74.379583 im/s
Epoch 43, Train Loss: 9509.5644531, Time: 67.1153s, Throughput: 74.379434 im/s
Epoch 44, Iter 39, Loss: 9220.5166016, Throughput: 74.630545 im/s
Epoch 44, Train Loss: 9444.7968750, Time: 66.8897s, Throughput: 74.630377 im/s
Epoch 45, Iter 39, Loss: 9567.8164062, Throughput: 75.098953 im/s
Epoch 45, Train Loss: 9408.1806641, Time: 66.4724s, Throughput: 75.098790 im/s
Epoch 46, Iter 39, Loss: 9540.9882812, Throughput: 75.215465 im/s
Epoch 46, Train Loss: 9380.7431641, Time: 66.3695s, Throughput: 75.215292 im/s
Epoch 47, Iter 39, Loss: 9119.8398438, Throughput: 75.313463 im/s
Epoch 47, Train Loss: 9413.9443359, Time: 66.2831s, Throughput: 75.313291 im/s
Epoch 48, Iter 39, Loss: 9527.5722656, Throughput: 75.020239 im/s
Epoch 48, Train Loss: 9379.7099609, Time: 66.5422s, Throughput: 75.020060 im/s
Epoch 49, Iter 39, Loss: 9459.9980469, Throughput: 74.325339 im/s
Epoch 49, Train Loss: 9348.1777344, Time: 67.1643s, Throughput: 74.325174 im/s
Epoch 50, Iter 39, Loss: 9292.8681641, Throughput: 75.094220 im/s
Epoch 50, Train Loss: 9316.5976562, Time: 66.4766s, Throughput: 75.094057 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 1.12.4
Commit 01a2eadb047 (2026-01-06 16:56 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.