VAE · MNIST Playground

🎯

Status

Not Trained

📈

Epoch

0 / 0

⚡

Current Loss

—

⚙️ Hyperparameters

Epochs

Batch Size

Learning Rate

Hidden Dim

Latent Dim

📉 Training Loss

📊 Loss curve appears here after training starts

🏗️ Network Topology

Input · 784-D

28 × 28 flattened pixel values

↓

Encoder FC · 400-D

ReLU activation

↓ split ↓

μ head & log σ² head · 2-D

Two parallel linear layers

↓ reparameterize ↓

Latent vector z · 2-D

z = μ + σ · ε ε ∼ 𝒩(0, I)

↓

Decoder FC · 400-D

ReLU activation

↓

Output · 784-D

Sigmoid → reconstructed image

📐 Loss Function

ELBO Loss

ℒ = ℒ_recon + β · KL

Reconstruction Loss (Binary Cross-Entropy)

ℒ_recon = −Σ [ x·log(x̂) + (1−x)·log(1−x̂) ]

KL Divergence (closed form)

KL = −½ Σ [ 1 + log σ² − μ² − σ² ]

Reparameterization Trick

The trick decouples stochasticity from parameters, making backpropagation through sampling possible:

z = μ + σ ⊙ ε where ε ∼ 𝒩(0, I)

Why 2-D Latent Space?

A 2-D latent space lets us visualise the full manifold as a 2-D scatter plot. Higher dimensions improve quality but lose direct interpretability.

⚠️ Train the model first (Training tab). Latent space visualisation requires a 2-D latent dimension.

🌐 2-D Latent Space — MNIST

Each point is an MNIST digit encoded via the VAE's encoder. Colour = digit class (0–9). Well-separated clusters indicate a structured latent manifold.

🌐 Train the model, then click Generate Plot

⚠️ Train the model first (Training tab) to enable reconstruction.

🔁 Original vs Reconstructed Digits

Row 1: original MNIST samples | Row 2: VAE reconstructions. Blurriness reflects the smoothing nature of the reconstruction loss.

🔁 Train then click Random Batch

ℹ️ Adjust the latent sliders to navigate the learned manifold and decode new digit-like images. Grid view requires a 2-D latent space.

🎛️ Latent Controls

Z₁ — Latent Dim 1 0.00

Z₂ — Latent Dim 2 0.00

🖼️ Generated Image

✨ Train the model then click Generate