Interactive Explainer
ELBO, Decomposed
The Evidence Lower Bound is the VAE's loss — and it's just two things added: reconstruction cost and KL to the prior. Watch them fight as you train.
Step 1
The loss
$\mathcal{L} = \underbrace{-\mathbb{E}_{q_\phi(z|x)}[\log p_\theta(x|z)]}_{\text{reconstruction}} + \beta \cdot \underbrace{\text{KL}(q_\phi(z|x) \,\Vert\, p(z))}_{\text{regularizer}}$
$\beta = 1$ gives the classical VAE; $\beta = 0$ degenerates to a plain AE; large $\beta$ pushes toward disentangled latents at reconstruction cost.
Try it
The widget
Train a tiny MNIST VAE in the browser.
Live: two bars (recon + KL), 2D latent scatter, reconstruction grid.
Slider: β from 0 to 50.
Status: scaffold. Implementation pending.
Step 2
What you should see
- $\beta = 0$ · sharp reconstructions, latent is a mess.
- $\beta = 1$ · balanced; samples look like digits.
- $\beta = 50$ · blurry reconstructions, but the latent axes pick up clean factors (stroke width, slant).