{ "cells": [ { "cell_type": "markdown", "id": "11c48eac", "metadata": {}, "source": [ "# VAE lecture demo (Week 10) — CS6140\n", "\n", "Companion to the lecture note **VAE_claude_0929.pdf**. Each cell checks one board computation numerically, and the last one trains a tiny\n", "autoencoder and a tiny VAE side by side. Data here: sklearn's **8×8 digits** with a **Gaussian** decoder (squared error);\n", "HW5 Problem 3 uses 28×28 MNIST with a Bernoulli decoder (binary cross-entropy) — nothing here is its solution.\n", "\n", "| Cell | Board segment | What it checks |\n", "|---|---|---|\n", "| 1 | setup | imports, device (tiny models: CPU) |\n", "| 2 | KL from scratch | discrete KL, asymmetry, cross-entropy = entropy + KL |\n", "| 3 | KL of Gaussians | closed form vs Monte-Carlo; what the KL penalty \"costs\" |\n", "| 4 | ELBO on a 2-state latent | ELBO + KL(q‖posterior) = log p(x) for any q; q = posterior is EM's E-step |\n", "| 5 | linear decoder (probabilistic PCA) | the exact posterior is Gaussian with a *linear* mean: a one-layer encoder |\n", "| 6 | reparameterization | `sample()` has no gradient, `rsample()` = μ + σε does; gradient of E[z²] |\n", "| 7 | AE vs VAE | same network ± KL term: latent layout and decoding a grid of z |\n", "\n", "Total run time: well under a minute on a laptop CPU." ] }, { "cell_type": "code", "execution_count": 1, "id": "589908b8", "metadata": { "execution": { "iopub.execute_input": "2026-09-29T22:30:22.629965Z", "iopub.status.busy": "2026-09-29T22:30:22.629868Z", "iopub.status.idle": "2026-09-29T22:30:24.442191Z", "shell.execute_reply": "2026-09-29T22:30:24.441684Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "best available device: mps\n" ] } ], "source": [ "import math, numpy as np, torch, torch.nn as nn, matplotlib.pyplot as plt, os\n", "from sklearn.datasets import load_digits\n", "torch.set_num_threads(4)\n", "def get_device():\n", " if torch.cuda.is_available(): return torch.device('cuda')\n", " if torch.backends.mps.is_available(): return torch.device('mps')\n", " return torch.device('cpu')\n", "print('best available device:', get_device())\n", "DEVICE = torch.device('cpu') # tiny models: the CPU is fastest\n", "FIG = 'figures_0929'; os.makedirs(FIG, exist_ok=True)" ] }, { "cell_type": "markdown", "id": "c408f7b6", "metadata": {}, "source": [ "## 2. KL divergence from scratch (discrete)\n", "$\\mathrm{KL}(p\\|q)=\\sum_x p(x)\\log\\frac{p(x)}{q(x)}$ — the extra \"surprise\" you pay for believing $q$ when the truth is $p$." ] }, { "cell_type": "code", "execution_count": 2, "id": "8e681a79", "metadata": { "execution": { "iopub.execute_input": "2026-09-29T22:30:24.443972Z", "iopub.status.busy": "2026-09-29T22:30:24.443775Z", "iopub.status.idle": "2026-09-29T22:30:24.446755Z", "shell.execute_reply": "2026-09-29T22:30:24.446223Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "KL(p||q) = 0.0589 KL(q||p) = 0.0566 (not symmetric; both >= 0)\n", "entropy H(p) = 1.0397, cross-entropy H(p,q) = 1.0986 = H(p) + KL(p||q) = 1.0986\n", "=> minimizing cross-entropy (= the softmax/logistic loss, = maximizing likelihood) over q <=> minimizing KL(p_data || q)\n" ] } ], "source": [ "p = np.array([.5, .25, .25]); q = np.array([1/3, 1/3, 1/3])\n", "KL = lambda a, b: np.sum(a*np.log(a/b))\n", "H = -np.sum(p*np.log(p)); CE = -np.sum(p*np.log(q))\n", "print(f'KL(p||q) = {KL(p,q):.4f} KL(q||p) = {KL(q,p):.4f} (not symmetric; both >= 0)')\n", "print(f'entropy H(p) = {H:.4f}, cross-entropy H(p,q) = {CE:.4f} = H(p) + KL(p||q) = {H+KL(p,q):.4f}')\n", "print('=> minimizing cross-entropy (= the softmax/logistic loss, = maximizing likelihood) over q <=> minimizing KL(p_data || q)')" ] }, { "cell_type": "markdown", "id": "f40c3ccb", "metadata": {}, "source": [ "## 3. KL between Gaussians: closed form vs. Monte-Carlo\n", "$\\mathrm{KL}(\\mathcal N(\\mu,\\sigma^2)\\,\\|\\,\\mathcal N(0,1))=\\tfrac12(\\mu^2+\\sigma^2-1-\\log\\sigma^2)$." ] }, { "cell_type": "code", "execution_count": 3, "id": "bb5703ce", "metadata": { "execution": { "iopub.execute_input": "2026-09-29T22:30:24.448192Z", "iopub.status.busy": "2026-09-29T22:30:24.448075Z", "iopub.status.idle": "2026-09-29T22:30:24.681529Z", "shell.execute_reply": "2026-09-29T22:30:24.680911Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " mu sigma closed form Monte-Carlo (10^6 samples of log q(z) - log p(z))\n", " 0.0 1.00 0.0000 0.0000\n", " 1.0 1.00 0.5000 0.5008\n", " 0.0 2.00 0.8069 0.8058\n", " 0.0 0.50 0.3181 0.3181\n", " 1.0 0.50 0.8181 0.8185\n", " 0.0 0.10 1.8076 1.8081\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "kl_gauss = lambda mu, s: 0.5*(mu**2 + s**2 - 1 - np.log(s**2))\n", "rng = np.random.default_rng(0)\n", "print(' mu sigma closed form Monte-Carlo (10^6 samples of log q(z) - log p(z))')\n", "for mu, s in [(0, 1), (1, 1), (0, 2), (0, .5), (1, .5), (0, .1)]:\n", " z = mu + s*rng.standard_normal(10**6)\n", " mc = np.mean((-0.5*np.log(2*np.pi*s*s) - (z-mu)**2/(2*s*s)) - (-0.5*np.log(2*np.pi) - z**2/2))\n", " print(f'{mu:5.1f} {s:6.2f} {kl_gauss(mu, s):10.4f} {mc:10.4f}')\n", "fig, ax = plt.subplots(1, 2, figsize=(9, 2.8))\n", "m = np.linspace(-3, 3, 200); ax[0].plot(m, kl_gauss(m, 1.0)); ax[0].set_xlabel('mu (sigma = 1)'); ax[0].set_title('moving the mean: KL = mu^2 / 2')\n", "s = np.linspace(0.05, 3, 300); ax[1].plot(s, kl_gauss(0, s)); ax[1].set_xlabel('sigma (mu = 0)'); ax[1].set_title('shrinking sigma -> 0 costs without bound')\n", "for a in ax: a.set_ylabel('KL to N(0,1)'); a.grid(alpha=.3)\n", "plt.tight_layout(); plt.savefig(f'{FIG}/fig_kl_gauss.png', dpi=130); plt.show()" ] }, { "cell_type": "markdown", "id": "c342ba99", "metadata": {}, "source": [ "## 4. The ELBO on a two-state latent variable (HW4's mixture, with K = 2)\n", "Prior $p(z)=(0.5,0.5)$; for the observed point, $p(x\\mid z=1)=0.2$, $p(x\\mid z=2)=0.6$. So $p(x)=0.4$ and the posterior is $(0.25, 0.75)$." ] }, { "cell_type": "code", "execution_count": 4, "id": "65c3da4b", "metadata": { "execution": { "iopub.execute_input": "2026-09-29T22:30:24.683181Z", "iopub.status.busy": "2026-09-29T22:30:24.683045Z", "iopub.status.idle": "2026-09-29T22:30:24.686842Z", "shell.execute_reply": "2026-09-29T22:30:24.686239Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "log p(x) = -0.9163, posterior = [0.25 0.75]\n", " q(z) recon E_q[log p(x|z)] KL(q||prior) ELBO gap KL(q||posterior)\n", "[0.5 0.5] -1.0601 0.0000 -1.0601 0.1438 0.1438\n", "[0.1 0.9] -0.6207 0.3681 -0.9888 0.0725 0.0725\n", "[0.25 0.75] -0.7855 0.1308 -0.9163 -0.0000 0.0000\n", "q = posterior closes the gap: that is exactly what the EM E-step (responsibilities) computes.\n" ] } ], "source": [ "pz = np.array([.5, .5]); px_z = np.array([.2, .6])\n", "px = pz @ px_z; post = pz*px_z/px\n", "print(f'log p(x) = {np.log(px):.4f}, posterior = {post}')\n", "print(' q(z) recon E_q[log p(x|z)] KL(q||prior) ELBO gap KL(q||posterior)')\n", "for qz in [np.array([.5, .5]), np.array([.1, .9]), post]:\n", " recon = qz @ np.log(px_z); klp = KL(qz, pz); elbo = recon - klp\n", " print(f'{str(qz.round(2)):14s} {recon:12.4f} {klp:10.4f} {elbo:8.4f} {np.log(px)-elbo:6.4f} {KL(qz, post):8.4f}')\n", "print('q = posterior closes the gap: that is exactly what the EM E-step (responsibilities) computes.')" ] }, { "cell_type": "markdown", "id": "6bd4a79c", "metadata": {}, "source": [ "## 5. A linear decoder: everything is computable (probabilistic PCA)\n", "$z\\sim\\mathcal N(0,1)$, $x = wz+\\varepsilon$, $\\varepsilon\\sim\\mathcal N(0,s^2I)$ with $w=(2,1)$, $s^2=1$. Bayes' rule gives\n", "$p(z\\mid x)=\\mathcal N\\big(w^\\top x/M,\\ s^2/M\\big)$, $M=w^\\top w+s^2=6$. Check it by brute force on a grid for $x=(3,1)$." ] }, { "cell_type": "code", "execution_count": 5, "id": "c3c7941a", "metadata": { "execution": { "iopub.execute_input": "2026-09-29T22:30:24.688207Z", "iopub.status.busy": "2026-09-29T22:30:24.688100Z", "iopub.status.idle": "2026-09-29T22:30:24.697783Z", "shell.execute_reply": "2026-09-29T22:30:24.697323Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "formula: mean = w.x/M = 1.1667, var = s^2/M = 0.1667 grid: mean = 1.1667, var = 0.1667\n", "the exact \"encoder\" is linear: mu(x) = [0.333, 0.167] . x — one nn.Linear(2, 1) layer.\n", "as s^2 -> 0 the mean becomes w.x/|w|^2 = 1.40: the projection onto w, i.e. PCA (HW3)\n", "marginal: p(x) = N(0, w w^T + s^2 I) =\n", " [[5. 2.]\n", " [2. 2.]]\n" ] } ], "source": [ "w = np.array([2., 1.]); s2 = 1.; x = np.array([3., 1.]); M = w@w + s2\n", "zz = np.linspace(-6, 6, 200001)\n", "logjoint = -zz**2/2 - ((x[None, :] - np.outer(zz, w))**2).sum(1)/(2*s2) # log p(z) + log p(x|z), up to constants\n", "pj = np.exp(logjoint - logjoint.max()); pj /= pj.sum()\n", "mean = (zz*pj).sum(); var = ((zz-mean)**2*pj).sum()\n", "print(f'formula: mean = w.x/M = {w@x/M:.4f}, var = s^2/M = {s2/M:.4f} grid: mean = {mean:.4f}, var = {var:.4f}')\n", "print(f'the exact \"encoder\" is linear: mu(x) = [{w[0]/M:.3f}, {w[1]/M:.3f}] . x — one nn.Linear(2, 1) layer.')\n", "print(f'as s^2 -> 0 the mean becomes w.x/|w|^2 = {w@x/(w@w):.2f}: the projection onto w, i.e. PCA (HW3)')\n", "print('marginal: p(x) = N(0, w w^T + s^2 I) =\\n', np.outer(w, w) + s2*np.eye(2))" ] }, { "cell_type": "markdown", "id": "6c21c1e4", "metadata": {}, "source": [ "## 6. The reparameterization trick\n", "We need $\\frac{\\partial}{\\partial\\mu}$ and $\\frac{\\partial}{\\partial\\sigma}$ of $\\mathbb E_{z\\sim\\mathcal N(\\mu,\\sigma^2)}[f(z)]$. For $f(z)=z^2$ the answer is known:\n", "$\\mathbb E[z^2]=\\mu^2+\\sigma^2$, so the gradients are $2\\mu$ and $2\\sigma$." ] }, { "cell_type": "code", "execution_count": 6, "id": "ee00ad48", "metadata": { "execution": { "iopub.execute_input": "2026-09-29T22:30:24.699335Z", "iopub.status.busy": "2026-09-29T22:30:24.699220Z", "iopub.status.idle": "2026-09-29T22:30:24.706650Z", "shell.execute_reply": "2026-09-29T22:30:24.706163Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sample(): requires_grad = False -> backprop stops here\n", "rsample(): requires_grad = True (rsample computes mu + sigma*eps)\n", "2 samples eps=(-1,+1): d/dmu = 2.000 (exact 2mu = 2), d/dsigma = 1.000 (exact 2sigma = 1)\n", "100k samples: d/dmu = 1.998, d/dsigma = 0.998\n" ] } ], "source": [ "mu = torch.tensor(1.0, requires_grad=True); sigma = torch.tensor(0.5, requires_grad=True)\n", "dist = torch.distributions.Normal(mu, sigma)\n", "z_plain = dist.sample((4,)); print('sample(): requires_grad =', z_plain.requires_grad, ' -> backprop stops here')\n", "z_rep = dist.rsample((4,)); print('rsample(): requires_grad =', z_rep.requires_grad, ' (rsample computes mu + sigma*eps)')\n", "\n", "eps = torch.tensor([-1., 1.]) # the two board samples\n", "z = mu + sigma*eps; (z**2).mean().backward()\n", "print(f'2 samples eps=(-1,+1): d/dmu = {mu.grad.item():.3f} (exact 2mu = 2), d/dsigma = {sigma.grad.item():.3f} (exact 2sigma = 1)')\n", "mu.grad = None; sigma.grad = None\n", "torch.manual_seed(0); z = mu + sigma*torch.randn(100000); (z**2).mean().backward()\n", "print(f'100k samples: d/dmu = {mu.grad.item():.3f}, d/dsigma = {sigma.grad.item():.3f}')" ] }, { "cell_type": "markdown", "id": "c7aa3c28", "metadata": {}, "source": [ "## 7. Autoencoder vs. VAE: same network, one extra term\n", "Encoder 64 → 128 → (2 means, 2 log-variances); decoder 2 → 128 → 64 with sigmoid outputs. The **AE** uses the mean only and minimizes reconstruction error.\n", "The **VAE** samples $z=\\mu+\\sigma\\epsilon$ and adds the KL term. Reconstruction term: Gaussian likelihood with $\\sigma_x=0.25$, i.e. $\\|x-\\hat x\\|^2/(2\\cdot0.25^2)$ — Week 1's \"squared error = Gaussian log-likelihood\".\n", "\n", "What to look for: with 2 latent dimensions and small 8×8 images, *both* decoders produce digit-like pictures somewhere.\n", "The difference is **where the codes are**: the AE's code scale and location are arbitrary (whatever reconstruction happened to like),\n", "so \"pick a random z\" has no answer; the VAE's KL term pins the codes to $\\mathcal N(0,I)$, so sampling the prior *is* the answer." ] }, { "cell_type": "code", "execution_count": 7, "id": "3d7cd755", "metadata": { "execution": { "iopub.execute_input": "2026-09-29T22:30:24.707998Z", "iopub.status.busy": "2026-09-29T22:30:24.707906Z", "iopub.status.idle": "2026-09-29T22:30:30.632470Z", "shell.execute_reply": "2026-09-29T22:30:30.631858Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "AE : reconstruction term 13.7, KL term 0.00\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "VAE: reconstruction term 14.3, KL term 4.60\n" ] } ], "source": [ "X, y = load_digits(return_X_y=True); X = torch.tensor(X/16., dtype=torch.float32)\n", "class AEorVAE(nn.Module):\n", " def __init__(self, variational):\n", " super().__init__(); self.variational = variational\n", " self.trunk = nn.Sequential(nn.Linear(64, 128), nn.ReLU())\n", " self.head_mu, self.head_logvar = nn.Linear(128, 2), nn.Linear(128, 2) # two heads, one trunk\n", " self.decoder = nn.Sequential(nn.Linear(2, 128), nn.ReLU(), nn.Linear(128, 64), nn.Sigmoid())\n", " def forward(self, x):\n", " h = self.trunk(x); mu = self.head_mu(h)\n", " if not self.variational: return self.decoder(mu), mu, None\n", " logvar = self.head_logvar(h)\n", " z = mu + torch.exp(0.5*logvar)*torch.randn_like(mu) # reparameterization\n", " return self.decoder(z), mu, logvar\n", "\n", "def fit(variational, epochs=1500, sx=0.25):\n", " torch.manual_seed(0); net = AEorVAE(variational); opt = torch.optim.Adam(net.parameters(), lr=3e-3)\n", " for ep in range(epochs): # full batch: only 1797 images\n", " xhat, mu, logvar = net(X)\n", " recon = ((X - xhat)**2).sum(1).mean()/(2*sx**2)\n", " kl = 0.5*(mu**2 + logvar.exp() - 1 - logvar).sum(1).mean() if variational else torch.tensor(0.)\n", " loss = recon + kl; opt.zero_grad(); loss.backward(); opt.step()\n", " print(f\"{'VAE' if variational else 'AE ':3s}: reconstruction term {recon.item():6.1f}, KL term {kl.item():5.2f}\")\n", " return net\n", "ae, vae = fit(False), fit(True)" ] }, { "cell_type": "code", "execution_count": 8, "id": "3e102cd6", "metadata": { "execution": { "iopub.execute_input": "2026-09-29T22:30:30.634242Z", "iopub.status.busy": "2026-09-29T22:30:30.634009Z", "iopub.status.idle": "2026-09-29T22:30:30.898070Z", "shell.execute_reply": "2026-09-29T22:30:30.897425Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "with torch.no_grad():\n", " codes = {'autoencoder': ae(X)[1].numpy(), 'VAE (means)': vae(X)[1].numpy()}\n", "fig, ax = plt.subplots(1, 2, figsize=(10, 4.2))\n", "for a, (name, c) in zip(ax, codes.items()):\n", " sc = a.scatter(c[:, 0], c[:, 1], c=y, cmap='tab10', s=6); a.set_title(f'{name}: code std = {c.std(0).round(1)}')\n", " a.set_aspect('equal', 'datalim')\n", "fig.colorbar(sc, ax=ax, ticks=range(10), label='digit'); plt.savefig(f'{FIG}/fig_ae_vs_vae_latent.png', dpi=130, bbox_inches='tight'); plt.show()" ] }, { "cell_type": "code", "execution_count": 9, "id": "a217477f", "metadata": { "execution": { "iopub.execute_input": "2026-09-29T22:30:30.899485Z", "iopub.status.busy": "2026-09-29T22:30:30.899376Z", "iopub.status.idle": "2026-09-29T22:30:31.046324Z", "shell.execute_reply": "2026-09-29T22:30:31.045756Z" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def tile(imgs, n_cols, pad=1):\n", " # lay out 8x8 images on a white canvas with a 1-pixel gap between tiles\n", " n_rows = int(np.ceil(len(imgs)/n_cols)); canvas = np.zeros((n_rows*(8+pad)+pad, n_cols*(8+pad)+pad))\n", " for k, im in enumerate(imgs):\n", " r, c = divmod(k, n_cols); canvas[pad+r*(8+pad):pad+r*(8+pad)+8, pad+c*(8+pad):pad+c*(8+pad)+8] = im.reshape(8, 8)\n", " return canvas\n", "def decode_grid(net, lim_x, lim_y, n=10):\n", " gx, gy = np.linspace(*lim_x, n), np.linspace(*lim_y, n)\n", " Z = torch.tensor([[a, b] for b in gy[::-1] for a in gx], dtype=torch.float32)\n", " with torch.no_grad(): return tile(net.decoder(Z).numpy(), n)\n", "c = codes['autoencoder']; lo, hi = np.percentile(c, 1, axis=0), np.percentile(c, 99, axis=0)\n", "fig, ax = plt.subplots(1, 2, figsize=(10, 5.2))\n", "ax[0].imshow(decode_grid(ae, (lo[0], hi[0]), (lo[1], hi[1])), cmap='gray_r')\n", "ax[0].set_title('AE: even grid over the box holding 98% of its codes (about -30..30)\\n(the decoder works, but you had to look up where the codes are)', fontsize=9)\n", "ax[1].imshow(decode_grid(vae, (-2.5, 2.5), (-2.5, 2.5)), cmap='gray_r')\n", "ax[1].set_title('VAE: even grid over [-2.5, 2.5]^2, i.e. where N(0, I) puts its mass\\n(all ten digits; neighbouring cells change gradually)', fontsize=9)\n", "for a in ax: a.axis('off')\n", "plt.tight_layout(); plt.savefig(f'{FIG}/fig_decode_grids.png', dpi=130); plt.show()" ] }, { "cell_type": "code", "execution_count": 10, "id": "efb6d51d", "metadata": { "execution": { "iopub.execute_input": "2026-09-29T22:30:31.047939Z", "iopub.status.busy": "2026-09-29T22:30:31.047810Z", "iopub.status.idle": "2026-09-29T22:30:31.142720Z", "shell.execute_reply": "2026-09-29T22:30:31.142139Z" } }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "torch.manual_seed(1); zs = torch.randn(12, 2)\n", "with torch.no_grad(): rows = [ae.decoder(zs).numpy(), vae.decoder(zs).numpy()]\n", "fig, ax = plt.subplots(2, 1, figsize=(9, 2.4))\n", "for a, r, t in zip(ax, rows, ['AE decoder on z ~ N(0, I): these z cover only the centre of its code space (code std about 8), so only the few classes clustered near 0 appear',\n", " 'VAE decoder on the same z: N(0, I) is where the KL term put the codes, so the samples spread over many classes (this is \"generation\")']):\n", " a.imshow(tile(r, 12), cmap='gray_r'); a.set_title(t, fontsize=8.5, loc='left'); a.axis('off')\n", "plt.tight_layout(); plt.savefig(f'{FIG}/fig_prior_samples.png', dpi=130); plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.14.0" } }, "nbformat": 4, "nbformat_minor": 5 }