From 5efef8c41f9de76a878eb46ba50de3c81ad20669 Mon Sep 17 00:00:00 2001 From: jsboige Date: Thu, 27 Aug 2026 11:06:05 +0200 Subject: [PATCH 1/2] feat(dl,#12959): 3.6 VAE/GAN/diffusion NumPy -- rebase post-conflit main MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Grain: DEEP/notebook-python — lane myia-po-2023:CoursIA-2 — prev: MED/notebook-python #13071 🤖 Generated with [Claude Code](https://claude.com/claude-code) Co-Authored-By: Claude Opus 4.6 --- .../3.5-Phenomenes-de-Generalisation.ipynb | 2 +- .../3.6-Modeles-Generatifs.ipynb | 1243 +++++++++++++++++ .../03-DeepLearning/README.md | 5 +- 3 files changed, 1247 insertions(+), 3 deletions(-) create mode 100644 MyIA.AI.Notebooks/ML/DataScienceWithAgents/03-DeepLearning/3.6-Modeles-Generatifs.ipynb diff --git a/MyIA.AI.Notebooks/ML/DataScienceWithAgents/03-DeepLearning/3.5-Phenomenes-de-Generalisation.ipynb b/MyIA.AI.Notebooks/ML/DataScienceWithAgents/03-DeepLearning/3.5-Phenomenes-de-Generalisation.ipynb index f05a286bd4..b13989a7c3 100644 --- a/MyIA.AI.Notebooks/ML/DataScienceWithAgents/03-DeepLearning/3.5-Phenomenes-de-Generalisation.ipynb +++ b/MyIA.AI.Notebooks/ML/DataScienceWithAgents/03-DeepLearning/3.5-Phenomenes-de-Generalisation.ipynb @@ -9,7 +9,7 @@ "source": [ "# 3.5 — Grokking et double descente : quand la généralisation défie le manuel\n", "\n", - "**Navigation** : [<< 2.9-Grokking (boîte noire)](../02-ML-Cours/2.9-Grokking-Generalisation.ipynb) · [2.8-Théorie-PAC](../02-ML-Cours/2.8-Theorie-PAC.ipynb) · [Feuille de route de la série](README.md)\n", + "**Navigation** : [<< 2.9-Grokking (boîte noire)](../02-ML-Cours/2.9-Grokking-Generalisation.ipynb) · [2.8-Théorie-PAC](../02-ML-Cours/2.8-Theorie-PAC.ipynb) · [Feuille de route de la série](README.md) · [3.6-Modeles-Generatifs >](3.6-Modeles-Generatifs.ipynb)\n", "\n", "Le notebook [2.9](../02-ML-Cours/2.9-Grokking-Generalisation.ipynb) vous a montré un réseau PyTorch qui mémorise pendant des milliers de pas, puis généralise **d'un coup** — le *grokking*. Le notebook [2.8](../02-ML-Cours/2.8-Theorie-PAC.ipynb) vous a donné l'outil théorique classique : une borne qui dit qu'ajouter de la capacité **coûte** en généralisation.\n", "\n", diff --git a/MyIA.AI.Notebooks/ML/DataScienceWithAgents/03-DeepLearning/3.6-Modeles-Generatifs.ipynb b/MyIA.AI.Notebooks/ML/DataScienceWithAgents/03-DeepLearning/3.6-Modeles-Generatifs.ipynb new file mode 100644 index 0000000000..538d834590 --- /dev/null +++ b/MyIA.AI.Notebooks/ML/DataScienceWithAgents/03-DeepLearning/3.6-Modeles-Generatifs.ipynb @@ -0,0 +1,1243 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "45d48ce2", + "metadata": { + "papermill": { + "duration": 0.003596, + "end_time": "2026-08-25T18:10:40.553684", + "exception": false, + "start_time": "2026-08-25T18:10:40.550088", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "# 3.6 — Modèles génératifs : trois objectifs, trois échecs — VAE, GAN et diffusion sur une distribution multimodale bornée\n", + "\n", + "**Navigation** : [<< 3.5-Grokking et double descente](3.5-Phenomenes-de-Generalisation.ipynb) · [Feuille de route de la série](README.md) · VAE applicatif : [QC-Py-24 (autoencodeurs d'anomalies)](../../QuantConnect/Python/QC-Py-24-Autoencoders-Anomaly.ipynb)\n", + "\n", + "Nos notebooks consomment des modèles génératifs partout — les autoencodeurs d'anomalies de [QC-Py-24](../../QuantConnect/Python/QC-Py-24-Autoencoders-Anomaly.ipynb), les diffuseurs des notebooks GenAI/Image — mais toujours comme des boîtes noires. Ce notebook ouvre trois de ces boîtes **côte à côte** : un **VAE**, un **GAN** et un petit **modèle de diffusion (DDPM)**, chacun écrit en NumPy pur sur la machinerie du [3.1](3.1-Retropropagation.ipynb) (backward à la main) et l'Adam du [3.2](3.2-Optimisateurs.ipynb). Pas une ligne de PyTorch.\n", + "\n", + "La thèse : **les trois familles n'optimisent pas la même chose**, donc elles n'échouent pas de la même façon. Le VAE maximise une borne de la log-vraisemblance (reconstruction + régularisation vers le prior) — il couvre, mais il **moyenne**. Le GAN optimise un duel minimax — ses échantillons sont nets, mais rien dans son objectif ne force la **couverture des modes**. La diffusion apprend à débruiter pas à pas — elle raffine itérativement, au prix d'un **échantillonnage séquentiel**. Pour rendre ces échecs *mesurables*, les trois modèles s'entraînent sur la même distribution bornée — huit modes sur un cercle — avec le même budget (pas, batch, largeur), contre une baseline **GMM ajustée par EM** qui fixe la barre : quand le biais inductif colle au problème, l'apprentissage profond est superflu.\n", + "\n", + "Ce notebook ne prétend pas reproduire FLUX ou Stable Diffusion — il isole les **mécanismes** que ces moteurs SOTA consomment (discussion finale)." + ] + }, + { + "cell_type": "markdown", + "id": "941e4cc1", + "metadata": { + "papermill": { + "duration": 0.002091, + "end_time": "2026-08-25T18:10:40.558413", + "exception": false, + "start_time": "2026-08-25T18:10:40.556322", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "***" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "927614b1", + "metadata": { + "execution": { + "iopub.execute_input": "2026-08-25T18:10:40.564003Z", + "iopub.status.busy": "2026-08-25T18:10:40.563394Z", + "iopub.status.idle": "2026-08-25T18:10:41.055482Z", + "shell.execute_reply": "2026-08-25T18:10:41.054982Z" + }, + "papermill": { + "duration": 0.495792, + "end_time": "2026-08-25T18:10:41.056420", + "exception": false, + "start_time": "2026-08-25T18:10:40.560628", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Jeu d'entrainement : 8192 points, 8 modes separes, rayon 1.6, std intra-mode 0.06\n", + "Domaine observe : x1 in [-1.80, 1.78] ; x2 in [-1.81, 1.84]\n" + ] + }, + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Imports, hyperparametres canoniques, donnees : huit modes sur un cercle (domaine borne)\n", + "import time\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "%matplotlib inline\n", + "\n", + "N_MODES = 8 # nombre de modes de la cible\n", + "RADIUS = 1.6 # rayon du cercle portant les modes\n", + "STD = 0.06 # ecart-type intra-mode (modes bien separes)\n", + "N_TRAIN = 8192 # jeu d'entrainement commun a tous les modeles\n", + "SEED = 42 # graine de la demonstration ; le protocole multi-graines vient en fin de notebook\n", + "SEEDS = [0, 1, 7, 42]\n", + "\n", + "def centres_modes():\n", + " ang = 2 * np.pi * np.arange(N_MODES) / N_MODES\n", + " return np.column_stack([RADIUS * np.cos(ang), RADIUS * np.sin(ang)])\n", + "\n", + "CENTERS = centres_modes()\n", + "\n", + "def make_data(n, rng):\n", + " ks = rng.integers(0, N_MODES, n)\n", + " return CENTERS[ks] + rng.normal(0, STD, (n, 2))\n", + "\n", + "X = make_data(N_TRAIN, np.random.default_rng(SEED))\n", + "print(f\"Jeu d'entrainement : {N_TRAIN} points, {N_MODES} modes separes, rayon {RADIUS}, std intra-mode {STD}\")\n", + "print(f\"Domaine observe : x1 in [{X[:,0].min():.2f}, {X[:,0].max():.2f}] ; x2 in [{X[:,1].min():.2f}, {X[:,1].max():.2f}]\")\n", + "\n", + "fig, ax = plt.subplots(figsize=(5.2, 4.6))\n", + "ax.scatter(X[:3000, 0], X[:3000, 1], s=3, alpha=0.35, color=\"tab:blue\", label=\"donnees\")\n", + "ax.scatter(CENTERS[:, 0], CENTERS[:, 1], s=60, marker=\"x\", color=\"tab:red\", label=\"centres des modes\")\n", + "ax.set_title(\"La cible : huit modes separes sur un cercle\")\n", + "ax.set_xlabel(\"x1\"); ax.set_ylabel(\"x2\"); ax.legend(); ax.set_aspect(\"equal\")\n", + "plt.tight_layout(); plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "448d15ae", + "metadata": { + "execution": { + "iopub.execute_input": "2026-08-25T18:10:41.063473Z", + "iopub.status.busy": "2026-08-25T18:10:41.063211Z", + "iopub.status.idle": "2026-08-25T18:10:43.291566Z", + "shell.execute_reply": "2026-08-25T18:10:43.291051Z" + }, + "papermill": { + "duration": 2.233247, + "end_time": "2026-08-25T18:10:43.292901", + "exception": false, + "start_time": "2026-08-25T18:10:41.059654", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "GMM (EM x3, 2.22 s de fit, 0 gradient) : couverture 8/8 | equilibre 0.999 | dispersion 0.99\n", + "Centres retrouves par EM (apparies au plus proche vrai centre) : ecart max 0.0036\n" + ] + } + ], + "source": [ + "# Metriques communes + baseline GMM ajustee par EM\n", + "# Trois mesures, appliquees a TOUT modele (GMM, VAE, GAN, diffusion), 4096 echantillons :\n", + "# - couverture : modes recevant >= 2 % des echantillons (le collapse se voit ici)\n", + "# - equilibre : entropie de l'occupation normalisee par log(8) (1.0 = masse parfaitement repartie)\n", + "# - dispersion : distance mediane au mode le plus proche, RELATIVE a celle des vraies donnees (1.0 = net)\n", + "def occupation(echantillons):\n", + " d2 = ((echantillons[:, None, :] - CENTERS[None, :, :]) ** 2).sum(-1)\n", + " return np.bincount(d2.argmin(1), minlength=N_MODES) / len(echantillons)\n", + "\n", + "def couverture(echantillons, part_min=0.02):\n", + " parts = occupation(echantillons)\n", + " return int((parts >= part_min).sum())\n", + "\n", + "def equilibre(echantillons):\n", + " parts = occupation(echantillons)\n", + " return float(-(parts * np.log(parts + 1e-12)).sum() / np.log(N_MODES))\n", + "\n", + "def dispersion_relative(echantillons):\n", + " d_vrai = np.sqrt(((X[:, None, :] - CENTERS[None, :, :]) ** 2).sum(-1)).min(1)\n", + " d_ech = np.sqrt(((echantillons[:, None, :] - CENTERS[None, :, :]) ** 2).sum(-1)).min(1)\n", + " return float(np.median(d_ech) / np.median(d_vrai))\n", + "\n", + "# --- Baseline : GMM diagonal ajuste par EM (aucun gradient, aucun reseau) ---\n", + "def gmm_em(X, K, rng, iters=100):\n", + " n = len(X)\n", + " mu = X[rng.choice(n, K, replace=False)].copy()\n", + " var = np.full((K, 2), X.var(0))\n", + " pi = np.full(K, 1 / K)\n", + " for _ in range(iters):\n", + " logcomp = np.log(pi)[None] - 0.5 * np.sum(np.log(2 * np.pi * var[None])\n", + " + (X[:, None, :] - mu[None]) ** 2 / var[None], -1)\n", + " m = logcomp.max(1, keepdims=True)\n", + " ll = float((m[:, 0] + np.log(np.exp(logcomp - m).sum(1))).sum()) # log-vraisemblance (log-sum-exp)\n", + " r = np.exp(logcomp - m); r /= r.sum(1, keepdims=True)\n", + " Nk = r.sum(0) + 1e-9\n", + " mu = (r.T @ X) / Nk[:, None]\n", + " var = (r[:, :, None] * (X[:, None, :] - mu[None]) ** 2).sum(0) / Nk[:, None] + 1e-6\n", + " pi = Nk / n\n", + " return mu, var, pi, ll\n", + "\n", + "def gmm_echantillon(mu, var, pi, n, rng):\n", + " ks = rng.choice(len(pi), n, p=pi / pi.sum())\n", + " return mu[ks] + rng.normal(0, 1, (n, 2)) * np.sqrt(var[ks])\n", + "\n", + "def gmm_em_multistart(X, K, n_restarts=3):\n", + " \"\"\"L'EM depend de son initialisation : une seule relance tombe parfois dans un\n", + " optimum local (un composant chevauche son voisin). Pratique standard : quelques\n", + " relances, on garde la meilleure log-vraisemblance.\"\"\"\n", + " best = None\n", + " for i in range(n_restarts):\n", + " res = gmm_em(X, K, np.random.default_rng(i))\n", + " if best is None or res[3] > best[3]:\n", + " best = res\n", + " return best\n", + "\n", + "t0 = time.time()\n", + "GMM_MU, GMM_VAR, GMM_PI, LL_GMM = gmm_em_multistart(X, N_MODES)\n", + "T_FIT_GMM = time.time() - t0\n", + "S_GMM = gmm_echantillon(GMM_MU, GMM_VAR, GMM_PI, 4096, np.random.default_rng(100))\n", + "print(f\"GMM (EM x3, {T_FIT_GMM:.2f} s de fit, 0 gradient) : couverture {couverture(S_GMM)}/8 | equilibre {equilibre(S_GMM):.3f} | dispersion {dispersion_relative(S_GMM):.2f}\")\n", + "ecart_centres = np.sqrt(((GMM_MU[:, None, :] - CENTERS[None, :, :]) ** 2).sum(-1)).min(1)\n", + "print(f\"Centres retrouves par EM (apparies au plus proche vrai centre) : ecart max {ecart_centres.max():.4f}\")" + ] + }, + { + "cell_type": "markdown", + "id": "ee430fb8", + "metadata": { + "papermill": { + "duration": 0.00278, + "end_time": "2026-08-25T18:10:43.298319", + "exception": false, + "start_time": "2026-08-25T18:10:43.295539", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "**Lecture — la barre est fixée.** Le GMM couvre 8/8 modes, équilibre quasi parfait, dispersion ~1,0 (aussi net que les vraies données). Ce n'est pas de la triche : son biais inductif — huit ellipses gaussiennes — colle *exactement* à la cible choisie, et l'EM retrouve les centres au millième près. Un détail honnête : l'EM dépend de son **initialisation** — une seule relance tombe parfois dans un optimum local où un composant chevauche son voisin (essayez `n_restarts=1` : un centre reste décalé) — d'où les trois relances, on garde la meilleure log-vraisemblance. C'est le témoin qui rend les échecs des modèles profonds **mesurables** : si un réseau entraîné 6 000 pas fait moins bien qu'un EM de deux secondes, l'échec est dans l'*objectif*, pas dans la capacité.\n", + "\n", + "Pourquoi alors des réseaux ? Parce que la vie réelle — images, audio, texte — n'est pas un mélange de huit gaussiennes : le GMM y explose (covariances en O(d²), modes mal définis). Les trois familles qui suivent échangent le biais inductif gratuit contre de la flexibilité — et chacune paie un prix différent, visible dans les mêmes trois métriques." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "10fd2c0f", + "metadata": { + "execution": { + "iopub.execute_input": "2026-08-25T18:10:43.304538Z", + "iopub.status.busy": "2026-08-25T18:10:43.304313Z", + "iopub.status.idle": "2026-08-25T18:10:43.311949Z", + "shell.execute_reply": "2026-08-25T18:10:43.311535Z" + }, + "papermill": { + "duration": 0.011769, + "end_time": "2026-08-25T18:10:43.312654", + "exception": false, + "start_time": "2026-08-25T18:10:43.300885", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Budget commun aux trois familles : 6000 pas de gradient, batch 256, couches cachees de largeur 64\n" + ] + } + ], + "source": [ + "# La machinerie commune : MLP NumPy (backward a la main, style 3.1) + Adam (style 3.2)\n", + "class MLP:\n", + " \"\"\"MLP a activations tangentes, dernier couche lineaire par defaut.\n", + " backward(dA) renvoie dX (gradient par rapport a l'entree) ET la liste des gradients parametres.\"\"\"\n", + " def __init__(self, dims, rng, out_linear=True):\n", + " self.W = [rng.normal(0, 0.5 ** 0.5 / np.sqrt(dims[i]), (dims[i], dims[i + 1])) for i in range(len(dims) - 1)]\n", + " self.b = [np.zeros(d) for d in dims[1:]]\n", + " self.out_linear = out_linear\n", + " def params(self):\n", + " return self.W + self.b\n", + " def n_params(self):\n", + " return int(sum(p.size for p in self.params()))\n", + " def forward(self, X):\n", + " self.cache = [X]\n", + " A = X\n", + " L = len(self.W)\n", + " for i in range(L):\n", + " Z = A @ self.W[i] + self.b[i]\n", + " H = Z if (i == L - 1 and self.out_linear) else np.tanh(Z)\n", + " self.cache.append((A, H))\n", + " A = H\n", + " return A\n", + " def backward(self, dA):\n", + " gW = [None] * len(self.W); gb = [None] * len(self.b)\n", + " L = len(self.W)\n", + " for i in range(L - 1, -1, -1):\n", + " A, H = self.cache[i + 1]\n", + " dZ = dA if (i == L - 1 and self.out_linear) else dA * (1 - H ** 2)\n", + " gW[i] = A.T @ dZ\n", + " gb[i] = dZ.sum(0)\n", + " dA = dZ @ self.W[i].T\n", + " return dA, gW + gb\n", + "\n", + "class Adam:\n", + " def __init__(self, params, lr=1e-3):\n", + " self.p = params\n", + " self.m = [np.zeros_like(p) for p in params]; self.v = [np.zeros_like(p) for p in params]\n", + " self.t = 0; self.lr = lr\n", + " def step(self, grads):\n", + " self.t += 1\n", + " for i, (p, g) in enumerate(zip(self.p, grads)):\n", + " self.m[i] = 0.9 * self.m[i] + 0.1 * g\n", + " self.v[i] = 0.999 * self.v[i] + 0.001 * g * g\n", + " mh = self.m[i] / (1 - 0.9 ** self.t); vh = self.v[i] / (1 - 0.999 ** self.t)\n", + " p -= self.lr * mh / (np.sqrt(vh) + 1e-8)\n", + "\n", + "H = 64 # largeur commune des couches cachees\n", + "BATCH = 256 # taille de batch commune\n", + "STEPS = 6000 # budget de pas de gradient commun aux trois familles\n", + "N_ECH = 4096 # nombre d'echantillons pour chaque evaluation\n", + "print(f\"Budget commun aux trois familles : {STEPS} pas de gradient, batch {BATCH}, couches cachees de largeur {H}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "83c7d605", + "metadata": { + "execution": { + "iopub.execute_input": "2026-08-25T18:10:43.319271Z", + "iopub.status.busy": "2026-08-25T18:10:43.318856Z", + "iopub.status.idle": "2026-08-25T18:10:43.330207Z", + "shell.execute_reply": "2026-08-25T18:10:43.329764Z" + }, + "papermill": { + "duration": 0.015532, + "end_time": "2026-08-25T18:10:43.330984", + "exception": false, + "start_time": "2026-08-25T18:10:43.315452", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Garde VAE (ELBO + reparametrisation) : ecart relatif max = 1.39e-08\n", + "Garde diffusion (eps-net, x_t conditionne en t) : ecart relatif max = 3.22e-10\n" + ] + } + ], + "source": [ + "# Garde (la discipline du 3.1) : gradient numerique vs analytique sur les deux chaines les plus risquees\n", + "# Chaine 1 : l'ELBO complet du VAE — reconstruction MOINS le chemin de reparametrisation z = mu + sigma*eps\n", + "B_G = 16\n", + "Xg = make_data(B_G, np.random.default_rng(0))\n", + "EPS_G = np.random.default_rng(1).normal(0, 1, (B_G, 2))\n", + "enc_g = MLP([2, 4, 4, 4], np.random.default_rng(0))\n", + "dec_g = MLP([2, 4, 4, 2], np.random.default_rng(2))\n", + "\n", + "def elbo_et_grads():\n", + " h = enc_g.forward(Xg); mu, lv = h[:, :2], h[:, 2:]\n", + " z = mu + np.exp(0.5 * lv) * EPS_G\n", + " xr = dec_g.forward(z)\n", + " L = ((xr - Xg) ** 2).sum(1).mean() + 0.5 * (np.exp(lv) + mu ** 2 - 1 - lv).sum(1).mean()\n", + " dz, gd = dec_g.backward(2 * (xr - Xg) / B_G)\n", + " dmu = dz + mu / B_G\n", + " dlv = dz * np.exp(0.5 * lv) * EPS_G * 0.5 + 0.5 * (np.exp(lv) - 1) / B_G\n", + " _, ge = enc_g.backward(np.concatenate([dmu, dlv], 1))\n", + " return L, ge + gd\n", + "\n", + "def ecart_max_garde(modeles, loss_et_grads):\n", + " \"\"\"Pour chaque couche de chaque modele, sonde la plus grande composante analytique par difference finie.\"\"\"\n", + " _, g = loss_et_grads()\n", + " worst = 0.0\n", + " k = 0\n", + " for net in modeles:\n", + " for couche in net.params():\n", + " gi = g[k]; k += 1\n", + " idx = np.unravel_index(np.argmax(np.abs(gi)), couche.shape)\n", + " orig, eps = couche[idx], 1e-6\n", + " couche[idx] = orig + eps; Lp, _ = loss_et_grads()\n", + " couche[idx] = orig - eps; Lm, _ = loss_et_grads()\n", + " couche[idx] = orig\n", + " num = (Lp - Lm) / (2 * eps)\n", + " worst = max(worst, abs(num - gi[idx]) / max(abs(num), 1e-10))\n", + " return worst\n", + "\n", + "print(f\"Garde VAE (ELBO + reparametrisation) : ecart relatif max = {ecart_max_garde([enc_g, dec_g], elbo_et_grads):.2e}\")\n", + "\n", + "# Chaine 2 : la MSE de prediction de bruit du DDPM (entree x_t conditionnee en t)\n", + "T = 100 # nombre de pas de diffusion\n", + "BETAS = np.linspace(1e-4, 0.09, T) # schedule lineaire ; cf. lecture de la section diffusion\n", + "ALPHAS_CUM = np.cumprod(1 - BETAS)\n", + "\n", + "def t_feat(t):\n", + " \"\"\"Encodage du temps discre'tise en 7 features : t normalise + sin/cos a 3 frequences.\"\"\"\n", + " x = t[:, None]\n", + " return np.concatenate([x, np.sin(2*np.pi*x), np.cos(2*np.pi*x),\n", + " np.sin(8*np.pi*x), np.cos(8*np.pi*x),\n", + " np.sin(24*np.pi*x), np.cos(24*np.pi*x)], 1)\n", + "\n", + "net_g = MLP([2 + 7, 4, 4, 2], np.random.default_rng(5))\n", + "Xg2 = Xg[:8]; EPS_G2 = np.random.default_rng(6).normal(0, 1, (8, 2))\n", + "INP_G = np.concatenate([Xg2, t_feat(np.arange(8) / T)], 1)\n", + "\n", + "def mse_bruit_et_grads():\n", + " eh = net_g.forward(INP_G)\n", + " L = ((eh - EPS_G2) ** 2).sum(1).mean()\n", + " _, g = net_g.backward(2 * (eh - EPS_G2) / 8)\n", + " return L, g\n", + "\n", + "print(f\"Garde diffusion (eps-net, x_t conditionne en t) : ecart relatif max = {ecart_max_garde([net_g], mse_bruit_et_grads):.2e}\")" + ] + }, + { + "cell_type": "markdown", + "id": "fe7dd2ba", + "metadata": { + "papermill": { + "duration": 0.002491, + "end_time": "2026-08-25T18:10:43.336036", + "exception": false, + "start_time": "2026-08-25T18:10:43.333545", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "**Lecture.** Les deux chaînes les plus risquées — l'ELBO du VAE avec son chemin de reparamétrisation (le gradient doit traverser $z = \\mu + \\sigma \\odot \\epsilon$ en traitant $\\epsilon$ comme une constante), et l'eps-net de la diffusion conditionné en $t$ — retombent sur le gradient numérique à ~1e-8 relatif. Le backward à la main reste exact sur tout ce que la suite construit : VAE, GAN et diffusion partagent cette machinerie vérifiée.\n", + "\n", + "*Note de craft (leçon apprise en construisant ce notebook)* : la garde a une vraie valeur de **débuggage**, pas seulement de rituel — c'est elle qui a attrapé une double-division par la taille de batch (Adam, invariant d'échelle globale, masquait le bug pendant que l'entraînement « marchait ») et un gradient KL non normalisé qui surpondérait la régularisation d'un facteur 256. Un entraînement qui converge n'est **pas** une preuve que l'objectif implémenté est celui qu'on croit." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "93a9c828", + "metadata": { + "execution": { + "iopub.execute_input": "2026-08-25T18:10:43.341915Z", + "iopub.status.busy": "2026-08-25T18:10:43.341692Z", + "iopub.status.idle": "2026-08-25T18:10:59.695374Z", + "shell.execute_reply": "2026-08-25T18:10:59.694376Z" + }, + "papermill": { + "duration": 16.358042, + "end_time": "2026-08-25T18:10:59.696434", + "exception": false, + "start_time": "2026-08-25T18:10:43.338392", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "VAE : 9094 parametres, 6000 pas, 16.2 s\n", + "ELBO final : reconstruction 0.700 + KL 1.05\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# --- Modele 1 : le VAE --- encoder mu/logvar, reparametrisation, decodeur, ELBO\n", + "def train_vae(seed, beta=1.0, verbose=False):\n", + " rng = np.random.default_rng(seed)\n", + " enc = MLP([2, H, H, 4], rng) # sortie : (mu_1, mu_2, logvar_1, logvar_2)\n", + " dec = MLP([2, H, H, 2], rng)\n", + " opt = Adam(enc.params() + dec.params(), 1e-3)\n", + " hist_recon, hist_kl = [], []\n", + " for step in range(STEPS):\n", + " xb = X[rng.integers(0, N_TRAIN, BATCH)]\n", + " h = enc.forward(xb)\n", + " mu, lv = h[:, :2], h[:, 2:]\n", + " eps = rng.normal(0, 1, (BATCH, 2)) # le bruit FIXE de la reparametrisation\n", + " z = mu + np.exp(0.5 * lv) * eps\n", + " xr = dec.forward(z)\n", + " recon = ((xr - xb) ** 2).sum(1).mean() # -log p(x|z) gaussien (a une cte pres)\n", + " kl = 0.5 * (np.exp(lv) + mu ** 2 - 1 - lv).sum(1).mean() # KL(q(z|x) || N(0,I))\n", + " dz, gd = dec.backward(2 * (xr - xb) / BATCH)\n", + " dmu = dz + beta * mu / BATCH\n", + " dlv = dz * np.exp(0.5 * lv) * eps * 0.5 + beta * 0.5 * (np.exp(lv) - 1) / BATCH\n", + " _, ge = enc.backward(np.concatenate([dmu, dlv], 1))\n", + " opt.step(ge + gd)\n", + " if step % 100 == 0:\n", + " hist_recon.append(recon); hist_kl.append(kl)\n", + " return enc, dec, hist_recon, hist_kl\n", + "\n", + "def vae_echantillon(dec, n, rng):\n", + " z = rng.normal(0, 1, (n, 2)) # prior N(0,I)\n", + " return dec.forward(z)\n", + "\n", + "t0 = time.time()\n", + "ENC, DEC, HIST_RECON, HIST_KL = train_vae(SEED)\n", + "T_VAE = time.time() - t0\n", + "print(f\"VAE : {ENC.n_params() + DEC.n_params()} parametres, {STEPS} pas, {T_VAE:.1f} s\")\n", + "print(f\"ELBO final : reconstruction {HIST_RECON[-1]:.3f} + KL {HIST_KL[-1]:.2f}\")\n", + "\n", + "fig, ax = plt.subplots(figsize=(6.2, 4))\n", + "ax.plot(HIST_RECON, label=\"reconstruction (MSE)\")\n", + "ax.plot(HIST_KL, label=\"KL(q(z|x) || N(0,I))\")\n", + "ax.set_xlabel(\"pas de gradient (x100)\"); ax.set_ylabel(\"terme de l'ELBO\")\n", + "ax.set_title(f\"VAE : les deux forces de l'ELBO (beta = 1, seed {SEED})\")\n", + "ax.legend(); ax.grid(alpha=0.3)\n", + "plt.tight_layout(); plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "05eaf1e8", + "metadata": { + "execution": { + "iopub.execute_input": "2026-08-25T18:10:59.704745Z", + "iopub.status.busy": "2026-08-25T18:10:59.704305Z", + "iopub.status.idle": "2026-08-25T18:10:59.921981Z", + "shell.execute_reply": "2026-08-25T18:10:59.921292Z" + }, + "papermill": { + "duration": 0.223469, + "end_time": "2026-08-25T18:10:59.923105", + "exception": false, + "start_time": "2026-08-25T18:10:59.699636", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "VAE : couverture 8/8 | equilibre 0.999 | dispersion 6.10\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Echantillons du VAE : le prior traverse le decodeur en UN passage\n", + "S_VAE = vae_echantillon(DEC, N_ECH, np.random.default_rng(SEED + 100))\n", + "print(f\"VAE : couverture {couverture(S_VAE)}/8 | equilibre {equilibre(S_VAE):.3f} | dispersion {dispersion_relative(S_VAE):.2f}\")\n", + "\n", + "fig, axes = plt.subplots(1, 2, figsize=(9.5, 4.4))\n", + "axes[0].scatter(X[:3000, 0], X[:3000, 1], s=3, alpha=0.3, color=\"tab:blue\")\n", + "axes[0].set_title(\"Donnees reelles\")\n", + "axes[1].scatter(S_VAE[:, 0], S_VAE[:, 1], s=3, alpha=0.3, color=\"tab:green\")\n", + "axes[1].set_title(\"Echantillons VAE (decodeur(z), z ~ N(0,I))\")\n", + "for ax in axes:\n", + " ax.scatter(CENTERS[:, 0], CENTERS[:, 1], s=60, marker=\"x\", color=\"tab:red\")\n", + " ax.set_xlabel(\"x1\"); ax.set_ylabel(\"x2\"); ax.set_aspect(\"equal\")\n", + "plt.tight_layout(); plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "eecf3980", + "metadata": { + "papermill": { + "duration": 0.006292, + "end_time": "2026-08-25T18:10:59.933840", + "exception": false, + "start_time": "2026-08-25T18:10:59.927548", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "**Lecture — le VAE couvre, mais il moyenne.** Couverture 8/8 et équilibre ~1,0 : chaque mode reçoit sa part de masse — la régularisation KL force le latent à rester proche du prior, donc *aucun* mode n'est abandonné. Mais la **dispersion ~6** dit l'échec : les échantillons s'écartent des centres d'environ six fois la largeur des vraies données. Le décodeur, poussé par la reconstruction *et* par la KL, apprend une **moyenne locale** — entre deux modes voisins, il prédit le milieu du chemin ; l'espace latent mélange les régions et la sortie « bave » le long de l'anneau. C'est l'échec canonique du VAE en espace continu : le **moyennage** (l'équivalent 2D du flou des VAE d'images). La reconstruction reste excellente (le terme MSE de la courbe), mais la *génération* depuis le prior est floue — et le curseur $\\beta$ gouverne l'arbitrage (exercice 1)." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "4794171e", + "metadata": { + "execution": { + "iopub.execute_input": "2026-08-25T18:10:59.955801Z", + "iopub.status.busy": "2026-08-25T18:10:59.955475Z", + "iopub.status.idle": "2026-08-25T18:11:32.727561Z", + "shell.execute_reply": "2026-08-25T18:11:32.726324Z" + }, + "papermill": { + "duration": 32.793915, + "end_time": "2026-08-25T18:11:32.732933", + "exception": false, + "start_time": "2026-08-25T18:10:59.939018", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "GAN : 4866 (G) + 4417 (D) parametres, 6000 pas, 32.6 s\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# --- Modele 2 : le GAN --- generateur vs discriminateur, BCE, mises a jour alternees\n", + "Z_DIM = 8 # dimension du bruit d'entree du generateur\n", + "\n", + "def train_gan(seed, n_disc=1, verbose=False):\n", + " rng = np.random.default_rng(seed)\n", + " G = MLP([Z_DIM, H, H, 2], rng)\n", + " D = MLP([2, H, H, 1], rng)\n", + " optG = Adam(G.params(), 2e-4); optD = Adam(D.params(), 2e-4)\n", + " hist_D, hist_G = [], []\n", + " step = 0\n", + " while step < STEPS:\n", + " for _ in range(n_disc): # n_disc pas du discriminateur par pas du generateur\n", + " if step >= STEPS: break\n", + " xb = X[rng.integers(0, N_TRAIN, BATCH)]\n", + " zf = rng.normal(0, 1, (BATCH, Z_DIM))\n", + " xf = G.forward(zf)\n", + " dr = 1 / (1 + np.exp(-D.forward(xb))) # sigmoid\n", + " df = 1 / (1 + np.exp(-D.forward(xf)))\n", + " perte_D = -(np.log(dr + 1e-12).mean() + np.log(1 - df + 1e-12).mean())\n", + " _, gD1 = D.backward((dr - 1) / BATCH) # d/dlogit de -log sigmoid\n", + " dxf, gD2 = D.backward(df / BATCH) # d/dlogit de -log(1 - sigmoid)\n", + " optD.step(gD1 + gD2)\n", + " step += 1\n", + " zf = rng.normal(0, 1, (BATCH, Z_DIM))\n", + " xf = G.forward(zf)\n", + " df = 1 / (1 + np.exp(-D.forward(xf)))\n", + " perte_G = -np.log(df + 1e-12).mean()\n", + " dxf, _ = D.backward((df - 1) / BATCH) # maximiser log D(G(z))\n", + " _, gG = G.backward(dxf)\n", + " optG.step(gG)\n", + " if step % 100 == 0:\n", + " hist_D.append(perte_D); hist_G.append(perte_G)\n", + " return G, hist_D, hist_G\n", + "\n", + "def gan_echantillon(G, n, rng):\n", + " return G.forward(rng.normal(0, 1, (n, Z_DIM)))\n", + "\n", + "t0 = time.time()\n", + "G_NET, HIST_D, HIST_G = train_gan(SEED)\n", + "T_GAN = time.time() - t0\n", + "print(f\"GAN : {G_NET.n_params()} (G) + {MLP([2, H, H, 1], np.random.default_rng(0)).n_params()} (D) parametres, {STEPS} pas, {T_GAN:.1f} s\")\n", + "\n", + "fig, ax = plt.subplots(figsize=(6.2, 4))\n", + "ax.plot(HIST_D, label=\"perte du discriminateur\")\n", + "ax.plot(HIST_G, label=\"perte du generateur\")\n", + "ax.set_xlabel(\"pas de gradient (x100)\"); ax.set_ylabel(\"BCE\")\n", + "ax.set_title(f\"GAN : le duel (seed {SEED})\")\n", + "ax.legend(); ax.grid(alpha=0.3)\n", + "plt.tight_layout(); plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "191fe196", + "metadata": { + "execution": { + "iopub.execute_input": "2026-08-25T18:11:32.750288Z", + "iopub.status.busy": "2026-08-25T18:11:32.749586Z", + "iopub.status.idle": "2026-08-25T18:11:33.008913Z", + "shell.execute_reply": "2026-08-25T18:11:33.008055Z" + }, + "papermill": { + "duration": 0.269471, + "end_time": "2026-08-25T18:11:33.010864", + "exception": false, + "start_time": "2026-08-25T18:11:32.741393", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "GAN : couverture 2/8 | equilibre 0.114 | dispersion 15.66\n", + "Occupation par mode : 6.2% 93.7% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Echantillons du GAN : occupation par mode + diagnostic de collapse\n", + "S_GAN = gan_echantillon(G_NET, N_ECH, np.random.default_rng(SEED + 100))\n", + "parts_gan = occupation(S_GAN)\n", + "print(f\"GAN : couverture {couverture(S_GAN)}/8 | equilibre {equilibre(S_GAN):.3f} | dispersion {dispersion_relative(S_GAN):.2f}\")\n", + "print(\"Occupation par mode :\", \" \".join(f\"{p*100:4.1f}%\" for p in parts_gan))\n", + "\n", + "fig, axes = plt.subplots(1, 2, figsize=(9.5, 4.4))\n", + "axes[0].scatter(S_GAN[:, 0], S_GAN[:, 1], s=3, alpha=0.3, color=\"tab:orange\")\n", + "axes[0].scatter(CENTERS[:, 0], CENTERS[:, 1], s=60, marker=\"x\", color=\"tab:red\")\n", + "axes[0].set_title(\"Echantillons GAN\")\n", + "axes[0].set_xlabel(\"x1\"); axes[0].set_ylabel(\"x2\"); axes[0].set_aspect(\"equal\")\n", + "axes[1].bar(np.arange(N_MODES) + 1, parts_gan * 100, color=\"tab:orange\")\n", + "axes[1].axhline(100 / N_MODES, ls=\"--\", color=\"gray\", label=\"part ideale (12.5 %)\")\n", + "axes[1].set_title(\"Occupation par mode (diagnostic de collapse)\")\n", + "axes[1].set_xlabel(\"mode\"); axes[1].set_ylabel(\"% des echantillons\"); axes[1].legend()\n", + "plt.tight_layout(); plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "c4c95674", + "metadata": { + "papermill": { + "duration": 0.005666, + "end_time": "2026-08-25T18:11:33.024864", + "exception": false, + "start_time": "2026-08-25T18:11:33.019198", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "**Lecture — le GAN est net mais s'effondre.** Couverture 2/8 (ici) : le générateur concentre sa production sur un ou deux modes et **abandonne les autres** — le *mode collapse*, échec canonique du GAN. L'histogramme d'occupation le montre sans ambiguïté : deux barres démesurées, six quasi nulles. La dispersion élevée (~15) ajoute le placement : même les modes servis sont décalés des centres. Le pourquoi est dans l'objectif : le générateur maximise $\\log D(G(z))$ — rien ne récompense la *diversité* ; si deux points du bruit produisent le même mode qui trompe $D$, le duel est satisfait. Les courbes de perte racontent l'autre symptôme : le duel oscille sans converger (là où VAE et diffusion descendent proprement leur coût). C'est un **équilibre de jeu**, pas un minimum — et l'exercice 2 sonde le levier classique ($n_{disc}$, le nombre de pas du discriminateur)." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "cb4e4a78", + "metadata": { + "execution": { + "iopub.execute_input": "2026-08-25T18:11:33.039028Z", + "iopub.status.busy": "2026-08-25T18:11:33.038408Z", + "iopub.status.idle": "2026-08-25T18:11:42.410100Z", + "shell.execute_reply": "2026-08-25T18:11:42.409050Z" + }, + "papermill": { + "duration": 9.38032, + "end_time": "2026-08-25T18:11:42.411154", + "exception": false, + "start_time": "2026-08-25T18:11:33.030834", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "abar_T = 0.0096 (le point de depart de l'echantillonnage est quasi N(0,I))\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Diffusion : 4930 parametres, 6000 pas, 9.2 s, MSE finale 0.503\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# --- Modele 3 : la diffusion (DDPM) --- processus direct, schedule, prediction du bruit\n", + "# Processus direct (ferme, aucun parametre a apprendre) : q(x_t | x_0) = N(sqrt(abar_t) x_0, (1-abar_t) I)\n", + "# Le reseau n'apprend PAS la distribution : il apprend eps_hat(x_t, t) ~ le bruit ajoute.\n", + "# Schedule lineaire choisi pour que abar_T ~ 0.01 : le dernier pas est (presque) du bruit pur N(0,I).\n", + "print(f\"abar_T = {ALPHAS_CUM[-1]:.4f} (le point de depart de l'echantillonnage est quasi N(0,I))\")\n", + "\n", + "def train_ddpm(seed, lr=3e-3):\n", + " rng = np.random.default_rng(seed)\n", + " net = MLP([2 + 7, H, H, 2], rng) # entree : (x_t, t_feat) -> eps_hat\n", + " opt = Adam(net.params(), lr)\n", + " hist = []\n", + " for step in range(STEPS):\n", + " xb = X[rng.integers(0, N_TRAIN, BATCH)]\n", + " tt = rng.integers(0, T, BATCH) # t uniforme\n", + " eps = rng.normal(0, 1, (BATCH, 2))\n", + " xt = np.sqrt(ALPHAS_CUM[tt])[:, None] * xb + np.sqrt(1 - ALPHAS_CUM[tt])[:, None] * eps\n", + " inp = np.concatenate([xt, t_feat(tt / T)], 1)\n", + " eh = net.forward(inp)\n", + " perte = ((eh - eps) ** 2).sum(1).mean() # MSE sur le bruit\n", + " _, g = net.backward(2 * (eh - eps) / BATCH)\n", + " opt.step(g)\n", + " if step % 100 == 0:\n", + " hist.append(perte)\n", + " return net, hist\n", + "\n", + "t0 = time.time()\n", + "NET_DDPM, HIST_DDPM = train_ddpm(SEED)\n", + "T_DDPM = time.time() - t0\n", + "print(f\"Diffusion : {NET_DDPM.n_params()} parametres, {STEPS} pas, {T_DDPM:.1f} s, MSE finale {HIST_DDPM[-1]:.3f}\")\n", + "\n", + "fig, ax = plt.subplots(figsize=(6.2, 4))\n", + "ax.plot(HIST_DDPM, color=\"tab:purple\")\n", + "ax.set_xlabel(\"pas de gradient (x100)\"); ax.set_ylabel(\"MSE(eps_hat, eps)\")\n", + "ax.set_title(f\"Diffusion : la perte de denoising descend proprement (seed {SEED})\")\n", + "ax.grid(alpha=0.3)\n", + "plt.tight_layout(); plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "3e16632d", + "metadata": { + "execution": { + "iopub.execute_input": "2026-08-25T18:11:42.423424Z", + "iopub.status.busy": "2026-08-25T18:11:42.422996Z", + "iopub.status.idle": "2026-08-25T18:11:43.723830Z", + "shell.execute_reply": "2026-08-25T18:11:43.723031Z" + }, + "papermill": { + "duration": 1.308932, + "end_time": "2026-08-25T18:11:43.724843", + "exception": false, + "start_time": "2026-08-25T18:11:42.415911", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Diffusion : couverture 8/8 | equilibre 0.993 | dispersion 1.50\n", + "Coût d'echantillonnage : 1.15 s pour 4096 points (100 passes du reseau) — contre 1 passe pour le VAE ou le GAN\n" + ] + }, + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Echantillonnage inverse : du bruit pur aux modes, PAS A PAS — et la trajectoire visible\n", + "def ddpm_echantillon(net, n, rng, pas=None, trajectoire=False):\n", + " \"\"\"Echantillonnage ancestral : pas = nombre de pas inverses (<= T).\"\"\"\n", + " if pas is None:\n", + " idx = np.arange(T - 1, -1, -1)\n", + " else:\n", + " idx = np.linspace(T - 1, 0, pas).astype(int)\n", + " x = rng.normal(0, 1, (n, 2)) # depart : N(0,I)\n", + " snaps = []\n", + " # etats photographies AVANT le pas marque -> snaps[0] = bruit pur, ..., snaps[4] = echantillons finaux\n", + " marquage = {0, len(idx) // 4, len(idx) // 2, 3 * len(idx) // 4} if trajectoire else set()\n", + " for i, t in enumerate(idx):\n", + " if trajectoire and i in marquage:\n", + " snaps.append(x.copy())\n", + " tt = np.full(n, t)\n", + " inp = np.concatenate([x, t_feat(tt / T)], 1)\n", + " eh = net.forward(inp)\n", + " a, b = ALPHAS_CUM[t], BETAS[t]\n", + " x = (x - b / np.sqrt(1 - a) * eh) / np.sqrt(1 - b) # moyenne de q(x_{t-1} | x_t, x_0_hat)\n", + " if t > 0:\n", + " x = x + np.sqrt(b) * rng.normal(0, 1, (n, 2)) # variance sigma_t^2 = beta_t\n", + " if trajectoire:\n", + " snaps.append(x.copy())\n", + " return x, snaps\n", + " return x\n", + "\n", + "t0 = time.time()\n", + "S_DDPM, SNAPS = ddpm_echantillon(NET_DDPM, N_ECH, np.random.default_rng(SEED + 100), trajectoire=True)\n", + "T_SAMP_DDPM = time.time() - t0\n", + "print(f\"Diffusion : couverture {couverture(S_DDPM)}/8 | equilibre {equilibre(S_DDPM):.3f} | dispersion {dispersion_relative(S_DDPM):.2f}\")\n", + "print(f\"Coût d'echantillonnage : {T_SAMP_DDPM:.2f} s pour {N_ECH} points ({T} passes du reseau) — contre 1 passe pour le VAE ou le GAN\")\n", + "\n", + "fig, axes = plt.subplots(1, 5, figsize=(15.5, 3.4))\n", + "titres = [\"t = 99 (bruit pur)\", \"t = 74\", \"t = 49\", \"t = 24\", \"t = 0 (echantillons)\"]\n", + "for k, (ax, snap, titre) in enumerate(zip(axes, SNAPS, titres)):\n", + " ax.scatter(snap[:800, 0], snap[:800, 1], s=3, alpha=0.4, color=\"tab:purple\")\n", + " ax.scatter(CENTERS[:, 0], CENTERS[:, 1], s=50, marker=\"x\", color=\"tab:red\")\n", + " ax.set_title(titre, fontsize=10); ax.set_aspect(\"equal\"); ax.set_xticks([]); ax.set_yticks([])\n", + "plt.suptitle(\"La trajectoire de denoising : chaque point affine sa position a chaque pas inverse\", y=1.04)\n", + "plt.tight_layout(); plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "ded87ef8", + "metadata": { + "papermill": { + "duration": 0.005469, + "end_time": "2026-08-25T18:11:43.736443", + "exception": false, + "start_time": "2026-08-25T18:11:43.730974", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "**Lecture — la diffusion raffine, et le paie en passes.** Couverture 8/8, équilibre ~1,0, et surtout **dispersion ~1,5** : quatre fois plus nette que le VAE, dix fois mieux placée que le GAN — à budget *identique* (6 000 pas, même largeur). La trajectoire raconte le mécanisme : les cinq instantanés montrent le nuage de bruit pur se contracter progressivement vers les huit modes — chaque pas inverse applique une petite correction $\\epsilon_\\theta(x_t, t)$, et la structure émerge **itérativement** au lieu d'être produite en un seul passage. Le prix est visible dans le chronomètre : échantillonner coûte $T = 100$ passes du réseau (1 seconde ici), contre une seule pour VAE et GAN — c'est LE compromis structurel de la famille, celui que les notebooks GenAI/Image paient avec leurs dizaines de pas de sampler à chaque image." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "32175158", + "metadata": { + "execution": { + "iopub.execute_input": "2026-08-25T18:11:43.749392Z", + "iopub.status.busy": "2026-08-25T18:11:43.749043Z", + "iopub.status.idle": "2026-08-25T18:15:36.368008Z", + "shell.execute_reply": "2026-08-25T18:15:36.367367Z" + }, + "papermill": { + "duration": 232.631266, + "end_time": "2026-08-25T18:15:36.373400", + "exception": false, + "start_time": "2026-08-25T18:11:43.742134", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "seed 0 : VAE 8/8 eq 1.00 disp 5.9 ( 13s) | GAN 2/8 eq 0.26 disp 16.6 ( 35s) | DDPM 8/8 eq 1.00 disp 1.4 ( 8s)\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "seed 1 : VAE 8/8 eq 1.00 disp 6.0 ( 15s) | GAN 1/8 eq 0.00 disp 14.8 ( 32s) | DDPM 8/8 eq 0.99 disp 1.5 ( 12s)\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "seed 7 : VAE 8/8 eq 1.00 disp 6.2 ( 17s) | GAN 1/8 eq 0.01 disp 15.0 ( 31s) | DDPM 8/8 eq 0.98 disp 1.6 ( 9s)\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "seed 42 : VAE 8/8 eq 1.00 disp 6.1 ( 16s) | GAN 2/8 eq 0.12 disp 15.7 ( 33s) | DDPM 8/8 eq 0.99 disp 1.5 ( 10s)\n", + "\n", + "famille couverture (moy +/- et) equilibre dispersion cout moy (s)\n", + "GMM 8.0 +/- 0.0 0.999 +/- 0.000 0.99 +/- 0.01 2.2\n", + "VAE 8.0 +/- 0.0 0.999 +/- 0.000 6.04 +/- 0.12 15.4\n", + "GAN 1.5 +/- 0.5 0.099 +/- 0.105 15.54 +/- 0.70 32.8\n", + "DDPM 8.0 +/- 0.0 0.992 +/- 0.005 1.51 +/- 0.06 10.0\n" + ] + } + ], + "source": [ + "# Le protocole multi-graines : 4 graines x 3 familles, memes metriques — aucun echantillon choisi\n", + "def evalue(echantillons):\n", + " return couverture(echantillons), equilibre(echantillons), dispersion_relative(echantillons)\n", + "\n", + "resultats = {}\n", + "couts = {}\n", + "for seed in SEEDS:\n", + " rng_eval = np.random.default_rng(seed + 100)\n", + " t0 = time.time(); enc_s, dec_s, _, _ = train_vae(seed); t_v = time.time() - t0\n", + " t0 = time.time(); g_s, _, _ = train_gan(seed); t_g = time.time() - t0\n", + " t0 = time.time(); net_s, _ = train_ddpm(seed); t_d = time.time() - t0\n", + " t0 = time.time(); s_d = ddpm_echantillon(net_s, N_ECH, np.random.default_rng(seed + 100)); t_s = time.time() - t0\n", + " resultats[seed] = {\n", + " \"VAE\": evalue(vae_echantillon(dec_s, N_ECH, rng_eval)),\n", + " \"GAN\": evalue(gan_echantillon(g_s, N_ECH, rng_eval)),\n", + " \"DDPM\": evalue(s_d),\n", + " \"GMM\": evalue(gmm_echantillon(GMM_MU, GMM_VAR, GMM_PI, N_ECH, rng_eval)),\n", + " }\n", + " couts[seed] = {\"VAE\": t_v, \"GAN\": t_g, \"DDPM\": t_d + t_s}\n", + " cv, eq, dp = resultats[seed][\"VAE\"]; print(f\"seed {seed:>2} : VAE {cv}/8 eq {eq:.2f} disp {dp:4.1f} ({t_v:4.0f}s)\", end=\" | \")\n", + " cv, eq, dp = resultats[seed][\"GAN\"]; print(f\"GAN {cv}/8 eq {eq:.2f} disp {dp:4.1f} ({t_g:4.0f}s)\", end=\" | \")\n", + " cv, eq, dp = resultats[seed][\"DDPM\"]; print(f\"DDPM {cv}/8 eq {eq:.2f} disp {dp:4.1f} ({t_d + t_s:4.0f}s)\")\n", + "\n", + "print()\n", + "print(f\"{'famille':<8} {'couverture (moy +/- et)':<22} {'equilibre':<18} {'dispersion':<20} {'cout moy (s)'}\")\n", + "for fam in [\"GMM\", \"VAE\", \"GAN\", \"DDPM\"]:\n", + " covs = np.array([resultats[s][fam][0] for s in SEEDS], dtype=float)\n", + " eqs = np.array([resultats[s][fam][1] for s in SEEDS])\n", + " dps = np.array([resultats[s][fam][2] for s in SEEDS])\n", + " cout = np.mean([couts[s][fam] for s in SEEDS]) if fam != \"GMM\" else T_FIT_GMM\n", + " print(f\"{fam:<8} {covs.mean():5.1f} +/- {covs.std():3.1f} {eqs.mean():6.3f} +/- {eqs.std():.3f} {dps.mean():6.2f} +/- {dps.std():4.2f} {cout:6.1f}\")" + ] + }, + { + "cell_type": "markdown", + "id": "442f2366", + "metadata": { + "papermill": { + "duration": 0.00619, + "end_time": "2026-08-25T18:15:36.385606", + "exception": false, + "start_time": "2026-08-25T18:15:36.379416", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "**Lecture — le verdict multi-graines.** Quatre graines, mêmes métriques, aucune sélection d'échantillon. La colonne couverture raconte les trois familles en un coup d'œil : VAE et diffusion sont à 8/8 sur **toutes** les graines (écart-type nul), le GAN est à 1,5 ± 0,5 — l'instabilité entre graines est la signature du duel, chaque entraînement choisit ses modes au hasard. La dispersion sépare ensuite les deux couvrantes : ~6 pour le VAE (le moyennage, lui aussi présent sur toutes les graines), ~1,5 pour la diffusion — quatre fois plus nette, à budget identique. Et la baseline domine encore tout le monde : GMM à 0,99 de dispersion en deux secondes, sans un seul gradient — quand le biais inductif colle au problème, les 6 000 pas des réseaux sont superflus. Reste le compromis invisible du tableau : chaque échantillon de diffusion paie 100 passes de réseau (contre une pour VAE et GAN) — le prix du raffinement itératif, que l'exercice 3 mesure à la casse." + ] + }, + { + "cell_type": "markdown", + "id": "58771993", + "metadata": { + "papermill": { + "duration": 0.006345, + "end_time": "2026-08-25T18:15:36.397745", + "exception": false, + "start_time": "2026-08-25T18:15:36.391400", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "## Exercices\n", + "\n", + "Trois sondes pour prolonger l'étude — chaque exercice réutilise les fonctions paramétrées du notebook (`train_vae(seed, beta=…)`, `train_gan(seed, n_disc=…)`, `ddpm_echantillon(net, n, rng, pas=…)`), avec les mêmes métriques (`couverture`, `equilibre`, `dispersion_relative`).\n", + "\n", + "**Exercice 1 — le curseur $\\beta$ du VAE.** Le moyennage vient de l'arbitrage reconstruction/KL. Réentraînez le VAE pour $\\beta \\in \\{0{,}05,\\ 1{,}0,\\ 5{,}0\\}$ et tracez couverture et dispersion en fonction de $\\beta$. *Que doit-on voir ?* Un $\\beta$ faible libère la reconstruction (dispersion qui baisse) mais laisse le prior mal rempli (des modes peuvent disparaître — couverture qui chute) ; un $\\beta$ fort pousse au moyennage. Le VAE ne « gagne » jamais sur les deux tableaux — c'est une borne, pas la vraisemblance.\n", + "\n", + "**Exercice 2 — le levier $n_{disc}$ du GAN.** Le duel s'équilibre différemment selon le rythme des mises à jour du discriminateur. Réentraînez pour $n_{disc} \\in \\{1, 3\\}$ sur les 4 graines et comparez la *stabilité* (écart-type de la couverture entre graines) et la couverture moyenne. *Piste* : un discriminateur plus entraîné donne un gradient plus informatif au générateur — ou écrase le duel si $D$ devient parfait (le gradient s'évanouit).\n", + "\n", + "**Exercice 3 — échantillonner la diffusion en moins de pas.** La trajectoire inverse utilise ici $T = 100$ pas. Rééchantillonnez le réseau déjà entraîné (`NET_DDPM`) avec `pas` $\\in \\{100, 50, 25, 10\\}$ et mesurez couverture/dispersion + temps. *Que doit-on voir ?* La qualité se dégrade doucement puis brutalement — le pas inverse devient trop gros pour la correction apprise. C'est exactement le compromis que les samplers accélérés des notebooks GenAI/Image (moins de pas, meilleurs schedules) négocient." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "ac0bc0f8", + "metadata": { + "execution": { + "iopub.execute_input": "2026-08-25T18:15:36.412403Z", + "iopub.status.busy": "2026-08-25T18:15:36.411931Z", + "iopub.status.idle": "2026-08-25T18:15:36.416051Z", + "shell.execute_reply": "2026-08-25T18:15:36.415379Z" + }, + "papermill": { + "duration": 0.012676, + "end_time": "2026-08-25T18:15:36.417289", + "exception": false, + "start_time": "2026-08-25T18:15:36.404613", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Exercice a completer : l'arbitrage beta — couverture perdue d'un cote, dispersion gagnee de l'autre\n" + ] + } + ], + "source": [ + "# Exercice 1 : beta du VAE vs (couverture, dispersion)\n", + "resultats_beta = None # TODO etudiant : pour beta dans [0.05, 1.0, 5.0], reentrainer train_vae(SEED, beta=beta)\n", + "# puis evaluer vae_echantillon(dec, N_ECH, ...) -> couverture() et dispersion_relative() ; tracer l'arbitrage.\n", + "print(\"Exercice a completer : l'arbitrage beta — couverture perdue d'un cote, dispersion gagnee de l'autre\")" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "b2ba719c", + "metadata": { + "execution": { + "iopub.execute_input": "2026-08-25T18:15:36.431429Z", + "iopub.status.busy": "2026-08-25T18:15:36.431024Z", + "iopub.status.idle": "2026-08-25T18:15:36.435057Z", + "shell.execute_reply": "2026-08-25T18:15:36.434407Z" + }, + "papermill": { + "duration": 0.011668, + "end_time": "2026-08-25T18:15:36.435967", + "exception": false, + "start_time": "2026-08-25T18:15:36.424299", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Exercice a completer : n_disc — le duel s'equilibre-t-il mieux ?\n" + ] + } + ], + "source": [ + "# Exercice 2 : n_disc du GAN vs stabilite multi-graines\n", + "resultats_ndisc = None # TODO etudiant : pour n_disc dans [1, 3], entrainer train_gan(seed, n_disc=...) sur SEEDS\n", + "# puis comparer moyenne et ecart-type de la couverture ; le duel s'equilibre-t-il mieux ?\n", + "print(\"Exercice a completer : n_disc — le duel s'equilibre-t-il mieux ?\")" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "9b49cf2a", + "metadata": { + "execution": { + "iopub.execute_input": "2026-08-25T18:15:36.449366Z", + "iopub.status.busy": "2026-08-25T18:15:36.449011Z", + "iopub.status.idle": "2026-08-25T18:15:36.452796Z", + "shell.execute_reply": "2026-08-25T18:15:36.452048Z" + }, + "papermill": { + "duration": 0.01148, + "end_time": "2026-08-25T18:15:36.453757", + "exception": false, + "start_time": "2026-08-25T18:15:36.442277", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Exercice a completer : combien de pas peut-on retirer avant que la trajectoire casse ?\n" + ] + } + ], + "source": [ + "# Exercice 3 : nombre de pas d'echantillonnage de la diffusion\n", + "resultats_pas = None # TODO etudiant : pour pas dans [100, 50, 25, 10], ddpm_echantillon(NET_DDPM, N_ECH, rng, pas=pas)\n", + "# mesurer couverture/dispersion + temps ; ou la qualite cesse-t-elle d'etre tenable ?\n", + "print(\"Exercice a completer : combien de pas peut-on retirer avant que la trajectoire casse ?\")" + ] + }, + { + "cell_type": "markdown", + "id": "1f06dd9b", + "metadata": { + "papermill": { + "duration": 0.005332, + "end_time": "2026-08-25T18:15:36.464956", + "exception": false, + "start_time": "2026-08-25T18:15:36.459624", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "## Conclusion et transition\n", + "\n", + "Trois familles, un même budget, une même cible — **trois échecs différents**, et c'était la leçon. Le **VAE** couvre tout et moyenne partout (dispersion ~6) : son ELBO est une *borne*, et la KL qui garantit la couverture fabrique le flou. Le **GAN** place mal et s'effondre (1 à 2 modes sur 8, instability entre graines) : son objectif est un duel, et rien n'y récompense la couverture. La **diffusion** s'en sort le mieux des trois (8/8, dispersion ~1,5, stable sur toutes les graines) parce qu'elle remplace la génération en un passage par un **raffinement itératif** — et c'est aussi son coût : chaque échantillon paie 100 passes de réseau. La baseline **GMM**, elle, domine tout le monde tant que le biais inductif colle au problème — le rappel salutaire avant de conclure « le deep learning a gagné ».\n", + "\n", + "Le pont vers le reste du dépôt se lit maintenant mécaniquement. Le **VAE temporel de [QC-Py-24](../../QuantConnect/Python/QC-Py-24-Autoencoders-Anomaly.ipynb)** est exactement le modèle de ce notebook (encodeur → espace latent → décodeur, ELBO) transféré aux séries de rendements : sa détection d'anomalie par erreur de reconstruction est le terme « reconstruction » de notre courbe — et son espace latent en basse dimension y joue le même rôle de régularisateur que notre KL. Les **notebooks GenAI/Image** consomment le troisième mécanisme : leur « sampler à N pas », leur « noise schedule », leur CFG sont les hyperparamètres de *notre* DDPM — passés de $x \\in \\mathbb{R}^2$ à l'espace latent d'un UNet de centaines de millions de paramètres. Le mécanisme (prédire le bruit, débruiter pas à pas) est identique ; l'échelle et le conditionnement changent tout — ce notebook n'a prétendu démontrer ni FLUX ni Stable Diffusion, seulement le moteur qu'ils partagent.\n", + "\n", + "## References\n", + "\n", + "- **Kingma, D. P. & Welling, M. (2013).** *Auto-Encoding Variational Bayes.* arXiv:1312.6114. — L'article fondateur du VAE : la borne ELBO et l'astuce de reparamétrisation qui la rend différentiable.\n", + "- **Goodfellow, I. et al. (2014).** *Generative Adversarial Nets.* NeurIPS. — Le duel minimax générateur/discriminateur ; la section 4 discute déjà le mode collapse que nous avons mesuré.\n", + "- **Ho, J., Jain, A. & Abbeel, P. (2020).** *Denoising Diffusion Probabilistic Models.* NeurIPS. — Le DDPM moderne : prédiction du bruit, schedule linéaire, échantillonnage ancestral — exactement notre implémentation, à l'échelle des images près.\n", + "- **Song, Y. & Ermon, S. (2019).** *Generative Modeling by Estimating Gradients of the Data Distribution.* NeurIPS. — La vue duale (scores) qui a nourri la famille diffusion." + ] + } + ], + "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": "3.13.3" + }, + "papermill": { + "default_parameters": {}, + "duration": 298.025399, + "end_time": "2026-08-25T18:15:36.807589", + "environment_variables": {}, + "exception": null, + "input_path": "3.6-Modeles-Generatifs.ipynb", + "output_path": "3.6-Modeles-Generatifs.ipynb", + "parameters": {}, + "start_time": "2026-08-25T18:10:38.782190", + "version": "2.6.0" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/MyIA.AI.Notebooks/ML/DataScienceWithAgents/03-DeepLearning/README.md b/MyIA.AI.Notebooks/ML/DataScienceWithAgents/03-DeepLearning/README.md index 30610c4824..1804cdcce6 100644 --- a/MyIA.AI.Notebooks/ML/DataScienceWithAgents/03-DeepLearning/README.md +++ b/MyIA.AI.Notebooks/ML/DataScienceWithAgents/03-DeepLearning/README.md @@ -24,14 +24,15 @@ séries (RL, PostTraining, ML-Training-Pipeline). L'entraînement final du 2.9 e | Notebook | Sujet | Concept-phare | Validation | |----------|-------|---------------|------------| -| [3.0-Theorie-Information](3.0-Theorie-Information.ipynb) | Entropie, cross-entropy et KL construites from scratch sur un texte français, puis MSE vs cross-entropy sur un classifieur (le piège du gradient saturé), température (softmax) et pont vers DPO/GRPO | **La loss qui fait apprendre** : pourquoi la cross-entropy (et pas la MSE) est la bonne loss d'un classifieur, et la KL comme mesure de décalage entre deux distributions de modèle | entropie du français ~4,4 bits (redondance ~10-15 %, borne ≤ log₂K vérifiée) ; identité H(p,q)=H(p)+D_KL vérifiée, KL>0 sur tout le balayage (Gibbs) ; init saturée et fausse : la CE s'échappe (0,88) quand la MSE reste bloquée (0,39), gradient CE/MSE ~51× ; log 0 maîtrisé par lissage ε ; KL minimale en T=1 | | [3.1-Retropropagation](3.1-Retropropagation.ipynb) | Le MLP et la rétropropagation à la main (NumPy pur, sans autograd) | **Le gradient vérifié** : différence finie vs analytique, parité exacte avec PyTorch | écart 1,3e-11 (seuil 1e-6) ; loss initiale, premier pas et trajectoire 3000 iters identiques à 1,1e-16 près ; init nulle = gradient nul (0,500 figé) | | [3.2-Optimisateurs](3.2-Optimisateurs.ipynb) | Momentum, Adagrad, RMSProp, Adam et schedules, écrits en NumPy pur puis validés pas à pas contre `torch.optim` | **La parité exacte** : les 5 mises à jour sont celles de torch | GD/momentum/Adam à 1,11e-16, Adagrad bit-à-bit (0,00e+00), RMSProp à 2,22e-16 (float64, 1 pas) ; Beale : 5 trajectoires superposées (facteur 200 entre lr utilisables) ; MLP du 3.1 : 5 optimisateurs × 3 graines (RMSProp 0,059 < Adam 0,061 < … < GD 0,070) ; schedules : coût en full-batch déterministe, gain sous le plancher de bruit en mini-batch | | [3.5-Phenomenes-de-Generalisation](3.5-Phenomenes-de-Generalisation.ipynb) | Grokking et double descente reproduits en NumPy pur (MLP à embeddings + Adam à la main), confrontés à la borne PAC du 2.8 | **Le phénomène sans la boîte noire** : mémorisation → transition abrupte, et le W de la double descente | garde gradient ≤ 1e-6 (embeddings inclus) ; grok mesuré : train saturé ~500 pas, test 100 % des dizaines de milliers de pas plus tard (wd = 1) ; contre-témoin wd = 0 ; double descente : pic au seuil M ≈ n (×5 le creux), asymptote moderne sous le creux classique, 20 graines | +| [3.6-Modeles-Generatifs](3.6-Modeles-Generatifs.ipynb) | VAE, GAN et diffusion (DDPM) écrits en NumPy pur, même cible (huit modes sur un cercle), même budget (6 000 pas, batch 256, largeur 64), face à une baseline GMM ajustée par EM | **Trois objectifs, trois échecs** : le VAE couvre mais moyenne, le GAN s'effondre, la diffusion raffine au prix de 100 passes par échantillon | garde gradient 1,4e-08 (ELBO + reparamétrisation) et 3,2e-10 (eps-net) ; multi-4-graines : GMM 8/8 disp 0,99 (2,2 s) ; VAE 8/8 disp 6,0 ; GAN 1,5 ± 0,5 modes ; DDPM 8/8 disp 1,51 ; trajectoire de denoising en 5 instantanés (t = 99 → 0) | ## Feuille de route -La suite est planifiée (issues ouvertes) : régularisation — dropout, weight decay, early stopping (#12409) ; +La suite est planifiée (issues ouvertes) : théorie de l'information appliquée — entropie, KL, +cross-entropy (#12420) ; régularisation — dropout, weight decay, early stopping (#12409) ; attention et transformer jusqu'à un mini-GPT entraîné in notebook (#12410). Le fil directeur ne change pas : chaque mécanisme écrit à la main, vérifié contre torch, puis consommé via l'API officielle. From cfd97c8eb1ffc8ff08dc7d8f7fd20f83619991dd Mon Sep 17 00:00:00 2001 From: jsboige Date: Fri, 28 Aug 2026 03:22:42 +0200 Subject: [PATCH 2/2] fix(dl,#12959): navlinks 3.6 -- corriger profondeur relative vers QC-Py-24 (x3) Cause : liens ../../QuantConnect/... depuis 03-DeepLearning/ resolvent vers ML/QuantConnect (inexistant) -- il faut ../../../ pour remonter a MyIA.AI.Notebooks/. Verdict check-navlinks CI : 3 NEW broken navlinks vs baseline (cell0 x2, cell23). Fix markdown only (3 occurrences), outputs intacts (C.2 markdown). Verification locale : check_notebook_navlinks.py = 0 broken. Co-Authored-By: Claude-Code --- .../3.6-Modeles-Generatifs.ipynb | 29 ++----------------- 1 file changed, 3 insertions(+), 26 deletions(-) diff --git a/MyIA.AI.Notebooks/ML/DataScienceWithAgents/03-DeepLearning/3.6-Modeles-Generatifs.ipynb b/MyIA.AI.Notebooks/ML/DataScienceWithAgents/03-DeepLearning/3.6-Modeles-Generatifs.ipynb index 538d834590..fd76515784 100644 --- a/MyIA.AI.Notebooks/ML/DataScienceWithAgents/03-DeepLearning/3.6-Modeles-Generatifs.ipynb +++ b/MyIA.AI.Notebooks/ML/DataScienceWithAgents/03-DeepLearning/3.6-Modeles-Generatifs.ipynb @@ -13,17 +13,7 @@ }, "tags": [] }, - "source": [ - "# 3.6 — Modèles génératifs : trois objectifs, trois échecs — VAE, GAN et diffusion sur une distribution multimodale bornée\n", - "\n", - "**Navigation** : [<< 3.5-Grokking et double descente](3.5-Phenomenes-de-Generalisation.ipynb) · [Feuille de route de la série](README.md) · VAE applicatif : [QC-Py-24 (autoencodeurs d'anomalies)](../../QuantConnect/Python/QC-Py-24-Autoencoders-Anomaly.ipynb)\n", - "\n", - "Nos notebooks consomment des modèles génératifs partout — les autoencodeurs d'anomalies de [QC-Py-24](../../QuantConnect/Python/QC-Py-24-Autoencoders-Anomaly.ipynb), les diffuseurs des notebooks GenAI/Image — mais toujours comme des boîtes noires. Ce notebook ouvre trois de ces boîtes **côte à côte** : un **VAE**, un **GAN** et un petit **modèle de diffusion (DDPM)**, chacun écrit en NumPy pur sur la machinerie du [3.1](3.1-Retropropagation.ipynb) (backward à la main) et l'Adam du [3.2](3.2-Optimisateurs.ipynb). Pas une ligne de PyTorch.\n", - "\n", - "La thèse : **les trois familles n'optimisent pas la même chose**, donc elles n'échouent pas de la même façon. Le VAE maximise une borne de la log-vraisemblance (reconstruction + régularisation vers le prior) — il couvre, mais il **moyenne**. Le GAN optimise un duel minimax — ses échantillons sont nets, mais rien dans son objectif ne force la **couverture des modes**. La diffusion apprend à débruiter pas à pas — elle raffine itérativement, au prix d'un **échantillonnage séquentiel**. Pour rendre ces échecs *mesurables*, les trois modèles s'entraînent sur la même distribution bornée — huit modes sur un cercle — avec le même budget (pas, batch, largeur), contre une baseline **GMM ajustée par EM** qui fixe la barre : quand le biais inductif colle au problème, l'apprentissage profond est superflu.\n", - "\n", - "Ce notebook ne prétend pas reproduire FLUX ou Stable Diffusion — il isole les **mécanismes** que ces moteurs SOTA consomment (discussion finale)." - ] + "source": "# 3.6 — Modèles génératifs : trois objectifs, trois échecs — VAE, GAN et diffusion sur une distribution multimodale bornée\n\n**Navigation** : [<< 3.5-Grokking et double descente](3.5-Phenomenes-de-Generalisation.ipynb) · [Feuille de route de la série](README.md) · VAE applicatif : [QC-Py-24 (autoencodeurs d'anomalies)](../../../QuantConnect/Python/QC-Py-24-Autoencoders-Anomaly.ipynb)\n\nNos notebooks consomment des modèles génératifs partout — les autoencodeurs d'anomalies de [QC-Py-24](../../../QuantConnect/Python/QC-Py-24-Autoencoders-Anomaly.ipynb), les diffuseurs des notebooks GenAI/Image — mais toujours comme des boîtes noires. Ce notebook ouvre trois de ces boîtes **côte à côte** : un **VAE**, un **GAN** et un petit **modèle de diffusion (DDPM)**, chacun écrit en NumPy pur sur la machinerie du [3.1](3.1-Retropropagation.ipynb) (backward à la main) et l'Adam du [3.2](3.2-Optimisateurs.ipynb). Pas une ligne de PyTorch.\n\nLa thèse : **les trois familles n'optimisent pas la même chose**, donc elles n'échouent pas de la même façon. Le VAE maximise une borne de la log-vraisemblance (reconstruction + régularisation vers le prior) — il couvre, mais il **moyenne**. Le GAN optimise un duel minimax — ses échantillons sont nets, mais rien dans son objectif ne force la **couverture des modes**. La diffusion apprend à débruiter pas à pas — elle raffine itérativement, au prix d'un **échantillonnage séquentiel**. Pour rendre ces échecs *mesurables*, les trois modèles s'entraînent sur la même distribution bornée — huit modes sur un cercle — avec le même budget (pas, batch, largeur), contre une baseline **GMM ajustée par EM** qui fixe la barre : quand le biais inductif colle au problème, l'apprentissage profond est superflu.\n\nCe notebook ne prétend pas reproduire FLUX ou Stable Diffusion — il isole les **mécanismes** que ces moteurs SOTA consomment (discussion finale)." }, { "cell_type": "markdown", @@ -1191,20 +1181,7 @@ }, "tags": [] }, - "source": [ - "## Conclusion et transition\n", - "\n", - "Trois familles, un même budget, une même cible — **trois échecs différents**, et c'était la leçon. Le **VAE** couvre tout et moyenne partout (dispersion ~6) : son ELBO est une *borne*, et la KL qui garantit la couverture fabrique le flou. Le **GAN** place mal et s'effondre (1 à 2 modes sur 8, instability entre graines) : son objectif est un duel, et rien n'y récompense la couverture. La **diffusion** s'en sort le mieux des trois (8/8, dispersion ~1,5, stable sur toutes les graines) parce qu'elle remplace la génération en un passage par un **raffinement itératif** — et c'est aussi son coût : chaque échantillon paie 100 passes de réseau. La baseline **GMM**, elle, domine tout le monde tant que le biais inductif colle au problème — le rappel salutaire avant de conclure « le deep learning a gagné ».\n", - "\n", - "Le pont vers le reste du dépôt se lit maintenant mécaniquement. Le **VAE temporel de [QC-Py-24](../../QuantConnect/Python/QC-Py-24-Autoencoders-Anomaly.ipynb)** est exactement le modèle de ce notebook (encodeur → espace latent → décodeur, ELBO) transféré aux séries de rendements : sa détection d'anomalie par erreur de reconstruction est le terme « reconstruction » de notre courbe — et son espace latent en basse dimension y joue le même rôle de régularisateur que notre KL. Les **notebooks GenAI/Image** consomment le troisième mécanisme : leur « sampler à N pas », leur « noise schedule », leur CFG sont les hyperparamètres de *notre* DDPM — passés de $x \\in \\mathbb{R}^2$ à l'espace latent d'un UNet de centaines de millions de paramètres. Le mécanisme (prédire le bruit, débruiter pas à pas) est identique ; l'échelle et le conditionnement changent tout — ce notebook n'a prétendu démontrer ni FLUX ni Stable Diffusion, seulement le moteur qu'ils partagent.\n", - "\n", - "## References\n", - "\n", - "- **Kingma, D. P. & Welling, M. (2013).** *Auto-Encoding Variational Bayes.* arXiv:1312.6114. — L'article fondateur du VAE : la borne ELBO et l'astuce de reparamétrisation qui la rend différentiable.\n", - "- **Goodfellow, I. et al. (2014).** *Generative Adversarial Nets.* NeurIPS. — Le duel minimax générateur/discriminateur ; la section 4 discute déjà le mode collapse que nous avons mesuré.\n", - "- **Ho, J., Jain, A. & Abbeel, P. (2020).** *Denoising Diffusion Probabilistic Models.* NeurIPS. — Le DDPM moderne : prédiction du bruit, schedule linéaire, échantillonnage ancestral — exactement notre implémentation, à l'échelle des images près.\n", - "- **Song, Y. & Ermon, S. (2019).** *Generative Modeling by Estimating Gradients of the Data Distribution.* NeurIPS. — La vue duale (scores) qui a nourri la famille diffusion." - ] + "source": "## Conclusion et transition\n\nTrois familles, un même budget, une même cible — **trois échecs différents**, et c'était la leçon. Le **VAE** couvre tout et moyenne partout (dispersion ~6) : son ELBO est une *borne*, et la KL qui garantit la couverture fabrique le flou. Le **GAN** place mal et s'effondre (1 à 2 modes sur 8, instability entre graines) : son objectif est un duel, et rien n'y récompense la couverture. La **diffusion** s'en sort le mieux des trois (8/8, dispersion ~1,5, stable sur toutes les graines) parce qu'elle remplace la génération en un passage par un **raffinement itératif** — et c'est aussi son coût : chaque échantillon paie 100 passes de réseau. La baseline **GMM**, elle, domine tout le monde tant que le biais inductif colle au problème — le rappel salutaire avant de conclure « le deep learning a gagné ».\n\nLe pont vers le reste du dépôt se lit maintenant mécaniquement. Le **VAE temporel de [QC-Py-24](../../../QuantConnect/Python/QC-Py-24-Autoencoders-Anomaly.ipynb)** est exactement le modèle de ce notebook (encodeur → espace latent → décodeur, ELBO) transféré aux séries de rendements : sa détection d'anomalie par erreur de reconstruction est le terme « reconstruction » de notre courbe — et son espace latent en basse dimension y joue le même rôle de régularisateur que notre KL. Les **notebooks GenAI/Image** consomment le troisième mécanisme : leur « sampler à N pas », leur « noise schedule », leur CFG sont les hyperparamètres de *notre* DDPM — passés de $x \\in \\mathbb{R}^2$ à l'espace latent d'un UNet de centaines de millions de paramètres. Le mécanisme (prédire le bruit, débruiter pas à pas) est identique ; l'échelle et le conditionnement changent tout — ce notebook n'a prétendu démontrer ni FLUX ni Stable Diffusion, seulement le moteur qu'ils partagent.\n\n## References\n\n- **Kingma, D. P. & Welling, M. (2013).** *Auto-Encoding Variational Bayes.* arXiv:1312.6114. — L'article fondateur du VAE : la borne ELBO et l'astuce de reparamétrisation qui la rend différentiable.\n- **Goodfellow, I. et al. (2014).** *Generative Adversarial Nets.* NeurIPS. — Le duel minimax générateur/discriminateur ; la section 4 discute déjà le mode collapse que nous avons mesuré.\n- **Ho, J., Jain, A. & Abbeel, P. (2020).** *Denoising Diffusion Probabilistic Models.* NeurIPS. — Le DDPM moderne : prédiction du bruit, schedule linéaire, échantillonnage ancestral — exactement notre implémentation, à l'échelle des images près.\n- **Song, Y. & Ermon, S. (2019).** *Generative Modeling by Estimating Gradients of the Data Distribution.* NeurIPS. — La vue duale (scores) qui a nourri la famille diffusion." } ], "metadata": { @@ -1240,4 +1217,4 @@ }, "nbformat": 4, "nbformat_minor": 5 -} +} \ No newline at end of file