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    "# 07 · Construir un transformer: atención y redes de propagación hacia adelante\n",
    "\n",
    "En 2017, *\"Attention Is All You Need\"* (Vaswani et al.) eliminó por completo la recurrencia. Un transformer es una pila de bloques idénticos, cada uno formado por solo dos subcapas:\n",
    "\n",
    "1. **Autoatención multicabeza:** cada token reúne información de todos los demás tokens (comunicación).\n",
    "2. **Red de propagación hacia adelante (MLP):** cada token procesa lo que reunió, por separado (cálculo).\n",
    "\n",
    "Ambas van envueltas en **conexiones residuales** y **normalización de capa**. Este notebook construye cada pieza desde cero, primero en NumPy para ver cada número y después en PyTorch para entrenar un modelo real y observar cómo la atención propaga la información a través de las capas.\n",
    "\n",
    "**Contenido**\n",
    "1. ¿Por qué transformers?\n",
    "2. Embeddings de tokens y codificaciones posicionales\n",
    "3. Atención de producto escalar escalado, paso a paso\n",
    "4. Máscaras: causal y de relleno\n",
    "5. Atención multicabeza\n",
    "6. La red de propagación hacia adelante (MLP)\n",
    "7. El flujo residual y LayerNorm: un bloque transformer completo\n",
    "8. Un transformer codificador-decodificador completo en PyTorch, entrenado para ordenar números\n",
    "9. Cómo se propaga la atención: mapas por capa, rollout de atención y saliencia por gradiente\n",
    "10. Dónde viven los parámetros y qué cambiaron los transformers modernos\n",
    "11. Ejercicios"
   ]
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   "id": "c15a960c",
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    "execution": {
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     "shell.execute_reply": "2026-10-16T09:08:59.225092Z"
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   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "import math, time\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as F\n",
    "\n",
    "np.random.seed(0); torch.manual_seed(0)\n",
    "np.set_printoptions(precision=3, suppress=True)\n",
    "\n",
    "def softmax(x, axis=-1):\n",
    "    x = x - x.max(axis=axis, keepdims=True)\n",
    "    e = np.exp(x)\n",
    "    return e / e.sum(axis=axis, keepdims=True)\n",
    "\n",
    "def show_matrix(ax, M, xlabels, ylabels, title, cmap=\"Blues\", vmin=None, vmax=None):\n",
    "    ax.imshow(M, cmap=cmap, vmin=vmin, vmax=vmax)\n",
    "    ax.set_xticks(range(len(xlabels))); ax.set_xticklabels(xlabels, rotation=45, ha=\"right\")\n",
    "    ax.set_yticks(range(len(ylabels))); ax.set_yticklabels(ylabels)\n",
    "    ax.set_title(title, fontsize=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bc6042e7",
   "metadata": {},
   "source": [
    "## 1. ¿Por qué transformers?\n",
    "\n",
    "| | RNN (notebook 05) | Transformer |\n",
    "|---|---|---|\n",
    "| Cómo ve el token *i* al token *j* | a través de $|i-j|$ pasos recurrentes | **directamente**, en un solo paso de atención |\n",
    "| Paralelismo en el entrenamiento | secuencial en el tiempo | todas las posiciones a la vez (ideal para GPU) |\n",
    "| Dependencias de largo alcance | los gradientes se desvanecen tras muchos pasos | longitud de camino 1 |\n",
    "| Coste por capa | $O(n\\,d^2)$ | $O(n^2 d)$ (atención) + $O(n\\,d^2)$ (MLP) |\n",
    "\n",
    "El coste cuadrático en la longitud de la secuencia $n$ es el precio; el paralelismo y las conexiones directas son la recompensa. Ese intercambio hizo posible entrenar con billones de tokens, que es lo que hace GPT (notebook 08).\n",
    "\n",
    "## 2. Embeddings de tokens y codificaciones posicionales\n",
    "\n",
    "El texto se divide en **tokens**, cada uno se asigna a un identificador entero, y cada identificador a un vector aprendido de tamaño $d_{model}$ mediante una **tabla de embeddings** (una matriz con una fila por token).\n",
    "\n",
    "La atención por sí sola no tiene noción de orden: trata la entrada como un *conjunto*. Lo demostramos más abajo. Por eso **sumamos** una señal posicional a cada embedding. El artículo original usaba sinusoides fijas con frecuencias espaciadas geométricamente:\n",
    "\n",
    "$$ PE_{(pos,\\,2i)} = \\sin\\!\\left(\\frac{pos}{10000^{2i/d}}\\right), \\qquad PE_{(pos,\\,2i+1)} = \\cos\\!\\left(\\frac{pos}{10000^{2i/d}}\\right) $$\n",
    "\n",
    "Las dimensiones bajas oscilan rápido (posición fina) y las altas despacio (posición gruesa), como las manecillas de un reloj. Una propiedad útil: el producto escalar $PE_{pos}\\cdot PE_{pos+k}$ solo depende del desfase $k$, lo que hace fácil detectar posiciones relativas."
   ]
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   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 1800x400 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def sinusoidal_pe(n_pos, d):\n",
    "    pos = np.arange(n_pos)[:, None]\n",
    "    i = np.arange(0, d, 2)[None, :]\n",
    "    angle = pos / (10000 ** (i / d))\n",
    "    pe = np.zeros((n_pos, d))\n",
    "    pe[:, 0::2], pe[:, 1::2] = np.sin(angle), np.cos(angle)\n",
    "    return pe\n",
    "\n",
    "pe = sinusoidal_pe(64, 64)\n",
    "fig, axes = plt.subplots(1, 3, figsize=(18, 4))\n",
    "axes[0].imshow(pe.T, cmap=\"RdBu\", aspect=\"auto\"); axes[0].set_xlabel(\"posición\"); axes[0].set_ylabel(\"dimensión\")\n",
    "axes[0].set_title(\"Codificación posicional sinusoidal\")\n",
    "for dim in [0, 10, 30]:\n",
    "    axes[1].plot(pe[:, dim], label=f\"dim. {dim}\")\n",
    "axes[1].legend(); axes[1].set_xlabel(\"posición\"); axes[1].set_title(\"Cada dimensión es una onda de distinta frecuencia\")\n",
    "axes[2].imshow(pe @ pe.T, cmap=\"viridis\"); axes[2].set_title(\"PE · PE: la similitud solo depende de la distancia\")\n",
    "axes[2].set_xlabel(\"posición\"); axes[2].set_ylabel(\"posición\")\n",
    "plt.tight_layout(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4fada5a3",
   "metadata": {},
   "source": [
    "## 3. Atención de producto escalar escalado, paso a paso\n",
    "\n",
    "El vector $x_i$ de cada token se proyecta de tres formas con matrices aprendidas:\n",
    "\n",
    "* **Consulta** (query) $q_i = x_i W_Q$: \"¿qué estoy buscando?\"\n",
    "* **Clave** (key) $k_j = x_j W_K$: \"¿qué contengo?\" (un anuncio)\n",
    "* **Valor** (value) $v_j = x_j W_V$: \"¿qué entregaré si me eliges?\"\n",
    "\n",
    "El token $i$ compara su consulta con todas las claves, convierte las puntuaciones en pesos con softmax y toma la media ponderada de los valores:\n",
    "\n",
    "$$ \\text{Atención}(Q,K,V) = \\text{softmax}\\!\\left(\\frac{QK^\\top}{\\sqrt{d_k}}\\right)V $$\n",
    "\n",
    "Es una **búsqueda en diccionario suave y derivable**: en lugar de devolver el valor de la única clave que coincide, devuelve una mezcla ponderada según lo bien que coincide cada clave.\n",
    "\n",
    "Ejecutémosla sobre una frase de 6 tokens con pesos aleatorios para que cada paso intermedio sea visible."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "2cebed3f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-16T09:09:00.089283Z",
     "iopub.status.busy": "2026-10-16T09:09:00.088975Z",
     "iopub.status.idle": "2026-10-16T09:09:00.575793Z",
     "shell.execute_reply": "2026-10-16T09:09:00.574559Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X: (6, 8)  Q,K,V: (6, 4)  puntuaciones: (6, 6)  salida: (6, 4)\n",
      "sumas por fila de A: [1. 1. 1. 1. 1. 1.]\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1700x450 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tokens = [\"the\", \"cat\", \"sat\", \"on\", \"the\", \"mat\"]\n",
    "vocab = sorted(set(tokens))\n",
    "d_model, d_k = 8, 4\n",
    "E = np.random.randn(len(vocab), d_model)                     # tabla de embeddings\n",
    "X = np.array([E[vocab.index(t)] for t in tokens]) + sinusoidal_pe(len(tokens), d_model)\n",
    "W_Q, W_K, W_V = (np.random.randn(d_model, d_k) / np.sqrt(d_model) for _ in range(3))\n",
    "\n",
    "Q, K, V = X @ W_Q, X @ W_K, X @ W_V\n",
    "scores = Q @ K.T / np.sqrt(d_k)                              # (6, 6): cada consulta frente a cada clave\n",
    "A = softmax(scores, axis=-1)                                  # cada fila suma 1\n",
    "out = A @ V                                                   # (6, 4): nueva representación por token\n",
    "\n",
    "print(\"X:\", X.shape, \" Q,K,V:\", Q.shape, \" puntuaciones:\", scores.shape, \" salida:\", out.shape)\n",
    "print(\"sumas por fila de A:\", A.sum(axis=1))\n",
    "fig, axes = plt.subplots(1, 3, figsize=(17, 4.5))\n",
    "show_matrix(axes[0], scores, tokens, tokens, \"1) puntuaciones  QKᵀ/√d_k\", cmap=\"RdBu_r\")\n",
    "show_matrix(axes[1], A, tokens, tokens, \"2) pesos  softmax(puntuaciones)  (fila = consulta)\", vmin=0, vmax=1)\n",
    "show_matrix(axes[2], out, [f\"v{i}\" for i in range(d_k)], tokens, \"3) salida  A·V\", cmap=\"RdBu_r\")\n",
    "plt.tight_layout(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aff5a05a",
   "metadata": {},
   "source": [
    "### ¿Por qué dividir entre $\\sqrt{d_k}$?\n",
    "\n",
    "Si las entradas de $q$ y $k$ tienen varianza unitaria, $q\\cdot k$ es una suma de $d_k$ términos y tiene varianza $d_k$. Con un $d_k$ grande las puntuaciones se vuelven enormes, softmax colapsa a un vector one-hot y su gradiente se vuelve casi cero (el problema de saturación del notebook 01). Dividir entre $\\sqrt{d_k}$ devuelve la varianza a 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b4a427db",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-16T09:09:00.579018Z",
     "iopub.status.busy": "2026-10-16T09:09:00.578724Z",
     "iopub.status.idle": "2026-10-16T09:09:03.030905Z",
     "shell.execute_reply": "2026-10-16T09:09:03.028928Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dims = [4, 16, 64, 256, 1024]\n",
    "ent_raw, ent_scaled = [], []\n",
    "for d in dims:\n",
    "    q, k = np.random.randn(1000, d), np.random.randn(1000, 32, d)\n",
    "    s = np.einsum(\"nd,nkd->nk\", q, k)\n",
    "    for store, ss in [(ent_raw, s), (ent_scaled, s / np.sqrt(d))]:\n",
    "        p = softmax(ss)\n",
    "        store.append(-(p * np.log(p + 1e-12)).sum(1).mean())\n",
    "plt.figure(figsize=(7, 4))\n",
    "plt.semilogx(dims, ent_raw, \"o-\", label=\"sin escalar  q·k\"); plt.semilogx(dims, ent_scaled, \"o-\", label=\"escalada  q·k/√d\")\n",
    "plt.axhline(np.log(32), color=\"gray\", ls=\"--\", label=\"uniforme sobre 32 claves\")\n",
    "plt.xlabel(\"d_k\"); plt.ylabel(\"entropía de los pesos de atención\"); plt.legend(); plt.grid(alpha=0.3)\n",
    "plt.title(\"Sin escalar, la atención colapsa a one-hot al crecer d\"); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "39a7ef00",
   "metadata": {},
   "source": [
    "### La atención sin posiciones no ve el orden\n",
    "\n",
    "Si se barajan los tokens de entrada, las salidas se barajan exactamente igual, pero el vector de salida de cada token no cambia. La autoatención es **equivariante a permutaciones**; de ahí la necesidad de las codificaciones posicionales."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "02d81724",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-16T09:09:03.034709Z",
     "iopub.status.busy": "2026-10-16T09:09:03.034417Z",
     "iopub.status.idle": "2026-10-16T09:09:03.043403Z",
     "shell.execute_reply": "2026-10-16T09:09:03.041525Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "permutación: [1 0 4 5 3 2]\n",
      "atención(X barajada) == atención(X) barajada: True\n"
     ]
    }
   ],
   "source": [
    "def attention(Xin):\n",
    "    q, k, v = Xin @ W_Q, Xin @ W_K, Xin @ W_V\n",
    "    return softmax(q @ k.T / np.sqrt(d_k)) @ v\n",
    "\n",
    "X_nopos = np.array([E[vocab.index(t)] for t in tokens])\n",
    "perm = np.random.permutation(len(tokens))\n",
    "print(\"permutación:\", perm)\n",
    "print(\"atención(X barajada) == atención(X) barajada:\", np.allclose(attention(X_nopos[perm]), attention(X_nopos)[perm]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c64e784f",
   "metadata": {},
   "source": [
    "## 4. Máscaras\n",
    "\n",
    "* **Máscara de relleno:** las secuencias de un lote se rellenan hasta la misma longitud; no se debe atender a las posiciones de relleno.\n",
    "* **Máscara causal (de anticipación):** en un decodificador o en GPT, el token $i$ solo puede atender a los tokens $\\le i$; si no, podría \"hacer trampa\" mirando la palabra que se supone que debe predecir.\n",
    "\n",
    "Ambas se aplican poniendo las puntuaciones prohibidas a $-\\infty$ **antes** del softmax, de modo que sus pesos queden exactamente en 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "da301c2a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-16T09:09:03.047134Z",
     "iopub.status.busy": "2026-10-16T09:09:03.046843Z",
     "iopub.status.idle": "2026-10-16T09:09:03.536744Z",
     "shell.execute_reply": "2026-10-16T09:09:03.535880Z"
    }
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 1700x450 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = len(tokens)\n",
    "causal = np.tril(np.ones((n, n), dtype=bool))\n",
    "A_causal = softmax(np.where(causal, scores, -np.inf))\n",
    "\n",
    "pad = np.array([True, True, True, True, False, False])      # supongamos que los dos últimos tokens son relleno\n",
    "A_pad = softmax(np.where(pad[None, :], scores, -np.inf))\n",
    "\n",
    "fig, axes = plt.subplots(1, 3, figsize=(17, 4.5))\n",
    "show_matrix(axes[0], causal.astype(float), tokens, tokens, \"máscara causal (1 = permitido)\", cmap=\"Greys\")\n",
    "show_matrix(axes[1], A_causal, tokens, tokens, \"atención causal: triangular inferior\", vmin=0, vmax=1)\n",
    "show_matrix(axes[2], A_pad, tokens, tokens, \"máscara de relleno: se ignoran las 2 últimas columnas\", vmin=0, vmax=1)\n",
    "plt.tight_layout(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cbc34049",
   "metadata": {},
   "source": [
    "## 5. Atención multicabeza\n",
    "\n",
    "Un solo patrón de atención por capa es limitante: un token puede necesitar mirar a la vez su palabra anterior (sintaxis) **y** un sustantivo relacionado que está lejos (significado). La **atención multicabeza** ejecuta $h$ operaciones de atención en paralelo, cada una en un subespacio más pequeño de tamaño $d_k = d_{model}/h$, y después las concatena y las mezcla con una proyección de salida $W_O$:\n",
    "\n",
    "$$ \\text{MHA}(X) = \\text{Concat}(\\text{cabeza}_1,\\dots,\\text{cabeza}_h)\\,W_O, \\qquad \\text{cabeza}_i = \\text{Atención}(XW_Q^{(i)}, XW_K^{(i)}, XW_V^{(i)}) $$\n",
    "\n",
    "En la práctica todas las cabezas se calculan con **una sola** multiplicación de matrices grande y un cambio de forma, como abajo. El coste es el mismo que el de una sola cabeza de anchura completa."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "1812e45b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-16T09:09:03.541310Z",
     "iopub.status.busy": "2026-10-16T09:09:03.541004Z",
     "iopub.status.idle": "2026-10-16T09:09:04.121961Z",
     "shell.execute_reply": "2026-10-16T09:09:04.120122Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "entrada (6, 8) -> salida (6, 8) | mapas de atención (4, 6, 6) (cabezas, consulta, clave)\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1800x400 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def multi_head_attention(X, Wq, Wk, Wv, Wo, n_heads, mask=None):\n",
    "    n, d = X.shape\n",
    "    dh = d // n_heads\n",
    "    def split(M):                                   # (n, d) -> (heads, n, dh)\n",
    "        return M.reshape(n, n_heads, dh).transpose(1, 0, 2)\n",
    "    Q, K, V = split(X @ Wq), split(X @ Wk), split(X @ Wv)\n",
    "    scores = Q @ K.transpose(0, 2, 1) / np.sqrt(dh)  # (heads, n, n)\n",
    "    if mask is not None:\n",
    "        scores = np.where(mask, scores, -np.inf)\n",
    "    A = softmax(scores)\n",
    "    heads = A @ V                                   # (heads, n, dh)\n",
    "    concat = heads.transpose(1, 0, 2).reshape(n, d) # de vuelta a (n, d)\n",
    "    return concat @ Wo, A\n",
    "\n",
    "d_model, n_heads = 8, 4\n",
    "Wq, Wk, Wv, Wo = (np.random.randn(d_model, d_model) / np.sqrt(d_model) for _ in range(4))\n",
    "Y, A_heads = multi_head_attention(X, Wq, Wk, Wv, Wo, n_heads)\n",
    "print(\"entrada\", X.shape, \"-> salida\", Y.shape, \"| mapas de atención\", A_heads.shape, \"(cabezas, consulta, clave)\")\n",
    "fig, axes = plt.subplots(1, n_heads, figsize=(18, 4))\n",
    "for h, ax in enumerate(axes):\n",
    "    show_matrix(ax, A_heads[h], tokens, tokens, f\"cabeza {h}\", vmin=0, vmax=1)\n",
    "plt.tight_layout(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7b14a64",
   "metadata": {},
   "source": [
    "## 6. La red de propagación hacia adelante (MLP)\n",
    "\n",
    "Después de que la atención *mezcla información entre tokens*, cada token pasa **por separado** por el mismo MLP de dos capas (notebook 02), normalmente 4 veces más ancho en el medio:\n",
    "\n",
    "$$ \\text{FFN}(x) = W_2\\,\\text{GELU}(W_1 x + b_1) + b_2, \\qquad W_1 \\in \\mathbb{R}^{4d\\times d},\\; W_2 \\in \\mathbb{R}^{d\\times 4d} $$\n",
    "\n",
    "Formas de pensarlo:\n",
    "* **Atención = comunicación, MLP = cálculo.** La atención mueve la información de un lado a otro; el MLP la transforma.\n",
    "* **Memoria clave-valor** (Geva et al., 2021): los pesos de entrada de cada neurona oculta (una fila de $W_1$) actúan como una *clave* que detecta un patrón; sus pesos de salida (una columna de $W_2$) son el *valor* que se escribe en el token cuando el patrón se activa. Se cree que buena parte del conocimiento factual de un modelo de lenguaje vive aquí.\n",
    "* Contiene aproximadamente **dos tercios** de los parámetros de un transformer (sección 10).\n",
    "\n",
    "\"Por posición\" significa que se aplican los mismos pesos a cada token por separado: la celda de abajo comprueba que procesar los tokens uno a uno da el mismo resultado que procesar la secuencia completa."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "41828f56",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-16T09:09:04.125308Z",
     "iopub.status.busy": "2026-10-16T09:09:04.125033Z",
     "iopub.status.idle": "2026-10-16T09:09:04.135291Z",
     "shell.execute_reply": "2026-10-16T09:09:04.133645Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "FFN aplicada a la secuencia == FFN aplicada a cada token por separado: True\n",
      "parámetros de la FFN: 552  frente a  parámetros de la atención: 256\n"
     ]
    }
   ],
   "source": [
    "def gelu(x):\n",
    "    return 0.5 * x * (1 + np.tanh(np.sqrt(2 / np.pi) * (x + 0.044715 * x ** 3)))   # la aproximación de GPT-2\n",
    "\n",
    "d_ff = 4 * d_model\n",
    "W1, b1 = np.random.randn(d_model, d_ff) / np.sqrt(d_model), np.zeros(d_ff)\n",
    "W2, b2 = np.random.randn(d_ff, d_model) / np.sqrt(d_ff), np.zeros(d_model)\n",
    "ffn = lambda x: gelu(x @ W1 + b1) @ W2 + b2\n",
    "\n",
    "whole = ffn(X)\n",
    "one_by_one = np.stack([ffn(X[i:i + 1])[0] for i in range(len(X))])\n",
    "print(\"FFN aplicada a la secuencia == FFN aplicada a cada token por separado:\", np.allclose(whole, one_by_one))\n",
    "print(f\"parámetros de la FFN: {W1.size + b1.size + W2.size + b2.size}  frente a  parámetros de la atención: {4 * d_model * d_model}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2927ced9",
   "metadata": {},
   "source": [
    "## 7. El flujo residual y LayerNorm: un bloque transformer completo\n",
    "\n",
    "Dos ingredientes más hacen entrenables las pilas profundas:\n",
    "\n",
    "* **Conexiones residuales** $x \\leftarrow x + \\text{Subcapa}(x)$. Cada subcapa solo *suma* una actualización a un vector en curso llamado **flujo residual** (residual stream). Los gradientes atraviesan directamente las sumas (la misma idea que el estado de celda de la LSTM y que ResNet), así que se pueden entrenar más de 100 capas.\n",
    "* La **normalización de capa** reescala cada vector de token a media cero y varianza unitaria, y después aplica una escala aprendida $\\gamma$ y un desplazamiento $\\beta$. Mantiene las activaciones en un rango sano.\n",
    "\n",
    "Los modelos modernos usan la disposición **pre-LN** (normalizar *antes* de cada subcapa), que es más estable que la post-LN original:\n",
    "\n",
    "```\n",
    "x ─┬─► LayerNorm ─► Atención multicabeza ─┐\n",
    "   └──────────────────────────────────────(+)─┬─► LayerNorm ─► FFN (MLP) ─┐\n",
    "                                              └───────────────────────────(+)─► siguiente bloque\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "61a0a07a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-16T09:09:04.139490Z",
     "iopub.status.busy": "2026-10-16T09:09:04.139184Z",
     "iopub.status.idle": "2026-10-16T09:09:04.166130Z",
     "shell.execute_reply": "2026-10-16T09:09:04.164334Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "bloque 0: forma (6, 8), tamaño de la actualización ‖Δ‖ = 5.29\n",
      "bloque 1: forma (6, 8), tamaño de la actualización ‖Δ‖ = 5.11\n",
      "bloque 2: forma (6, 8), tamaño de la actualización ‖Δ‖ = 5.46\n",
      "LayerNorm coincide con PyTorch: True\n"
     ]
    }
   ],
   "source": [
    "def layer_norm(x, gamma, beta, eps=1e-5):\n",
    "    mu = x.mean(axis=-1, keepdims=True)\n",
    "    var = x.var(axis=-1, keepdims=True)\n",
    "    return gamma * (x - mu) / np.sqrt(var + eps) + beta\n",
    "\n",
    "def transformer_block(x, p, mask=None):\n",
    "    a, attn = multi_head_attention(layer_norm(x, *p[\"ln1\"]), *p[\"attn\"], n_heads=p[\"heads\"], mask=mask)\n",
    "    x = x + a                                         # residual 1: la atención suma al flujo\n",
    "    x = x + p[\"ffn\"](layer_norm(x, *p[\"ln2\"]))        # residual 2: el MLP suma al flujo\n",
    "    return x, attn\n",
    "\n",
    "params = {\"ln1\": (np.ones(d_model), np.zeros(d_model)), \"ln2\": (np.ones(d_model), np.zeros(d_model)),\n",
    "          \"attn\": (Wq, Wk, Wv, Wo), \"heads\": n_heads, \"ffn\": ffn}\n",
    "h = X\n",
    "for layer in range(3):                               # pesos compartidos por brevedad; los modelos reales usan pesos distintos en cada capa\n",
    "    h_new, _ = transformer_block(h, params, mask=causal)\n",
    "    print(f\"bloque {layer}: forma {h_new.shape}, tamaño de la actualización ‖Δ‖ = {np.linalg.norm(h_new - h):.2f}\")\n",
    "    h = h_new\n",
    "\n",
    "# Comparamos nuestra LayerNorm con la de PyTorch\n",
    "x_t = torch.randn(5, 8)\n",
    "ours = layer_norm(x_t.numpy(), np.ones(8), np.zeros(8))\n",
    "print(\"LayerNorm coincide con PyTorch:\", np.allclose(ours, F.layer_norm(x_t, (8,)).numpy(), atol=1e-5))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb672d49",
   "metadata": {},
   "source": [
    "## 8. Un transformer completo en PyTorch, entrenado para ordenar números\n",
    "\n",
    "Ahora lo de verdad: un **transformer codificador-decodificador** exactamente como en el artículo de 2017 (con pre-LN), escrito desde cero con capas `nn.Linear`. Sin `nn.Transformer`. Los módulos de atención guardan sus pesos para que podamos inspeccionarlos después.\n",
    "\n",
    "**Tarea:** la entrada son 10 dígitos aleatorios y la salida, los mismos dígitos ordenados. *\"3 9 1 1 7 0 4 2 8 5\"* → *\"0 1 1 2 3 4 5 7 8 9\"*. Ordenar es un buen juguete porque:\n",
    "* **requiere** atención: cada posición de salida debe encontrar el $k$-ésimo dígito más pequeño, esté donde esté,\n",
    "* hay $10^{10}$ entradas posibles, así que el modelo no puede memorizar; debe aprender el algoritmo,\n",
    "* los patrones de atención aprendidos son interpretables.\n",
    "\n",
    "```\n",
    " dígitos de origen ─► Embedding + PE ─► [Bloque codificador] × N ─► memoria ─────────────┐\n",
    "                                        (autoatención + MLP)                             │\n",
    "                                                                                         ▼\n",
    " <sos> + ordenados[:-1] ─► Embedding + PE ─► [Bloque decodificador] × N ─► Lineal ─► softmax sobre dígitos\n",
    "                                             (autoatención causal + atención cruzada a la memoria + MLP)\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "11b491b1",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-16T09:09:04.171169Z",
     "iopub.status.busy": "2026-10-16T09:09:04.170496Z",
     "iopub.status.idle": "2026-10-16T09:09:04.379923Z",
     "shell.execute_reply": "2026-10-16T09:09:04.378566Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "parámetros: 235,851\n",
      "origen de ejemplo       : [8, 8, 5, 5, 5, 0, 6, 7, 1, 6]\n",
      "entrada del decodificador: [10, 0, 1, 5, 5, 5, 6, 6, 7, 8] (10 = <sos>)\n",
      "objetivo                : [0, 1, 5, 5, 5, 6, 6, 7, 8, 8]\n"
     ]
    }
   ],
   "source": [
    "class MultiHeadAttention(nn.Module):\n",
    "    def __init__(self, d_model, n_heads):\n",
    "        super().__init__()\n",
    "        assert d_model % n_heads == 0\n",
    "        self.h, self.dh = n_heads, d_model // n_heads\n",
    "        self.Wq, self.Wk, self.Wv, self.Wo = (nn.Linear(d_model, d_model) for _ in range(4))\n",
    "        self.last_attn = None\n",
    "    def forward(self, x_q, x_kv, mask=None):\n",
    "        B, Tq, D = x_q.shape\n",
    "        Tk = x_kv.shape[1]\n",
    "        q = self.Wq(x_q).view(B, Tq, self.h, self.dh).transpose(1, 2)    # (B, h, Tq, dh)\n",
    "        k = self.Wk(x_kv).view(B, Tk, self.h, self.dh).transpose(1, 2)\n",
    "        v = self.Wv(x_kv).view(B, Tk, self.h, self.dh).transpose(1, 2)\n",
    "        scores = q @ k.transpose(-2, -1) / math.sqrt(self.dh)            # (B, h, Tq, Tk)\n",
    "        if mask is not None:\n",
    "            scores = scores.masked_fill(~mask, float(\"-inf\"))\n",
    "        attn = scores.softmax(-1)\n",
    "        self.last_attn = attn.detach()\n",
    "        out = (attn @ v).transpose(1, 2).reshape(B, Tq, D)\n",
    "        return self.Wo(out)\n",
    "\n",
    "class FeedForward(nn.Module):\n",
    "    def __init__(self, d_model, mult=4):\n",
    "        super().__init__()\n",
    "        self.net = nn.Sequential(nn.Linear(d_model, mult * d_model), nn.GELU(), nn.Linear(mult * d_model, d_model))\n",
    "    def forward(self, x):\n",
    "        return self.net(x)\n",
    "\n",
    "class EncoderBlock(nn.Module):\n",
    "    def __init__(self, d, h):\n",
    "        super().__init__()\n",
    "        self.ln1, self.attn, self.ln2, self.ffn = nn.LayerNorm(d), MultiHeadAttention(d, h), nn.LayerNorm(d), FeedForward(d)\n",
    "    def forward(self, x):\n",
    "        y = self.ln1(x)\n",
    "        x = x + self.attn(y, y)\n",
    "        return x + self.ffn(self.ln2(x))\n",
    "\n",
    "class DecoderBlock(nn.Module):\n",
    "    def __init__(self, d, h):\n",
    "        super().__init__()\n",
    "        self.ln1, self.self_attn = nn.LayerNorm(d), MultiHeadAttention(d, h)\n",
    "        self.ln2, self.cross_attn = nn.LayerNorm(d), MultiHeadAttention(d, h)\n",
    "        self.ln3, self.ffn = nn.LayerNorm(d), FeedForward(d)\n",
    "    def forward(self, x, memory, causal_mask):\n",
    "        y = self.ln1(x)\n",
    "        x = x + self.self_attn(y, y, causal_mask)                  # solo mira las salidas anteriores\n",
    "        x = x + self.cross_attn(self.ln2(x), memory)               # mira el origen codificado\n",
    "        return x + self.ffn(self.ln3(x))\n",
    "\n",
    "class Transformer(nn.Module):\n",
    "    def __init__(self, vocab, d=64, heads=4, n_enc=2, n_dec=2, max_len=32):\n",
    "        super().__init__()\n",
    "        self.src_emb, self.tgt_emb = nn.Embedding(vocab, d), nn.Embedding(vocab, d)\n",
    "        self.register_buffer(\"pe\", torch.tensor(sinusoidal_pe(max_len, d), dtype=torch.float32))\n",
    "        self.enc = nn.ModuleList(EncoderBlock(d, heads) for _ in range(n_enc))\n",
    "        self.dec = nn.ModuleList(DecoderBlock(d, heads) for _ in range(n_dec))\n",
    "        self.ln_enc, self.ln_dec = nn.LayerNorm(d), nn.LayerNorm(d)\n",
    "        self.out = nn.Linear(d, vocab)\n",
    "        self.d = d\n",
    "    def encode(self, src):\n",
    "        x = self.src_emb(src) * math.sqrt(self.d) + self.pe[:src.shape[1]]\n",
    "        for blk in self.enc:\n",
    "            x = blk(x)\n",
    "        return self.ln_enc(x)\n",
    "    def decode(self, tgt_in, memory):\n",
    "        T = tgt_in.shape[1]\n",
    "        causal = torch.tril(torch.ones(T, T, dtype=torch.bool, device=tgt_in.device))\n",
    "        x = self.tgt_emb(tgt_in) * math.sqrt(self.d) + self.pe[:T]\n",
    "        for blk in self.dec:\n",
    "            x = blk(x, memory, causal)\n",
    "        return self.out(self.ln_dec(x))\n",
    "    def forward(self, src, tgt_in):\n",
    "        return self.decode(tgt_in, self.encode(src))\n",
    "\n",
    "N_DIGITS, SEQ, SOS = 10, 10, 10\n",
    "VOCAB = N_DIGITS + 1\n",
    "\n",
    "def make_batch(B):\n",
    "    src = torch.randint(0, N_DIGITS, (B, SEQ))\n",
    "    tgt = src.sort(dim=1).values\n",
    "    tgt_in = torch.cat([torch.full((B, 1), SOS), tgt[:, :-1]], dim=1)     # desplazamiento a la derecha: teacher forcing\n",
    "    return src, tgt_in, tgt\n",
    "\n",
    "torch.manual_seed(0)\n",
    "model = Transformer(VOCAB)\n",
    "print(f\"parámetros: {sum(p.numel() for p in model.parameters()):,}\")\n",
    "src, tgt_in, tgt = make_batch(2)\n",
    "print(\"origen de ejemplo       :\", src[0].tolist())\n",
    "print(\"entrada del decodificador:\", tgt_in[0].tolist(), \"(10 = <sos>)\")\n",
    "print(\"objetivo                :\", tgt[0].tolist())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "c49d01ef",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-16T09:09:04.384670Z",
     "iopub.status.busy": "2026-10-16T09:09:04.384261Z",
     "iopub.status.idle": "2026-10-16T09:11:58.023570Z",
     "shell.execute_reply": "2026-10-16T09:11:58.021679Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "paso    0  pérdida 2.4649  (0 s)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "paso  300  pérdida 0.0492  (81 s)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "paso  600  pérdida 0.0290  (111 s)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "paso  900  pérdida 0.0024  (141 s)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "paso 1199  pérdida 0.0018  (171 s)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "opt = torch.optim.AdamW(model.parameters(), lr=1e-3, weight_decay=0.01)\n",
    "steps = 1200\n",
    "sched = torch.optim.lr_scheduler.OneCycleLR(opt, max_lr=1e-3, total_steps=steps, pct_start=0.1)   # calentamiento y después decaimiento\n",
    "t0, losses = time.time(), []\n",
    "for step in range(steps):\n",
    "    src, tgt_in, tgt = make_batch(128)\n",
    "    logits = model(src, tgt_in)\n",
    "    loss = F.cross_entropy(logits.reshape(-1, VOCAB), tgt.reshape(-1))\n",
    "    opt.zero_grad(); loss.backward(); nn.utils.clip_grad_norm_(model.parameters(), 1.0); opt.step(); sched.step()\n",
    "    losses.append(loss.item())\n",
    "    if step % 300 == 0 or step == steps - 1:\n",
    "        print(f\"paso {step:4d}  pérdida {loss.item():.4f}  ({time.time() - t0:.0f} s)\")\n",
    "plt.figure(figsize=(7, 3.5)); plt.semilogy(losses); plt.xlabel(\"paso\"); plt.ylabel(\"pérdida\"); plt.grid(alpha=0.3)\n",
    "plt.title(\"Entrenando el transformer para ordenar\"); plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "3b8bd25a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-16T09:11:58.027511Z",
     "iopub.status.busy": "2026-10-16T09:11:58.027114Z",
     "iopub.status.idle": "2026-10-16T09:11:59.868209Z",
     "shell.execute_reply": "2026-10-16T09:11:59.866967Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "secuencias totalmente correctas: 99.8%   exactitud por dígito: 99.97%\n",
      "entrada [2, 9, 2, 0, 0, 2, 6, 7, 9, 4] \n",
      "salida  [0, 0, 2, 2, 2, 4, 6, 7, 9, 9] ✓\n",
      "entrada [1, 1, 6, 1, 2, 9, 4, 1, 3, 0] \n",
      "salida  [0, 1, 1, 1, 1, 2, 3, 4, 6, 9] ✓\n",
      "entrada [0, 6, 5, 7, 9, 2, 1, 6, 0, 6] \n",
      "salida  [0, 0, 1, 2, 5, 6, 6, 6, 7, 9] ✓\n",
      "entrada [6, 5, 3, 9, 4, 6, 1, 8, 0, 5] \n",
      "salida  [0, 1, 3, 4, 5, 5, 6, 6, 8, 9] ✓\n"
     ]
    }
   ],
   "source": [
    "@torch.no_grad()\n",
    "def greedy_sort(model, src):\n",
    "    memory = model.encode(src)\n",
    "    out = torch.full((src.shape[0], 1), SOS)\n",
    "    for _ in range(SEQ):                                   # autorregresivo: un dígito cada vez\n",
    "        nxt = model.decode(out, memory)[:, -1].argmax(-1, keepdim=True)\n",
    "        out = torch.cat([out, nxt], dim=1)\n",
    "    return out[:, 1:]\n",
    "\n",
    "model.eval()\n",
    "torch.manual_seed(123)\n",
    "src, _, tgt = make_batch(2000)\n",
    "pred = greedy_sort(model, src)\n",
    "print(f\"secuencias totalmente correctas: {(pred == tgt).all(1).float().mean():.1%}   exactitud por dígito: {(pred == tgt).float().mean():.2%}\")\n",
    "for i in range(4):\n",
    "    print(\"entrada\", src[i].tolist(), \"\\nsalida \", pred[i].tolist(), \"✓\" if (pred[i] == tgt[i]).all() else \"✗\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6624c9c3",
   "metadata": {},
   "source": [
    "## 9. Cómo se propaga la atención\n",
    "\n",
    "### 9a. Qué mira cada capa y cada cabeza\n",
    "\n",
    "Ejecutamos un ejemplo y dibujamos cada mapa de atención:\n",
    "* **Autoatención del codificador** (entrada ↔ entrada): cómo intercambian información los tokens de origen, por ejemplo para averiguar la posición de cada dígito en el orden.\n",
    "* **Atención cruzada del decodificador** (salida → entrada): para la posición de salida $k$, qué posiciones de origen lee. Al ordenar, deberías ver que cada paso de salida se fija en la posición o posiciones de entrada que contienen el dígito que está a punto de escribir (un \"puntero\" aprendido), a menudo con algo de peso en su vecino en el orden, lo que ayuda al modelo a decidir cuándo pasar al siguiente valor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "0d94b1ac",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-16T09:11:59.872192Z",
     "iopub.status.busy": "2026-10-16T09:11:59.871888Z",
     "iopub.status.idle": "2026-10-16T09:12:03.150653Z",
     "shell.execute_reply": "2026-10-16T09:12:03.149089Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "entrada: [7, 2, 9, 0, 4, 4, 1, 8, 3, 6] \n",
      "salida : [0, 1, 2, 3, 4, 4, 6, 7, 8, 9]\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1600x800 with 8 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1600x800 with 8 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "example = torch.tensor([[7, 2, 9, 0, 4, 4, 1, 8, 3, 6]])\n",
    "with torch.no_grad():\n",
    "    memory = model.encode(example)\n",
    "    res = greedy_sort(model, example)\n",
    "    tgt_in = torch.cat([torch.tensor([[SOS]]), res[:, :-1]], dim=1)\n",
    "    model.decode(tgt_in, memory)                         # rellena last_attn para toda la secuencia decodificada\n",
    "src_lbl = [f\"{d}\" for d in example[0].tolist()]\n",
    "out_lbl = [f\"→{d}\" for d in res[0].tolist()]\n",
    "print(\"entrada:\", example[0].tolist(), \"\\nsalida :\", res[0].tolist())\n",
    "\n",
    "H = model.enc[0].attn.h\n",
    "fig, axes = plt.subplots(2, H, figsize=(4 * H, 8))\n",
    "for l, blk in enumerate(model.enc):\n",
    "    for h in range(H):\n",
    "        show_matrix(axes[l, h], blk.attn.last_attn[0, h], src_lbl, src_lbl, f\"codificador C{l} cabeza {h}\", vmin=0, vmax=1)\n",
    "fig.suptitle(\"Autoatención del codificador (filas = dígito de consulta, columnas = dígito clave)\"); plt.tight_layout(); plt.show()\n",
    "\n",
    "fig, axes = plt.subplots(2, H, figsize=(4 * H, 8))\n",
    "for l, blk in enumerate(model.dec):\n",
    "    for h in range(H):\n",
    "        show_matrix(axes[l, h], blk.cross_attn.last_attn[0, h], src_lbl, out_lbl, f\"decodificador C{l} at. cruzada cabeza {h}\", cmap=\"Greens\", vmin=0, vmax=1)\n",
    "fig.suptitle(\"Atención cruzada del decodificador (filas = paso de salida, columnas = posición de entrada)\"); plt.tight_layout(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c5f43e19",
   "metadata": {},
   "source": [
    "### 9b. Rollout de atención: seguir la información a través de la pila\n",
    "\n",
    "Un solo mapa de atención solo muestra un salto. Después de la capa 1, el vector del token $j$ ya contiene información de otros tokens, así que cuando la capa 2 atiende a $j$ también lee indirectamente *esos* tokens. El **rollout de atención** (Abnar y Zuidema, 2020) lo sigue multiplicando los mapas de cada capa. Por la conexión residual, cada capa transmite también la mitad del token original, lo que modelamos como $\\tfrac12 A + \\tfrac12 I$:\n",
    "\n",
    "$$ R^{(L)} = \\prod_{\\ell=1}^{L} \\left(\\tfrac12 \\bar A^{(\\ell)} + \\tfrac12 I\\right) \\qquad (\\bar A = \\text{media sobre las cabezas}) $$\n",
    "\n",
    "La fila $i$ de $R$ estima cuánto de cada token de entrada ha llegado a la representación final del token $i$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "40836903",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-16T09:12:03.154403Z",
     "iopub.status.busy": "2026-10-16T09:12:03.154125Z",
     "iopub.status.idle": "2026-10-16T09:12:03.930724Z",
     "shell.execute_reply": "2026-10-16T09:12:03.929134Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1600x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def rollout(attn_maps):\n",
    "    R = torch.eye(attn_maps[0].shape[-1])\n",
    "    for A in attn_maps:\n",
    "        A_bar = A.mean(0)                                       # promedio de las cabezas\n",
    "        A_res = 0.5 * A_bar + 0.5 * torch.eye(A_bar.shape[0])   # tiene en cuenta el camino residual\n",
    "        A_res = A_res / A_res.sum(-1, keepdim=True)\n",
    "        R = A_res @ R\n",
    "    return R\n",
    "\n",
    "enc_maps = [blk.attn.last_attn[0] for blk in model.enc]\n",
    "fig, axes = plt.subplots(1, 3, figsize=(16, 4.8))\n",
    "show_matrix(axes[0], enc_maps[0].mean(0), src_lbl, src_lbl, \"capa 0 (media de las cabezas)\", cmap=\"Purples\")\n",
    "show_matrix(axes[1], enc_maps[1].mean(0), src_lbl, src_lbl, \"capa 1 (media de las cabezas)\", cmap=\"Purples\")\n",
    "show_matrix(axes[2], rollout(enc_maps), src_lbl, src_lbl, \"rollout a través de ambas capas\", cmap=\"Purples\")\n",
    "plt.tight_layout(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ce5ae90",
   "metadata": {},
   "source": [
    "### 9c. Flujo del gradiente: ¿qué entradas influyen realmente en una salida?\n",
    "\n",
    "Los pesos de atención nos dicen por dónde *podría* fluir la información. Los gradientes nos dicen a qué es realmente *sensible* la salida. Calculamos $\\left\\|\\partial\\, \\text{logit}_k / \\partial\\, \\text{embedding}_j\\right\\|$ para cada paso de salida $k$ y cada posición de entrada $j$. Es retropropagación (notebook 02) usada para interpretar, y fluye exactamente por los caminos de atención visualizados arriba."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "63c14e7c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-16T09:12:03.935204Z",
     "iopub.status.busy": "2026-10-16T09:12:03.934926Z",
     "iopub.status.idle": "2026-10-16T09:12:04.480288Z",
     "shell.execute_reply": "2026-10-16T09:12:04.478670Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1200x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.zero_grad()\n",
    "emb = (model.src_emb(example) * math.sqrt(model.d)).detach().requires_grad_(True)\n",
    "x = emb + model.pe[:SEQ]\n",
    "for blk in model.enc:\n",
    "    x = blk(x)\n",
    "memory = model.ln_enc(x)\n",
    "logits = model.decode(tgt_in, memory)                        # (1, SEQ, VOCAB)\n",
    "\n",
    "saliency = torch.zeros(SEQ, SEQ)\n",
    "for k in range(SEQ):\n",
    "    chosen = logits[0, k, res[0, k]]                         # el logit del dígito que realmente escribió\n",
    "    g, = torch.autograd.grad(chosen, emb, retain_graph=True)\n",
    "    saliency[k] = g[0].norm(dim=-1)\n",
    "saliency = saliency / saliency.sum(1, keepdim=True)\n",
    "\n",
    "fig, axes = plt.subplots(1, 2, figsize=(12, 4.8))\n",
    "show_matrix(axes[0], saliency, src_lbl, out_lbl, \"saliencia por gradiente (normalizada por fila)\", cmap=\"Oranges\")\n",
    "show_matrix(axes[1], model.dec[-1].cross_attn.last_attn[0].mean(0), src_lbl, out_lbl, \"atención cruzada de la última capa (media de las cabezas)\", cmap=\"Greens\")\n",
    "plt.tight_layout(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a7f13f9",
   "metadata": {},
   "source": [
    "Cómo leer las gráficas:\n",
    "* La atención cruzada y la saliencia coinciden en gran medida: cada paso de salida depende sobre todo de la entrada que contiene el dígito que se está escribiendo y de sus vecinos en el orden (el valor anterior o el siguiente).\n",
    "* No coinciden del todo, y esa es la lección: la atención muestra por dónde se *enruta* la información, el gradiente muestra a qué es *sensible* la decisión. Para saber que el \"4\" va en quinto lugar, el modelo debe tener en cuenta cuántos dígitos menores hay; ese conteo ocurre en la autoatención del codificador y en los MLP, y aparece como una sensibilidad repartida.\n",
    "* Los resultados varían un poco entre ejecuciones de entrenamiento (semillas aleatorias distintas aprenden estrategias distintas pero igual de correctas).\n",
    "\n",
    "## 10. Dónde viven los parámetros\n",
    "\n",
    "Para un bloque con anchura de modelo $d$ y expansión 4 en el MLP:\n",
    "\n",
    "| Componente | Parámetros | Proporción |\n",
    "|---|---|---|\n",
    "| Atención $W_Q, W_K, W_V, W_O$ | $4d^2$ | ≈ 1/3 |\n",
    "| Propagación hacia adelante $W_1, W_2$ | $2 \\cdot d \\cdot 4d = 8d^2$ | ≈ 2/3 |\n",
    "| LayerNorm, sesgos | $O(d)$ | despreciable |\n",
    "\n",
    "Así que un bloque tiene unos $12d^2$ parámetros, la fórmula que usaremos para GPT en el notebook 08."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "12f16887",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-16T09:12:04.483881Z",
     "iopub.status.busy": "2026-10-16T09:12:04.483537Z",
     "iopub.status.idle": "2026-10-16T09:12:04.493401Z",
     "shell.execute_reply": "2026-10-16T09:12:04.491730Z"
    }
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "bloque codificador (d=64): atención 16,640  FFN 33,088  LayerNorm 256\n",
      "proporción de la FFN: 66%,  12·d² = 49,152\n",
      "GPT-2 small  d=  768 layers= 12  ->  12·L·d² ≈   0.08 mil millones de parámetros en los bloques\n",
      "GPT-2 XL     d= 1600 layers= 48  ->  12·L·d² ≈   1.47 mil millones de parámetros en los bloques\n",
      "GPT-3        d=12288 layers= 96  ->  12·L·d² ≈ 173.95 mil millones de parámetros en los bloques\n"
     ]
    }
   ],
   "source": [
    "def count(m): return sum(p.numel() for p in m.parameters())\n",
    "blk = model.enc[0]\n",
    "attn_p, ffn_p, ln_p = count(blk.attn), count(blk.ffn), count(blk.ln1) + count(blk.ln2)\n",
    "print(f\"bloque codificador (d=64): atención {attn_p:,}  FFN {ffn_p:,}  LayerNorm {ln_p:,}\")\n",
    "print(f\"proporción de la FFN: {ffn_p / (attn_p + ffn_p + ln_p):.0%},  12·d² = {12 * 64 ** 2:,}\")\n",
    "for name, d, L in [(\"GPT-2 small\", 768, 12), (\"GPT-2 XL\", 1600, 48), (\"GPT-3\", 12288, 96)]:\n",
    "    print(f\"{name:12s} d={d:5d} layers={L:3d}  ->  12·L·d² ≈ {12 * L * d * d / 1e9:6.2f} mil millones de parámetros en los bloques\")"
   ]
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   "id": "7f54dd18",
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   "source": [
    "### Qué cambiaron (y qué conservaron) los transformers modernos\n",
    "\n",
    "El bloque que construiste sigue siendo el núcleo de todos los modelos grandes. Mejoras habituales desde 2017:\n",
    "\n",
    "| Original (2017) | Moderno (LLaMA, Mistral, modelos de clase GPT-4) | Por qué |\n",
    "|---|---|---|\n",
    "| Post-LN | **Pre-LN**, a menudo **RMSNorm** | entrenamiento más estable de pilas profundas |\n",
    "| Posiciones absolutas sinusoidales | **RoPE** (embeddings rotatorios) | codifica la posición relativa dentro de $q\\cdot k$, extrapola mejor |\n",
    "| MLP con ReLU / GELU | MLP con compuerta **SwiGLU** | mejor calidad por parámetro |\n",
    "| Una K,V por cabeza | **Atención de consultas agrupadas** (K,V compartidas) | caché KV más pequeña, generación más rápida |\n",
    "| MLP denso | **Mezcla de expertos** (cada token se envía a 2 de N MLP) | más parámetros con el mismo cálculo |\n",
    "| Atención ingenua | **FlashAttention** (núcleo fusionado y por bloques) | las mismas matemáticas, mucho menos tráfico de memoria |\n",
    "\n",
    "## Ideas clave\n",
    "\n",
    "* Atención = softmax$(QK^\\top/\\sqrt{d_k})V$: una búsqueda derivable en la que cada token puede leer a cualquier otro token en un solo paso.\n",
    "* La atención multicabeza ejecuta varias búsquedas en paralelo en subespacios; las máscaras controlan quién puede ver a quién.\n",
    "* El **MLP** procesa cada token por separado y contiene la mayoría de los parámetros (el \"conocimiento\").\n",
    "* Las **conexiones residuales + LayerNorm** crean un flujo residual del que cada subcapa lee y en el que escribe, lo que hace entrenables las pilas profundas.\n",
    "* Los patrones de atención se componen a lo largo de las capas (rollout); los gradientes revelan qué entradas importan de verdad.\n",
    "\n",
    "## Ejercicios\n",
    "\n",
    "1. Quita la codificación posicional del codificador y vuelve a entrenar. ¿Sigue funcionando la ordenación? ¿Por qué podría funcionar? (Pista: ¿ordenar depende del orden en el lado de la *entrada*?) Ahora prueba con una tarea de **inversión**.\n",
    "2. Pon `heads=1` y compara la exactitud y los mapas de atención.\n",
    "3. Sustituye `FeedForward` por un MLP SwiGLU: $W_2(\\text{SiLU}(W_1x) \\odot W_3x)$.\n",
    "4. Entrena con secuencias de longitud 10 y prueba con longitud 15 (aumenta `max_len`). ¿Qué se rompe?\n",
    "5. Sustituye el decodificador por un modelo **solo codificador** que prediga, en cada posición, el lugar que ocupa ese dígito en el orden. Visualiza su atención."
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