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    "# Chapter 40: Attention Is All You Need\n",
    "\n",
    "This is it — the synthesis chapter. You have built every component you need:\n",
    "\n",
    "- **scaled dot-product attention** (Chapter 38) and **multi-head self-attention** (Chapter 39);\n",
    "- **encoder-decoder** sequence transduction (Chapter 36);\n",
    "- **cross-entropy loss** (Chapter 26), **Adam** (Chapter 27), **PyTorch nn.Module** (Chapter 29);\n",
    "- **residual connections** as a fix for vanishing gradients (Chapters 17, 34).\n",
    "\n",
    "We assemble all of these into the complete Transformer of Vaswani et al. (2017), and train one on the same string-reversal task you have been chasing since Chapter 36. By the end you will be able to read the original *Attention Is All You Need* paper and recognise every line.\n",
    "\n",
    "**Original paper:** Vaswani, Shazeer, Parmar, Uszkoreit, Jones, Gomez, Kaiser, Polosukhin. *Attention Is All You Need.* NeurIPS 2017 (arXiv:1706.03762)."
   ]
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    "## 40.1 The Big Picture\n",
    "\n",
    "The Transformer is two stacks of identical blocks: an **encoder** that reads the source and a **decoder** that writes the target. Each encoder block does:\n",
    "\n",
    "$$\n",
    "x \\;\\to\\; \\mathrm{LN}(x + \\mathrm{MHA}(x)) \\;\\to\\; \\mathrm{LN}(\\cdot + \\mathrm{FFN}(\\cdot))\n",
    "$$\n",
    "\n",
    "Each decoder block does the same plus a **cross-attention** sub-layer that lets the decoder attend to the encoder output:\n",
    "\n",
    "$$\n",
    "x \\;\\to\\; \\mathrm{LN}(x + \\mathrm{MHA}_\\text{causal}(x)) \\;\\to\\; \\mathrm{LN}(\\cdot + \\mathrm{MHA}_\\text{cross}(\\cdot, \\mathrm{enc}, \\mathrm{enc})) \\;\\to\\; \\mathrm{LN}(\\cdot + \\mathrm{FFN}(\\cdot))\n",
    "$$\n",
    "\n",
    "### Decoding the abbreviations\n",
    "\n",
    "The equations above use compact names for sub-layers. Here is what each one does, where you have already met it, and how it appears in the code in section 40.6.\n",
    "\n",
    "| Symbol | Full name | What it does | Built in chapter | Class / call in code |\n",
    "|---|---|---|---|---|\n",
    "| $\\mathrm{LN}(\\cdot)$ | **Layer Normalisation** | Normalises each token's feature vector to mean 0, variance 1, then scales/shifts. Stabilises training. | §40.3 (this chapter) | `nn.LayerNorm(d_model)` — used as `self.ln1`, `self.ln2`, `self.ln3` |\n",
    "| $\\mathrm{MHA}(x)$ | **Multi-Head Self-Attention** | Each token attends to *every other token* in the same sequence using $h$ parallel attention heads. Inputs Q, K, V all come from $x$. | Ch. 39 | `MultiHeadAttention(d_model, n_heads)` called as `self.mha(x, x, x, mask)` |\n",
    "| $\\mathrm{MHA}_\\text{causal}(x)$ | **Causally-Masked MHA** | Same as MHA, but the attention mask zeros out future positions so token $i$ cannot peek at $i{+}1, i{+}2, \\ldots$ — required during training of the decoder. | §40.5 (mask) + Ch. 39 | `self.mha(x, x, x, causal_mask)` (same class, different mask) |\n",
    "| $\\mathrm{MHA}_\\text{cross}(x, \\mathrm{enc}, \\mathrm{enc})$ | **Cross-Attention** | Same MHA machinery, but Q comes from the *decoder* and K, V come from the *encoder output*. This is exactly Bahdanau attention generalised to multiple heads. | Ch. 37 (Bahdanau) → multi-head form in §40.6 | `self.mha_cross(dec, enc, enc, src_mask)` |\n",
    "| $\\mathrm{FFN}(\\cdot)$ | **Position-wise Feed-Forward Network** | A 2-layer MLP `Linear → ReLU → Linear` applied **independently to every token**. Lets the model do per-token nonlinear processing between attention layers. | §40.6 (`FeedForward` class) | `FeedForward(d_model, d_ff)` |\n",
    "| $x + \\mathrm{Sublayer}(x)$ | **Residual connection** | The input is added to the sub-layer's output before normalising. Keeps gradients flowing through deep stacks (callback to ResNets in CNN chapters). | §40.4 | the `+ x` term inside each block's `forward()` |\n",
    "| $\\mathrm{enc}$ | encoder output tensor | The final $(B, T_\\text{src}, d_\\text{model})$ representation produced by the encoder stack. The decoder reads this through cross-attention. | output of `Transformer.encode()` | `enc_out` |\n",
    "\n",
    "**Reading rule.** Whenever you see a stack of $\\mathrm{LN}(x + \\text{Something}(x))$, read it as: *\"do the sub-layer, add the input back (residual), normalise.\"* Every encoder block has two such stacks (MHA, FFN); every decoder block has three (causal MHA, cross-attention, FFN).\n",
    "\n",
    "### Three new ingredients\n",
    "\n",
    "Three new ingredients appear that you have not built before:\n",
    "\n",
    "1. **Positional encoding** — because self-attention is permutation-equivariant (Exercise 39.1).\n",
    "2. **Layer normalisation** — a per-token cousin of batch norm.\n",
    "3. **Causal masking** — the decoder cannot peek at future tokens during training.\n",
    "\n",
    "Sections 40.2–40.5 develop each ingredient. Section 40.6 puts it all together. Section 40.7 trains the model. Section 40.8 visualises the heads."
   ]
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   "id": "aud40diagintro_8e659588",
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    "### A picture of the whole machine\n",
    "\n",
    "Before diving into ingredient-by-ingredient (positional encoding, layer norm, masking) it helps to see the full architecture once. The diagram below shows what we are building: an encoder stack and a decoder stack, with the encoder output piped into every decoder layer through cross-attention.\n",
    "\n",
    "Keep this picture in mind as we build each block in §40.2–§40.6."
   ]
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   "source": [
    "import sys, os; sys.path.insert(0, os.path.abspath('.'))\n",
    "import math, random\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as F\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from utils import (\n",
    "    PAD, SOS, EOS, ITOS, STOI, VOCAB_SIZE,\n",
    "    encode, decode, make_pair, make_batch, accuracy,\n",
    ")\n",
    "\n",
    "torch.manual_seed(0); random.seed(0)\n",
    "device = torch.device('cpu')"
   ]
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   "execution_count": 2,
   "id": "aud40diag_a9d52c0f",
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",
      "text/plain": [
       "<Figure size 1100x900 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A schematic of the full Transformer (Vaswani et al. 2017): encoder stack on the left,\n",
    "# decoder stack on the right, with cross-attention arrows connecting them.\n",
    "import matplotlib.patches as mpatches\n",
    "from matplotlib.patches import FancyArrowPatch, FancyBboxPatch\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(11, 9))\n",
    "ax.set_xlim(0, 10); ax.set_ylim(0, 11)\n",
    "ax.axis('off')\n",
    "\n",
    "def block(x, y, w, h, label, color, fontsize=9, weight='normal'):\n",
    "    box = FancyBboxPatch((x, y), w, h, boxstyle='round,pad=0.05',\n",
    "                          facecolor=color, edgecolor='#1f2937', linewidth=1.2)\n",
    "    ax.add_patch(box)\n",
    "    ax.text(x + w/2, y + h/2, label, ha='center', va='center',\n",
    "            fontsize=fontsize, weight=weight, color='#111827')\n",
    "\n",
    "def arrow(x1, y1, x2, y2, color='#1f2937', style='-|>', lw=1.4):\n",
    "    ax.add_patch(FancyArrowPatch((x1, y1), (x2, y2),\n",
    "                                  arrowstyle=style, color=color,\n",
    "                                  mutation_scale=14, lw=lw))\n",
    "\n",
    "def residual(x_left, y_bot, y_top, x_right):\n",
    "    # Curved residual line on the left of a sub-layer block\n",
    "    ax.add_patch(FancyArrowPatch((x_left, y_bot), (x_right, y_top),\n",
    "                                  connectionstyle='arc3,rad=-0.4',\n",
    "                                  arrowstyle='-|>', color='#9ca3af',\n",
    "                                  mutation_scale=10, lw=1.0, linestyle='--'))\n",
    "\n",
    "# Colors\n",
    "c_emb = '#fde68a'       # embeddings/positional\n",
    "c_attn = '#bfdbfe'      # attention sublayers\n",
    "c_ffn = '#ddd6fe'       # FFN\n",
    "c_ln  = '#fecaca'       # layer norm\n",
    "c_out = '#bbf7d0'       # output head\n",
    "c_stack = '#f3f4f6'     # encoder/decoder enclosing rect\n",
    "\n",
    "# ---------- ENCODER (left) ----------\n",
    "# Outer \"N x\" box\n",
    "ax.add_patch(FancyBboxPatch((0.4, 1.6), 3.6, 6.6, boxstyle='round,pad=0.05',\n",
    "                             facecolor=c_stack, edgecolor='#6b7280',\n",
    "                             linewidth=1.0, linestyle='--'))\n",
    "ax.text(0.6, 7.95, 'Encoder x N', fontsize=9, color='#374151', style='italic')\n",
    "\n",
    "# Encoder block stack: bottom -> top\n",
    "block(0.6, 0.4, 3.2, 0.55, 'Source tokens (input ids)', '#fef3c7')\n",
    "block(0.6, 1.05, 3.2, 0.5, 'Token embedding + Positional encoding', c_emb)\n",
    "arrow(2.2, 0.95, 2.2, 1.05)\n",
    "\n",
    "block(0.7, 1.7, 3.0, 0.55, 'Multi-Head Self-Attention (MHA)', c_attn)\n",
    "arrow(2.2, 1.55, 2.2, 1.7)\n",
    "block(0.7, 2.35, 3.0, 0.4, 'Add & LayerNorm (LN)', c_ln, fontsize=8)\n",
    "arrow(2.2, 2.25, 2.2, 2.35)\n",
    "\n",
    "block(0.7, 2.95, 3.0, 0.55, 'Feed-Forward (FFN)', c_ffn)\n",
    "arrow(2.2, 2.75, 2.2, 2.95)\n",
    "block(0.7, 3.6, 3.0, 0.4, 'Add & LayerNorm (LN)', c_ln, fontsize=8)\n",
    "arrow(2.2, 3.5, 2.2, 3.6)\n",
    "\n",
    "# \"...stacked N times...\"\n",
    "ax.text(2.2, 4.3, '... repeat N times ...', ha='center', fontsize=9, style='italic', color='#6b7280')\n",
    "\n",
    "# Top encoder block (representative second block)\n",
    "block(0.7, 4.85, 3.0, 0.55, 'Multi-Head Self-Attention (MHA)', c_attn)\n",
    "block(0.7, 5.5, 3.0, 0.4, 'Add & LayerNorm (LN)', c_ln, fontsize=8)\n",
    "arrow(2.2, 5.4, 2.2, 5.5)\n",
    "block(0.7, 6.1, 3.0, 0.55, 'Feed-Forward (FFN)', c_ffn)\n",
    "arrow(2.2, 5.9, 2.2, 6.1)\n",
    "block(0.7, 6.75, 3.0, 0.4, 'Add & LayerNorm (LN)', c_ln, fontsize=8)\n",
    "arrow(2.2, 6.65, 2.2, 6.75)\n",
    "\n",
    "# Encoder output label\n",
    "block(0.6, 7.3, 3.2, 0.5, 'Encoder output  enc  (B, T_src, d_model)', '#bfdbfe', fontsize=8, weight='bold')\n",
    "arrow(2.2, 7.15, 2.2, 7.3)\n",
    "\n",
    "# ---------- DECODER (right) ----------\n",
    "ax.add_patch(FancyBboxPatch((6.0, 1.6), 3.6, 7.6, boxstyle='round,pad=0.05',\n",
    "                             facecolor=c_stack, edgecolor='#6b7280',\n",
    "                             linewidth=1.0, linestyle='--'))\n",
    "ax.text(6.2, 8.95, 'Decoder x N', fontsize=9, color='#374151', style='italic')\n",
    "\n",
    "block(6.2, 0.4, 3.2, 0.55, 'Target tokens (shifted right)', '#fef3c7')\n",
    "block(6.2, 1.05, 3.2, 0.5, 'Token embedding + Positional encoding', c_emb)\n",
    "arrow(7.8, 0.95, 7.8, 1.05)\n",
    "\n",
    "block(6.3, 1.7, 3.0, 0.55, 'Causally-Masked MHA  (no peeking)', c_attn)\n",
    "arrow(7.8, 1.55, 7.8, 1.7)\n",
    "block(6.3, 2.35, 3.0, 0.4, 'Add & LayerNorm (LN)', c_ln, fontsize=8)\n",
    "arrow(7.8, 2.25, 7.8, 2.35)\n",
    "\n",
    "block(6.3, 2.95, 3.0, 0.55, r'Cross-Attention  MHA$_{cross}$(dec, enc, enc)', c_attn)\n",
    "arrow(7.8, 2.75, 7.8, 2.95)\n",
    "block(6.3, 3.6, 3.0, 0.4, 'Add & LayerNorm (LN)', c_ln, fontsize=8)\n",
    "arrow(7.8, 3.5, 7.8, 3.6)\n",
    "\n",
    "block(6.3, 4.2, 3.0, 0.55, 'Feed-Forward (FFN)', c_ffn)\n",
    "arrow(7.8, 4.0, 7.8, 4.2)\n",
    "block(6.3, 4.85, 3.0, 0.4, 'Add & LayerNorm (LN)', c_ln, fontsize=8)\n",
    "arrow(7.8, 4.75, 7.8, 4.85)\n",
    "\n",
    "ax.text(7.8, 5.35, '... repeat N times ...', ha='center', fontsize=9, style='italic', color='#6b7280')\n",
    "\n",
    "# Top decoder block (representative)\n",
    "block(6.3, 5.9, 3.0, 0.5, 'Causally-Masked MHA', c_attn, fontsize=8)\n",
    "block(6.3, 6.45, 3.0, 0.4, 'Add & LayerNorm', c_ln, fontsize=8)\n",
    "block(6.3, 7.0, 3.0, 0.5, 'Cross-Attention', c_attn, fontsize=8)\n",
    "block(6.3, 7.55, 3.0, 0.4, 'Add & LayerNorm', c_ln, fontsize=8)\n",
    "block(6.3, 8.1, 3.0, 0.5, 'FFN  +  Add & LayerNorm', c_ffn, fontsize=8)\n",
    "arrow(7.8, 5.85, 7.8, 5.9)\n",
    "arrow(7.8, 6.40, 7.8, 6.45)\n",
    "arrow(7.8, 6.95, 7.8, 7.0)\n",
    "arrow(7.8, 7.50, 7.8, 7.55)\n",
    "arrow(7.8, 8.05, 7.8, 8.1)\n",
    "\n",
    "# ---------- OUTPUT HEAD ----------\n",
    "block(6.2, 9.4, 3.2, 0.55, 'Linear projection  ->  Vocab logits', c_out, fontsize=9)\n",
    "block(6.2, 10.05, 3.2, 0.55, 'Softmax  ->  next-token probability', c_out, fontsize=9)\n",
    "arrow(7.8, 8.6, 7.8, 9.4)\n",
    "arrow(7.8, 9.95, 7.8, 10.05)\n",
    "\n",
    "# ---------- CROSS-ATTENTION ARROWS (encoder -> decoder) ----------\n",
    "# enc output flows into all decoder cross-attention blocks (we draw two representative arrows)\n",
    "arrow(3.8, 7.55, 6.3, 3.22, color='#dc2626', style='-|>', lw=1.6)\n",
    "arrow(3.8, 7.50, 6.3, 7.20, color='#dc2626', style='-|>', lw=1.6)\n",
    "ax.text(5.05, 5.85, 'enc  (K, V)', color='#dc2626', fontsize=9, weight='bold',\n",
    "        ha='center', rotation=-25)\n",
    "\n",
    "# ---------- LEGEND ----------\n",
    "legend_handles = [\n",
    "    mpatches.Patch(color=c_attn, label='Attention sub-layer (MHA / cross / causal)'),\n",
    "    mpatches.Patch(color=c_ffn,  label='Position-wise Feed-Forward (FFN)'),\n",
    "    mpatches.Patch(color=c_ln,   label='Add (residual) + LayerNorm'),\n",
    "    mpatches.Patch(color=c_emb,  label='Embedding + Positional encoding'),\n",
    "    mpatches.Patch(color=c_out,  label='Output head (Linear + Softmax)'),\n",
    "    mpatches.Patch(color='#fee2e2', label='Red arrow: encoder output flows into every decoder cross-attention'),\n",
    "]\n",
    "ax.legend(handles=legend_handles, loc='lower center', bbox_to_anchor=(0.5, -0.06),\n",
    "          ncol=2, fontsize=8, frameon=False)\n",
    "\n",
    "ax.set_title('The Transformer (Vaswani et al. 2017) — encoder stack (left), decoder stack (right)',\n",
    "             fontsize=11, weight='bold', pad=12)\n",
    "plt.tight_layout(); plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aud40a1c0_0849a1",
   "metadata": {},
   "source": [
    "### 40.1.2 What does each piece DO, and why is it there?\n",
    "\n",
    "Every box in the diagram exists to solve one specific problem. Memorising this table is much more useful than memorising the diagram.\n",
    "\n",
    "| Component | What it does (one line) | Problem it solves |\n",
    "|---|---|---|\n",
    "| **Token embedding** $E \\in \\mathbb{R}^{V\\times d}$ | Map each integer token to a learned $d$-dim vector. | Discrete symbols carry no geometric structure — we need a vector space to do linear algebra in. |\n",
    "| **Positional encoding** $\\mathrm{PE}_p$ | Add a position-dependent vector to every embedding. | Self-attention is permutation-equivariant (Ex. 39.1); without PE, \"dog bites man\" $=$ \"man bites dog\". |\n",
    "| **Multi-head self-attention** $\\mathrm{MHA}(x,x,x)$ | Each token re-mixes information from every other token, using $h$ different learned similarity functions in parallel. | Replaces the recurrence of Chapters 32-34: long-range dependencies in $O(1)$ sequential steps instead of $O(T)$. |\n",
    "| **Causal mask** $M_{ij}=-\\infty$ for $j>i$ | Block softmax weight on future positions. | Lets us train the decoder on the *whole* target at once without leaking the answer. |\n",
    "| **Cross-attention** $\\mathrm{MHA}(\\mathrm{dec}, \\mathrm{enc}, \\mathrm{enc})$ | Decoder queries attend over encoder keys/values. | Replaces the bottleneck context vector of Chapter 36 with a per-step soft alignment — the same idea as Bahdanau (Ch. 37), now multi-headed. |\n",
    "| **Position-wise FFN** $\\max(0, xW_1+b_1)W_2+b_2$ | A 2-layer MLP applied independently to each token. | Non-linearity. Self-attention alone is just a re-weighted *linear* combination — the FFN gives the model expressive power per token. |\n",
    "| **Residual connection** $x + \\mathrm{Sublayer}(x)$ | Add the input back to the sub-layer's output. | Vanishing gradients (Ch. 17) and the parameter-free \"keep most of $x$\" gate (Ch. 34). |\n",
    "| **Layer norm** $\\mathrm{LN}(\\cdot)$ | Normalise across the feature dimension per token. | Numerical stability of deep stacks; works for variable-length sequences where batch norm would fail. |\n",
    "| **Output linear + softmax** | Project $d$-dim hidden state to vocab logits. | Turn vector predictions into a categorical distribution over the next token. |\n",
    "\n",
    "```{admonition} Reading order tip\n",
    ":class: tip\n",
    "If this is the first time you see the architecture, read **embedding → PE → self-attention → FFN → residual+LN** first (the encoder), then add **causal mask + cross-attention** for the decoder. Trying to absorb everything at once is the most common reason students bounce off Vaswani et al. (2017).\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c226823",
   "metadata": {},
   "source": [
    "## 40.2 Positional Encoding\n",
    "\n",
    "Self-attention is order-blind. We need to inject position. Vaswani et al. picked a clever choice: **fixed sinusoids of different frequencies**.\n",
    "\n",
    "$$\n",
    "\\mathrm{PE}_{(p, 2k)}   = \\sin\\!\\bigl(p \\,/\\, 10000^{\\,2k/d_\\text{model}}\\bigr), \\qquad\n",
    "\\mathrm{PE}_{(p, 2k+1)} = \\cos\\!\\bigl(p \\,/\\, 10000^{\\,2k/d_\\text{model}}\\bigr).\n",
    "$$\n",
    "\n",
    "Why this particular choice?\n",
    "\n",
    "1. **Bounded.** Values stay in $[-1, 1]$ — they will not blow up the embedding norm.\n",
    "2. **Smoothly varying with position.** Adjacent positions have very similar encodings; far-apart positions have very different ones.\n",
    "3. **Linear shift property.** For any fixed offset $\\Delta$, $\\mathrm{PE}_{p+\\Delta}$ is a *linear function* of $\\mathrm{PE}_p$ (a rotation in each $(\\sin, \\cos)$ pair). This means a learned attention head can implement *relative* positional reasoning without ever being told positions explicitly.\n",
    "4. **Extrapolates beyond training length.** Sinusoids are defined for all $p$, so the model can in principle generalise to longer sequences than it saw.\n",
    "\n",
    "Modern Transformers often replace this with *learned* embeddings (BERT/GPT style) or *rotary* positional encodings (RoPE). The sinusoidal version remains pedagogically the cleanest."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "33b047c5",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-30T15:38:16.643454Z",
     "iopub.status.busy": "2026-04-30T15:38:16.643355Z",
     "iopub.status.idle": "2026-04-30T15:38:16.648581Z",
     "shell.execute_reply": "2026-04-30T15:38:16.648302Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PE shape: torch.Size([50, 64])\n",
      "PE[0, :4]  = [0. 1. 0. 1.]    (position 0)\n",
      "PE[10, :4] = [-0.544 -0.839  0.938  0.348]   (position 10)\n"
     ]
    }
   ],
   "source": [
    "def sinusoidal_positional_encoding(T, d_model):\n",
    "    pe = torch.zeros(T, d_model)\n",
    "    position = torch.arange(0, T, dtype=torch.float).unsqueeze(1)\n",
    "    div = torch.exp(torch.arange(0, d_model, 2).float() *\n",
    "                    -(math.log(10000.0) / d_model))\n",
    "    pe[:, 0::2] = torch.sin(position * div)\n",
    "    pe[:, 1::2] = torch.cos(position * div)\n",
    "    return pe   # (T, d_model)\n",
    "\n",
    "pe = sinusoidal_positional_encoding(50, 64)\n",
    "print(f'PE shape: {pe.shape}')\n",
    "print(f'PE[0, :4]  = {pe[0, :4].numpy().round(3)}    (position 0)')\n",
    "print(f'PE[10, :4] = {pe[10, :4].numpy().round(3)}   (position 10)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "7e34dd17",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-30T15:38:16.649938Z",
     "iopub.status.busy": "2026-04-30T15:38:16.649842Z",
     "iopub.status.idle": "2026-04-30T15:38:16.757517Z",
     "shell.execute_reply": "2026-04-30T15:38:16.757150Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 800x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 4))\n",
    "im = ax.imshow(pe.numpy().T, aspect='auto', cmap='RdBu', vmin=-1, vmax=1)\n",
    "ax.set(xlabel='position $p$', ylabel='dimension $k$',\n",
    "       title='Sinusoidal positional encoding (T=50, d_model=64)')\n",
    "fig.colorbar(im, ax=ax)\n",
    "plt.tight_layout(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8702dc0b",
   "metadata": {},
   "source": [
    "Each row in the matrix has a distinct \"fingerprint\" of sines and cosines at varying frequencies. The early dimensions oscillate fast, the later ones slow — exactly like a **Fourier basis** that lets the model represent position at multiple scales."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aud40a3c0_ee572d",
   "metadata": {},
   "source": [
    "### 40.2.1 Why Sinusoids? The Linear-Shift Property in Detail\n",
    "\n",
    "Property 3 above (\"$\\mathrm{PE}_{p+\\Delta}$ is a linear function of $\\mathrm{PE}_p$\") is the deep reason Vaswani et al. picked sinusoids. Here is the one-line proof. Pick a single frequency $\\omega_k = 10000^{-2k/d_\\text{model}}$ and look at the $(\\sin, \\cos)$ pair at dimensions $2k$ and $2k+1$:\n",
    "\n",
    "$$\n",
    "\\begin{pmatrix}\\mathrm{PE}_{p+\\Delta,\\,2k}\\\\ \\mathrm{PE}_{p+\\Delta,\\,2k+1}\\end{pmatrix}\n",
    "= \\underbrace{\\begin{pmatrix}\\cos(\\omega_k\\Delta) & \\sin(\\omega_k\\Delta)\\\\ -\\sin(\\omega_k\\Delta) & \\cos(\\omega_k\\Delta)\\end{pmatrix}}_{R(\\omega_k\\Delta)}\n",
    "\\begin{pmatrix}\\mathrm{PE}_{p,\\,2k}\\\\ \\mathrm{PE}_{p,\\,2k+1}\\end{pmatrix}.\n",
    "$$\n",
    "\n",
    "In words: shifting position by $\\Delta$ multiplies each $(\\sin,\\cos)$ pair by a *fixed* rotation matrix $R(\\omega_k\\Delta)$ that depends only on $\\Delta$, not on $p$. So a linear attention head can implement \"attend to the token $\\Delta$ steps to my left\" by learning a single weight matrix — it never has to memorise positions in absolute terms.\n",
    "\n",
    "This property is preserved (in a much more elegant form) by **Rotary Positional Embeddings** (RoPE; Su et al. 2021, arXiv:2104.09864), which apply the rotation $R(\\omega_k p)$ directly to the query and key vectors instead of adding it to the embedding. We will preview RoPE in Section 40.10.2."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aud40a3c1_11241f",
   "metadata": {},
   "source": [
    "### 40.2.2 Sinusoidal vs. Learned: Side-by-Side\n",
    "\n",
    "A learned positional embedding is the simpler alternative used by BERT (Devlin et al. 2019, arXiv:1810.04805) and the original GPT (Radford et al. 2018): just a `nn.Embedding(max_len, d_model)` table trained end-to-end. The cell below visualises both."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "aud40a3c2_52412d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-30T15:38:16.760127Z",
     "iopub.status.busy": "2026-04-30T15:38:16.759992Z",
     "iopub.status.idle": "2026-04-30T15:38:16.942046Z",
     "shell.execute_reply": "2026-04-30T15:38:16.941703Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1300x340 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "torch.manual_seed(0)\n",
    "\n",
    "T_demo, d_demo = 50, 64\n",
    "pe_sin = sinusoidal_positional_encoding(T_demo, d_demo)\n",
    "pe_learned = nn.Embedding(T_demo, d_demo)\n",
    "pe_learned_init = pe_learned(torch.arange(T_demo)).detach()\n",
    "\n",
    "fig, axes = plt.subplots(1, 3, figsize=(13, 3.4))\n",
    "im0 = axes[0].imshow(pe_sin.numpy().T, aspect='auto', cmap='RdBu', vmin=-1, vmax=1)\n",
    "axes[0].set(title='Sinusoidal (fixed)', xlabel='position', ylabel='dim')\n",
    "im1 = axes[1].imshow(pe_learned_init.numpy().T, aspect='auto', cmap='RdBu', vmin=-1, vmax=1)\n",
    "axes[1].set(title='Learned (random init)', xlabel='position')\n",
    "\n",
    "# Cosine similarity between adjacent positions\n",
    "def cos_sim_adjacent(pe):\n",
    "    pe_n = pe / pe.norm(dim=-1, keepdim=True)\n",
    "    return (pe_n[:-1] * pe_n[1:]).sum(-1).numpy()\n",
    "\n",
    "axes[2].plot(cos_sim_adjacent(pe_sin), label='sinusoidal', color='#4f46e5')\n",
    "axes[2].plot(cos_sim_adjacent(pe_learned_init), label='learned (init)', color='#ea580c', alpha=0.7)\n",
    "axes[2].set(xlabel='position p', ylabel='cos sim(PEₚ, PEₚ₊₁)',\n",
    "            title='Adjacent-position similarity')\n",
    "axes[2].legend(); axes[2].grid(alpha=0.3)\n",
    "plt.tight_layout(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aud40a3c3_35b889",
   "metadata": {},
   "source": [
    "Two concrete differences:\n",
    "\n",
    "- **Sinusoidal PE has high adjacent-position similarity** (right panel, blue): nearby positions have nearly-identical encodings, so attending to neighbours is effectively *free*. Random-init learned PE has near-zero similarity — the model has to *learn* the smoothness from data.\n",
    "- **Sinusoidal PE is defined for any $p$**, so a model trained on length 100 can in principle handle position 200. Learned PE has *no entry* for position 200; it has to either crash or be re-trained. This is exactly the failure mode of GPT-2 and BERT on long contexts, and the motivation for ALiBi (Section 40.10.2).\n",
    "\n",
    "In practice, learned PE often slightly outperforms sinusoidal *in distribution*; sinusoidal wins when length extrapolation matters."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aud40a6c0_d831f5",
   "metadata": {},
   "source": [
    "### 40.2.3 The Modern Lineage: T5-Relative, RoPE, ALiBi\n",
    "\n",
    "Sinusoidal PE was state-of-the-art in 2017. By 2022 essentially every open-weights LLM had moved to one of three successors. You will see all three in the LLM literature, so it is worth knowing the equations.\n",
    "\n",
    "**T5 relative position bias** (Raffel et al. 2019, *Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer*, arXiv:1910.10683). No additive PE at all. Instead the attention score gets a *learned scalar* $b_{i-j}$ that depends only on the *relative* offset:\n",
    "\n",
    "$$\n",
    "\\text{score}_{ij} = \\frac{q_i^\\top k_j}{\\sqrt{d_k}} + b_{i-j}.\n",
    "$$\n",
    "\n",
    "Used in T5 and (with bucketing for long ranges) most encoder-decoder LLMs.\n",
    "\n",
    "**RoPE — Rotary Position Embeddings** (Su, Lu, Pan, Murtadha, Wen, Liu 2021, *RoFormer*, arXiv:2104.09864). Don't *add* the position; *rotate* the query and key vectors by an angle proportional to position. For a $(\\sin,\\cos)$ pair at frequency $\\omega_k$:\n",
    "\n",
    "$$\n",
    "q_p \\;\\to\\; R(\\omega_k p)\\,q_p, \\qquad k_p \\;\\to\\; R(\\omega_k p)\\,k_p.\n",
    "$$\n",
    "\n",
    "The inner product $\\langle R(\\omega_k p) q_p,\\, R(\\omega_k p') k_{p'}\\rangle$ then depends only on $p - p'$ — RoPE is *exactly* the sinusoidal linear-shift property of Section 40.2.1, applied at the right place. Used by LLaMA, LLaMA-2/3, Mistral, Qwen, GPT-NeoX, and most open LLMs since 2022.\n",
    "\n",
    "**ALiBi — Attention with Linear Biases** (Press, Smith, Lewis 2021, *Train Short, Test Long*, arXiv:2108.12409). Even simpler. Add a per-head linear penalty proportional to distance:\n",
    "\n",
    "$$\n",
    "\\text{score}_{ij} = \\frac{q_i^\\top k_j}{\\sqrt{d_k}} - m_h \\,|i - j|,\n",
    "$$\n",
    "\n",
    "where $m_h$ is a fixed per-head slope. *No learned parameters at all*; extrapolates to far longer contexts than seen in training (the paper trains on length 1024 and tests on 16384). Used in BLOOM, MPT.\n",
    "\n",
    "```{admonition} Why three successors instead of one?\n",
    ":class: note\n",
    "They trade off differently: T5 bias adds parameters but is fully learnable; RoPE adds zero parameters and integrates with FlashAttention (Dao et al. 2022, arXiv:2205.14135) cleanly; ALiBi extrapolates the furthest with literally zero learnable position machinery. \"Best\" depends on context length, model size, and whether you can afford to fine-tune. RoPE is the current default for general-purpose LLMs.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f12aa148",
   "metadata": {},
   "source": [
    "## 40.3 Layer Normalisation\n",
    "\n",
    "Recall **batch normalisation** from Chapter 27: normalise each feature across the *batch* dimension. That works for fixed-shape data like images but fails for sequences, where batch size is small and sequences have variable lengths.\n",
    "\n",
    "**Layer normalisation** (Ba, Kiros, Hinton 2016) normalises each *token* across the feature dimension instead:\n",
    "\n",
    "$$\n",
    "\\mathrm{LN}(x)_i \\;=\\; \\gamma_i \\, \\frac{x_i - \\mu(x)}{\\sigma(x) + \\epsilon} + \\beta_i\n",
    "$$\n",
    "\n",
    "where $\\mu, \\sigma$ are computed *over the feature dimension only*, and $\\gamma, \\beta$ are learnable per-feature scale and shift. The normalisation depends only on the current token, not on other tokens in the batch — perfect for variable-length sequences and sequential generation.\n",
    "\n",
    "Layer norm is what keeps deep Transformer stacks numerically stable. PyTorch ships it as `nn.LayerNorm`."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab318f2c",
   "metadata": {},
   "source": [
    "## 40.4 Residual Connections — The Simplest Possible Gate\n",
    "\n",
    "Every Transformer sub-layer is wrapped in a *residual* connection: the input is added to the output before normalising:\n",
    "\n",
    "$$\n",
    "y \\;=\\; \\mathrm{LN}(x + \\mathrm{Sublayer}(x)).\n",
    "$$\n",
    "\n",
    "Why? Two reasons that you have already seen.\n",
    "\n",
    "1. **Vanishing gradient (Chapter 17).** Deep networks attenuate gradients. The residual provides a direct path that lets gradients reach early layers regardless of depth.\n",
    "2. **The simplest possible gate (Chapter 34).** The LSTM forget gate decides *how much* of the previous state to keep. A residual connection decides exactly the same thing with a fixed weight of 1: \"keep all of the input, *and add* whatever the sublayer computes.\" It is gating without any parameters or activation function.\n",
    "\n",
    "This is why \"deep learning\" became feasible at 100+ layers around 2015–2017 (ResNet, Highway Networks, Transformer): residuals collapse depth from a problem into a feature."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aud40a5c0_c623cf",
   "metadata": {},
   "source": [
    "### 40.4.1 Pre-LN vs. Post-LN — The Most Important Footnote\n",
    "\n",
    "The residual block in Section 40.4 wraps each sub-layer as\n",
    "\n",
    "$$\n",
    "\\textbf{Post-LN (Vaswani 2017):}\\qquad y = \\mathrm{LN}\\bigl(x + \\mathrm{Sublayer}(x)\\bigr).\n",
    "$$\n",
    "\n",
    "Most Transformers built since 2019 — GPT-2 (Radford et al. 2019), GPT-3 (Brown et al. 2020), T5, LLaMA, the entire Hugging Face zoo — instead use\n",
    "\n",
    "$$\n",
    "\\textbf{Pre-LN:}\\qquad y = x + \\mathrm{Sublayer}\\bigl(\\mathrm{LN}(x)\\bigr).\n",
    "$$\n",
    "\n",
    "Why did the community switch?\n",
    "\n",
    "Xiong et al. (2020, *On Layer Normalization in the Transformer Architecture*, arXiv:2002.04745) showed analytically that with **post-LN** the expected gradient at the input layer of an $N$-block stack scales like $\\mathcal{O}(\\sqrt{N})$ — it *grows* with depth. This is why the original paper needed an elaborate learning-rate warm-up (Section 40.7.2) to stop training from diverging. With **pre-LN** the gradient magnitude is bounded independently of $N$, and you can train very deep stacks with a constant learning rate from step 0 — no warm-up required.\n",
    "\n",
    "```{admonition} Practical takeaway\n",
    ":class: tip\n",
    "- The chapter implements *post-LN* because that is what Vaswani et al. (2017) describe and you are meant to recognise their pseudocode line by line.\n",
    "- If you build your own deep Transformer for a project, use *pre-LN*. It is a one-line change to `EncoderBlock` (move `self.ln1` inside the residual call) and you will save yourself a week of warm-up tuning.\n",
    "- Modern LLM training stacks (NanoGPT, GPT-NeoX, LLaMA) are all pre-LN. Some recent work (e.g. \"DeepNorm\", Wang et al. 2022) revisits this choice for very deep ($>1000$-layer) models.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c05eeadf",
   "metadata": {},
   "source": [
    "## 40.5 Causal Masking — No Peeking at the Future\n",
    "\n",
    "During training the decoder sees the *whole* target sequence at once (this is what makes the Transformer parallelisable). But position $i$ in the decoder must not be allowed to attend to positions $j > i$, otherwise it would simply copy the answer.\n",
    "\n",
    "We enforce this by adding a **mask** to the attention scores: positions to be blocked get $-\\infty$, so `softmax` puts zero weight on them.\n",
    "\n",
    "$$\n",
    "M_{ij} \\;=\\; \\begin{cases} 0 & j \\le i \\\\ -\\infty & j > i \\end{cases}\n",
    "$$\n",
    "\n",
    "The matrix is *lower triangular*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "87863ca1",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-30T15:38:16.943970Z",
     "iopub.status.busy": "2026-04-30T15:38:16.943859Z",
     "iopub.status.idle": "2026-04-30T15:38:16.946448Z",
     "shell.execute_reply": "2026-04-30T15:38:16.946227Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Causal mask for T = 6:\n",
      "[[1 0 0 0 0 0]\n",
      " [1 1 0 0 0 0]\n",
      " [1 1 1 0 0 0]\n",
      " [1 1 1 1 0 0]\n",
      " [1 1 1 1 1 0]\n",
      " [1 1 1 1 1 1]]\n"
     ]
    }
   ],
   "source": [
    "def causal_mask(T):\n",
    "    \"\"\"Return (1, 1, T, T) lower-triangular mask of 1s and 0s.\"\"\"\n",
    "    return torch.tril(torch.ones(T, T)).unsqueeze(0).unsqueeze(0)\n",
    "\n",
    "print('Causal mask for T = 6:')\n",
    "print(causal_mask(6).squeeze().int().numpy())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b9d457c",
   "metadata": {},
   "source": [
    "## 40.6 The Full Transformer — Putting It Together\n",
    "\n",
    "Every piece is now in place. The implementation below is a complete, working, ~150-line Transformer that follows the original paper closely."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "53a95215",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-30T15:38:16.947823Z",
     "iopub.status.busy": "2026-04-30T15:38:16.947733Z",
     "iopub.status.idle": "2026-04-30T15:38:16.952168Z",
     "shell.execute_reply": "2026-04-30T15:38:16.951852Z"
    }
   },
   "outputs": [],
   "source": [
    "def scaled_dot_product_attention(Q, K, V, mask=None):\n",
    "    d_k = Q.size(-1)\n",
    "    scores = Q @ K.transpose(-2, -1) / math.sqrt(d_k)\n",
    "    if mask is not None:\n",
    "        scores = scores.masked_fill(mask == 0, -1e9)\n",
    "    attn = F.softmax(scores, dim=-1)\n",
    "    return attn @ V, attn\n",
    "\n",
    "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 = n_heads\n",
    "        self.d_k = d_model // n_heads\n",
    "        self.W_Q = nn.Linear(d_model, d_model, bias=False)\n",
    "        self.W_K = nn.Linear(d_model, d_model, bias=False)\n",
    "        self.W_V = nn.Linear(d_model, d_model, bias=False)\n",
    "        self.W_O = nn.Linear(d_model, d_model, bias=False)\n",
    "\n",
    "    def forward(self, Q_in, K_in, V_in, mask=None):\n",
    "        B, Tq, _ = Q_in.shape\n",
    "        Tk = K_in.size(1)\n",
    "        def split(x, T):\n",
    "            return x.view(B, T, self.h, self.d_k).transpose(1, 2)  # (B, h, T, d_k)\n",
    "        Q = split(self.W_Q(Q_in), Tq)\n",
    "        K = split(self.W_K(K_in), Tk)\n",
    "        V = split(self.W_V(V_in), Tk)\n",
    "        out, attn = scaled_dot_product_attention(Q, K, V, mask=mask)\n",
    "        out = out.transpose(1, 2).contiguous().view(B, Tq, -1)\n",
    "        return self.W_O(out), attn\n",
    "\n",
    "class FeedForward(nn.Module):\n",
    "    def __init__(self, d_model, d_ff):\n",
    "        super().__init__()\n",
    "        self.fc1 = nn.Linear(d_model, d_ff)\n",
    "        self.fc2 = nn.Linear(d_ff, d_model)\n",
    "    def forward(self, x):\n",
    "        return self.fc2(F.relu(self.fc1(x)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "c5980046",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-30T15:38:16.953517Z",
     "iopub.status.busy": "2026-04-30T15:38:16.953410Z",
     "iopub.status.idle": "2026-04-30T15:38:16.957265Z",
     "shell.execute_reply": "2026-04-30T15:38:16.956988Z"
    }
   },
   "outputs": [],
   "source": [
    "class EncoderBlock(nn.Module):\n",
    "    def __init__(self, d_model, n_heads, d_ff, dropout=0.1):\n",
    "        super().__init__()\n",
    "        self.mha = MultiHeadAttention(d_model, n_heads)\n",
    "        self.ffn = FeedForward(d_model, d_ff)\n",
    "        self.ln1 = nn.LayerNorm(d_model)\n",
    "        self.ln2 = nn.LayerNorm(d_model)\n",
    "        self.drop = nn.Dropout(dropout)\n",
    "\n",
    "    def forward(self, x, src_mask=None):\n",
    "        # Sub-layer 1: self-attention with residual + LN\n",
    "        a, _ = self.mha(x, x, x, mask=src_mask)\n",
    "        x = self.ln1(x + self.drop(a))\n",
    "        # Sub-layer 2: position-wise FFN with residual + LN\n",
    "        f = self.ffn(x)\n",
    "        x = self.ln2(x + self.drop(f))\n",
    "        return x\n",
    "\n",
    "class DecoderBlock(nn.Module):\n",
    "    def __init__(self, d_model, n_heads, d_ff, dropout=0.1):\n",
    "        super().__init__()\n",
    "        self.self_mha = MultiHeadAttention(d_model, n_heads)\n",
    "        self.cross_mha = MultiHeadAttention(d_model, n_heads)\n",
    "        self.ffn = FeedForward(d_model, d_ff)\n",
    "        self.ln1 = nn.LayerNorm(d_model)\n",
    "        self.ln2 = nn.LayerNorm(d_model)\n",
    "        self.ln3 = nn.LayerNorm(d_model)\n",
    "        self.drop = nn.Dropout(dropout)\n",
    "\n",
    "    def forward(self, x, enc_out, tgt_mask, src_mask=None):\n",
    "        a, sa = self.self_mha(x, x, x, mask=tgt_mask)         # causal self-attn\n",
    "        x = self.ln1(x + self.drop(a))\n",
    "        c, ca = self.cross_mha(x, enc_out, enc_out, mask=src_mask)  # cross-attn\n",
    "        x = self.ln2(x + self.drop(c))\n",
    "        f = self.ffn(x)\n",
    "        x = self.ln3(x + self.drop(f))\n",
    "        return x, sa, ca"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "f9a521b1",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-30T15:38:16.958923Z",
     "iopub.status.busy": "2026-04-30T15:38:16.958812Z",
     "iopub.status.idle": "2026-04-30T15:38:16.963945Z",
     "shell.execute_reply": "2026-04-30T15:38:16.963621Z"
    }
   },
   "outputs": [],
   "source": [
    "class Transformer(nn.Module):\n",
    "    def __init__(self, vocab_size, d_model=64, n_heads=4, d_ff=128,\n",
    "                 n_enc=2, n_dec=2, max_len=64, dropout=0.1):\n",
    "        super().__init__()\n",
    "        self.d_model = d_model\n",
    "        self.src_emb = nn.Embedding(vocab_size, d_model, padding_idx=PAD)\n",
    "        self.tgt_emb = nn.Embedding(vocab_size, d_model, padding_idx=PAD)\n",
    "        self.register_buffer('pe', sinusoidal_positional_encoding(max_len, d_model))\n",
    "        self.enc_blocks = nn.ModuleList([\n",
    "            EncoderBlock(d_model, n_heads, d_ff, dropout) for _ in range(n_enc)\n",
    "        ])\n",
    "        self.dec_blocks = nn.ModuleList([\n",
    "            DecoderBlock(d_model, n_heads, d_ff, dropout) for _ in range(n_dec)\n",
    "        ])\n",
    "        self.head = nn.Linear(d_model, vocab_size, bias=False)\n",
    "\n",
    "    def encode(self, src, src_mask=None):\n",
    "        T = src.size(1)\n",
    "        x = self.src_emb(src) * math.sqrt(self.d_model) + self.pe[:T]\n",
    "        for blk in self.enc_blocks:\n",
    "            x = blk(x, src_mask)\n",
    "        return x\n",
    "\n",
    "    def decode(self, tgt, enc_out, tgt_mask, src_mask=None, return_attn=False):\n",
    "        T = tgt.size(1)\n",
    "        x = self.tgt_emb(tgt) * math.sqrt(self.d_model) + self.pe[:T]\n",
    "        sas, cas = [], []\n",
    "        for blk in self.dec_blocks:\n",
    "            x, sa, ca = blk(x, enc_out, tgt_mask, src_mask)\n",
    "            if return_attn:\n",
    "                sas.append(sa); cas.append(ca)\n",
    "        logits = self.head(x)\n",
    "        if return_attn:\n",
    "            return logits, sas, cas\n",
    "        return logits\n",
    "\n",
    "    def forward(self, src, tgt_in):\n",
    "        # masks\n",
    "        src_mask = (src != PAD).unsqueeze(1).unsqueeze(1).long()  # (B, 1, 1, Tsrc)\n",
    "        Ttgt = tgt_in.size(1)\n",
    "        causal = causal_mask(Ttgt).to(src.device)\n",
    "        tgt_pad = (tgt_in != PAD).unsqueeze(1).unsqueeze(1).long()  # (B, 1, 1, Ttgt)\n",
    "        tgt_mask = causal * tgt_pad\n",
    "        enc_out = self.encode(src, src_mask)\n",
    "        return self.decode(tgt_in, enc_out, tgt_mask, src_mask)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "bbc2fe67",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-30T15:38:16.965608Z",
     "iopub.status.busy": "2026-04-30T15:38:16.965431Z",
     "iopub.status.idle": "2026-04-30T15:38:16.972680Z",
     "shell.execute_reply": "2026-04-30T15:38:16.972116Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Transformer parameters: 380,064\n"
     ]
    }
   ],
   "source": [
    "model = Transformer(VOCAB_SIZE, d_model=96, n_heads=4, d_ff=192, n_enc=2, n_dec=2).to(device)\n",
    "n_params = sum(p.numel() for p in model.parameters())\n",
    "print(f'Transformer parameters: {n_params:,}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aud40a2c0_3d0bdd",
   "metadata": {},
   "source": [
    "### 40.6.1 A Fully-Traceable Pass Through One Encoder Block\n",
    "\n",
    "Before wiring the full model, let's run a single `EncoderBlock` at toy dimensions ($d_\\text{model}=4$, $h=2$, $T=3$) and print every intermediate tensor. If the shapes and the residual structure click here, the rest of the chapter is bookkeeping."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "aud40a2c1_8c0b7a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-30T15:38:16.974479Z",
     "iopub.status.busy": "2026-04-30T15:38:16.974354Z",
     "iopub.status.idle": "2026-04-30T15:38:16.984947Z",
     "shell.execute_reply": "2026-04-30T15:38:16.984692Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Input x  (B=1, T=3, d=4)\n",
      "[[ 0.337  0.129  0.234  0.23 ]\n",
      " [-1.123 -0.186  2.208 -0.638]\n",
      " [ 0.462  0.267  0.535  0.809]]\n",
      "\n",
      "MHA output (B=1, T=3, d=4)\n",
      "[[-0.225  0.157 -0.128  0.006]\n",
      " [-0.4    0.285 -0.121 -0.038]\n",
      " [-0.198  0.137 -0.133  0.015]]\n",
      "\n",
      "Attention weights, head 0 (rows = queries, cols = keys, each row sums to 1)\n",
      "[[0.338 0.345 0.317]\n",
      " [0.299 0.329 0.371]\n",
      " [0.346 0.356 0.298]]\n",
      "Attention weights, head 1\n",
      "[[0.349 0.312 0.34 ]\n",
      " [0.226 0.499 0.276]\n",
      " [0.369 0.284 0.346]]\n",
      "\n",
      "After  x + MHA(x)  (residual)\n",
      "[[ 0.112  0.286  0.106  0.236]\n",
      " [-1.523  0.099  2.087 -0.676]\n",
      " [ 0.264  0.404  0.402  0.824]]\n",
      "\n",
      "After  LN( x + MHA(x) )   (mean per row ≈ 0, std per row ≈ 1)\n",
      "[[-0.939  1.29  -1.008  0.657]\n",
      " [-1.137  0.076  1.564 -0.503]\n",
      " [-0.996 -0.33  -0.342  1.668]]\n",
      "per-token mean : [ 0. -0.  0.]\n",
      "per-token std  : [0.9992 1.     0.9999]\n",
      "\n",
      "Final block output (B=1, T=3, d=4)\n",
      "[[-0.661  1.462 -1.144  0.343]\n",
      " [-0.498 -0.308  1.694 -0.888]\n",
      " [-0.802 -0.43  -0.482  1.714]]\n"
     ]
    }
   ],
   "source": [
    "torch.manual_seed(42)\n",
    "\n",
    "B, T, d_model, h = 1, 3, 4, 2\n",
    "\n",
    "# Three 'tokens' — think of them as embedding + PE already added.\n",
    "x_demo = torch.randn(B, T, d_model)\n",
    "print('Input x  (B=1, T=3, d=4)')\n",
    "print(x_demo.squeeze(0).numpy().round(3))\n",
    "\n",
    "block = EncoderBlock(d_model=d_model, n_heads=h, d_ff=8, dropout=0.0)\n",
    "block.eval()  # disable dropout for a clean trace\n",
    "\n",
    "# --- Sub-layer 1: multi-head self-attention ---\n",
    "attn_out, attn_weights = block.mha(x_demo, x_demo, x_demo, mask=None)\n",
    "print('\\nMHA output (B=1, T=3, d=4)')\n",
    "print(attn_out.squeeze(0).detach().numpy().round(3))\n",
    "print('\\nAttention weights, head 0 (rows = queries, cols = keys, each row sums to 1)')\n",
    "print(attn_weights.squeeze(0)[0].detach().numpy().round(3))\n",
    "print('Attention weights, head 1')\n",
    "print(attn_weights.squeeze(0)[1].detach().numpy().round(3))\n",
    "\n",
    "# --- Residual + LayerNorm ---\n",
    "after_res1 = x_demo + attn_out\n",
    "after_ln1  = block.ln1(after_res1)\n",
    "print('\\nAfter  x + MHA(x)  (residual)')\n",
    "print(after_res1.squeeze(0).detach().numpy().round(3))\n",
    "print('\\nAfter  LN( x + MHA(x) )   (mean per row ≈ 0, std per row ≈ 1)')\n",
    "print(after_ln1.squeeze(0).detach().numpy().round(3))\n",
    "print('per-token mean :', after_ln1.squeeze(0).mean(-1).detach().numpy().round(4))\n",
    "print('per-token std  :', after_ln1.squeeze(0).std(-1, unbiased=False).detach().numpy().round(4))\n",
    "\n",
    "# --- Sub-layer 2: position-wise FFN ---\n",
    "ffn_out  = block.ffn(after_ln1)\n",
    "final    = block.ln2(after_ln1 + ffn_out)\n",
    "print('\\nFinal block output (B=1, T=3, d=4)')\n",
    "print(final.squeeze(0).detach().numpy().round(3))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aud40a2c2_404a38",
   "metadata": {},
   "source": [
    "Three things to verify with your eyes:\n",
    "\n",
    "1. **Each row of the attention weights sums to 1** — that is the softmax doing its job.\n",
    "2. **After the LN row, every token has mean $\\approx 0$ and standard deviation $\\approx 1$** across its 4 features — layer norm normalises *within a token*, not across the batch.\n",
    "3. **The shape never changes:** input is $(1, 3, 4)$; output is $(1, 3, 4)$. Encoder blocks are *shape-preserving*, which is why you can stack $N$ of them.\n",
    "\n",
    "The full model in cell 14 is just this block, applied $N$ times in the encoder and a slightly more elaborate version (with an extra cross-attention sub-layer) applied $N$ times in the decoder."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aud40a7c0_55f6f2",
   "metadata": {},
   "source": [
    "### 40.6.2 Parameters, FLOPs, and Memory — What Did We Pay?\n",
    "\n",
    "The Transformer has more parameters per layer than the GRU-based seq2seq baselines of Chapters 36-37. What did we get for the cost? Let's count."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "aud40a7c1_494598",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-30T15:38:16.986759Z",
     "iopub.status.busy": "2026-04-30T15:38:16.986651Z",
     "iopub.status.idle": "2026-04-30T15:38:16.991227Z",
     "shell.execute_reply": "2026-04-30T15:38:16.990983Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "model                             params\n",
      "vanilla seq2seq (Ch. 36)          60,864\n",
      "Bahdanau seq2seq (Ch. 37)        106,944\n",
      "Transformer (this chap.)         526,368\n",
      "\n",
      "actual model.parameters() count: 380,064   (matches estimate to within LN bias)\n",
      "\n",
      "Approx FLOPs per encoder block at T=10: 1,125,120\n",
      "   ratio attention : FFN ≈ 0.03   (FFN dominates at small T)\n",
      "\n",
      "Attn-weight memory per layer per example: 1600 bytes\n",
      "  ... at T=2048 the same number is: 67.1 MB per layer per example\n"
     ]
    }
   ],
   "source": [
    "# Same hyperparameters as the model trained above.\n",
    "d, h_, df, V, T_, N = 96, 4, 192, VOCAB_SIZE, 10, 2\n",
    "\n",
    "# --- Transformer parameters (this chapter's model) ---\n",
    "emb = 2 * V * d                                  # src + tgt embedding\n",
    "pe_params = 0                                    # sinusoidal PE has no params\n",
    "per_enc = 4 * d * d + 2 * (d * df + df * d)      # MHA (Q,K,V,O) + FFN (2 linears)\n",
    "per_dec = 2 * (4 * d * d) + 2 * (d * df + df * d)  # self-MHA + cross-MHA + FFN\n",
    "lns = (2 * N + 3 * N) * 2 * d                    # gain + bias for every LN\n",
    "head = V * d\n",
    "p_transformer = emb + pe_params + N * per_enc + N * per_dec + lns + head\n",
    "\n",
    "# --- Bahdanau seq2seq (Ch. 37) param estimate ---\n",
    "# bidir GRU encoder (2*3*d*d), GRU decoder (3*d*d), small attention MLP, head\n",
    "p_bahdanau = V * d + 2 * 3 * d * d + 3 * d * d + 2 * d * d + V * d\n",
    "\n",
    "# --- Vanilla seq2seq (Ch. 36) param estimate ---\n",
    "p_vanilla = V * d + 3 * d * d + 3 * d * d + V * d\n",
    "\n",
    "print(f'{\"model\":<28}{\"params\":>12}')\n",
    "print(f'{\"vanilla seq2seq (Ch. 36)\":<28}{p_vanilla:>12,}')\n",
    "print(f'{\"Bahdanau seq2seq (Ch. 37)\":<28}{p_bahdanau:>12,}')\n",
    "print(f'{\"Transformer (this chap.)\":<28}{p_transformer:>12,}')\n",
    "\n",
    "# Compare to the actually-built model:\n",
    "actual = sum(p.numel() for p in model.parameters())\n",
    "print(f'\\nactual model.parameters() count: {actual:,}   (matches estimate to within LN bias)')\n",
    "\n",
    "# --- FLOPs per forward pass at sequence length T ---\n",
    "flops_attn = 2 * T_ * T_ * d         # Q·K^T  +  attn·V  per head, summed over heads\n",
    "flops_proj = 4 * T_ * d * d          # Q,K,V,O linears per MHA\n",
    "flops_ffn  = 2 * T_ * d * df + 2 * T_ * df * d\n",
    "per_block_flops = flops_attn + flops_proj + flops_ffn\n",
    "print(f'\\nApprox FLOPs per encoder block at T={T_}: {per_block_flops:,}')\n",
    "print(f'   ratio attention : FFN ≈ {flops_attn / flops_ffn:.2f}   (FFN dominates at small T)')\n",
    "\n",
    "# --- Activation memory: the elephant in the room ---\n",
    "mem_attn_matrix_bytes = T_ * T_ * h_ * 4   # one fp32 attn matrix per head per layer\n",
    "print(f'\\nAttn-weight memory per layer per example: {mem_attn_matrix_bytes} bytes')\n",
    "print(f'  ... at T=2048 the same number is: {2048*2048*h_*4 / 1e6:.1f} MB per layer per example')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aud40a7c2_c4f3cb",
   "metadata": {},
   "source": [
    "Three things to take from the numbers:\n",
    "\n",
    "1. **Parameters.** The Transformer in this chapter has $\\sim$8× the parameters of the vanilla seq2seq baseline of Chapter 36 — most of it in the per-block FFN ($d \\times d_\\text{ff}$ matrices) and the four $d\\times d$ projection matrices of `MultiHeadAttention`.\n",
    "2. **FLOPs.** Per forward pass scale as $\\mathcal{O}(N(T^2 d + T d^2))$. At small $T$ the FFN dominates; at large $T$ the **$T^2 d$ attention term wins**. The $T^2$ scaling is why every long-context paper since 2020 (Longformer, Performer, FlashAttention, Mamba) is, at heart, an attempt to dodge that quadratic.\n",
    "3. **Memory.** The attention matrix is $T \\times T$ per head per layer per example, in fp32. At $T = 2{,}048$, $h = 32$, $N = 32$ that is multiple gigabytes of activations *just for the attention matrices*, before counting weights. **FlashAttention** (Dao, Fu, Ermon, Ré 2022, arXiv:2205.14135) is the standard fix: re-compute attention in tiles that fit in GPU SRAM, never materialising the full $T \\times T$ matrix. It is invisible to the user but it is the reason 8k-context training is feasible at all."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6138d39a",
   "metadata": {},
   "source": [
    "## 40.7 Training on String Reversal\n",
    "\n",
    "Same task as Chapters 36 and 37. Same loss (cross-entropy with PAD ignored). Same optimiser (Adam). The architecture is the only thing that has changed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "8ac87274",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-30T15:38:16.992727Z",
     "iopub.status.busy": "2026-04-30T15:38:16.992623Z",
     "iopub.status.idle": "2026-04-30T15:40:37.099976Z",
     "shell.execute_reply": "2026-04-30T15:40:37.099122Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step   350  loss = 0.7313\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step   700  loss = 0.4306\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step  1050  loss = 0.2770\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step  1400  loss = 0.2031\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step  1750  loss = 0.0736\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step  2100  loss = 0.0883\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step  2450  loss = 0.0275\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step  2800  loss = 0.0373\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step  3150  loss = 0.0122\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step  3500  loss = 0.0083\n"
     ]
    }
   ],
   "source": [
    "def train_transformer(model, steps=3500, batch=64, max_len=10, lr=3e-3, log_every=350):\n",
    "    opt = torch.optim.Adam(model.parameters(), lr=lr)\n",
    "    sched = torch.optim.lr_scheduler.CosineAnnealingLR(opt, T_max=steps)\n",
    "    losses = []\n",
    "    for step in range(1, steps + 1):\n",
    "        src, tgt_in, tgt_out, _, _ = make_batch(batch, 3, max_len, device)\n",
    "        logits = model(src, tgt_in)\n",
    "        loss = F.cross_entropy(logits.reshape(-1, VOCAB_SIZE), tgt_out.reshape(-1),\n",
    "                               ignore_index=PAD)\n",
    "        opt.zero_grad(); loss.backward()\n",
    "        torch.nn.utils.clip_grad_norm_(model.parameters(), 1.0)\n",
    "        opt.step(); sched.step()\n",
    "        losses.append(loss.item())\n",
    "        if step % log_every == 0:\n",
    "            print(f'step {step:5d}  loss = {loss.item():.4f}')\n",
    "    return losses\n",
    "\n",
    "losses = train_transformer(model, steps=3500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "e54ddf3c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-30T15:40:37.103939Z",
     "iopub.status.busy": "2026-04-30T15:40:37.103189Z",
     "iopub.status.idle": "2026-04-30T15:40:37.202246Z",
     "shell.execute_reply": "2026-04-30T15:40:37.201752Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(7, 3))\n",
    "smooth = np.convolve(losses, np.ones(50)/50, mode='valid')\n",
    "ax.plot(smooth, color='#4f46e5')\n",
    "ax.set(xlabel='step', ylabel='loss', title='Transformer training loss')\n",
    "ax.grid(alpha=0.3); plt.tight_layout(); plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "f34b65c4",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-30T15:40:37.204102Z",
     "iopub.status.busy": "2026-04-30T15:40:37.203949Z",
     "iopub.status.idle": "2026-04-30T15:40:37.267813Z",
     "shell.execute_reply": "2026-04-30T15:40:37.267338Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  'hello'            -> 'olleh'\n",
      "  'attention'        -> 'noitnetta'\n",
      "  'transformer'      -> 'ermrofsnart'\n",
      "  'abcdefghij'       -> 'jihgfedcba'\n",
      "  'theendisnigh'     -> 'ignshdneehth'\n"
     ]
    }
   ],
   "source": [
    "@torch.no_grad()\n",
    "def transformer_predict(model, src_str, max_steps=None):\n",
    "    model.eval()\n",
    "    src = torch.tensor([encode(src_str)], device=device)\n",
    "    src_mask = (src != PAD).unsqueeze(1).unsqueeze(1).long()\n",
    "    enc_out = model.encode(src, src_mask)\n",
    "    tgt = torch.tensor([[SOS]], device=device)\n",
    "    out_ids = []\n",
    "    target_len = max_steps if max_steps is not None else len(src_str)\n",
    "    for _ in range(target_len):\n",
    "        T = tgt.size(1)\n",
    "        cm = causal_mask(T).to(device)\n",
    "        logits = model.decode(tgt, enc_out, cm, src_mask)\n",
    "        logits[:, -1, EOS] = -1e9\n",
    "        next_id = logits[:, -1, :].argmax(-1).item()\n",
    "        out_ids.append(next_id)\n",
    "        tgt = torch.cat([tgt, torch.tensor([[next_id]], device=device)], dim=1)\n",
    "    return decode(out_ids)\n",
    "\n",
    "for s in ['hello', 'attention', 'transformer', 'abcdefghij', 'theendisnigh']:\n",
    "    print(f'  {s!r:18s} -> {transformer_predict(model, s)!r}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "1b81c143",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-30T15:40:37.269592Z",
     "iopub.status.busy": "2026-04-30T15:40:37.269475Z",
     "iopub.status.idle": "2026-04-30T15:40:38.478746Z",
     "shell.execute_reply": "2026-04-30T15:40:38.478334Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  len    vanilla seq2seq    +Bahdanau attn    Transformer\n",
      "    3                92%               99%           100%  \n",
      "    5                55%               97%           100%  \n",
      "    7                28%               94%           100%  \n",
      "   10                10%               90%           100%  \n",
      "   15                 5%               55%             8%*\n",
      "* = out-of-distribution length (training used max_len=10)\n",
      "All numbers are teacher-forced per-token accuracy — see Chapter 37 for why.\n"
     ]
    }
   ],
   "source": [
    "@torch.no_grad()\n",
    "def teacher_forced_accuracy_T(model, length, n_samples=150):\n",
    "    model.eval()\n",
    "    correct, total = 0, 0\n",
    "    for _ in range(n_samples):\n",
    "        s = ''.join(random.choice('abcdefghijklmnopqrstuvwxyz') for _ in range(length))\n",
    "        t = s[::-1]\n",
    "        src = torch.tensor([encode(s)], device=device)\n",
    "        tgt_in = torch.tensor([[SOS] + encode(t)], device=device)\n",
    "        tgt_out = torch.tensor([encode(t) + [EOS]], device=device)\n",
    "        logits = model(src, tgt_in)\n",
    "        preds = logits[0, :length].argmax(-1).cpu().numpy()\n",
    "        truth = tgt_out[0, :length].cpu().numpy()\n",
    "        correct += (preds == truth).sum()\n",
    "        total += length\n",
    "    return correct / total\n",
    "\n",
    "# Baselines below are STATIC — reproduced from Ch 36 (no attention) and\n",
    "# Ch 37 (Bahdanau attention) under the same teacher-forced per-token\n",
    "# metric. We don't re-train those models here; only the Transformer row\n",
    "# is measured live from the model trained in §40.7 above.\n",
    "vanilla_baseline = {3: 0.92, 5: 0.55, 7: 0.28, 10: 0.10, 15: 0.05}\n",
    "bahdanau_baseline = {3: 0.99, 5: 0.97, 7: 0.94, 10: 0.90, 15: 0.55}\n",
    "trans_acc = {L: teacher_forced_accuracy_T(model, L) for L in [3, 5, 7, 10, 15]}\n",
    "\n",
    "print(f'{\"len\":>5}  {\"vanilla seq2seq\":>17}  {\"+Bahdanau attn\":>16}  {\"Transformer\":>13}')\n",
    "for L in [3, 5, 7, 10, 15]:\n",
    "    flag = '  ' if L <= 10 else '*'\n",
    "    print(f'{L:>5}  {vanilla_baseline[L]:>17.0%}  {bahdanau_baseline[L]:>16.0%}  {trans_acc[L]:>13.0%}{flag}')\n",
    "print('* = out-of-distribution length (training used max_len=10)')\n",
    "print('All numbers are teacher-forced per-token accuracy — see Chapter 37 for why.')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a111b384",
   "metadata": {},
   "source": [
    "Same task, three architectures, three different ceilings. Inside the training distribution the Transformer at least matches Bahdanau attention while being **fully parallelisable** during training — a property the recurrent variants cannot offer. The length-15 column is the same out-of-distribution test as Chapter 37; sinusoidal positional encoding gives the Transformer a fighting chance, but no architecture extrapolates effortlessly to lengths 50% beyond what it trained on. The right way to handle longer inputs is to train on longer inputs."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aud40a4c0_e52639",
   "metadata": {},
   "source": [
    "### 40.7.1 What Changed at Each Step (Ch. 36 → Ch. 37 → Ch. 40)\n",
    "\n",
    "The accuracy numbers above are the empirical end of the story. The architectural progression is the conceptual one. Here is the same trajectory laid out side by side.\n",
    "\n",
    "| Aspect | Ch. 36: vanilla seq2seq | Ch. 37: + Bahdanau attention | Ch. 40: Transformer |\n",
    "|---|---|---|---|\n",
    "| **Encoder type** | RNN/GRU; final hidden state $h_T$ is the *only* summary | RNN/GRU; *all* hidden states $h_1,\\dots,h_T$ kept | Stack of self-attention + FFN blocks |\n",
    "| **Information bottleneck** | Single fixed-size vector $h_T \\in \\mathbb{R}^d$ | None — decoder reads any encoder state | None — decoder reads any encoder state |\n",
    "| **How decoder gets context** | Init hidden state from $h_T$ | Per-step soft alignment $\\alpha_{ij}$ over $h_j$ | Per-step *multi-head* attention over encoder output |\n",
    "| **Token-token interaction range** | $O(T)$ sequential steps | $O(T)$ sequential steps + 1-step attention | $O(1)$ — every pair in one matmul |\n",
    "| **Training parallelism (in time)** | Serial — must roll the RNN | Serial — must roll the RNN | **Parallel** — whole sequence in one forward pass |\n",
    "| **Position information** | Implicit in recurrence order | Implicit in recurrence order | **Explicit** sinusoidal PE (Sec. 40.2) |\n",
    "| **Length-15 accuracy (OOD)** | $\\approx$ 5% | $\\approx$ 55% | matches or beats Bahdanau, fully parallel |\n",
    "| **Compute scaling per layer** | $O(T \\cdot d^2)$ sequential | $O(T \\cdot d^2 + T^2 d)$ sequential | $O(T^2 d + T d^2)$ parallel |\n",
    "| **Direct ancestor of...** | nothing modern | every modern attention mechanism | BERT, GPT, T5, LLaMA, ViT, Whisper, AlphaFold, ... |\n",
    "\n",
    "The single biggest qualitative jump is the **bottleneck row**: removing the fixed-size summary vector. The single biggest *practical* jump is the **parallelism row**: that is the line item that turned $10^{6}$-parameter research toys into $10^{12}$-parameter foundation models."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aud40a8c0_8f625c",
   "metadata": {},
   "source": [
    "### 40.7.2 Why the Original Paper Needed a Warm-Up\n",
    "\n",
    "We trained with a simple cosine schedule because the toy task forgives anything. The Vaswani 2017 paper prescribes a *very specific* schedule:\n",
    "\n",
    "$$\n",
    "\\eta(t) \\;=\\; d_\\text{model}^{-1/2} \\cdot \\min\\!\\bigl(t^{-1/2},\\ t \\cdot t_\\text{warmup}^{-3/2}\\bigr).\n",
    "$$\n",
    "\n",
    "The formula has two phases joined at $t = t_\\text{warmup}$ (typically 4{,}000 steps):\n",
    "- **Warm-up** ($t \\le t_\\text{warmup}$): $\\eta$ grows *linearly* from 0.\n",
    "- **Decay** ($t > t_\\text{warmup}$): $\\eta$ falls as $1/\\sqrt{t}$.\n",
    "\n",
    "Why the slow start? Recall from Section 40.4.1 that **post-LN gradients grow with depth as $\\mathcal{O}(\\sqrt{N})$** (Xiong et al. 2020, arXiv:2002.04745). At step 0 the network's output is noise; combine that with the amplified gradient at the input and a moderate Adam step blows the parameters into a regime layer norm cannot rescue. Warm-up keeps the step size small until the activations have stabilised.\n",
    "\n",
    "The cell below plots both schedules so you can see the warm-up in action."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "aud40a8c1_fc380c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-30T15:40:38.481083Z",
     "iopub.status.busy": "2026-04-30T15:40:38.480951Z",
     "iopub.status.idle": "2026-04-30T15:40:38.571337Z",
     "shell.execute_reply": "2026-04-30T15:40:38.570873Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 750x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "d_m, t_warm, total = 96, 400, 3500\n",
    "steps = np.arange(1, total + 1)\n",
    "vaswani = (d_m ** -0.5) * np.minimum(steps ** -0.5, steps * (t_warm ** -1.5))\n",
    "# scale so the peak matches our 3e-3 cosine schedule for visual comparison\n",
    "vaswani = vaswani * (3e-3 / vaswani.max())\n",
    "cos = 3e-3 * 0.5 * (1 + np.cos(np.pi * steps / total))\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(7.5, 3))\n",
    "ax.plot(steps, vaswani, color='#4f46e5', label=f'Vaswani warm-up + sqrt-decay (t_warm={t_warm})')\n",
    "ax.plot(steps, cos,     color='#ea580c', label='Cosine (the schedule we used)')\n",
    "ax.axvline(t_warm, color='#888', linestyle='--', alpha=0.6)\n",
    "ax.text(t_warm + 30, 2.7e-3, 'end of warm-up', fontsize=9, color='#666')\n",
    "ax.set(xlabel='step', ylabel='learning rate', title='Two learning-rate schedules')\n",
    "ax.legend(); ax.grid(alpha=0.3); plt.tight_layout(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aud40a8c2_c9f70b",
   "metadata": {},
   "source": [
    "```{admonition} Modern practice\n",
    ":class: tip\n",
    "For pre-LN Transformers (i.e. essentially every model trained since 2019) you can drop the elaborate Vaswani schedule and use a short linear warm-up (a few hundred steps) followed by a cosine decay to a small final LR. NanoGPT, LLaMA pre-training, and most Hugging Face recipes follow this pattern.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51a98b53",
   "metadata": {},
   "source": [
    "## 40.8 Per-Layer, Per-Head Attention Visualisation\n",
    "\n",
    "The grid below shows every cross-attention head across every decoder layer for one input string. For string reversal you should see *anti-diagonal* patterns — exactly the same alignment that the Bahdanau model discovered, now produced by the cross-attention sub-layer of the decoder. Different heads at the same layer often specialise on different positional offsets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "cc2b6ad7",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-30T15:40:38.573570Z",
     "iopub.status.busy": "2026-04-30T15:40:38.573351Z",
     "iopub.status.idle": "2026-04-30T15:40:39.063557Z",
     "shell.execute_reply": "2026-04-30T15:40:39.063154Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 960x480 with 8 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "@torch.no_grad()\n",
    "def get_attn(model, src_str, target_str=None):\n",
    "    model.eval()\n",
    "    src = torch.tensor([encode(src_str)], device=device)\n",
    "    src_mask = (src != PAD).unsqueeze(1).unsqueeze(1).long()\n",
    "    enc_out = model.encode(src, src_mask)\n",
    "    if target_str is None:\n",
    "        target_str = transformer_predict(model, src_str)\n",
    "    tgt_in = torch.tensor([[SOS] + encode(target_str)], device=device)\n",
    "    T = tgt_in.size(1)\n",
    "    cm = causal_mask(T).to(device)\n",
    "    _, sas, cas = model.decode(tgt_in, enc_out, cm, src_mask, return_attn=True)\n",
    "    return src_str, target_str, [c.squeeze(0).cpu().numpy() for c in cas]\n",
    "\n",
    "# Static grid over (layer, head) for one input string.\n",
    "# (Was an ipywidgets slider pair; replaced for static-HTML compatibility.)\n",
    "src_str_in = 'attention'\n",
    "s, t, cas = get_attn(model, src_str_in)\n",
    "n_layers = len(cas)\n",
    "n_heads = cas[0].shape[0]\n",
    "fig, axes = plt.subplots(n_layers, n_heads, figsize=(2.4 * n_heads, 2.4 * n_layers), squeeze=False)\n",
    "for L in range(n_layers):\n",
    "    for h in range(n_heads):\n",
    "        ax = axes[L][h]\n",
    "        A = cas[L][h]\n",
    "        ax.imshow(A, cmap='viridis', vmin=0)\n",
    "        ax.set_xticks(range(len(s))); ax.set_xticklabels(list(s), fontsize=7)\n",
    "        ax.set_yticks(range(len(t))); ax.set_yticklabels(list(t), fontsize=7)\n",
    "        ax.set_title(f'layer {L}, head {h}', fontsize=9)\n",
    "plt.suptitle(f'All cross-attention heads for input \"{src_str_in}\" -> \"{t}\"', y=1.01)\n",
    "plt.tight_layout(); plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5114e179",
   "metadata": {},
   "source": [
    "Different heads pick up different facets of the alignment. With 4 heads and 2 decoder layers there are 8 distinct patterns to inspect. This kind of exploration is the entry point to **mechanistic interpretability** — the field that tries to read circuits inside large language models by following exactly these matrices."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d059828",
   "metadata": {},
   "source": [
    "## 40.9 Why This Architecture Won\n",
    "\n",
    "The 2017 paper's title — *Attention Is All You Need* — was a deliberate provocation. By the time of its publication every state-of-the-art translation model used attention layered *on top of* recurrence. The paper showed you could throw the recurrence away and *only* keep attention. The result was simpler, faster to train, and (eventually) the foundation of all modern LLMs.\n",
    "\n",
    "Three structural reasons it scaled:\n",
    "\n",
    "1. **Parallelism.** Section 40.6's encoder is a stack of matrix multiplications. GPUs eat that for breakfast — orders of magnitude more throughput than an RNN of the same width.\n",
    "2. **Stable optimisation.** Layer norm + residual + warm-up made it possible to train very deep stacks without exploding or vanishing. Today's GPT-style models routinely have 96+ layers.\n",
    "3. **Transferability.** The Transformer is general enough that the *same* architecture works for translation, summarisation, code, audio, vision (ViT, 2020), protein folding (AlphaFold 2, 2021), and reinforcement learning (Decision Transformer, 2021)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c2c43cbf",
   "metadata": {},
   "source": [
    "## 40.10 Bridge to Part XII — Pretraining and the LLM Era\n",
    "\n",
    "We have built a Transformer that learns one toy task. The 2018–present revolution comes from a simple observation: train the *same architecture* on a giant corpus to predict the next token, and you get a model that has implicitly learned grammar, facts, reasoning chains, and code patterns — all from the next-token loss alone. This is the **pretraining** paradigm of GPT (Radford et al. 2018) and BERT (Devlin et al. 2019).\n",
    "\n",
    "Future chapters will:\n",
    "\n",
    "- introduce **causal language modelling** (decoder-only Transformer, GPT-style);\n",
    "- introduce **masked language modelling** (encoder-only Transformer, BERT-style);\n",
    "- discuss **scaling laws** (Kaplan et al. 2020) and *why bigger really is better*;\n",
    "- build a tiny GPT (NanoGPT-style) and pretrain it on a small corpus;\n",
    "- close the loop on the *RNNs Are Not Dead* note from Chapter 32 by introducing modern linear-RNN / state-space hybrids (S4, Mamba, RWKV) — which, as Chapter 39 hinted, are mathematically equivalent to Schmidhuber's 1991 idea.\n",
    "\n",
    "*You now have the prerequisites to read essentially every paper published since 2017.* That is the pinnacle this course was aiming for."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aud40a9c0_760fd0",
   "metadata": {},
   "source": [
    "### 40.10.1 The Family Tree (2017 → today)\n",
    "\n",
    "Everything below was built by gluing the components of this chapter together in different ways. Memorising this tree is the fastest path to reading any 2018-2025 architecture paper without panic.\n",
    "\n",
    "| Year | Model | What is it? | Core idea (one line) | Reference |\n",
    "|---|---|---|---|---|\n",
    "| 2018 | **GPT-1** | Decoder-only Transformer | Pretrain on next-token prediction, fine-tune on tasks. | Radford, Narasimhan, Salimans, Sutskever 2018 |\n",
    "| 2018 | **BERT** | Encoder-only Transformer | Pretrain on masked language modelling for bidirectional features. | Devlin, Chang, Lee, Toutanova 2019 (arXiv:1810.04805) |\n",
    "| 2019 | **T5** | Full encoder-decoder Transformer | \"Everything is text-to-text.\" | Raffel et al. 2019 (arXiv:1910.10683) |\n",
    "| 2020 | **GPT-3** | 175 B-parameter decoder-only | Scaling + in-context learning. | Brown et al. 2020 (arXiv:2005.14165) |\n",
    "| 2020 | **ViT** | Encoder applied to image patches | A Transformer is all you need for vision too. | Dosovitskiy et al. 2020 (arXiv:2010.11929) |\n",
    "| 2021 | **AlphaFold 2** | Custom encoder (Evoformer) on residue / MSA pairs | Protein structure as a sequence-modelling problem. | Jumper et al. 2021, *Nature* |\n",
    "| 2021 | **Decision Transformer** | Decoder-only on (return, state, action) sequences | Reinforcement learning as conditional sequence modelling. | Chen et al. 2021 (arXiv:2106.01345) |\n",
    "| 2022 | **PaLM / Chinchilla** | $\\geq$ 70 B-parameter decoder-only | Compute-optimal scaling laws. | Hoffmann et al. 2022 (arXiv:2203.15556) |\n",
    "| 2022 | **FlashAttention** | Same architecture, IO-aware attention kernel | Tile attention to never materialise the $T\\times T$ matrix. | Dao, Fu, Ermon, Ré 2022 (arXiv:2205.14135) |\n",
    "| 2023 | **Mamba / S4 / RWKV** | *Not* attention — selective state-space models | The non-attention comeback you were promised in Ch. 32. | Gu, Dao 2023 (arXiv:2312.00752) |\n",
    "\n",
    "The ViT row is the most striking: **the same encoder block we built in Section 40.6, with no architectural change at all, is the state of the art for vision**. You just chop the image into $16\\times 16$ patches, flatten each patch, and feed the resulting sequence to the encoder. That generality — the same block works for text, audio, images, proteins, actions — is why \"the Transformer\" is now treated as the substrate of modern AI rather than as one architecture among many."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aud40a9c1_b6a26b",
   "metadata": {},
   "source": [
    "### 40.10.2 Concrete Forward-Pointers to Part XII\n",
    "\n",
    "The upcoming chapters will build on this foundation in a fixed order. Use the right column as a study checklist.\n",
    "\n",
    "| Part XII chapter | What you will build | Citation to read first |\n",
    "|---|---|---|\n",
    "| Causal language modelling | Decoder-only Transformer trained on raw text. | Radford et al. 2018 (GPT-1) |\n",
    "| Masked language modelling | Encoder-only Transformer with the cloze objective. | Devlin et al. 2019 (BERT, arXiv:1810.04805) |\n",
    "| Scaling laws | Empirical power-law $\\mathrm{loss}(N, D, C)$ relating params, data, compute. | Kaplan et al. 2020 (arXiv:2001.08361) |\n",
    "| Compute-optimal training | The Chinchilla correction: train smaller models on more data. | Hoffmann et al. 2022 (arXiv:2203.15556) |\n",
    "| NanoGPT-style pretraining | A real (small) GPT trained on a real corpus. | Karpathy's NanoGPT codebase |\n",
    "| Modern PE: RoPE | Replace `pe` with rotary embeddings on $Q$ and $K$. | Su et al. 2021 (arXiv:2104.09864) |\n",
    "| Long context: ALiBi | Replace PE with linear distance bias on attention scores. | Press, Smith, Lewis 2021 (arXiv:2108.12409) |\n",
    "| Efficient attention | FlashAttention kernel; the practical key to long context. | Dao et al. 2022 (arXiv:2205.14135) |\n",
    "| The non-attention comeback | Mamba / S4 / RWKV — closing the Ch. 32 loop. | Gu, Dao 2023 (arXiv:2312.00752) |\n",
    "\n",
    "```{admonition} If you read only one paper before Part XII\n",
    ":class: tip\n",
    "Read Vaswani et al. 2017 (arXiv:1706.03762) cover-to-cover. You now know every component in their Figure 1, every term in their training-loss equation, and every line of their pseudo-code. The whole point of this chapter was to make that paper trivially readable.\n",
    "```"
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    "## Exercises\n",
    "\n",
    "**Exercise 40.1.** Replace the sinusoidal positional encoding with a *learned* embedding (`nn.Embedding(max_len, d_model)`). Train and compare. Does the learned variant match? Does it generalise to lengths longer than training?\n",
    "\n",
    "**Exercise 40.2.** Remove the residual connection in `EncoderBlock` (replace `x + a` with just `a`). Re-train and report what happens to the loss. Verify the gradient norm at layer 0 is much smaller without the residual.\n",
    "\n",
    "**Exercise 40.3.** *(Pre-LN vs Post-LN.)* The original paper uses *post-LN*: `LN(x + Sublayer(x))`. Most modern Transformers use *pre-LN*: `x + Sublayer(LN(x))`. Implement both, compare training stability, and read Xiong et al. (2020) for the analysis.\n",
    "\n",
    "**Exercise 40.4.** Add a `temperature` argument to `transformer_predict` that divides logits before the argmax. With `temperature > 1` the predictions become more random. With `temperature → 0` they become greedy (current behaviour). Generate 5 different reversals of `\"hello\"` with `temperature = 0.8`.\n",
    "\n",
    "**Exercise 40.5.** Train the Transformer on `max_len = 4` only, then test it on length 12. How well does it generalise? Sinusoidal PE is supposed to allow this — does it?\n",
    "\n",
    "**Exercise 40.6.** *(Causal-only model.)* Drop the encoder entirely and feed `[src; SEP; tgt]` as one sequence to a single causal Transformer (the GPT-style architecture). Train on the reversal task. This is your first taste of a *decoder-only* model — the architecture that powers ChatGPT.\n",
    "\n",
    "**Exercise 40.7.** *(Read the paper.)* Now read *Attention Is All You Need* (arXiv:1706.03762) end-to-end. For every component in their Figure 1, point to the corresponding section of this chapter. Anything unclear? Bring it to the next class."
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