ML-Explainability/NLP/dissecting_gpt2.ipynb

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   "source": [
    "# Dissecting a GPT model\n",
    "\n",
    "Return to the [Castle](https://github.com/Nkluge-correa/TeenyTinyCastle)\n",
    "\n",
    "In this notebook, we will explore how a GPT-2 (Generative Pre-trained Transformer 2) model works. This walkthrough is based on the two-video series created by [Neel Nanda](https://www.neelnanda.io/) and serves as a great introduction to how GPT-style models work and the field of [mechanistic interpretability](https://www.neelnanda.io/mechanistic-interpretability/getting-started).\n",
    "\n",
    "- [What is a Transformer? (Transformer Walkthrough Part 1/2)](https://www.youtube.com/watch?v=bOYE6E8JrtU).\n",
    "- [Implementing GPT-2 From Scratch (Transformer Walkthrough Part 2/2)](https://www.youtube.com/watch?v=dsjUDacBw8o).\n",
    "\n",
    "For other resources related to building and interpreting transformer models, check these other tutorials:\n",
    "\n",
    "- [Building the original transformer architecture for sequence-to-sequence translation](https://github.com/Nkluge-correa/TeenyTinyCastle/blob/12eeb87cbb2abfa66c518c40785c47cdb6b62978/ML-Intro-Course/16_seuqnece_to_sequence.ipynb).\n",
    "- [Building a miniGPT model to generate text](https://github.com/Nkluge-correa/TeenyTinyCastle/blob/12eeb87cbb2abfa66c518c40785c47cdb6b62978/ML-Intro-Course/17_text_generation.ipynb).\n",
    "- [Interpret BERT models via integrated gradients](https://github.com/Nkluge-correa/TeenyTinyCastle/blob/12eeb87cbb2abfa66c518c40785c47cdb6b62978/ML-Explainability/NLP/gradient_explanations_BERT.ipynb).\n",
    "\n",
    "This implementation uses many utilities from the [`TransformerLens`](https://github.com/neelnanda-io/TransformerLens) library, so we will install some prerequisites before running anything."
   ]
  },
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   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
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     "text": [
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "  Running command git clone --filter=blob:none --quiet https://github.com/neelnanda-io/TransformerLens 'C:\\Users\\CWLINK\\AppData\\Local\\Temp\\pip-req-build-2p8me9mz'\n"
     ]
    }
   ],
   "source": [
    "# library for doing mechanistic interpretability of GPT-2 Style language models\n",
    "%pip install git+https://github.com/neelnanda-io/TransformerLens"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What does a GPT model do?\n",
    "\n",
    "Before implementing anything, we need a GPT model to work with. Let us load a small version of GPT-2 (117M) so we can gain some understanding of what process this model performs during a forward pass."
   ]
  },
  {
   "cell_type": "code",
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      "Using pad_token, but it is not set yet.\n"
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     "text": [
      "Loaded pretrained model gpt2-small into HookedTransformer\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "HookedTransformer(\n",
       "  (embed): Embed()\n",
       "  (hook_embed): HookPoint()\n",
       "  (pos_embed): PosEmbed()\n",
       "  (hook_pos_embed): HookPoint()\n",
       "  (blocks): ModuleList(\n",
       "    (0): TransformerBlock(\n",
       "      (ln1): LayerNorm(\n",
       "        (hook_scale): HookPoint()\n",
       "        (hook_normalized): HookPoint()\n",
       "      )\n",
       "      (ln2): LayerNorm(\n",
       "        (hook_scale): HookPoint()\n",
       "        (hook_normalized): HookPoint()\n",
       "      )\n",
       "      (attn): Attention(\n",
       "        (hook_k): HookPoint()\n",
       "        (hook_q): HookPoint()\n",
       "        (hook_v): HookPoint()\n",
       "        (hook_z): HookPoint()\n",
       "        (hook_attn_scores): HookPoint()\n",
       "        (hook_pattern): HookPoint()\n",
       "        (hook_result): HookPoint()\n",
       "      )\n",
       "      (mlp): MLP(\n",
       "        (hook_pre): HookPoint()\n",
       "        (hook_post): HookPoint()\n",
       "      )\n",
       "      (hook_q_input): HookPoint()\n",
       "      (hook_k_input): HookPoint()\n",
       "      (hook_v_input): HookPoint()\n",
       "      (hook_attn_out): HookPoint()\n",
       "      (hook_mlp_out): HookPoint()\n",
       "      (hook_resid_pre): HookPoint()\n",
       "      (hook_resid_mid): HookPoint()\n",
       "      (hook_resid_post): HookPoint()\n",
       "    )\n",
       "    (1): TransformerBlock(\n",
       "      (ln1): LayerNorm(\n",
       "        (hook_scale): HookPoint()\n",
       "        (hook_normalized): HookPoint()\n",
       "      )\n",
       "      (ln2): LayerNorm(\n",
       "        (hook_scale): HookPoint()\n",
       "        (hook_normalized): HookPoint()\n",
       "      )\n",
       "      (attn): Attention(\n",
       "        (hook_k): HookPoint()\n",
       "        (hook_q): HookPoint()\n",
       "        (hook_v): HookPoint()\n",
       "        (hook_z): HookPoint()\n",
       "        (hook_attn_scores): HookPoint()\n",
       "        (hook_pattern): HookPoint()\n",
       "        (hook_result): HookPoint()\n",
       "      )\n",
       "      (mlp): MLP(\n",
       "        (hook_pre): HookPoint()\n",
       "        (hook_post): HookPoint()\n",
       "      )\n",
       "      (hook_q_input): HookPoint()\n",
       "      (hook_k_input): HookPoint()\n",
       "      (hook_v_input): HookPoint()\n",
       "      (hook_attn_out): HookPoint()\n",
       "      (hook_mlp_out): HookPoint()\n",
       "      (hook_resid_pre): HookPoint()\n",
       "      (hook_resid_mid): HookPoint()\n",
       "      (hook_resid_post): HookPoint()\n",
       "    )\n",
       "    (2): TransformerBlock(\n",
       "      (ln1): LayerNorm(\n",
       "        (hook_scale): HookPoint()\n",
       "        (hook_normalized): HookPoint()\n",
       "      )\n",
       "      (ln2): LayerNorm(\n",
       "        (hook_scale): HookPoint()\n",
       "        (hook_normalized): HookPoint()\n",
       "      )\n",
       "      (attn): Attention(\n",
       "        (hook_k): HookPoint()\n",
       "        (hook_q): HookPoint()\n",
       "        (hook_v): HookPoint()\n",
       "        (hook_z): HookPoint()\n",
       "        (hook_attn_scores): HookPoint()\n",
       "        (hook_pattern): HookPoint()\n",
       "        (hook_result): HookPoint()\n",
       "      )\n",
       "      (mlp): MLP(\n",
       "        (hook_pre): HookPoint()\n",
       "        (hook_post): HookPoint()\n",
       "      )\n",
       "      (hook_q_input): HookPoint()\n",
       "      (hook_k_input): HookPoint()\n",
       "      (hook_v_input): HookPoint()\n",
       "      (hook_attn_out): HookPoint()\n",
       "      (hook_mlp_out): HookPoint()\n",
       "      (hook_resid_pre): HookPoint()\n",
       "      (hook_resid_mid): HookPoint()\n",
       "      (hook_resid_post): HookPoint()\n",
       "    )\n",
       "    (3): TransformerBlock(\n",
       "      (ln1): LayerNorm(\n",
       "        (hook_scale): HookPoint()\n",
       "        (hook_normalized): HookPoint()\n",
       "      )\n",
       "      (ln2): LayerNorm(\n",
       "        (hook_scale): HookPoint()\n",
       "        (hook_normalized): HookPoint()\n",
       "      )\n",
       "      (attn): Attention(\n",
       "        (hook_k): HookPoint()\n",
       "        (hook_q): HookPoint()\n",
       "        (hook_v): HookPoint()\n",
       "        (hook_z): HookPoint()\n",
       "        (hook_attn_scores): HookPoint()\n",
       "        (hook_pattern): HookPoint()\n",
       "        (hook_result): HookPoint()\n",
       "      )\n",
       "      (mlp): MLP(\n",
       "        (hook_pre): HookPoint()\n",
       "        (hook_post): HookPoint()\n",
       "      )\n",
       "      (hook_q_input): HookPoint()\n",
       "      (hook_k_input): HookPoint()\n",
       "      (hook_v_input): HookPoint()\n",
       "      (hook_attn_out): HookPoint()\n",
       "      (hook_mlp_out): HookPoint()\n",
       "      (hook_resid_pre): HookPoint()\n",
       "      (hook_resid_mid): HookPoint()\n",
       "      (hook_resid_post): HookPoint()\n",
       "    )\n",
       "    (4): TransformerBlock(\n",
       "      (ln1): LayerNorm(\n",
       "        (hook_scale): HookPoint()\n",
       "        (hook_normalized): HookPoint()\n",
       "      )\n",
       "      (ln2): LayerNorm(\n",
       "        (hook_scale): HookPoint()\n",
       "        (hook_normalized): HookPoint()\n",
       "      )\n",
       "      (attn): Attention(\n",
       "        (hook_k): HookPoint()\n",
       "        (hook_q): HookPoint()\n",
       "        (hook_v): HookPoint()\n",
       "        (hook_z): HookPoint()\n",
       "        (hook_attn_scores): HookPoint()\n",
       "        (hook_pattern): HookPoint()\n",
       "        (hook_result): HookPoint()\n",
       "      )\n",
       "      (mlp): MLP(\n",
       "        (hook_pre): HookPoint()\n",
       "        (hook_post): HookPoint()\n",
       "      )\n",
       "      (hook_q_input): HookPoint()\n",
       "      (hook_k_input): HookPoint()\n",
       "      (hook_v_input): HookPoint()\n",
       "      (hook_attn_out): HookPoint()\n",
       "      (hook_mlp_out): HookPoint()\n",
       "      (hook_resid_pre): HookPoint()\n",
       "      (hook_resid_mid): HookPoint()\n",
       "      (hook_resid_post): HookPoint()\n",
       "    )\n",
       "    (5): TransformerBlock(\n",
       "      (ln1): LayerNorm(\n",
       "        (hook_scale): HookPoint()\n",
       "        (hook_normalized): HookPoint()\n",
       "      )\n",
       "      (ln2): LayerNorm(\n",
       "        (hook_scale): HookPoint()\n",
       "        (hook_normalized): HookPoint()\n",
       "      )\n",
       "      (attn): Attention(\n",
       "        (hook_k): HookPoint()\n",
       "        (hook_q): HookPoint()\n",
       "        (hook_v): HookPoint()\n",
       "        (hook_z): HookPoint()\n",
       "        (hook_attn_scores): HookPoint()\n",
       "        (hook_pattern): HookPoint()\n",
       "        (hook_result): HookPoint()\n",
       "      )\n",
       "      (mlp): MLP(\n",
       "        (hook_pre): HookPoint()\n",
       "        (hook_post): HookPoint()\n",
       "      )\n",
       "      (hook_q_input): HookPoint()\n",
       "      (hook_k_input): HookPoint()\n",
       "      (hook_v_input): HookPoint()\n",
       "      (hook_attn_out): HookPoint()\n",
       "      (hook_mlp_out): HookPoint()\n",
       "      (hook_resid_pre): HookPoint()\n",
       "      (hook_resid_mid): HookPoint()\n",
       "      (hook_resid_post): HookPoint()\n",
       "    )\n",
       "    (6): TransformerBlock(\n",
       "      (ln1): LayerNorm(\n",
       "        (hook_scale): HookPoint()\n",
       "        (hook_normalized): HookPoint()\n",
       "      )\n",
       "      (ln2): LayerNorm(\n",
       "        (hook_scale): HookPoint()\n",
       "        (hook_normalized): HookPoint()\n",
       "      )\n",
       "      (attn): Attention(\n",
       "        (hook_k): HookPoint()\n",
       "        (hook_q): HookPoint()\n",
       "        (hook_v): HookPoint()\n",
       "        (hook_z): HookPoint()\n",
       "        (hook_attn_scores): HookPoint()\n",
       "        (hook_pattern): HookPoint()\n",
       "        (hook_result): HookPoint()\n",
       "      )\n",
       "      (mlp): MLP(\n",
       "        (hook_pre): HookPoint()\n",
       "        (hook_post): HookPoint()\n",
       "      )\n",
       "      (hook_q_input): HookPoint()\n",
       "      (hook_k_input): HookPoint()\n",
       "      (hook_v_input): HookPoint()\n",
       "      (hook_attn_out): HookPoint()\n",
       "      (hook_mlp_out): HookPoint()\n",
       "      (hook_resid_pre): HookPoint()\n",
       "      (hook_resid_mid): HookPoint()\n",
       "      (hook_resid_post): HookPoint()\n",
       "    )\n",
       "    (7): TransformerBlock(\n",
       "      (ln1): LayerNorm(\n",
       "        (hook_scale): HookPoint()\n",
       "        (hook_normalized): HookPoint()\n",
       "      )\n",
       "      (ln2): LayerNorm(\n",
       "        (hook_scale): HookPoint()\n",
       "        (hook_normalized): HookPoint()\n",
       "      )\n",
       "      (attn): Attention(\n",
       "        (hook_k): HookPoint()\n",
       "        (hook_q): HookPoint()\n",
       "        (hook_v): HookPoint()\n",
       "        (hook_z): HookPoint()\n",
       "        (hook_attn_scores): HookPoint()\n",
       "        (hook_pattern): HookPoint()\n",
       "        (hook_result): HookPoint()\n",
       "      )\n",
       "      (mlp): MLP(\n",
       "        (hook_pre): HookPoint()\n",
       "        (hook_post): HookPoint()\n",
       "      )\n",
       "      (hook_q_input): HookPoint()\n",
       "      (hook_k_input): HookPoint()\n",
       "      (hook_v_input): HookPoint()\n",
       "      (hook_attn_out): HookPoint()\n",
       "      (hook_mlp_out): HookPoint()\n",
       "      (hook_resid_pre): HookPoint()\n",
       "      (hook_resid_mid): HookPoint()\n",
       "      (hook_resid_post): HookPoint()\n",
       "    )\n",
       "    (8): TransformerBlock(\n",
       "      (ln1): LayerNorm(\n",
       "        (hook_scale): HookPoint()\n",
       "        (hook_normalized): HookPoint()\n",
       "      )\n",
       "      (ln2): LayerNorm(\n",
       "        (hook_scale): HookPoint()\n",
       "        (hook_normalized): HookPoint()\n",
       "      )\n",
       "      (attn): Attention(\n",
       "        (hook_k): HookPoint()\n",
       "        (hook_q): HookPoint()\n",
       "        (hook_v): HookPoint()\n",
       "        (hook_z): HookPoint()\n",
       "        (hook_attn_scores): HookPoint()\n",
       "        (hook_pattern): HookPoint()\n",
       "        (hook_result): HookPoint()\n",
       "      )\n",
       "      (mlp): MLP(\n",
       "        (hook_pre): HookPoint()\n",
       "        (hook_post): HookPoint()\n",
       "      )\n",
       "      (hook_q_input): HookPoint()\n",
       "      (hook_k_input): HookPoint()\n",
       "      (hook_v_input): HookPoint()\n",
       "      (hook_attn_out): HookPoint()\n",
       "      (hook_mlp_out): HookPoint()\n",
       "      (hook_resid_pre): HookPoint()\n",
       "      (hook_resid_mid): HookPoint()\n",
       "      (hook_resid_post): HookPoint()\n",
       "    )\n",
       "    (9): TransformerBlock(\n",
       "      (ln1): LayerNorm(\n",
       "        (hook_scale): HookPoint()\n",
       "        (hook_normalized): HookPoint()\n",
       "      )\n",
       "      (ln2): LayerNorm(\n",
       "        (hook_scale): HookPoint()\n",
       "        (hook_normalized): HookPoint()\n",
       "      )\n",
       "      (attn): Attention(\n",
       "        (hook_k): HookPoint()\n",
       "        (hook_q): HookPoint()\n",
       "        (hook_v): HookPoint()\n",
       "        (hook_z): HookPoint()\n",
       "        (hook_attn_scores): HookPoint()\n",
       "        (hook_pattern): HookPoint()\n",
       "        (hook_result): HookPoint()\n",
       "      )\n",
       "      (mlp): MLP(\n",
       "        (hook_pre): HookPoint()\n",
       "        (hook_post): HookPoint()\n",
       "      )\n",
       "      (hook_q_input): HookPoint()\n",
       "      (hook_k_input): HookPoint()\n",
       "      (hook_v_input): HookPoint()\n",
       "      (hook_attn_out): HookPoint()\n",
       "      (hook_mlp_out): HookPoint()\n",
       "      (hook_resid_pre): HookPoint()\n",
       "      (hook_resid_mid): HookPoint()\n",
       "      (hook_resid_post): HookPoint()\n",
       "    )\n",
       "    (10): TransformerBlock(\n",
       "      (ln1): LayerNorm(\n",
       "        (hook_scale): HookPoint()\n",
       "        (hook_normalized): HookPoint()\n",
       "      )\n",
       "      (ln2): LayerNorm(\n",
       "        (hook_scale): HookPoint()\n",
       "        (hook_normalized): HookPoint()\n",
       "      )\n",
       "      (attn): Attention(\n",
       "        (hook_k): HookPoint()\n",
       "        (hook_q): HookPoint()\n",
       "        (hook_v): HookPoint()\n",
       "        (hook_z): HookPoint()\n",
       "        (hook_attn_scores): HookPoint()\n",
       "        (hook_pattern): HookPoint()\n",
       "        (hook_result): HookPoint()\n",
       "      )\n",
       "      (mlp): MLP(\n",
       "        (hook_pre): HookPoint()\n",
       "        (hook_post): HookPoint()\n",
       "      )\n",
       "      (hook_q_input): HookPoint()\n",
       "      (hook_k_input): HookPoint()\n",
       "      (hook_v_input): HookPoint()\n",
       "      (hook_attn_out): HookPoint()\n",
       "      (hook_mlp_out): HookPoint()\n",
       "      (hook_resid_pre): HookPoint()\n",
       "      (hook_resid_mid): HookPoint()\n",
       "      (hook_resid_post): HookPoint()\n",
       "    )\n",
       "    (11): TransformerBlock(\n",
       "      (ln1): LayerNorm(\n",
       "        (hook_scale): HookPoint()\n",
       "        (hook_normalized): HookPoint()\n",
       "      )\n",
       "      (ln2): LayerNorm(\n",
       "        (hook_scale): HookPoint()\n",
       "        (hook_normalized): HookPoint()\n",
       "      )\n",
       "      (attn): Attention(\n",
       "        (hook_k): HookPoint()\n",
       "        (hook_q): HookPoint()\n",
       "        (hook_v): HookPoint()\n",
       "        (hook_z): HookPoint()\n",
       "        (hook_attn_scores): HookPoint()\n",
       "        (hook_pattern): HookPoint()\n",
       "        (hook_result): HookPoint()\n",
       "      )\n",
       "      (mlp): MLP(\n",
       "        (hook_pre): HookPoint()\n",
       "        (hook_post): HookPoint()\n",
       "      )\n",
       "      (hook_q_input): HookPoint()\n",
       "      (hook_k_input): HookPoint()\n",
       "      (hook_v_input): HookPoint()\n",
       "      (hook_attn_out): HookPoint()\n",
       "      (hook_mlp_out): HookPoint()\n",
       "      (hook_resid_pre): HookPoint()\n",
       "      (hook_resid_mid): HookPoint()\n",
       "      (hook_resid_post): HookPoint()\n",
       "    )\n",
       "  )\n",
       "  (ln_final): LayerNorm(\n",
       "    (hook_scale): HookPoint()\n",
       "    (hook_normalized): HookPoint()\n",
       "  )\n",
       "  (unembed): Unembed()\n",
       ")"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "device(type='cuda')"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import torch\n",
    "from transformer_lens import HookedTransformer\n",
    "\n",
    "gpt2 = HookedTransformer.from_pretrained(\"gpt2-small\", \n",
    "                                        fold_ln=False, \n",
    "                                        center_unembed=False, \n",
    "                                        center_writing_weights=False)\n",
    "\n",
    "device = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")\n",
    "\n",
    "display(gpt2, device)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "GPT-2 is a _decoder-only transformer._\n",
    "\n",
    "A `decoder-only` transformer is a type of transformer architecture that only contains the decoder part of the transformer model without the encoder part. In a [typical transformer architecture](https://arxiv.org/abs/1706.03762), the encoder processes an input sequence and generates a representation of that sequence in the form of a hidden/latent state. The decoder then takes this representation and generates an output based on it.\n",
    "\n",
    "A decoder-only transformer takes a fixed-length vector (usually called a \"_context vector_\") as input and generates an output sequence based on it. In a `decoder-only` transformer, this context is the prompt we feed our model. In other words, if you feed in a sentence, the model will generate a probability distribution over tokens, and you can repeatedly sample from this to generate text.\n",
    "\n",
    "Formally, you feed in a sequence of length $N$, then sample from the probability distribution over the $N+1-th$ word, use this to construct a new sequence of length $N+1$, then feed this new sequence into the model to get a probability distribution over the $N+2-th$ word, and so on.\n",
    "\n",
    "$$sample_t = The \\rightarrow_{model} The\\;cat$$\n",
    "$$sample_{t+1} = The\\;cat \\rightarrow_{model} The\\;cat\\;sat$$\n",
    "$$sample_{t+2} = The\\;cat\\;sat \\rightarrow_{model} The\\;cat\\;sat\\;on$$\n",
    "$$sample_{t+3} = The\\;cat\\;sat\\;on \\rightarrow_{model} The\\;cat\\;sat\\;on\\;the$$\n",
    "$$sample_{t+4} = The\\;cat\\;sat\\;on\\;the \\rightarrow_{model} The\\;cat\\;sat\\;on\\;the\\;floor.$$\n",
    "\n",
    "A decoder-only transformer like GPT-2 is trained on a large corpus of text data using a `causal language modeling` objective. \n",
    "\n",
    "> Causal language modeling is a type of language modeling where a model is trained to predict the next word in a sequence given the previous words, with the constraint that the model can only use information from the past, not the future. More precisely, we only allow the model to perform attention on the left side of the sentence. Thus, the prediction of what comes after token $5$ is only a function of the first $5$ tokens, not of token $6$. This is why we call such models autoregressive (they predict the future only using past information). Their objective during training is to predict the next token in a sequence given the previous tokens.\n",
    "\n",
    "<img src=\"https://jalammar.github.io/images/xlnet/gpt-2-autoregression-2.gif\" width=\"600\"/>\n",
    "\n",
    "Source: [The Illustrated GPT-2 (Visualizing Transformer Language Models)](https://jalammar.github.io/illustrated-gpt2/).\n",
    "\n",
    "Transformers are _sequence modeling engines_ that depend on a lot of linear algebra. They are (basically) a stack of `[linear + non-linear + linear]` operations, enclosed in blocks (`block = [attention, MLP, linear mapping]`), that read and write in a continuous stream of residual information.\n",
    "\n",
    "<img src=\"https://imgs.xkcd.com/comics/machine_learning_2x.png\" width=\"400\"/>\n",
    "\n",
    "Source: [xkcd](https://xkcd.com/1838/).\n",
    "\n",
    "But they need something friendly to perform linear algebra on. Not words, but `vectors`. How do we turn words into vectors? We `tokenize` the words and pass them by an `embedding layer`.\n",
    "\n",
    "To learn more about embedding layers:\n",
    "\n",
    "- [Check this tutorial on how to work with embedding layers and perform basic interpretability analysis](https://github.com/Nkluge-correa/TeenyTinyCastle/blob/12eeb87cbb2abfa66c518c40785c47cdb6b62978/ML-Explainability/NLP/investigating_word_embeddings.ipynb).\n",
    "- [Check this tutorial on how to train a word2vec model](https://github.com/Nkluge-correa/TeenyTinyCastle/blob/12eeb87cbb2abfa66c518c40785c47cdb6b62978/ML-Explainability/NLP/word2vec.ipynb).\n",
    "\n",
    "All the other transformer models we trained in this repository use a tokenization scheme that creates a vocabulary of words (like a dictionary). However, the lack of punctuation and many useful symbols present in natural language make this tokenization scheme brittle. GPT-2, and many other large language models, use a tokenization scheme called `Byte-Pair` encodings, which allows the model to tokenize \"chunks\" of words by their 256 ASCII combinations, where common pairs of tokens are merged into a new single token. For example, the word \"the,\" comprised of the ASCII characters `116 104 101`, quickly becomes a singular token in this schema since the word \"the\" always appears in English.\n",
    "\n",
    "The GPT-2 tokenizer has a vocabulary formed out of 50257 tokens corresponding to words, chunks of words, symbols, numbers, etc. Let us see some of these tokens."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of parameters in the reference model:  163087441\n",
      "Number of tokens in the reference model tokenizer:  50257\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[('Ġa', 257),\n",
       " ('he', 258),\n",
       " ('in', 259),\n",
       " ('re', 260),\n",
       " ('on', 261),\n",
       " ('Ġthe', 262),\n",
       " ('er', 263),\n",
       " ('Ġs', 264),\n",
       " ('at', 265),\n",
       " ('Ġw', 266)]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[('Ġ(/', 50247),\n",
       " ('âĢ¦.\"', 50248),\n",
       " ('Compar', 50249),\n",
       " ('Ġamplification', 50250),\n",
       " ('ominated', 50251),\n",
       " ('Ġregress', 50252),\n",
       " ('ĠCollider', 50253),\n",
       " ('Ġinformants', 50254),\n",
       " ('Ġgazed', 50255),\n",
       " ('<|endoftext|>', 50256)]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# number of parameters in gpt2\n",
    "print(\"Number of parameters in the reference model: \", sum(p.numel() for p in gpt2.parameters()))\n",
    "\n",
    "# numebr of tokens in gpt2 tokenizer\n",
    "print(\"Number of tokens in the reference model tokenizer: \", len(list(gpt2.tokenizer.vocab.items())))\n",
    "\n",
    "sorted_tokens = sorted(list(gpt2.tokenizer.vocab.items()), key=lambda n:n[1])\n",
    "\n",
    "# display tokens 257 to 267\n",
    "display(sorted_tokens[257:267])\n",
    "\n",
    "# display last 10 tokens\n",
    "display(sorted_tokens[-10:])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Tokens that start with the letter `Ġ` represent that this token starts with a space. That means that \"and\" and \" and\" are different tokens. Many tokens are weird, and explaining \"why\" the tokenizer chooses to add the token \" gazed\" as a singular token is hard. But it did. The only explanation is that these are the most common bite pairs found in the training corpus.\n",
    "\n",
    "You can use the `to_tokens` and `to_str_tokens` method from the `transformer_lens` library to explore how words are tokenized. You will see that spaces and capitalization matters in tokenization.\n",
    "\n",
    "> Note: `prepend_bos=False` prevents the `bos` token (beginning of the sentence token = 50256) from being appended at every sentence's beginning."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['Cat']\n",
      "'Cat' = token  21979\n",
      "[' Cat']\n",
      "' Cat' = token  5181\n",
      "[' cat']\n",
      "' cat' = token  3797\n",
      "['cat']\n",
      "'cat' = token  9246\n",
      "'8248247+939-100/70' =  ['8', '248', '247', '+', '9', '39', '-', '100', '/', '70']\n"
     ]
    }
   ],
   "source": [
    "# many types of cats\n",
    "print(gpt2.to_str_tokens(\"Cat\", prepend_bos=False))\n",
    "print(\"'Cat' = token \", gpt2.to_tokens(\"Cat\", prepend_bos=False)[0][0].cpu().numpy())\n",
    "print(gpt2.to_str_tokens(\" Cat\", prepend_bos=False))\n",
    "print(\"' Cat' = token \", gpt2.to_tokens(\" Cat\", prepend_bos=False)[0][0].cpu().numpy())\n",
    "print(gpt2.to_str_tokens(\" cat\", prepend_bos=False))\n",
    "print(\"' cat' = token \", gpt2.to_tokens(\" cat\", prepend_bos=False)[0][0].cpu().numpy())\n",
    "print(gpt2.to_str_tokens(\"cat\", prepend_bos=False))\n",
    "print(\"'cat' = token \", gpt2.to_tokens(\"cat\", prepend_bos=False)[0][0].cpu().numpy())\n",
    "\n",
    "# and much more crazy stuff\n",
    "print(\"'8248247+939-100/70' = \",gpt2.to_str_tokens(\"8248247+939-100/70\", prepend_bos=False))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The tokenizer is a look-up table that turns words and sub-words into integers. These integers are then turned into vectors by an embedding layer. This embedding layer is also a kind of look-up table, where each token in our vocabulary corresponds to a specific vector representation of dimensionality equal to the dimensionality of the embedding layer. GPT-2 works with $d_{embeddings} = 768$, and the ouput of embedding layer is shape $[d_{batch}, d_{length}, d_{dimensionality}]$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sentence:  The cat sat on the\n",
      "Tokenized Sentence:  tensor([[ 464, 3797, 3332,  319,  262]], device='cuda:0')\n",
      "String Tokens:  ['The', ' cat', ' sat', ' on', ' the']\n",
      "Sentence Embedding Shape:  torch.Size([1, 5, 768])\n"
     ]
    }
   ],
   "source": [
    "sentence = \"The cat sat on the\"\n",
    "print(\"Sentence: \", sentence)\n",
    "\n",
    "# convert the sentence to tokens\n",
    "sentence_tokens = gpt2.to_tokens(sentence, prepend_bos=False)\n",
    "print(\"Tokenized Sentence: \", sentence_tokens)\n",
    "\n",
    "# convert the tokens back to sentence\n",
    "string_tokens = gpt2.to_str_tokens(sentence, prepend_bos=False)\n",
    "print(\"String Tokens: \", string_tokens)\n",
    "\n",
    "# convert the tokenks to embedding vectors\n",
    "sentence_embed = gpt2.embed(sentence_tokens)\n",
    "print(\"Sentence Embedding Shape: \", sentence_embed.shape)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given this input, the goal of the model is to output a probability distribution over the next tokens for every prefix of the sequence (a $7$ token sequence generates $7$ next token predictions).\n",
    "\n",
    "The initial embedding matrix is passed by a series of transformer layers (GPT-2 small has 12 layers), which are made of multi-head attention layers and MLP layers (plus some normalization and skip connections). The final output of this process is a vector of logits, i.e.,  a vector of unnormalized scores over the vocabulary (50257 tokens).\n",
    "\n",
    "This vector is then normalized using a softmax function that turns the logits into a probability distribution (a positive distribution that sums up to 1):\n",
    "\n",
    "$$softmax(\\mathbf{x})_i = \\frac{e^{x_i}}{\\sum_{j=1}^{n} e^{x_j}}$$\n",
    "\n",
    "If we want to sample from this distribution greedily, we select the next token as the one with the highest probability score.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Logits Shape torch.Size([1, 5, 50257])\n",
      "Softmax Output torch.Size([1, 5, 50257])\n"
     ]
    }
   ],
   "source": [
    "# pytorch forces us to declare the device on which we want to perform the operations\n",
    "sentence_tokens = sentence_tokens.to(device)\n",
    "\n",
    "# pass the sentence through gpt2\n",
    "logits, cache = gpt2.run_with_cache(sentence_tokens)\n",
    "\n",
    "# print the logits shape (batch_size, sequence_length, vocab_size)\n",
    "print(\"Logits Shape\",logits.shape)\n",
    "\n",
    "# perform softmax on the logits to get the probabilities\n",
    "probs = torch.nn.functional.softmax(logits,dim=-1)\n",
    "\n",
    "# print the probabilities shape (batch_size, sequence_length, vocab_size)\n",
    "print(\"Softmax Output\", probs.shape)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see now that the model generated a `next_token_prediction` for every token in the seed sentence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Current token:  The\n",
      "Probability:  0.013599105179309845\n",
      "Next token with max probability:  ('Ċ', 198)\n",
      "\n",
      "Current token:   cat\n",
      "Probability:  0.1103605255484581\n",
      "Next token with max probability:  ('Ġwas', 373)\n",
      "\n",
      "Current token:   sat\n",
      "Probability:  0.223967045545578\n",
      "Next token with max probability:  ('Ġon', 319)\n",
      "\n",
      "Current token:   on\n",
      "Probability:  0.45369622111320496\n",
      "Next token with max probability:  ('Ġthe', 262)\n",
      "\n",
      "Current token:   the\n",
      "Probability:  0.07635769993066788\n",
      "Next token with max probability:  ('Ġfloor', 4314)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for i in range(probs.shape[1]):\n",
    "    print(\"Current token: \", string_tokens[i])\n",
    "    print(\"Probability: \", probs[0][i].max().item())\n",
    "    print(\"Next token with max probability: \", sorted_tokens[probs[0][i].argmax().item()])\n",
    "    print(\"\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us see what \"_other things_\" our cat could have seated on according to GPT-2 by sampling the first $k$ most likely next tokens for the final token in our seed sentence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Next token (top 1):  ('Ġfloor', 4314)\n",
      "Probability:  0.07635769993066788\n",
      "\n",
      "Next token (top 2):  ('Ġbed', 3996)\n",
      "Probability:  0.06527633219957352\n",
      "\n",
      "Next token (top 3):  ('Ġcouch', 18507)\n",
      "Probability:  0.0540718249976635\n",
      "\n",
      "Next token (top 4):  ('Ġground', 2323)\n",
      "Probability:  0.05208930745720863\n",
      "\n",
      "Next token (top 5):  ('Ġedge', 5743)\n",
      "Probability:  0.047842156141996384\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# get the top k values and their corresponding indices \n",
    "topk_values, topk_indices = torch.topk(probs[0][-1], k=5)\n",
    "\n",
    "# print the top k values and their corresponding indices\n",
    "for i in range(topk_values.shape[0]):\n",
    "    print(f\"Next token (top {i+1}): \", sorted_tokens[topk_indices[i].item()])\n",
    "    print(\"Probability: \", topk_values[i].item())\n",
    "    print(\"\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sentence at t:  The cat sat on the\n",
      "Sentence at t + 1:  The cat sat on the floor\n",
      "Sentence at t + 2:  The cat sat on the floor,\n",
      "Sentence at t + 3:  The cat sat on the floor, and\n",
      "Sentence at t + 4:  The cat sat on the floor, and the\n",
      "Sentence at t + 5:  The cat sat on the floor, and the cat\n",
      "Sentence at t + 6:  The cat sat on the floor, and the cat was\n",
      "Sentence at t + 7:  The cat sat on the floor, and the cat was still\n",
      "Sentence at t + 8:  The cat sat on the floor, and the cat was still asleep\n",
      "Sentence at t + 9:  The cat sat on the floor, and the cat was still asleep.\n",
      "Sentence at t + 10:  The cat sat on the floor, and the cat was still asleep.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "sentence = \"The cat sat on the\"\n",
    "print(\"Sentence at t: \", sentence)\n",
    "\n",
    "sentence_tokens = gpt2.to_tokens(sentence, prepend_bos=False).to(device)\n",
    "\n",
    "for i in range(10):\n",
    "\n",
    "    # pass the sentence through the reference model and get the logits\n",
    "    logits = gpt2(sentence_tokens)\n",
    "\n",
    "    # perform softmax on the logits to get the probabilities\n",
    "    probs = torch.nn.functional.softmax(logits,dim=-1)\n",
    "\n",
    "    # get the next token\n",
    "    next_token = probs[0, -1].argmax(dim=-1)\n",
    "\n",
    "    # append the next token to the sentence\n",
    "    sentence_tokens = torch.cat([sentence_tokens, next_token[None, None]], dim=-1)\n",
    "    \n",
    "    # convert the next token to string\n",
    "    next_char = gpt2.to_string(next_token)\n",
    "\n",
    "    # append the next token to the sentence\n",
    "    sentence = sentence + next_char\n",
    "    \n",
    "    print(f\"Sentence at t + {i+1}: \", sentence)\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we know:\n",
    "\n",
    "1. What are decoder-only transformers, and what is their main function (_sequence modeling_).\n",
    "2. How transformers encode language via tokenization.\n",
    "3. How tokens are converted into embeddings. Embeddings are a matrix/look-up table of shape $[d_{dimensionality}, d_{vocabulary}]$\n",
    "4. The output of the embedding layer is of shape $[d_{batch}, d_{length}, d_{dimensionality}]$\n",
    "4. That a GPT-style model is built of decoder blocks. Every block has a Multihead attention layer and an MLP layer combined (plus some extra stuff).\n",
    "5. Decoder-only transformers are trained via causal language modeling (they can only look at the past).\n",
    "6. They output a prediction for every prefix in their input sequence.\n",
    "7. These predictions are the final output of the model. A vector of logits that can be normalized (via softmax) into a probability distribution over $d_{vocabulary}$ of the model.\n",
    "7. Sampling from this distribution in an iterated fashion allows us to generate text.\n",
    "\n",
    "Let us take a look into what happens inside the decoder blocks of a GPT-style model.\n",
    "\n",
    "## Dissecting Attention Layers\n",
    "\n",
    "> Note: this explanation is based on the article \"_[A Mathematical Framework for Transformer Circuits](https://transformer-circuits.pub/2021/framework/index.html)_\", by [Anthropic](https://www.anthropic.com/).\n",
    "\n",
    "The transformer architecture can be taught at a high level as a sequence of transformer layers. Each layer has a fixed number of `attention heads` ($h_1$, $h_2$,...$h_n$) that are concatenated into a multi-head attention layer ($H_k$). Each layer has a multi-head attention layer and an MLP (multi-layer perceptron, $M_k$) ($Layer_k = (H_k, M_k)$), with each one performing operations on the residual stream. This residual stream is the central object of the transformer. The residual stream has a constant shape $[d_{batch}, d_{length}, d_{dimensionality}]$.\n",
    "\n",
    "Each one of the blocks in a transformer can be represented by the diagram below.\n",
    "\n",
    "> Note: Tokenization + Embedding (and positional embedding) only happen before the first transformer block. `Positional embedding` is an extra embedding layer used to give positional information to the sequence. We can input temporal information into our sequence since attention is permutation invariant and position agnostic. Positional information helps the model figure out that words are close to each other, which usually implies that they are relevant to each other.\n",
    "\n",
    "<img src=\"https://www.researchgate.net/publication/334288604/figure/fig1/AS:778232232148992@1562556431066/The-Transformer-encoder-structure_W640.jpg\" width=\"200\"/>\n",
    "\n",
    "Source: [Multi-lingual Intent Detection and Slot Filling in a Joint BERT-based Model](https://www.researchgate.net/publication/334288604_Multi-lingual_Intent_Detection_and_Slot_Filling_in_a_Joint_BERT-based_Model).\n",
    "\n",
    "Thus:\n",
    "\n",
    "1. The incomming residual stream ($[d_{batch}, d_{length}, d_{dimensionality}]$) passes by the MultiHead attention layer.\n",
    "2. Each attention head performs self-attention on the input in parallel, adding their results to the output.\n",
    "3. This output is then normalized by a layer norm.\n",
    "4. The MLP layer passes the normalized output.\n",
    "5. The output of the MLP layer is added to the output of the MultiHead attention layer, normalized, and passed through the next layer in the original shape of the residual stream ($[d_{batch}, d_{length}, d_{dimensionality}]$).\n",
    "6. Both the MLP and MultiHead attention layers read and write to the residual stream.\n",
    "\n",
    "We already talked about tokenization and embedding, so let us talk about attention.\n",
    "\n",
    "### `Attention`\n",
    "\n",
    "Attention (we are referring to self-attention) moves information from prior positions in the sequence to the current token. The word \"sat\" should be strongly tied to \"cat\" in our example sentence, and attention carries this information from token-to-token. Attention layers are the only bit of a transformer that moves information between positions. Attention heads act independently and additively, adding their outputs to the stream. This process is linear (addition and multiplication).\n",
    "\n",
    "Attention has three significant components:\n",
    "\n",
    "- Query: The query is a representation of the current token used to score against all the other tokens (_what we have at our current position_).\n",
    "- Key: Key vectors are what we match our query against (_what does the sequence have to offer_).\n",
    "- Value: Value vectors are actual word representations (like the word embeddings before the first attention block), we add the attention scores to each of these values to create a new representation of the current word (_what should you pay attention to at the end_).\n",
    "\n",
    "But the general \"_gist_\" of attention is this:\n",
    "\n",
    "Given our three input matrices: the query matrix ($Q$), the key matrix ($K$), and the value matrix ($V$), we compute a weighted sum of the value matrix ($V$) based on the similarity between the queries ($Q$) and the keys ($K$).\n",
    "\n",
    "The query, key, and value matrices are typically derived from the input data by applying a linear transformation to the input features. The dimensions of the matrices depend on the input size and the number of attention heads the model uses.\n",
    "\n",
    "First, we compute the dot product of the query and key matrices, which produce a matrix of dot products. The dot products are then divided by the square root of the dimensionality of the key matrix to ensure that the attention weights are under the same scale. Finally, the dot products are passed through a softmax function to produce a matrix of attention weights that sum to $1$.\n",
    "\n",
    "The attention weights are then used to weight the value matrix ($V$) and compute a weighted sum of the values, which is then used as the output of the attention head. This process is repeated for each attention head, and the output of all the attention heads is concatenated to produce the final output.\n",
    "\n",
    "$$ Attention(Q, K, V) = softmax(\\frac{QK^T}{\\sqrt{d_k}})V $$\n",
    "\n",
    "Where:\n",
    "- $Q$ is the query matrix.\n",
    "- $K$ is the key matrix.\n",
    "- $V$ is the value matrix.\n",
    "- $d_k$ is the dimensionality of the key matrix.\n",
    "\n",
    "### `Multi-Layer Perceptron`\n",
    "\n",
    "The MLP layers are just a standard neural network, with a singular hidden layer and a nonlinear activation function (usually [`GELU`](https://paperswithcode.com/method/gelu#:~:text=The%20Gaussian%20Error%20Linear%20Unit,x%201%20x%20%3E%200%20)). They are followed by a linear mapping layer that projects the output of the MLP back to the dimensionality of the residual stream (MLPs usually have a higher dimensionality than that of the residual stream) ($linear\\;map \\rightarrow non-linearity \\rightarrow linear\\;map$).\n",
    "\n",
    "The general intuition behind the MultiHead attention/MLP/linear projection sandwich is that after attention has moved relevant information to a single position in the residual stream, MLPs perform computation on the stream. \n",
    "\n",
    "This process is repeated until the last layer, where the residual stream is finally projected into a vector of logits representing the model's confidence distribution for next token predictions over $d_{vocabulary}$.\n",
    "\n",
    "### `LayerNorm`\n",
    "\n",
    "Layernorm is the normalization applied at the start of each layer (MLP, MultiHead attention, and before the unembedding) to convert each input vector to mean zero and variance 1.\n",
    "\n",
    "### `Activations` vs `Parameters`\n",
    "\n",
    "`Activations` are temporary numbers calculated during a forward pass that are input functions. Attention scores and patterns are examples of activations. The residual stream can be thought of as one flowing stream of activations.\n",
    "\n",
    "> Note: the `run_with_cache` method (from `transformer_lens`) allows us to store all information associated with a forward pass in a transformer model, which is quite useful for interpretability research. With it, we can access all matrices that compose the transformer network and monitor the residual stream (the residual flow of information that travels through the forward pass) as it progresses."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "hook_embed                     (1, 5, 768)\n",
      "hook_pos_embed                 (1, 5, 768)\n",
      "blocks.0.hook_resid_pre        (1, 5, 768)\n",
      "blocks.0.ln1.hook_scale        (1, 5, 1)\n",
      "blocks.0.ln1.hook_normalized   (1, 5, 768)\n",
      "blocks.0.attn.hook_q           (1, 5, 12, 64)\n",
      "blocks.0.attn.hook_k           (1, 5, 12, 64)\n",
      "blocks.0.attn.hook_v           (1, 5, 12, 64)\n",
      "blocks.0.attn.hook_attn_scores (1, 12, 5, 5)\n",
      "blocks.0.attn.hook_pattern     (1, 12, 5, 5)\n",
      "blocks.0.attn.hook_z           (1, 5, 12, 64)\n",
      "blocks.0.hook_attn_out         (1, 5, 768)\n",
      "blocks.0.hook_resid_mid        (1, 5, 768)\n",
      "blocks.0.ln2.hook_scale        (1, 5, 1)\n",
      "blocks.0.ln2.hook_normalized   (1, 5, 768)\n",
      "blocks.0.mlp.hook_pre          (1, 5, 3072)\n",
      "blocks.0.mlp.hook_post         (1, 5, 3072)\n",
      "blocks.0.hook_mlp_out          (1, 5, 768)\n",
      "blocks.0.hook_resid_post       (1, 5, 768)\n",
      "ln_final.hook_scale            (1, 5, 1)\n",
      "ln_final.hook_normalized       (1, 5, 768)\n"
     ]
    }
   ],
   "source": [
    "# names and shapes of the activation in the first layer of the reference model\n",
    "for activation_name, activation in cache.items():\n",
    "    if \".0.\" in activation_name or \"blocks\" not in activation_name:\n",
    "        print(f\"{activation_name:30} {tuple(activation.shape)}\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`Parameters` are the weights and biases that the model learned during training. These values do not change when the input changes. They are, for example, the weights (connections) in the MLP layers, or the values in the embedding layer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "embed.W_E          (50257, 768)\n",
      "pos_embed.W_pos    (1024, 768)\n",
      "blocks.0.ln1.w     (768,)\n",
      "blocks.0.ln1.b     (768,)\n",
      "blocks.0.ln2.w     (768,)\n",
      "blocks.0.ln2.b     (768,)\n",
      "blocks.0.attn.W_Q  (12, 768, 64)\n",
      "blocks.0.attn.W_K  (12, 768, 64)\n",
      "blocks.0.attn.W_V  (12, 768, 64)\n",
      "blocks.0.attn.W_O  (12, 64, 768)\n",
      "blocks.0.attn.b_Q  (12, 64)\n",
      "blocks.0.attn.b_K  (12, 64)\n",
      "blocks.0.attn.b_V  (12, 64)\n",
      "blocks.0.attn.b_O  (768,)\n",
      "blocks.0.mlp.W_in  (768, 3072)\n",
      "blocks.0.mlp.b_in  (3072,)\n",
      "blocks.0.mlp.W_out (3072, 768)\n",
      "blocks.0.mlp.b_out (768,)\n",
      "ln_final.w         (768,)\n",
      "ln_final.b         (768,)\n",
      "unembed.W_U        (768, 50257)\n",
      "unembed.b_U        (50257,)\n"
     ]
    }
   ],
   "source": [
    "# names and shapes of the parameters in the first layer of the reference model\n",
    "for name, param in gpt2.named_parameters():\n",
    "    if \".0.\" in name or \"blocks\" not in name:\n",
    "        print(f\"{name:18} {tuple(param.shape)}\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One of the central focuses on interpretability in transformer models is the inner workings of how activations change concerning an input, and one of the main activations of interest in transformers is attention maps. \n",
    "\n",
    "> Note: attention maps are a scalar matrix representing the relative importance of tokens assigned by the layer activations at different 2D spatial locations concerning the given attention head.  \n",
    "\n",
    "GPT-2 small has 12 layers, and every layer has 12 attention heads working in parallel and individually. `TransformerLens` gives access, via the run_with_cache method, in a very straightforward way to these activations, so we can pass them through any visualization library to plot our attention maps."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Layer 1 has 12 heads. Each outputs a pattern of shape torch.Size([15, 15])\n",
      "Layer 2 has 12 heads. Each outputs a pattern of shape torch.Size([15, 15])\n",
      "Layer 3 has 12 heads. Each outputs a pattern of shape torch.Size([15, 15])\n",
      "Layer 4 has 12 heads. Each outputs a pattern of shape torch.Size([15, 15])\n",
      "Layer 5 has 12 heads. Each outputs a pattern of shape torch.Size([15, 15])\n",
      "Layer 6 has 12 heads. Each outputs a pattern of shape torch.Size([15, 15])\n",
      "Layer 7 has 12 heads. Each outputs a pattern of shape torch.Size([15, 15])\n",
      "Layer 8 has 12 heads. Each outputs a pattern of shape torch.Size([15, 15])\n",
      "Layer 9 has 12 heads. Each outputs a pattern of shape torch.Size([15, 15])\n",
      "Layer 10 has 12 heads. Each outputs a pattern of shape torch.Size([15, 15])\n",
      "Layer 11 has 12 heads. Each outputs a pattern of shape torch.Size([15, 15])\n",
      "Layer 12 has 12 heads. Each outputs a pattern of shape torch.Size([15, 15])\n"
     ]
    }
   ],
   "source": [
    "sentence_tokens=gpt2.to_str_tokens(sentence, prepend_bos=False)\n",
    "\n",
    "tokens = gpt2.to_tokens(sentence, prepend_bos=False)\n",
    "tokens = tokens.to(device)\n",
    "\n",
    "_, cache = gpt2.run_with_cache(tokens)\n",
    "\n",
    "for i in range(len([x for x in cache.keys() if \"pattern\" in x])):\n",
    "    print(f\"Layer {i+1} has {cache['pattern', i][0].shape[0]} heads. Each outputs a pattern of shape {cache['pattern', i][0].shape[1:]}\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can do this using `matplotlib`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1600x1600 with 24 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "layer = 3 # choose the layer from 0 to 11\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "fig, axes = plt.subplots(nrows=4, ncols=3, figsize=(16, 16))\n",
    "\n",
    "for i, ax in enumerate(axes.flat):\n",
    "    im = ax.imshow(cache[\"pattern\", layer][0][i].cpu().numpy(), cmap='viridis')\n",
    "    ax.set_title('Attention Head {}'.format(i+1))\n",
    "\n",
    "    ax.xaxis.set_ticks(range(len(sentence_tokens)))\n",
    "    ax.yaxis.set_ticks(range(len(sentence_tokens)))\n",
    "    ax.set_xticklabels(sentence_tokens)\n",
    "    ax.set_yticklabels(sentence_tokens)\n",
    "    ax.tick_params(axis='x', which='major', pad=5, rotation=45)\n",
    "    ax.tick_params(axis='y', which='major', pad=5)\n",
    "    plt.colorbar(im, ax=ax)\n",
    "\n",
    "fig.suptitle(f'MultiHead Attention {layer + 1}', fontsize=16)\n",
    "fig.tight_layout()\n",
    "fig.subplots_adjust(top=0.94)\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or something like `Plotly`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "plotlyServerURL": "https://plot.ly"
       },
       "data": [
        {
         "hovertemplate": "Key: %{x}<br>Query: %{y}<br>Attention Score: %{z}<extra></extra>",
         "showscale": false,
         "texttemplate": "%{z}",
         "type": "heatmap",
         "xaxis": "x",
         "yaxis": "y",
         "z": [
          [
           0.24991253,
           0.028981432,
           0.009531758,
           0.01260268,
           0.04527378,
           0.009593936,
           0.012372253,
           0.02770322,
           0.04961477,
           0.0056860987,
           0.018354855,
           0.010530008,
           0.0071678013,
           0.18721324,
           0.32546166
          ],
          [
           0.16713348,
           0.043929424,
           0.019330805,
           0.013499817,
           0.035028253,
           0.013582961,
           0.04806789,
           0.05596802,
           0.06512582,
           0.016543169,
           0.03673533,
           0.022829872,
           0.019607661,
           0.4426175,
           0
          ],
          [
           0.059205852,
           0.1143097,
           0.032042306,
           0.06400789,
           0.065796375,
           0.06333642,
           0.11188167,
           0.15452825,
           0.061045,
           0.07307004,
           0.09673048,
           0.040535294,
           0.06351077,
           0,
           0
          ],
          [
           0.106551364,
           0.10276556,
           0.049193062,
           0.047915544,
           0.08997324,
           0.07428152,
           0.08060957,
           0.08104185,
           0.10214921,
           0.10642421,
           0.11862876,
           0.04046608,
           0,
           0,
           0
          ],
          [
           0.10567253,
           0.10933296,
           0.052234963,
           0.036176864,
           0.09040241,
           0.06606483,
           0.07258777,
           0.099005975,
           0.14164439,
           0.11386409,
           0.11301317,
           0,
           0,
           0,
           0
          ],
          [
           0.0753055,
           0.11862747,
           0.069101684,
           0.046247974,
           0.10170253,
           0.09266347,
           0.11912872,
           0.11333322,
           0.13158177,
           0.13230766,
           0,
           0,
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          ],
          [
           0.14120881,
           0.13764,
           0.048758592,
           0.051079545,
           0.12813911,
           0.074666746,
           0.09702248,
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           0,
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           0,
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          ],
          [
           0.1373992,
           0.12203711,
           0.07113402,
           0.06981584,
           0.1510667,
           0.118323006,
           0.13625343,
           0.19397067,
           0,
           0,
           0,
           0,
           0,
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   "source": [
    "import plotly.graph_objs as go\n",
    "from plotly.subplots import make_subplots\n",
    "\n",
    "\n",
    "fig = go.Figure()\n",
    "specs = [[{'type': 'heatmap'}]*3]*4\n",
    "subplot_titles = [f\"Attention Head {i+1}\" for i in range(12)]\n",
    "fig = make_subplots(rows=4, cols=3, specs=specs, subplot_titles=subplot_titles)\n",
    "\n",
    "for i in range(1, 13):\n",
    "    row = (i - 1) // 3 + 1\n",
    "    col = i % 3 if i % 3 != 0 else 3\n",
    "    fig.add_trace(\n",
    "        # plotly go.Heatmap requires the matrix to be flipped\n",
    "        go.Heatmap(z=cache[\"pattern\", layer][0][i-1].cpu().numpy()[::-1, :], \n",
    "            texttemplate=\"%{z}\",\n",
    "            showscale=False,\n",
    "            hovertemplate='Key: %{x}<br>Query: %{y}<br>Attention Score: %{z}<extra></extra>'), \n",
    "            row=row, col=col)\n",
    "\n",
    "    fig.update_xaxes(title_text=\"Key\", ticktext=sentence_tokens,row=row, col=col, tickmode='array', \n",
    "                    tickvals=list(range(len(sentence_tokens))), tickangle=45)\n",
    "    fig.update_yaxes(title_text=\"Query\", ticktext=sentence_tokens[::-1],row=row, col=col, tickmode='array', \n",
    "                    tickvals=list(range(len(sentence_tokens))))\n",
    "    fig.update_layout(template=\"plotly_dark\",\n",
    "                        title_text=f\"<b><i>MultiHead Attention - Layer {layer + 1}</i></b>\", \n",
    "                        font=dict(size=10), \n",
    "                        height=1300,\n",
    "                        paper_bgcolor='rgba(0, 0, 0, 0)',\n",
    "                        plot_bgcolor='rgba(0, 0, 0, 0)',\n",
    "                        )\n",
    "\n",
    "fig.show()"
   ]
  },
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   "source": [
    "These attention maps represent the relative importance of different tokens in the input sequence with respect to each other. A higher attention score between two tokens indicates that they are more relevant to each other. All attention head contributes to the final MultiHead Attention output. This output will be written to the residual stream together with the output of the MLP layer.\n",
    "\n",
    "One way to interpret these maps is by looking at how the queries are scored against each key. For example, at layer 12, head 11, the query \"_floor_\" focuses most on \"_sat_.\" This pattern emerges again in heads 9 and 4, where most of the attention associated with the query \"_floor_\" is again paid to the value \"_sat_.\" These heads independently agree that \"_sat_\" and \"_floor_\" are correlated in this context. These maps also help us visualize what `causal masking` is, wich is zeroing all the right-upper side of our attention matrix (queries cannot look to the keys in the future). \n",
    "\n",
    "Attention represents a vital part of transformer and GPT-style architectures, and understanding how attention heads coordinate, even in different layers, to help enrich the context of the residual stream is an open problem in interpretability research.\n",
    "\n",
    "Another point of interest is what happens inside the MLP layers, but this we will leave for another tutorial.\n",
    "\n",
    "---\n",
    "\n",
    "Return to the [Castle](https://github.com/Nkluge-correa/TeenyTinyCastle)"
   ]
  }
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