speculative_sampling.ipynb

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  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "## Installation & Libraries  "
      ],
      "metadata": {
        "id": "PSspO8KgV0ZV"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "\n",
        "# speculative_sampling\n",
        "@ Itai Shapira\n",
        "\n",
        "Harvard CS229."
      ],
      "metadata": {
        "id": "9h-gbFF-VxFr"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "!pip install transformers"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6_qdxsYdVoBr",
        "outputId": "313b1461-a85b-401a-be89-78370abf3bd9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
            "Collecting transformers\n",
            "  Downloading transformers-4.26.1-py3-none-any.whl (6.3 MB)\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m6.3/6.3 MB\u001b[0m \u001b[31m91.9 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hRequirement already satisfied: regex!=2019.12.17 in /usr/local/lib/python3.8/dist-packages (from transformers) (2022.6.2)\n",
            "Requirement already satisfied: numpy>=1.17 in /usr/local/lib/python3.8/dist-packages (from transformers) (1.21.6)\n",
            "Collecting tokenizers!=0.11.3,<0.14,>=0.11.1\n",
            "  Downloading tokenizers-0.13.2-cp38-cp38-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (7.6 MB)\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m7.6/7.6 MB\u001b[0m \u001b[31m105.9 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hRequirement already satisfied: requests in /usr/local/lib/python3.8/dist-packages (from transformers) (2.25.1)\n",
            "Requirement already satisfied: packaging>=20.0 in /usr/local/lib/python3.8/dist-packages (from transformers) (23.0)\n",
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            "Requirement already satisfied: pyyaml>=5.1 in /usr/local/lib/python3.8/dist-packages (from transformers) (6.0)\n",
            "Collecting huggingface-hub<1.0,>=0.11.0\n",
            "  Downloading huggingface_hub-0.12.1-py3-none-any.whl (190 kB)\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m190.3/190.3 KB\u001b[0m \u001b[31m25.0 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hRequirement already satisfied: tqdm>=4.27 in /usr/local/lib/python3.8/dist-packages (from transformers) (4.64.1)\n",
            "Requirement already satisfied: typing-extensions>=3.7.4.3 in /usr/local/lib/python3.8/dist-packages (from huggingface-hub<1.0,>=0.11.0->transformers) (4.5.0)\n",
            "Requirement already satisfied: idna<3,>=2.5 in /usr/local/lib/python3.8/dist-packages (from requests->transformers) (2.10)\n",
            "Requirement already satisfied: certifi>=2017.4.17 in /usr/local/lib/python3.8/dist-packages (from requests->transformers) (2022.12.7)\n",
            "Requirement already satisfied: urllib3<1.27,>=1.21.1 in /usr/local/lib/python3.8/dist-packages (from requests->transformers) (1.24.3)\n",
            "Requirement already satisfied: chardet<5,>=3.0.2 in /usr/local/lib/python3.8/dist-packages (from requests->transformers) (4.0.0)\n",
            "Installing collected packages: tokenizers, huggingface-hub, transformers\n",
            "Successfully installed huggingface-hub-0.12.1 tokenizers-0.13.2 transformers-4.26.1\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Transformers (huggingface)  provides APIs and tools to easily download and train state-of-the-art pretrained models.\n",
        "from transformers import GPT2Tokenizer, GPT2LMHeadModel  # Model configuration class\n",
        "\n",
        "import torch\n",
        "import time         # measuring speedups\n",
        "\n",
        "import numpy as np \n",
        "import pandas as pd\n",
        "pd.set_option('precision', 2)\n",
        "\n",
        "import seaborn as sns"
      ],
      "metadata": {
        "id": "CV2YNN5Ih3m2"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Import Models"
      ],
      "metadata": {
        "id": "KJxIEINxIOUs"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "device = \"cuda:0\" if torch.cuda.is_available() else \"cpu\"\n",
        "print(device)"
      ],
      "metadata": {
        "id": "Jd3Z7gMMWZR3",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f67ddcbd-f5a9-4702-93c0-a9c8b720eac3"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "cuda:0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "SMALL_MODEL_ID = \"gpt2\"\n",
        "BIG_MODEL_ID = \"gpt2-large\""
      ],
      "metadata": {
        "id": "pytXEJmbITgV"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "tokenizer = GPT2Tokenizer.from_pretrained(SMALL_MODEL_ID) \n",
        "\n",
        "small_model = GPT2LMHeadModel.from_pretrained(SMALL_MODEL_ID, pad_token_id = tokenizer.eos_token_id).to(device)\n",
        "big_model = GPT2LMHeadModel.from_pretrained(BIG_MODEL_ID, pad_token_id = tokenizer.eos_token_id).to(device)"
      ],
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      "execution_count": null,
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        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Downloading (…)olve/main/vocab.json:   0%|          | 0.00/1.04M [00:00<?, ?B/s]"
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    },
    {
      "cell_type": "code",
      "source": [
        "text_str = \"School Of Engineering And Applied\"\n",
        "input_ids = tokenizer.encode(text_str, return_tensors = \"pt\").to(device)\n",
        "print(len(input_ids[0]))\n",
        "output = small_model(input_ids)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vEkoGrISOWjS",
        "outputId": "56a2275c-fbee-43ee-d686-f3b93ffa693b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "5\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "##Rejection Sampling\n",
        "below we implement the algorithm "
      ],
      "metadata": {
        "id": "fgKtFtqcGP6_"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def createModelFunction(model):\n",
        "  \"\"\" generates the inference functions, inculding softmax \"\"\"\n",
        "  return lambda inputs: adjust_distribution(model(inputs).logits[0])\n",
        "\n",
        "def adjust_distribution(logits, top_k = 40):\n",
        "  if top_k is not None:\n",
        "    indices_to_remove = logits < torch.topk(logits, top_k)[0][..., -1, None]\n",
        "    logits[indices_to_remove] = -float('Inf')\n",
        "  return logits.softmax(dim=-1)\n",
        "\n",
        "def sample(p):\n",
        "  \"\"\" gets a distrubtion and returns a sample \"\"\"\n",
        "  return torch.multinomial(p, 1)       # slow :(  better: torch.argmax(p)\n",
        "\n",
        "def autoregressive_sampling(x, model, n):\n",
        "  \"\"\"\n",
        "  Given a t-token prefix x1, ..., xt, predict n next-token distributions sequentially\n",
        "  \"\"\"\n",
        "  t = len(x[0])\n",
        "  T = len(x[0]) + n\n",
        "\n",
        "  while t < T:\n",
        "    \n",
        "    # generate new sample:\n",
        "    new_pred = sample(model(x)[-1])\n",
        "\n",
        "    # concatenate to the sequence\n",
        "    x = torch.cat((x, new_pred.reshape(1,1)), dim = 1)\n",
        "\n",
        "    t += 1\n",
        "  return x\n",
        "\n",
        "\n",
        "def generate_delta_distribution(p, q):\n",
        "  \"\"\"\n",
        "  p,q: two distribution vectors \n",
        "  returns max(0, p-q) after normalization\n",
        "  \"\"\"\n",
        "  delta = p-q \n",
        "\n",
        "  # zero out negative values:\n",
        "  delta[delta < 0] = 0\n",
        "\n",
        "  # normalized \n",
        "  delta /= delta.norm(p=1)\n",
        "  return delta\n",
        "\n",
        "@torch.no_grad()\n",
        "def rejection_sampling(x, small_pred, big_pred, k, n):\n",
        "  t = len(x[0])\n",
        "  T = t + n\n",
        "\n",
        "  # repeat until n new tokens have been generated \n",
        "  while t < T:\n",
        "\n",
        "    # *step 1*: \n",
        "    # Given a t-token prefix x1, ..., xt, predict k next-token distributions\n",
        "    # {ps(xi|xs <i)| for t < i ≤ t + k} sequentially using a small_pred\n",
        "    xs = x\n",
        "    for _ in range(k):\n",
        "      new_pred = sample(small_pred(xs)[-1])\n",
        "      xs = torch.cat((xs, new_pred.reshape(1,1)), dim = 1)\n",
        "\n",
        "\n",
        "    # step 2: use the big model to compute {pb} in parallel\n",
        "    ps = small_pred(xs)     # shape = (t, vocab_size)\n",
        "    pb = big_pred(xs)       # shape = (t, vocab_size)\n",
        "\n",
        "    # step 3 - rejection sampling\n",
        "    counter = 0\n",
        "    for _ in range(k):\n",
        "      prev_token = t - 1\n",
        "      x_ts = xs[0][t]\n",
        "\n",
        "      # sample r ~ U(0,1), compare to the probs ratio:\n",
        "      if torch.rand(1).to(device) < (pb[prev_token][x_ts] / ps[prev_token][x_ts]):      # accepting\n",
        "        t += 1\n",
        "        counter += 1\n",
        "        if counter < k:\n",
        "          x = torch.cat((x, x_ts.reshape(1,1)), dim = 1)\n",
        "        else:  # all k tokens were accepted \n",
        "          new_sample = sample(pb[prev_token])\n",
        "          x = torch.cat((x, new_sample.reshape(1,1)), dim = 1)\n",
        "\n",
        "    \n",
        "      else:      # rejecting\n",
        "        # sample one additional token\n",
        "        p_delta = generate_delta_distribution(pb[prev_token], ps[prev_token])\n",
        "        new_sample = sample(p_delta)\n",
        "        x = torch.cat((x, new_sample.reshape(1,1)), dim = 1)\n",
        "        t += 1\n",
        "        break\n",
        "    \n",
        "  return x"
      ],
      "metadata": {
        "id": "25X4JhZfwRTN"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "small_pred = createModelFunction(small_model)\n",
        "big_pred = createModelFunction(big_model)\n",
        "\n",
        "def run_sim_autoregressive(input_str, n):\n",
        "  \"\"\"\n",
        "  run simultion on one prompt. measure the running time of the autoregressive \n",
        "  \"\"\"\n",
        "\n",
        "  inputs = tokenizer.encode(input_str, return_tensors = \"pt\").to(device)\n",
        "  \n",
        "  # autoregressive runtimes for the small model\n",
        "  start = time.perf_counter()\n",
        "  output = autoregressive_sampling(inputs, small_pred, n)\n",
        "  elapsed_time_small = time.perf_counter() - start\n",
        "  \n",
        "  # autoregressive runtimes for the large model\n",
        "  start = time.perf_counter()\n",
        "  output = autoregressive_sampling(inputs, big_pred, n)\n",
        "  elapsed_time_big = time.perf_counter() - start\n",
        "  return elapsed_time_small, elapsed_time_big\n",
        "\n",
        "def run_sim_rejection_sampling(input_str, k, n):\n",
        "  \"\"\"\n",
        "  run simultion on one prompt. measure the running time of the rejection_sampling \n",
        "  \"\"\"\n",
        "  inputs = tokenizer.encode(input_str, return_tensors = \"pt\").to(device)\n",
        "  \n",
        "  #runtimes for the efficient attention algorithm\n",
        "  start = time.perf_counter()\n",
        "  output = rejection_sampling(inputs, small_pred, big_pred,k, n)\n",
        "  elapsed_time = time.perf_counter() - start\n",
        "  return elapsed_time"
      ],
      "metadata": {
        "id": "pqOyK8Nbh69W"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Visualization \n",
        "We compare the performance of our algorithm to autoregressive inference of the large and small models. We run the following expermints:\n",
        "For 20 samples, 6 prompts and different values of k; record the running time of the three algorithms.\n",
        "\n",
        "Note: the speed-up increases with lower temperature, and with different ways to optimize the sampling method. "
      ],
      "metadata": {
        "id": "qiDEWffkqBI0"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "## visualization stuff\n",
        "fontfamily = \"monospace\"\n",
        "context = \"notebook\"\n",
        "\n",
        "color_main = 'gold'\n",
        "\n",
        "\n",
        "rc = {'axes.titlesize':18, 'axes.titleweight':'bold',\n",
        "      'axes.labelweight':'bold', 'figure.figsize':[12,8], \n",
        "      'lines.linewidth':5, 'axes.edgecolor':'black',\n",
        "     'boxplot.boxprops.color': color_main}\n",
        "\n",
        "sns.set(context=context, font=fontfamily, rc=rc, style=\"whitegrid\")"
      ],
      "metadata": {
        "id": "RG6WOExap-4R"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "prompts = [\n",
        "    # easy \n",
        "    \"A B C\",   \n",
        "    \"100, 99, 98, 97\",\n",
        "\n",
        "    # medium difficulty\n",
        "    \"The Rolling Stones first album is\",\n",
        "    \"It was the best of times, it was the worst of times, it was\",\n",
        "\n",
        "    # hard\n",
        "    \"what are you thinking about?\",\n",
        "    \"What is the maximum entropy probability density function for a continuous variable of given mean and standard deviation?\",\n",
        "    \n",
        "]\n",
        "\n",
        "samples = 30\n",
        "n = 21\n",
        "k_values = [2,3,4,5,6,7,8]\n",
        "\n",
        "# total different inputs settings: samples x prompts x k_values\n",
        "\n",
        "res = []\n",
        "for _ in range(samples):\n",
        "  for pmt in prompts:\n",
        "    elapsed_time_small, elapsed_time_big = run_sim_autoregressive(pmt, n)\n",
        "    res.append([\"autoregressive\",SMALL_MODEL_ID, pmt, 0, n, elapsed_time_small])\n",
        "    res.append([\"autoregressive\",BIG_MODEL_ID, pmt, 0, n, elapsed_time_big])\n",
        "    for k in k_values:\n",
        "      elapsed_time = run_sim_rejection_sampling(pmt, k, n)\n",
        "      res.append([\"rejection_sampling\",\"-\", pmt, k, n, elapsed_time])\n",
        "\n",
        "df = pd.DataFrame(res, columns = [\"algorithm\", \"model\", \"prompt\", \"k\",\"n\",\"time\"])\n",
        "df.to_csv(\"./results.csv\") # save"
      ],
      "metadata": {
        "id": "Bda3i-8wM2kB"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Running time for a given prompt, by different values of k"
      ],
      "metadata": {
        "id": "3uptsItkqLH1"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "prompt = \"A B C\"\n",
        "title = f\"Running time prompt='{prompt}'\"\n",
        "\n",
        "sns.lineplot(data=df[(df[\"prompt\"] == \"A B C\") & (df[\"algorithm\"] == \"rejection_sampling\")], x=\"k\", y=\"time\", ci=\"sd\", label=\"rejection_sampling\")\n",
        "\n",
        "sns.lineplot(y=df[(df[\"prompt\"] == \"A B C\") & (df[\"model\"] == \"gpt2\")][\"time\"].mean(), \n",
        "             x=df[(df[\"prompt\"] == \"A B C\") & (df[\"algorithm\"] == \"rejection_sampling\")][\"k\"], label=\"ar_gpt-large\", color=\"wheat\")\n",
        "\n",
        "sns.lineplot(y=df[(df[\"prompt\"] == \"A B C\") & (df[\"model\"] == \"gpt2-large\")][\"time\"].mean(), \n",
        "             x=df[(df[\"prompt\"] == \"A B C\") & (df[\"algorithm\"] == \"rejection_sampling\")][\"k\"], label=\"ar_gpt-small\", color=\"salmon\").set_title(title)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 540
        },
        "id": "K8rSGmYXZC-q",
        "outputId": "125f663b-cf27-4d0f-e03d-b12be7547b2a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, \"Running time prompt='A B C'\")"
            ]
          },
          "metadata": {},
          "execution_count": 27
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "*speed up by prompt*\n",
        "\n",
        "The mean running time of a prompt-k pairs. Great improvement for the easy prompt. Hard prompt and large k tend to be slow. "
      ],
      "metadata": {
        "id": "TUWB3QejqUkN"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "pd.pivot_table(data=df, columns = [\"algorithm\", \"model\",\"k\"], index=\"prompt\", values= \"time\", aggfunc=\"mean\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 332
        },
        "id": "3CaZDhGfE5J5",
        "outputId": "342aa670-e050-4da1-a519-daafad8eb2c1"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "algorithm                                          autoregressive             \\\n",
              "model                                                        gpt2 gpt2-large   \n",
              "k                                                               0          0   \n",
              "prompt                                                                         \n",
              "100, 99, 98, 97                                              0.33       0.95   \n",
              "A B C                                                        0.32       0.94   \n",
              "It was the best of times, it was the worst of t...           0.32       0.94   \n",
              "The Rolling Stones first album is                            0.33       0.95   \n",
              "What is the maximum entropy probability density...           0.33       0.95   \n",
              "what are you thinking about?                                 0.32       0.94   \n",
              "\n",
              "algorithm                                          rejection_sampling        \\\n",
              "model                                                               -         \n",
              "k                                                                   2     3   \n",
              "prompt                                                                        \n",
              "100, 99, 98, 97                                                  0.87  0.75   \n",
              "A B C                                                            0.85  0.65   \n",
              "It was the best of times, it was the worst of t...               1.01  1.02   \n",
              "The Rolling Stones first album is                                0.98  0.91   \n",
              "What is the maximum entropy probability density...               0.94  0.90   \n",
              "what are you thinking about?                                     0.94  0.85   \n",
              "\n",
              "algorithm                                                                   \\\n",
              "model                                                                        \n",
              "k                                                      4     5     6     7   \n",
              "prompt                                                                       \n",
              "100, 99, 98, 97                                     0.73  0.74  0.74  0.72   \n",
              "A B C                                               0.65  0.59  0.55  0.48   \n",
              "It was the best of times, it was the worst of t...  1.14  1.20  1.29  1.41   \n",
              "The Rolling Stones first album is                   0.86  0.93  0.95  1.09   \n",
              "What is the maximum entropy probability density...  0.86  0.91  0.92  1.11   \n",
              "what are you thinking about?                        0.86  0.90  0.90  1.02   \n",
              "\n",
              "algorithm                                                 \n",
              "model                                                     \n",
              "k                                                      8  \n",
              "prompt                                                    \n",
              "100, 99, 98, 97                                     0.73  \n",
              "A B C                                               0.52  \n",
              "It was the best of times, it was the worst of t...  1.52  \n",
              "The Rolling Stones first album is                   1.07  \n",
              "What is the maximum entropy probability density...  1.12  \n",
              "what are you thinking about?                        1.00  "
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-a896a1b1-a6d0-4f95-9222-5923288cab50\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead tr th {\n",
              "        text-align: left;\n",
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              "\n",
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              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr>\n",
              "      <th>algorithm</th>\n",
              "      <th colspan=\"2\" halign=\"left\">autoregressive</th>\n",
              "      <th colspan=\"7\" halign=\"left\">rejection_sampling</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>model</th>\n",
              "      <th>gpt2</th>\n",
              "      <th>gpt2-large</th>\n",
              "      <th colspan=\"7\" halign=\"left\">-</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>k</th>\n",
              "      <th>0</th>\n",
              "      <th>0</th>\n",
              "      <th>2</th>\n",
              "      <th>3</th>\n",
              "      <th>4</th>\n",
              "      <th>5</th>\n",
              "      <th>6</th>\n",
              "      <th>7</th>\n",
              "      <th>8</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>prompt</th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>100, 99, 98, 97</th>\n",
              "      <td>0.33</td>\n",
              "      <td>0.95</td>\n",
              "      <td>0.87</td>\n",
              "      <td>0.75</td>\n",
              "      <td>0.73</td>\n",
              "      <td>0.74</td>\n",
              "      <td>0.74</td>\n",
              "      <td>0.72</td>\n",
              "      <td>0.73</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>A B C</th>\n",
              "      <td>0.32</td>\n",
              "      <td>0.94</td>\n",
              "      <td>0.85</td>\n",
              "      <td>0.65</td>\n",
              "      <td>0.65</td>\n",
              "      <td>0.59</td>\n",
              "      <td>0.55</td>\n",
              "      <td>0.48</td>\n",
              "      <td>0.52</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>It was the best of times, it was the worst of times, it was</th>\n",
              "      <td>0.32</td>\n",
              "      <td>0.94</td>\n",
              "      <td>1.01</td>\n",
              "      <td>1.02</td>\n",
              "      <td>1.14</td>\n",
              "      <td>1.20</td>\n",
              "      <td>1.29</td>\n",
              "      <td>1.41</td>\n",
              "      <td>1.52</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>The Rolling Stones first album is</th>\n",
              "      <td>0.33</td>\n",
              "      <td>0.95</td>\n",
              "      <td>0.98</td>\n",
              "      <td>0.91</td>\n",
              "      <td>0.86</td>\n",
              "      <td>0.93</td>\n",
              "      <td>0.95</td>\n",
              "      <td>1.09</td>\n",
              "      <td>1.07</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>What is the maximum entropy probability density function for a continuous variable of given mean and standard deviation?</th>\n",
              "      <td>0.33</td>\n",
              "      <td>0.95</td>\n",
              "      <td>0.94</td>\n",
              "      <td>0.90</td>\n",
              "      <td>0.86</td>\n",
              "      <td>0.91</td>\n",
              "      <td>0.92</td>\n",
              "      <td>1.11</td>\n",
              "      <td>1.12</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>what are you thinking about?</th>\n",
              "      <td>0.32</td>\n",
              "      <td>0.94</td>\n",
              "      <td>0.94</td>\n",
              "      <td>0.85</td>\n",
              "      <td>0.86</td>\n",
              "      <td>0.90</td>\n",
              "      <td>0.90</td>\n",
              "      <td>1.02</td>\n",
              "      <td>1.00</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-a896a1b1-a6d0-4f95-9222-5923288cab50')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
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              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
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              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
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              "      fill: #174EA6;\n",
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              "\n",
              "    [theme=dark] .colab-df-convert {\n",
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              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
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              "  </style>\n",
              "\n",
              "      <script>\n",
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              "          document.querySelector('#df-a896a1b1-a6d0-4f95-9222-5923288cab50 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-a896a1b1-a6d0-4f95-9222-5923288cab50');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 33
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "average percent speed up for k=3, n=21:"
      ],
      "metadata": {
        "id": "4sl8eWSVII3o"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "tmp = pd.pivot_table(data=df[\n",
        "    (df[\"k\"] == 3) | (df[\"k\"] == 0)\n",
        "    ], columns = [\"algorithm\", \"model\",\"k\"], index=\"prompt\", values= \"time\", aggfunc=\"mean\")\n",
        "tmp.columns = [\"small\",\"big\",\"rejection_sampling\"]\n",
        "tmp[\"rejection_sampling\"] /= tmp[\"big\"]/100\n",
        "tmp[[\"rejection_sampling\"]]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 269
        },
        "id": "FyB2f_ASG7qb",
        "outputId": "6b5f32fe-fb13-49d9-a01a-02c4a47330ef"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "                                                    rejection_sampling\n",
              "prompt                                                                \n",
              "100, 99, 98, 97                                                  78.83\n",
              "A B C                                                            69.18\n",
              "It was the best of times, it was the worst of t...              108.46\n",
              "The Rolling Stones first album is                                95.87\n",
              "What is the maximum entropy probability density...               94.65\n",
              "what are you thinking about?                                     90.22"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-229593ef-6941-4a34-b48e-f84e02d610eb\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>rejection_sampling</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>prompt</th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>100, 99, 98, 97</th>\n",
              "      <td>78.83</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>A B C</th>\n",
              "      <td>69.18</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>It was the best of times, it was the worst of times, it was</th>\n",
              "      <td>108.46</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>The Rolling Stones first album is</th>\n",
              "      <td>95.87</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>What is the maximum entropy probability density function for a continuous variable of given mean and standard deviation?</th>\n",
              "      <td>94.65</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>what are you thinking about?</th>\n",
              "      <td>90.22</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-229593ef-6941-4a34-b48e-f84e02d610eb')\"\n",
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              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
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              "      gap: 12px;\n",
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              "\n",
              "    .colab-df-convert {\n",
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              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-229593ef-6941-4a34-b48e-f84e02d610eb button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-229593ef-6941-4a34-b48e-f84e02d610eb');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
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              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 51
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# export to html\n",
        "\n",
        "#!jupyter nbconvert --to html speculative_sampling.ipynb"
      ],
      "metadata": {
        "id": "abO8EX89JZpO",
        "outputId": "3847b6bc-3f98-433a-ecdb-3399d343dcc5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 131
        }
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "error",
          "ename": "SyntaxError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;36m  File \u001b[0;32m\"<ipython-input-3-e3dec00bb542>\"\u001b[0;36m, line \u001b[0;32m2\u001b[0m\n\u001b[0;31m    jupyter nbconvert --to script speculative_sampling.ipynb\u001b[0m\n\u001b[0m            ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
          ]
        }
      ]
    }
  ]
}