fact_editing_plots.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "from common_imports import *\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "sns.set_theme()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "rank1_reduction_results = joblib.load('rank1_to_subspace_results.joblib')\n",
    "rome_vs_subsp_rewrite_scores = joblib.load('rome_vs_subsp_results.joblib')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Analyzing rewrite scores"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_rewrite_score_df(rome_vs_subsp_rewrite_scores):\n",
    "    rows = []\n",
    "    for data in rome_vs_subsp_rewrite_scores:\n",
    "        for metric in ('rome', 'subsp', 'subsp_rowspace', 'subsp_rowspace_10', 'subsp_rowspace_50'):\n",
    "            rows.append({\n",
    "                'layer': data['layer'],\n",
    "                'fact_idx': data['fact_idx'],\n",
    "                'metric': metric,\n",
    "                'score': data[f'rewrite_score_{metric}'],\n",
    "            })\n",
    "    return pd.DataFrame(rows)\n",
    "\n",
    "rewrite_score_df = get_rewrite_score_df(rome_vs_subsp_rewrite_scores)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# make a dataframe comparing the rewrite scores of rome vs subsp\n",
    "y_axis_metric = 'subsp_rowspace'\n",
    "rewrite_score_rome_vs_subsp_df = rewrite_score_df.query(\n",
    "    f'metric in (\"rome\", \"{y_axis_metric}\")').pivot(\n",
    "        index=['layer', 'fact_idx'], columns='metric', values='score').reset_index()\n",
    "\n",
    "for layer in (20, 25, 30, 35):\n",
    "    sns.scatterplot(data=rewrite_score_rome_vs_subsp_df.query(f'layer == {layer}'), x='rome', y=y_axis_metric,)\n",
    "    # remove x axis and y axis labels\n",
    "    plt.gca().set(xlabel=None, ylabel=None,)\n",
    "    # set the number of ticks on x axis and y axis\n",
    "    plt.locator_params(axis='x', nbins=5)\n",
    "    plt.locator_params(axis='y', nbins=5)\n",
    "    # increase x, y tiks label size to 20\n",
    "    plt.xticks(fontsize=20)\n",
    "    plt.yticks(fontsize=20)\n",
    "    plt.title(f'layer {layer}', fontsize=20)\n",
    "    plt.savefig(f'layer_{layer}_rewrite_score_rome_vs_subsp.pdf', bbox_inches='tight')\n",
    "    plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Analyzing other metrics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [],
   "source": [
    "def analyze_reduction_results(rows):\n",
    "    # collect a dataframe of cosine simliarities between v and b \n",
    "    cosine_sim_rows = []\n",
    "    for row in rows:\n",
    "        cosine_sim_rows.append({\n",
    "            'layer': row['layer'],\n",
    "            'fact_idx': row['fact_idx'],\n",
    "            'cosine_sim': torch.cosine_similarity(row['v'], row['b'], dim=0).abs().item(),\n",
    "        })\n",
    "    cosine_sim_df = pd.DataFrame(cosine_sim_rows)\n",
    "    # collect a dataframe of the ratio of the variance introduced by our edit vs\n",
    "    # the ROME edit\n",
    "    variance_ratio_rows = []\n",
    "    for row in rows:\n",
    "        variance_ratio_rows.append({\n",
    "            'layer': row['layer'],\n",
    "            'fact_idx': row['fact_idx'],\n",
    "            'var_ratio': (row['var_full'] / row['var_rome']).item(),\n",
    "        })\n",
    "    variance_ratio_df = pd.DataFrame(variance_ratio_rows)\n",
    "    return cosine_sim_df, variance_ratio_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [],
   "source": [
    "cosine_sim_df, variance_ratio_df = analyze_reduction_results(rows)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# violin plot of cosine similarities with layer on the x axis\n",
    "# sns.violinplot(data=cosine_sim_df, x='layer', y='cosine_sim')\n",
    "# violin plot of ratios of variance introduced with layer on the x axis\n",
    "sns.violinplot(data=variance_ratio_df.query('15 <= layer < 40'), x='layer', y='var_ratio')\n",
    "# draw a horizontal line at 1\n",
    "plt.axhline(1, color='black', linestyle='--')\n",
    "# remove the y axis label\n",
    "plt.ylabel('')\n",
    "# set the x axis label\n",
    "plt.xlabel('')\n",
    "# increase the fontsize for the x axis ticks\n",
    "plt.xticks(fontsize=20)\n",
    "# increase the fontsize for the y axis ticks\n",
    "plt.yticks(fontsize=20)\n",
    "# save to pdf\n",
    "plt.savefig('figures/rank1_to_subspace_variance_ratio_violin.pdf', bbox_inches='tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# violin plot of cosine similarities with layer on the x axis\n",
    "sns.violinplot(data=cosine_sim_df, x='layer', y='cosine_sim')\n",
    "# draw a horizontal line at 1\n",
    "plt.axhline(1, color='black', linestyle='--')\n",
    "# remove the y axis label\n",
    "plt.ylabel('')\n",
    "# set the x axis label\n",
    "plt.xlabel('')\n",
    "# increase the fontsize for the x axis ticks\n",
    "plt.xticks(fontsize=20)\n",
    "# increase the fontsize for the y axis ticks\n",
    "plt.yticks(fontsize=20)\n",
    "# save to pdf\n",
    "plt.savefig('figures/rank1_to_subspace_cosine_sim_violin.pdf', bbox_inches='tight')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.10.12",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.12"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "fd8dbfdfd1a6a4c5f3a98a8b5f239185c4ac44e8c535538c941237e2ab93d1b0"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}