notebook/fDPO-propostion.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "fb9325bf2c197689",
   "metadata": {},
   "source": [
    "# Experimtal validation of Proposition B.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "initial_id",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-10-17T17:53:24.930558Z",
     "start_time": "2024-10-17T17:53:13.557932Z"
    },
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/rlhf-dev/filtered-dpo/.venv/lib/python3.10/site-packages/transformers/utils/generic.py:441: UserWarning: torch.utils._pytree._register_pytree_node is deprecated. Please use torch.utils._pytree.register_pytree_node instead.\n",
      "  _torch_pytree._register_pytree_node(\n",
      "/rlhf-dev/filtered-dpo/.venv/lib/python3.10/site-packages/transformers/utils/generic.py:309: UserWarning: torch.utils._pytree._register_pytree_node is deprecated. Please use torch.utils._pytree.register_pytree_node instead.\n",
      "  _torch_pytree._register_pytree_node(\n",
      "/rlhf-dev/filtered-dpo/.venv/lib/python3.10/site-packages/transformers/utils/generic.py:309: UserWarning: torch.utils._pytree._register_pytree_node is deprecated. Please use torch.utils._pytree.register_pytree_node instead.\n",
      "  _torch_pytree._register_pytree_node(\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from sympy import init_printing\n",
    "from transformers import GPT2Tokenizer, GPT2LMHeadModel\n",
    "import numpy as np\n",
    "import torch\n",
    "import random\n",
    "from tqdm import tqdm\n",
    "\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ba30942781f1598",
   "metadata": {},
   "source": [
    "## Preparation\n",
    "### load GPT-2 model and tokenizer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "eac8ca8df12d5641",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-10-17T17:53:33.844162Z",
     "start_time": "2024-10-17T17:53:24.944530Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model loaded GPT2LMHeadModel(\n",
      "  (transformer): GPT2Model(\n",
      "    (wte): Embedding(50257, 1280)\n",
      "    (wpe): Embedding(1024, 1280)\n",
      "    (drop): Dropout(p=0.1, inplace=False)\n",
      "    (h): ModuleList(\n",
      "      (0-35): 36 x GPT2Block(\n",
      "        (ln_1): LayerNorm((1280,), eps=1e-05, elementwise_affine=True)\n",
      "        (attn): GPT2Attention(\n",
      "          (c_attn): Conv1D()\n",
      "          (c_proj): Conv1D()\n",
      "          (attn_dropout): Dropout(p=0.1, inplace=False)\n",
      "          (resid_dropout): Dropout(p=0.1, inplace=False)\n",
      "        )\n",
      "        (ln_2): LayerNorm((1280,), eps=1e-05, elementwise_affine=True)\n",
      "        (mlp): GPT2MLP(\n",
      "          (c_fc): Conv1D()\n",
      "          (c_proj): Conv1D()\n",
      "          (act): NewGELUActivation()\n",
      "          (dropout): Dropout(p=0.1, inplace=False)\n",
      "        )\n",
      "      )\n",
      "    )\n",
      "    (ln_f): LayerNorm((1280,), eps=1e-05, elementwise_affine=True)\n",
      "  )\n",
      "  (lm_head): Linear(in_features=1280, out_features=50257, bias=False)\n",
      ")\n"
     ]
    }
   ],
   "source": [
    "# Load GPT-2 model and tokenizer\n",
    "# model_name = \"gpt2\"\n",
    "model_name = \"gpt2-large\"\n",
    "model = GPT2LMHeadModel.from_pretrained(model_name)\n",
    "tokenizer = GPT2Tokenizer.from_pretrained(model_name)\n",
    "print(\"Model loaded\", model)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b80aace5b7579ff",
   "metadata": {},
   "source": [
    "### define utility functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4fd9b280657acd5",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-10-17T17:53:34.027660Z",
     "start_time": "2024-10-17T17:53:34.021427Z"
    }
   },
   "outputs": [],
   "source": [
    "###\n",
    "# Calculate log probabilities and gradients\n",
    "def get_log_probs_and_gradients(input_ids, prompt_size):\n",
    "    # Forward pass\n",
    "    outputs = model(input_ids, labels=input_ids)\n",
    "    logits = outputs.logits[:, :-1, :]  # Shifted to predict next token\n",
    "    labels = input_ids[:, 1:]  # Shift labels to match logits for the next token\n",
    "\n",
    "    # Log-softmax for log probabilities\n",
    "    log_probs = torch.nn.functional.log_softmax(logits, dim=-1)\n",
    "\n",
    "    # Gather the log probabilities of the actual next tokens (labels)\n",
    "    token_log_probs = log_probs.gather(2, labels.unsqueeze(-1)).squeeze(-1)\n",
    "\n",
    "    # Exclude the prompt tokens from the log probability calculation\n",
    "    token_log_probs = token_log_probs[:, prompt_size:]  # Ignore the first prompt_size tokens\n",
    "\n",
    "    # Sum the log probabilities for the entire sequence\n",
    "    total_log_prob = token_log_probs.sum()\n",
    "\n",
    "    # Backward pass for gradients\n",
    "    model.zero_grad()  # Reset gradients\n",
    "    total_log_prob.backward()  # Compute gradients\n",
    "    # gradients = {name: param.grad for name, param in model.named_parameters() if param.grad is not None}\n",
    "    # Convert gradients to vectors (flattened tensors)\n",
    "    gradients = {name: param.grad.view(-1) for name, param in model.named_parameters() if param.grad is not None}\n",
    "\n",
    "    # Concatenate all gradient vectors into a single vector\n",
    "    gradients = torch.cat([grad for grad in gradients.values()])\n",
    "\n",
    "    return total_log_prob.cpu().item(), gradients.detach().cpu().numpy()\n",
    "\n",
    "\n",
    "# Set random seed for reproducibility\n",
    "def set_seed(seed):\n",
    "    random.seed(seed)\n",
    "    np.random.seed(seed)\n",
    "    torch.manual_seed(seed)\n",
    "    if torch.cuda.is_available():\n",
    "        torch.cuda.manual_seed_all(seed)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d167f313f80b84e",
   "metadata": {},
   "source": [
    "## Experiment\n",
    "### generate samples and calculate log probabilities and gradients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "b1c62ae5080f40f2",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-10-17T17:59:50.022443Z",
     "start_time": "2024-10-17T17:53:34.070728Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 16/16 [05:11<00:00, 19.48s/it]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Text 0: Let's talk about the most recent one: The \"We Can't Stop\" campaign.\n",
      "\n",
      "It is a very specific, yet very powerful, type of anti-gun sentiment that was brought to us by an individual named Dan Schoen, and we've seen its influence in all of our media coverage.\n",
      "\n",
      "\n",
      "Text 1: Let's talk about that, and I hope you guys will be back. This was an hour long podcast that I had a blast recording, and I want to give a huge thanks to all the listeners for being here.\n",
      "\n",
      "\n",
      "First things first, I wanted to give a big thanks to all the listeners. I appreciate\n",
      "Text 2: Let's talk about this again. What does it mean to \"go native?\"\n",
      "\n",
      "The answer is pretty much the same as it always was:\n",
      "\n",
      "Your design is your responsibility, and it is your responsibility to figure out what that design is doing and how it is affecting your users.\n",
      "\n",
      "But with native\n",
      "Text 3: Let's talk about the most common problem: an unresponsive application. The first thing I would do when I found the issue was to stop the application. Here is the code that I used.\n",
      "\n",
      "/** * Check whether the application has been started or not. */ function doInitialization() { var userId =\n",
      "Text 4: Let's talk about the third group: the \"disinterested parties\". They're not \"in\" the economy, in the way that the two groups are. This is why \"the third group\" is so important.\n",
      "\n",
      "Disinterested parties are people who don't have a stake in the economy, but are simply\n",
      "Text 5: Let's talk about how people interact with your app. Here are a couple of things you can do to keep people engaged:\n",
      "\n",
      "Create an engaging app\n",
      "\n",
      "You can create a rich app using an app like Zapier. But it requires a little more attention to detail to make it better. And it's not\n",
      "Text 6: Let's talk about the story itself. I was surprised at how well-constructed this book was, and that was mainly thanks to how well the story line is set up, with the various locations and locations in the story. It makes sense that such a large-scale book would have been written for an adult audience\n",
      "Text 7: Let's talk about the actual game and its contents a bit more.\n",
      "\n",
      "The game itself is a simple game which you can play by itself. There are a lot of puzzles and it's very difficult to complete. You are a detective whose job it is to find the missing daughter of the King, that's your\n",
      "Text 8: Let's talk about how they did their business.\"\n",
      "\n",
      "This isn't the first time that Clinton's campaign has made an issue of a company's political contributions, which she has highlighted as evidence of Wall Street corruption. During her first primary fight against Obama, for example, Clinton attacked a number of companies on the basis\n",
      "Text 9: Let's talk about what we have in common as a community. We're an incredibly supportive community,\" said Mike McGough, vice president of community relations for the Washington Area Transit Authority. \"We believe in the same things that you and I do. We value education. We value education for every day life. We value\n",
      "Text 10: Let's talk about the new rules that came into effect this past week, because I think it's going to make all kinds of life much better for everyone.\n",
      "\n",
      "The rule of six was originally devised by Robert Kahn in 1960. It basically states that a player can play six lands (and the top seven cards)\n",
      "Text 11: Let's talk about the film:\n",
      "\n",
      "I'd like to give credit to two people for this one:\n",
      "\n",
      "Firstly, my favorite people who have made movies about this:\n",
      "\n",
      "The guy who gave me the idea:\n",
      "\n",
      "The guy who shot the movie:\n",
      "\n",
      "And finally, the guy who wrote\n",
      "Text 12: Let's talk about what it means. The first line of the first section of this page is \"The \"real\" world\", but that is an image made up for your convenience. The real world is not real. It's all a figment of your imagination, just like all the other figments of your imagination\n",
      "Text 13: Let's talk about the future.\n",
      "\n",
      "When you look back on the last five or six years, there are some interesting things that you can see that are changing. We're not going to get rid of the nuclear weapon, but we're going to move toward less reliance on it, which means more flexibility in the\n",
      "Text 14: Let's talk about how to keep your money in the bank.\n",
      "\n",
      "You could choose to take out loans or to save money in a pension fund. These approaches can be very powerful if you know the right way to use them.\n",
      "\n",
      "But here's the catch:\n",
      "\n",
      "You could also make a huge mistake\n",
      "Text 15: Let's talk about that a bit. How did you first get into the business?\n",
      "\n",
      "A: Well, we've always done business outside of the state, but there was an interesting opportunity for a while when I had a lot of time with the band. I'd been living in Southern California for a long time\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "# Init parameter\n",
    "n_samples = 16\n",
    "max_length = 64\n",
    "seed = 0\n",
    "\n",
    "# Set the seed to a specific value\n",
    "set_seed(seed)\n",
    "\n",
    "# Generate sentences, calculate log probabilities, and store model's gradients\n",
    "generated_texts = []\n",
    "log_probs = []\n",
    "input_prompt = \"Let's talk about\"\n",
    "# input_prompt = \"Please have a conversation with me about\"\n",
    "# input_prompt = \"Could you please\"\n",
    "# input_prompt = \"I am a\"\n",
    "\n",
    "for i in tqdm(range(n_samples)):\n",
    "    input_ids = tokenizer.encode(input_prompt, return_tensors=\"pt\").to(model.device)\n",
    "    outputs = model.generate(\n",
    "        input_ids, max_length=max_length, do_sample=True, top_p=0.9, pad_token_id=tokenizer.eos_token_id\n",
    "    )\n",
    "    generated_text = tokenizer.decode(outputs[0], skip_special_tokens=True)\n",
    "    generated_texts.append(generated_text)\n",
    "\n",
    "    # Calculate log probs and model parameter gradients\n",
    "    log_prob, gradients = get_log_probs_and_gradients(outputs, prompt_size=input_ids[0].shape[0])\n",
    "    log_probs.append(log_prob)\n",
    "    np.save(f\"npy/{model_name}_gradients_{i}.npy\", gradients)\n",
    "    del gradients\n",
    "    torch.cuda.empty_cache()\n",
    "\n",
    "for i, generated_text in enumerate(generated_texts):\n",
    "    print(f\"Text {i}: {generated_text}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a341b243f440ea4f",
   "metadata": {},
   "source": [
    "### calculate inner products and cosine similarities between gradients of different texts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "74cb7b41f5d5b9e8",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-10-17T18:41:02.111666Z",
     "start_time": "2024-10-17T17:59:51.678461Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== index 0 vs 1 ===\n",
      "log delta: -34.63453674316406\n",
      "Norm ratio: -0.04096949100494385\n",
      "Cosine similarity: 0.010436630807816982\n",
      "=== index 0 vs 2 ===\n",
      "log delta: -39.711326599121094\n",
      "Norm ratio: 0.060503438115119934\n",
      "Cosine similarity: 0.06374682486057281\n",
      "=== index 0 vs 3 ===\n",
      "log delta: -28.649139404296875\n",
      "Norm ratio: 0.012578791938722134\n",
      "Cosine similarity: 0.03294891491532326\n",
      "=== index 0 vs 4 ===\n",
      "log delta: -30.735992431640625\n",
      "Norm ratio: 0.012080834247171879\n",
      "Cosine similarity: 0.05845014378428459\n",
      "=== index 0 vs 5 ===\n",
      "log delta: -31.09703826904297\n",
      "Norm ratio: 0.013283329084515572\n",
      "Cosine similarity: 0.018960298970341682\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== index 0 vs 6 ===\n",
      "log delta: -16.898239135742188\n",
      "Norm ratio: -0.08847668766975403\n",
      "Cosine similarity: 0.005629478022456169\n",
      "=== index 0 vs 7 ===\n",
      "log delta: -18.699554443359375\n",
      "Norm ratio: 0.08078710734844208\n",
      "Cosine similarity: 0.05208093300461769\n",
      "=== index 0 vs 8 ===\n",
      "log delta: -26.00146484375\n",
      "Norm ratio: 0.00750507740303874\n",
      "Cosine similarity: 0.03859593719244003\n",
      "=== index 0 vs 9 ===\n",
      "log delta: -29.740211486816406\n",
      "Norm ratio: -0.14447851479053497\n",
      "Cosine similarity: 0.03536652401089668\n",
      "=== index 0 vs 10 ===\n",
      "log delta: -8.344818115234375\n",
      "Norm ratio: -0.06497731059789658\n",
      "Cosine similarity: 0.04654870182275772\n",
      "=== index 0 vs 11 ===\n",
      "log delta: -34.10285186767578\n",
      "Norm ratio: -0.005609959829598665\n",
      "Cosine similarity: 0.046435896307229996\n",
      "=== index 0 vs 12 ===\n",
      "log delta: -30.98180389404297\n",
      "Norm ratio: -0.02521050162613392\n",
      "Cosine similarity: 0.04969289153814316\n",
      "=== index 0 vs 13 ===\n",
      "log delta: -42.327232360839844\n",
      "Norm ratio: 0.15785320103168488\n",
      "Cosine similarity: 0.040324755012989044\n",
      "=== index 0 vs 14 ===\n",
      "log delta: -33.016632080078125\n",
      "Norm ratio: 0.03751131519675255\n",
      "Cosine similarity: 0.05030199885368347\n",
      "=== index 0 vs 15 ===\n",
      "log delta: -25.764862060546875\n",
      "Norm ratio: 0.037633590400218964\n",
      "Cosine similarity: 0.0248660147190094\n",
      "=== index 1 vs 2 ===\n",
      "log delta: -5.076789855957031\n",
      "Norm ratio: 0.10147294402122498\n",
      "Cosine similarity: 0.0031155296601355076\n",
      "=== index 1 vs 3 ===\n",
      "log delta: 5.9853973388671875\n",
      "Norm ratio: 0.05354828014969826\n",
      "Cosine similarity: 0.052031148225069046\n",
      "=== index 1 vs 4 ===\n",
      "log delta: 3.8985443115234375\n",
      "Norm ratio: 0.05305042490363121\n",
      "Cosine similarity: 0.018347758799791336\n",
      "=== index 1 vs 5 ===\n",
      "log delta: 3.5374984741210938\n",
      "Norm ratio: 0.05425289273262024\n",
      "Cosine similarity: 0.04378625005483627\n",
      "=== index 1 vs 6 ===\n",
      "log delta: 17.736297607421875\n",
      "Norm ratio: -0.04750724509358406\n",
      "Cosine similarity: 0.05862932652235031\n",
      "=== index 1 vs 7 ===\n",
      "log delta: 15.934982299804688\n",
      "Norm ratio: 0.12175661325454712\n",
      "Cosine similarity: 0.07069245725870132\n",
      "=== index 1 vs 8 ===\n",
      "log delta: 8.633071899414062\n",
      "Norm ratio: 0.04847467690706253\n",
      "Cosine similarity: -0.008155076764523983\n",
      "=== index 1 vs 9 ===\n",
      "log delta: 4.894325256347656\n",
      "Norm ratio: -0.10350900888442993\n",
      "Cosine similarity: -0.010116204619407654\n",
      "=== index 1 vs 10 ===\n",
      "log delta: 26.289718627929688\n",
      "Norm ratio: -0.024007828906178474\n",
      "Cosine similarity: 0.04430598393082619\n",
      "=== index 1 vs 11 ===\n",
      "log delta: 0.5316848754882812\n",
      "Norm ratio: 0.03535956144332886\n",
      "Cosine similarity: 0.031928155571222305\n",
      "=== index 1 vs 12 ===\n",
      "log delta: 3.6527328491210938\n",
      "Norm ratio: 0.015758976340293884\n",
      "Cosine similarity: 0.029195785522460938\n",
      "=== index 1 vs 13 ===\n",
      "log delta: -7.692695617675781\n",
      "Norm ratio: 0.19882264733314514\n",
      "Cosine similarity: 0.00919010303914547\n",
      "=== index 1 vs 14 ===\n",
      "log delta: 1.6179046630859375\n",
      "Norm ratio: 0.07848083227872849\n",
      "Cosine similarity: 0.02248852699995041\n",
      "=== index 1 vs 15 ===\n",
      "log delta: 8.869674682617188\n",
      "Norm ratio: 0.07860316336154938\n",
      "Cosine similarity: 0.05054815486073494\n",
      "=== index 2 vs 3 ===\n",
      "log delta: 11.062187194824219\n",
      "Norm ratio: -0.04792461171746254\n",
      "Cosine similarity: 0.0018873742083087564\n",
      "=== index 2 vs 4 ===\n",
      "log delta: 8.975334167480469\n",
      "Norm ratio: -0.04842248186469078\n",
      "Cosine similarity: 0.06231001392006874\n",
      "=== index 2 vs 5 ===\n",
      "log delta: 8.614288330078125\n",
      "Norm ratio: -0.04722001403570175\n",
      "Cosine similarity: 0.06077854335308075\n",
      "=== index 2 vs 6 ===\n",
      "log delta: 22.813087463378906\n",
      "Norm ratio: -0.14898008108139038\n",
      "Cosine similarity: 0.02622465416789055\n",
      "=== index 2 vs 7 ===\n",
      "log delta: 21.01177215576172\n",
      "Norm ratio: 0.02028377167880535\n",
      "Cosine similarity: 0.057667411863803864\n",
      "=== index 2 vs 8 ===\n",
      "log delta: 13.709861755371094\n",
      "Norm ratio: -0.05299825966358185\n",
      "Cosine similarity: 0.006339346524327993\n",
      "=== index 2 vs 9 ===\n",
      "log delta: 9.971115112304688\n",
      "Norm ratio: -0.20498186349868774\n",
      "Cosine similarity: -0.008443514816462994\n",
      "=== index 2 vs 10 ===\n",
      "log delta: 31.36650848388672\n",
      "Norm ratio: -0.12548068165779114\n",
      "Cosine similarity: 0.027245597913861275\n",
      "=== index 2 vs 11 ===\n",
      "log delta: 5.6084747314453125\n",
      "Norm ratio: -0.06611338257789612\n",
      "Cosine similarity: 0.05674014985561371\n",
      "=== index 2 vs 12 ===\n",
      "log delta: 8.729522705078125\n",
      "Norm ratio: -0.08571388572454453\n",
      "Cosine similarity: 0.0417325384914875\n",
      "=== index 2 vs 13 ===\n",
      "log delta: -2.61590576171875\n",
      "Norm ratio: 0.09734974056482315\n",
      "Cosine similarity: 0.044696055352687836\n",
      "=== index 2 vs 14 ===\n",
      "log delta: 6.694694519042969\n",
      "Norm ratio: -0.022992119193077087\n",
      "Cosine similarity: 0.06907078623771667\n",
      "=== index 2 vs 15 ===\n",
      "log delta: 13.946464538574219\n",
      "Norm ratio: -0.0228697769343853\n",
      "Cosine similarity: -0.010140947066247463\n",
      "=== index 3 vs 4 ===\n",
      "log delta: -2.08685302734375\n",
      "Norm ratio: -0.000497882254421711\n",
      "Cosine similarity: 0.02881097048521042\n",
      "=== index 3 vs 5 ===\n",
      "log delta: -2.4478988647460938\n",
      "Norm ratio: 0.0007046361570246518\n",
      "Cosine similarity: 0.031853608787059784\n",
      "=== index 3 vs 6 ===\n",
      "log delta: 11.750900268554688\n",
      "Norm ratio: -0.10105550289154053\n",
      "Cosine similarity: 0.03275178000330925\n",
      "=== index 3 vs 7 ===\n",
      "log delta: 9.9495849609375\n",
      "Norm ratio: 0.06820835918188095\n",
      "Cosine similarity: 0.052962079644203186\n",
      "=== index 3 vs 8 ===\n",
      "log delta: 2.647674560546875\n",
      "Norm ratio: -0.005073640961199999\n",
      "Cosine similarity: -0.0075841606594622135\n",
      "=== index 3 vs 9 ===\n",
      "log delta: -1.0910720825195312\n",
      "Norm ratio: -0.15705722570419312\n",
      "Cosine similarity: 0.01709126867353916\n",
      "=== index 3 vs 10 ===\n",
      "log delta: 20.3043212890625\n",
      "Norm ratio: -0.07755611091852188\n",
      "Cosine similarity: 0.03137873113155365\n",
      "=== index 3 vs 11 ===\n",
      "log delta: -5.453712463378906\n",
      "Norm ratio: -0.01818874292075634\n",
      "Cosine similarity: 0.024448798969388008\n",
      "=== index 3 vs 12 ===\n",
      "log delta: -2.3326644897460938\n",
      "Norm ratio: -0.03778926655650139\n",
      "Cosine similarity: 0.042755186557769775\n",
      "=== index 3 vs 13 ===\n",
      "log delta: -13.678092956542969\n",
      "Norm ratio: 0.14527437090873718\n",
      "Cosine similarity: 0.01638634316623211\n",
      "=== index 3 vs 14 ===\n",
      "log delta: -4.36749267578125\n",
      "Norm ratio: 0.024932492524385452\n",
      "Cosine similarity: 0.0213862843811512\n",
      "=== index 3 vs 15 ===\n",
      "log delta: 2.88427734375\n",
      "Norm ratio: 0.025054801255464554\n",
      "Cosine similarity: 0.018274512141942978\n",
      "=== index 4 vs 5 ===\n",
      "log delta: -0.36104583740234375\n",
      "Norm ratio: 0.0012024559546262026\n",
      "Cosine similarity: 0.032419439405202866\n",
      "=== index 4 vs 6 ===\n",
      "log delta: 13.837753295898438\n",
      "Norm ratio: -0.10055762529373169\n",
      "Cosine similarity: 0.016436558216810226\n",
      "=== index 4 vs 7 ===\n",
      "log delta: 12.03643798828125\n",
      "Norm ratio: 0.06870630383491516\n",
      "Cosine similarity: 0.04489172622561455\n",
      "=== index 4 vs 8 ===\n",
      "log delta: 4.734527587890625\n",
      "Norm ratio: -0.004575751721858978\n",
      "Cosine similarity: 0.028174834325909615\n",
      "=== index 4 vs 9 ===\n",
      "log delta: 0.9957809448242188\n",
      "Norm ratio: -0.15655940771102905\n",
      "Cosine similarity: 0.04263533651828766\n",
      "=== index 4 vs 10 ===\n",
      "log delta: 22.39117431640625\n",
      "Norm ratio: -0.07705820351839066\n",
      "Cosine similarity: 0.044700831174850464\n",
      "=== index 4 vs 11 ===\n",
      "log delta: -3.3668594360351562\n",
      "Norm ratio: -0.01769089512526989\n",
      "Cosine similarity: 0.05571044608950615\n",
      "=== index 4 vs 12 ===\n",
      "log delta: -0.24581146240234375\n",
      "Norm ratio: -0.037291403859853745\n",
      "Cosine similarity: 0.08787855505943298\n",
      "=== index 4 vs 13 ===\n",
      "log delta: -11.591239929199219\n",
      "Norm ratio: 0.1457722783088684\n",
      "Cosine similarity: 0.07307735830545425\n",
      "=== index 4 vs 14 ===\n",
      "log delta: -2.2806396484375\n",
      "Norm ratio: 0.02543036639690399\n",
      "Cosine similarity: 0.061931151896715164\n",
      "=== index 4 vs 15 ===\n",
      "log delta: 4.97113037109375\n",
      "Norm ratio: 0.025552736595273018\n",
      "Cosine similarity: 0.014267626218497753\n",
      "=== index 5 vs 6 ===\n",
      "log delta: 14.198799133300781\n",
      "Norm ratio: -0.10176008939743042\n",
      "Cosine similarity: 0.049039874225854874\n",
      "=== index 5 vs 7 ===\n",
      "log delta: 12.397483825683594\n",
      "Norm ratio: 0.06750372052192688\n",
      "Cosine similarity: 0.07739417254924774\n",
      "=== index 5 vs 8 ===\n",
      "log delta: 5.095573425292969\n",
      "Norm ratio: -0.005778225138783455\n",
      "Cosine similarity: 0.0042105307802557945\n",
      "=== index 5 vs 9 ===\n",
      "log delta: 1.3568267822265625\n",
      "Norm ratio: -0.1577618569135666\n",
      "Cosine similarity: 0.02412496693432331\n",
      "=== index 5 vs 10 ===\n",
      "log delta: 22.752220153808594\n",
      "Norm ratio: -0.07826068997383118\n",
      "Cosine similarity: 0.028028616681694984\n",
      "=== index 5 vs 11 ===\n",
      "log delta: -3.0058135986328125\n",
      "Norm ratio: -0.018893400207161903\n",
      "Cosine similarity: 0.039522770792245865\n",
      "=== index 5 vs 12 ===\n",
      "log delta: 0.115234375\n",
      "Norm ratio: -0.03849387541413307\n",
      "Cosine similarity: 0.01214800775051117\n",
      "=== index 5 vs 13 ===\n",
      "log delta: -11.230194091796875\n",
      "Norm ratio: 0.14456982910633087\n",
      "Cosine similarity: 0.03400560840964317\n",
      "=== index 5 vs 14 ===\n",
      "log delta: -1.9195938110351562\n",
      "Norm ratio: 0.024227971211075783\n",
      "Cosine similarity: 0.048363324254751205\n",
      "=== index 5 vs 15 ===\n",
      "log delta: 5.332176208496094\n",
      "Norm ratio: 0.024350257590413094\n",
      "Cosine similarity: 0.03540729358792305\n",
      "=== index 6 vs 7 ===\n",
      "log delta: -1.8013153076171875\n",
      "Norm ratio: 0.16926386952400208\n",
      "Cosine similarity: 0.0744740441441536\n",
      "=== index 6 vs 8 ===\n",
      "log delta: -9.103225708007812\n",
      "Norm ratio: 0.0959818884730339\n",
      "Cosine similarity: -0.013967431150376797\n",
      "=== index 6 vs 9 ===\n",
      "log delta: -12.841972351074219\n",
      "Norm ratio: -0.05600178241729736\n",
      "Cosine similarity: -0.008512222208082676\n",
      "=== index 6 vs 10 ===\n",
      "log delta: 8.553421020507812\n",
      "Norm ratio: 0.02349943481385708\n",
      "Cosine similarity: -0.005344540346413851\n",
      "=== index 6 vs 11 ===\n",
      "log delta: -17.204612731933594\n",
      "Norm ratio: 0.08286676555871964\n",
      "Cosine similarity: 0.0445815809071064\n",
      "=== index 6 vs 12 ===\n",
      "log delta: -14.083564758300781\n",
      "Norm ratio: 0.06326616555452347\n",
      "Cosine similarity: 0.04682779312133789\n",
      "=== index 6 vs 13 ===\n",
      "log delta: -25.428993225097656\n",
      "Norm ratio: 0.2463298887014389\n",
      "Cosine similarity: 0.005779949948191643\n",
      "=== index 6 vs 14 ===\n",
      "log delta: -16.118392944335938\n",
      "Norm ratio: 0.1259879767894745\n",
      "Cosine similarity: -0.02248454838991165\n",
      "=== index 6 vs 15 ===\n",
      "log delta: -8.866622924804688\n",
      "Norm ratio: 0.12611030042171478\n",
      "Cosine similarity: 0.022530900314450264\n",
      "=== index 7 vs 8 ===\n",
      "log delta: -7.301910400390625\n",
      "Norm ratio: -0.07328202575445175\n",
      "Cosine similarity: -0.0017419893993064761\n",
      "=== index 7 vs 9 ===\n",
      "log delta: -11.040657043457031\n",
      "Norm ratio: -0.22526563704013824\n",
      "Cosine similarity: 0.011046070605516434\n",
      "=== index 7 vs 10 ===\n",
      "log delta: 10.354736328125\n",
      "Norm ratio: -0.14576444029808044\n",
      "Cosine similarity: 0.035081490874290466\n",
      "=== index 7 vs 11 ===\n",
      "log delta: -15.403297424316406\n",
      "Norm ratio: -0.08639714121818542\n",
      "Cosine similarity: 0.058427710086107254\n",
      "=== index 7 vs 12 ===\n",
      "log delta: -12.282249450683594\n",
      "Norm ratio: -0.10599765181541443\n",
      "Cosine similarity: 0.05855412036180496\n",
      "=== index 7 vs 13 ===\n",
      "log delta: -23.62767791748047\n",
      "Norm ratio: 0.07706604897975922\n",
      "Cosine similarity: 0.037304315716028214\n",
      "=== index 7 vs 14 ===\n",
      "log delta: -14.31707763671875\n",
      "Norm ratio: -0.04327583312988281\n",
      "Cosine similarity: 0.015896383672952652\n",
      "=== index 7 vs 15 ===\n",
      "log delta: -7.0653076171875\n",
      "Norm ratio: -0.043153535574674606\n",
      "Cosine similarity: 0.03180306777358055\n",
      "=== index 8 vs 9 ===\n",
      "log delta: -3.7387466430664062\n",
      "Norm ratio: -0.15198363363742828\n",
      "Cosine similarity: 0.0825844332575798\n",
      "=== index 8 vs 10 ===\n",
      "log delta: 17.656646728515625\n",
      "Norm ratio: -0.07248243689537048\n",
      "Cosine similarity: 0.013933965004980564\n",
      "=== index 8 vs 11 ===\n",
      "log delta: -8.101387023925781\n",
      "Norm ratio: -0.01311514526605606\n",
      "Cosine similarity: 0.017987653613090515\n",
      "=== index 8 vs 12 ===\n",
      "log delta: -4.980339050292969\n",
      "Norm ratio: -0.03271563723683357\n",
      "Cosine similarity: 0.04372876137495041\n",
      "=== index 8 vs 13 ===\n",
      "log delta: -16.325767517089844\n",
      "Norm ratio: 0.15034808218479156\n",
      "Cosine similarity: 0.038762956857681274\n",
      "=== index 8 vs 14 ===\n",
      "log delta: -7.015167236328125\n",
      "Norm ratio: 0.03000611439347267\n",
      "Cosine similarity: 0.0339365117251873\n",
      "=== index 8 vs 15 ===\n",
      "log delta: 0.236602783203125\n",
      "Norm ratio: 0.03012850321829319\n",
      "Cosine similarity: 0.03525810316205025\n",
      "=== index 9 vs 10 ===\n",
      "log delta: 21.39539337158203\n",
      "Norm ratio: 0.0795011967420578\n",
      "Cosine similarity: 0.027697598561644554\n",
      "=== index 9 vs 11 ===\n",
      "log delta: -4.362640380859375\n",
      "Norm ratio: 0.13886849582195282\n",
      "Cosine similarity: 0.02140246517956257\n",
      "=== index 9 vs 12 ===\n",
      "log delta: -1.2415924072265625\n",
      "Norm ratio: 0.11926797032356262\n",
      "Cosine similarity: 0.0425054170191288\n",
      "=== index 9 vs 13 ===\n",
      "log delta: -12.587020874023438\n",
      "Norm ratio: 0.3023316264152527\n",
      "Cosine similarity: 0.05666569992899895\n",
      "=== index 9 vs 14 ===\n",
      "log delta: -3.2764205932617188\n",
      "Norm ratio: 0.18198974430561066\n",
      "Cosine similarity: 0.03125656023621559\n",
      "=== index 9 vs 15 ===\n",
      "log delta: 3.9753494262695312\n",
      "Norm ratio: 0.18211208283901215\n",
      "Cosine similarity: 0.06801129877567291\n",
      "=== index 10 vs 11 ===\n",
      "log delta: -25.758033752441406\n",
      "Norm ratio: 0.0593673400580883\n",
      "Cosine similarity: 0.0374247208237648\n",
      "=== index 10 vs 12 ===\n",
      "log delta: -22.636985778808594\n",
      "Norm ratio: 0.039766825735569\n",
      "Cosine similarity: 0.04264835640788078\n",
      "=== index 10 vs 13 ===\n",
      "log delta: -33.98241424560547\n",
      "Norm ratio: 0.22283050417900085\n",
      "Cosine similarity: 0.06621678173542023\n",
      "=== index 10 vs 14 ===\n",
      "log delta: -24.67181396484375\n",
      "Norm ratio: 0.10248862951993942\n",
      "Cosine similarity: 0.043375372886657715\n",
      "=== index 10 vs 15 ===\n",
      "log delta: -17.4200439453125\n",
      "Norm ratio: 0.10261094570159912\n",
      "Cosine similarity: 0.010557271540164948\n",
      "=== index 11 vs 12 ===\n",
      "log delta: 3.1210479736328125\n",
      "Norm ratio: -0.01960049755871296\n",
      "Cosine similarity: 0.05829468369483948\n",
      "=== index 11 vs 13 ===\n",
      "log delta: -8.224380493164062\n",
      "Norm ratio: 0.16346310079097748\n",
      "Cosine similarity: 0.05064830929040909\n",
      "=== index 11 vs 14 ===\n",
      "log delta: 1.0862197875976562\n",
      "Norm ratio: 0.04312129318714142\n",
      "Cosine similarity: 0.04593370482325554\n",
      "=== index 11 vs 15 ===\n",
      "log delta: 8.337989807128906\n",
      "Norm ratio: 0.043243568390607834\n",
      "Cosine similarity: 0.030896499752998352\n",
      "=== index 12 vs 13 ===\n",
      "log delta: -11.345428466796875\n",
      "Norm ratio: 0.18306368589401245\n",
      "Cosine similarity: 0.03664659336209297\n",
      "=== index 12 vs 14 ===\n",
      "log delta: -2.0348281860351562\n",
      "Norm ratio: 0.06272174417972565\n",
      "Cosine similarity: 0.04063982516527176\n",
      "=== index 12 vs 15 ===\n",
      "log delta: 5.216941833496094\n",
      "Norm ratio: 0.06284410506486893\n",
      "Cosine similarity: 0.03830885887145996\n",
      "=== index 13 vs 14 ===\n",
      "log delta: 9.310600280761719\n",
      "Norm ratio: -0.12034183740615845\n",
      "Cosine similarity: 0.06589867174625397\n",
      "=== index 13 vs 15 ===\n",
      "log delta: 16.56237030029297\n",
      "Norm ratio: -0.12021955102682114\n",
      "Cosine similarity: 0.04103846475481987\n",
      "=== index 14 vs 15 ===\n",
      "log delta: 7.25177001953125\n",
      "Norm ratio: 0.00012230125139467418\n",
      "Cosine similarity: -0.0035700888838618994\n"
     ]
    }
   ],
   "source": [
    "cos_sims = []\n",
    "log_deltas = []\n",
    "log_norm_ratios = []\n",
    "\n",
    "for i in range(n_samples):\n",
    "    # print(f\"text {i}: {generated_texts[i]}\")\n",
    "    gradient_i = np.load(f\"npy/{model_name}_gradients_\" + str(i) + \".npy\")\n",
    "    norm_i = np.linalg.norm(gradient_i)\n",
    "    for j in range(i+1 , n_samples):\n",
    "        gradient_j = np.load(f\"npy/{model_name}_gradients_\" + str(j) + \".npy\")\n",
    "        # inner product\n",
    "        inner_product = np.dot(gradient_i, gradient_j)\n",
    "        \n",
    "        # norm of gradients\n",
    "        norm_j = np.linalg.norm(gradient_j)\n",
    "        \n",
    "        # log norm_i / norm_j\n",
    "        log_norm_ratio = np.log(norm_i / norm_j) \n",
    "        \n",
    "        # cos similarity\n",
    "        cosine_similarity = inner_product / (norm_i * norm_j)\n",
    "        \n",
    "        # log delta = log (p_i / p_j) \n",
    "        log_delta = log_probs[i] - log_probs[j]\n",
    "\n",
    "        # Store the results\n",
    "        cos_sims.append(cosine_similarity)\n",
    "        log_deltas.append(log_delta)\n",
    "        log_norm_ratios.append(log_norm_ratio)\n",
    "        \n",
    "        # Print the results\n",
    "        print(f\"=== index {i} vs {j} ===\")\n",
    "        print(f\"log delta: {log_delta}\")\n",
    "        print(f\"Norm ratio: {log_norm_ratio}\")\n",
    "        print(f\"Cosine similarity: {cosine_similarity}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dba0d29faa2eeee8",
   "metadata": {},
   "source": [
    "### plot the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "5fc0feaca0fd6766",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-10-18T02:30:05.738581Z",
     "start_time": "2024-10-18T02:30:03.475926Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 750x750 with 12 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prompt: Let's talk about\n",
      "Correlation matrix\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<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>Log delta</th>\n",
       "      <th>Log norm-ratio</th>\n",
       "      <th>Cosine similarity</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Log delta</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.332567</td>\n",
       "      <td>-0.035197</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Log norm-ratio</th>\n",
       "      <td>-0.332567</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.113806</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Cosine similarity</th>\n",
       "      <td>-0.035197</td>\n",
       "      <td>0.113806</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   Log delta  Log norm-ratio  Cosine similarity\n",
       "Log delta           1.000000       -0.332567          -0.035197\n",
       "Log norm-ratio     -0.332567        1.000000           0.113806\n",
       "Cosine similarity  -0.035197        0.113806           1.000000"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Data frame creation\n",
    "data = pd.DataFrame({\"Log delta\": log_deltas, \"Log norm-ratio\": log_norm_ratios, \"Cosine similarity\": cos_sims})\n",
    "\n",
    "# Create a scatter plot of all pairs\n",
    "sns.pairplot(data)\n",
    "\n",
    "# Adjust the font size\n",
    "plt.rcParams[\"font.size\"] = 12\n",
    "\n",
    "# Save as a PDF file\n",
    "# plt.savefig(f'fdpo-prop-{input_prompt}.pdf')\n",
    "\n",
    "# Display the plot\n",
    "plt.show()\n",
    "\n",
    "# etc.\n",
    "print(f\"Prompt: {input_prompt}\")\n",
    "print(\"Correlation matrix\")\n",
    "data.corr()"
   ]
  }
 ],
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   "language": "python",
   "name": "python3"
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    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.12"
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 },
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