zk-stats-lib/examples/variance/variance.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: ezkl==7.0.0 in /Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages (from -r ../../requirements.txt (line 1)) (7.0.0)\n",
      "Requirement already satisfied: torch in /Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages (from -r ../../requirements.txt (line 2)) (2.1.1)\n",
      "Requirement already satisfied: requests in /Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages (from -r ../../requirements.txt (line 3)) (2.31.0)\n",
      "Requirement already satisfied: scipy in /Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages (from -r ../../requirements.txt (line 4)) (1.11.4)\n",
      "Requirement already satisfied: numpy in /Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages (from -r ../../requirements.txt (line 5)) (1.26.2)\n",
      "Requirement already satisfied: matplotlib in /Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages (from -r ../../requirements.txt (line 6)) (3.8.2)\n",
      "Requirement already satisfied: statistics in /Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages (from -r ../../requirements.txt (line 7)) (1.0.3.5)\n",
      "Requirement already satisfied: onnx in /Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages (from -r ../../requirements.txt (line 8)) (1.15.0)\n",
      "Requirement already satisfied: filelock in /Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages (from torch->-r ../../requirements.txt (line 2)) (3.13.1)\n",
      "Requirement already satisfied: sympy in /Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages (from torch->-r ../../requirements.txt (line 2)) (1.12)\n",
      "Requirement already satisfied: jinja2 in /Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages (from torch->-r ../../requirements.txt (line 2)) (3.1.2)\n",
      "Requirement already satisfied: networkx in /Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages (from torch->-r ../../requirements.txt (line 2)) (3.2.1)\n",
      "Requirement already satisfied: fsspec in /Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages (from torch->-r ../../requirements.txt (line 2)) (2023.10.0)\n",
      "Requirement already satisfied: typing-extensions in /Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages (from torch->-r ../../requirements.txt (line 2)) (4.8.0)\n",
      "Requirement already satisfied: certifi>=2017.4.17 in /Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages (from requests->-r ../../requirements.txt (line 3)) (2023.11.17)\n",
      "Requirement already satisfied: urllib3<3,>=1.21.1 in /Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages (from requests->-r ../../requirements.txt (line 3)) (2.1.0)\n",
      "Requirement already satisfied: charset-normalizer<4,>=2 in /Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages (from requests->-r ../../requirements.txt (line 3)) (3.3.2)\n",
      "Requirement already satisfied: idna<4,>=2.5 in /Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages (from requests->-r ../../requirements.txt (line 3)) (3.6)\n",
      "Requirement already satisfied: contourpy>=1.0.1 in /Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages (from matplotlib->-r ../../requirements.txt (line 6)) (1.2.0)\n",
      "Requirement already satisfied: python-dateutil>=2.7 in /Users/jernkun/Library/Python/3.10/lib/python/site-packages (from matplotlib->-r ../../requirements.txt (line 6)) (2.8.2)\n",
      "Requirement already satisfied: pyparsing>=2.3.1 in /Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages (from matplotlib->-r ../../requirements.txt (line 6)) (3.1.1)\n",
      "Requirement already satisfied: pillow>=8 in /Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages (from matplotlib->-r ../../requirements.txt (line 6)) (10.1.0)\n",
      "Requirement already satisfied: kiwisolver>=1.3.1 in /Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages (from matplotlib->-r ../../requirements.txt (line 6)) (1.4.5)\n",
      "Requirement already satisfied: packaging>=20.0 in /Users/jernkun/Library/Python/3.10/lib/python/site-packages (from matplotlib->-r ../../requirements.txt (line 6)) (23.2)\n",
      "Requirement already satisfied: cycler>=0.10 in /Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages (from matplotlib->-r ../../requirements.txt (line 6)) (0.12.1)\n",
      "Requirement already satisfied: fonttools>=4.22.0 in /Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages (from matplotlib->-r ../../requirements.txt (line 6)) (4.45.1)\n",
      "Requirement already satisfied: docutils>=0.3 in /Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages (from statistics->-r ../../requirements.txt (line 7)) (0.20.1)\n",
      "Requirement already satisfied: protobuf>=3.20.2 in /Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages (from onnx->-r ../../requirements.txt (line 8)) (4.25.1)\n",
      "Requirement already satisfied: six>=1.5 in /Users/jernkun/Library/Python/3.10/lib/python/site-packages (from python-dateutil>=2.7->matplotlib->-r ../../requirements.txt (line 6)) (1.16.0)\n",
      "Requirement already satisfied: MarkupSafe>=2.0 in /Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages (from jinja2->torch->-r ../../requirements.txt (line 2)) (2.1.3)\n",
      "Requirement already satisfied: mpmath>=0.19 in /Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages (from sympy->torch->-r ../../requirements.txt (line 2)) (1.3.0)\n",
      "\u001b[33mWARNING: You are using pip version 21.2.3; however, version 23.3.2 is available.\n",
      "You should consider upgrading via the '/usr/local/bin/python3 -m pip install --upgrade pip' command.\u001b[0m\n",
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "pip install -r ../../requirements.txt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import ezkl\n",
    "import torch\n",
    "from torch import nn\n",
    "import json\n",
    "import os\n",
    "import time\n",
    "import scipy\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import statistics\n",
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "%run -i ../../zkstats/core.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# init path\n",
    "os.makedirs(os.path.dirname('shared/'), exist_ok=True)\n",
    "os.makedirs(os.path.dirname('prover/'), exist_ok=True)\n",
    "verifier_model_path = os.path.join('shared/verifier.onnx')\n",
    "prover_model_path = os.path.join('prover/prover.onnx')\n",
    "verifier_compiled_model_path = os.path.join('shared/verifier.compiled')\n",
    "prover_compiled_model_path = os.path.join('prover/prover.compiled')\n",
    "pk_path = os.path.join('shared/test.pk')\n",
    "vk_path = os.path.join('shared/test.vk')\n",
    "proof_path = os.path.join('shared/test.pf')\n",
    "settings_path = os.path.join('shared/settings.json')\n",
    "srs_path = os.path.join('shared/kzg.srs')\n",
    "witness_path = os.path.join('prover/witness.json')\n",
    "# this is private to prover since it contains actual data\n",
    "sel_data_path = os.path.join('prover/sel_data.json')\n",
    "# this is just dummy random value\n",
    "sel_dummy_data_path = os.path.join('shared/sel_dummy_data.json')"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "=======================  ZK-STATS FLOW ======================="
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_path = os.path.join('data.json')\n",
    "dummy_data_path = os.path.join('shared/dummy_data.json')\n",
    "\n",
    "data = json.loads(open(data_path, \"r\").read())['col_name']\n",
    "data_tensor = torch.reshape(torch.tensor(data),(1,-1, 1))\n",
    "\n",
    "create_dummy(data_path, dummy_data_path)\n",
    "dummy_data = json.loads(open(dummy_data_path, \"r\").read())['col_name']\n",
    "dummy_data_tensor = torch.reshape(torch.tensor(dummy_data), (1,-1,1))\n",
    "\n",
    "dummy_theory_output = torch.var(dummy_data_tensor, correction = 1)\n",
    "dummy_data_mean = torch.mean(dummy_data_tensor)\n",
    "theory_output = torch.var(data_tensor, correction = 1)\n",
    "data_mean = torch.mean(data_tensor)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "scales = [2]\n",
    "selected_columns = ['col_name']\n",
    "commitment_maps = get_data_commitment_maps(data_path, scales)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages/torch/onnx/symbolic_opset9.py:2174: FutureWarning: 'torch.onnx.symbolic_opset9._cast_Bool' is deprecated in version 2.0 and will be removed in the future. Please Avoid using this function and create a Cast node instead.\n",
      "  return fn(g, to_cast_func(g, input, False), to_cast_func(g, other, False))\n"
     ]
    }
   ],
   "source": [
    "# Verifier/ data consumer side:\n",
    "class verifier_model(nn.Module):\n",
    "    def __init__(self):\n",
    "        super(verifier_model, self).__init__()\n",
    "        # w represents mean in this case\n",
    "        self.w = nn.Parameter(data = dummy_theory_output, requires_grad = False)\n",
    "        self.data_mean = nn.Parameter(data = dummy_data_mean, requires_grad = False)\n",
    "\n",
    "    def forward(self,X):\n",
    "        x_mean_cons = torch.abs(torch.sum(X)-X.size()[1]*(self.data_mean))<=torch.abs(0.01*X.size()[1]*self.data_mean)\n",
    "        return (torch.logical_and(torch.abs(torch.sum((X-self.data_mean)*(X-self.data_mean))-self.w*(X.size()[1]-1))<=torch.abs(0.01*self.w*(X.size()[1]-1)),x_mean_cons ),self.w)\n",
    "\n",
    "verifier_define_calculation(dummy_data_path, selected_columns,sel_dummy_data_path,verifier_model, verifier_model_path)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "theory output:  tensor(212.5777)\n",
      "==== Generate & Calibrate Setting ====\n",
      "scale:  [2]\n",
      "setting:  {\"run_args\":{\"tolerance\":{\"val\":0.0,\"scale\":1.0},\"input_scale\":2,\"param_scale\":2,\"scale_rebase_multiplier\":10,\"lookup_range\":[-20332,8],\"logrows\":15,\"num_inner_cols\":2,\"variables\":[[\"batch_size\",1]],\"input_visibility\":{\"Hashed\":{\"hash_is_public\":true,\"outlets\":[]}},\"output_visibility\":\"Public\",\"param_visibility\":\"Private\"},\"num_rows\":14432,\"total_assignments\":1521,\"total_const_size\":8,\"model_instance_shapes\":[[1],[1]],\"model_output_scales\":[0,2],\"model_input_scales\":[2],\"module_sizes\":{\"kzg\":[],\"poseidon\":[14432,[1]],\"elgamal\":[0,[0]]},\"required_lookups\":[\"Abs\",{\"GreaterThan\":{\"a\":0.0}}],\"check_mode\":\"UNSAFE\",\"version\":\"7.0.0\",\"num_blinding_factors\":null}\n"
     ]
    }
   ],
   "source": [
    "# Prover/ data owner side\n",
    "print(\"theory output: \", theory_output)\n",
    "class prover_model(nn.Module):\n",
    "    def __init__(self):\n",
    "        super(prover_model, self).__init__()\n",
    "        # w represents mean in this case\n",
    "        self.w = nn.Parameter(data = theory_output, requires_grad = False)\n",
    "        self.data_mean = nn.Parameter(data = data_mean, requires_grad = False)\n",
    "    def forward(self,X):\n",
    "        x_mean_cons = torch.abs(torch.sum(X)-X.size()[1]*(self.data_mean))<=torch.abs(0.01*X.size()[1]*self.data_mean)\n",
    "        return (torch.logical_and(torch.abs(torch.sum((X-self.data_mean)*(X-self.data_mean))-self.w*(X.size()[1]-1))<=torch.abs(0.01*self.w*(X.size()[1]-1)),x_mean_cons ),self.w)\n",
    "\n",
    "\n",
    "prover_gen_settings(data_path, selected_columns, sel_data_path, prover_model,prover_model_path, scales, \"resources\", settings_path)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "spawning module 0\n",
      "spawning module 2\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "==== setting up ezkl ====\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "spawning module 0\n",
      "spawning module 2\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time setup: 3.455188035964966 seconds\n",
      "=======================================\n",
      "Theory output:  tensor(212.5777)\n",
      "!@# compiled_model exists? True\n",
      "!@# compiled_model exists? True\n",
      "==== Generating Witness ====\n",
      "witness boolean:  1.0\n",
      "witness result 1 : 212.5\n",
      "==== Generating Proof ====\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "spawning module 0\n",
      "spawning module 2\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "proof:  {'instances': [[[12907834141446617622, 16863260785082668294, 2215826187815521673, 2191547160659437828], [12436184717236109307, 3962172157175319849, 7381016538464732718, 1011752739694698287], [14958435514946940528, 17320992765071788231, 18318297740500540397, 2188255106962760522]]], 'proof': '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'transcript_type': 'EVM'}\n",
      "Time gen prf: 4.567595958709717 seconds\n"
     ]
    }
   ],
   "source": [
    "# Here verifier & prover can concurrently call setup since all params are public to get pk.\n",
    "# Here write as verifier function to emphasize that verifier must calculate its own vk to be sure\n",
    "setup(verifier_model_path, verifier_compiled_model_path, settings_path,vk_path, pk_path )\n",
    "\n",
    "print(\"=======================================\")\n",
    "# Prover generates proof\n",
    "print(\"Theory output: \", theory_output)\n",
    "prover_gen_proof(prover_model_path, sel_data_path, witness_path, prover_compiled_model_path, settings_path, proof_path, pk_path)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "num_inputs:  1\n",
      "prf instances:  [[[12907834141446617622, 16863260785082668294, 2215826187815521673, 2191547160659437828], [12436184717236109307, 3962172157175319849, 7381016538464732718, 1011752739694698287], [14958435514946940528, 17320992765071788231, 18318297740500540397, 2188255106962760522]]]\n",
      "proof boolean:  1.0\n",
      "proof result 1 : 212.5\n",
      "verified\n"
     ]
    }
   ],
   "source": [
    "# Verifier verifies\n",
    "verifier_verify(proof_path, settings_path, vk_path, selected_columns, commitment_maps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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