0.p_bits_101.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# p-Bits 101\n",
    "\n",
    "This is a series of notebooks which elaborates on the algorithmic aspects of probabilistic computing, which has emerged as an alternative computing technology in the last 5 years. Probabilistic computing is a descendant of stochastic computing - although, the two shouldn't be confused.\n",
    "\n",
    "Stochastic computing involves the use of uniform random bit-streams in conventional logic gates to arrive at analogues of computation - like flipping two coins and counting the pair of heads relative to coin flips and calling this multiplication of the two probabilities of a head on each individual coin.\n",
    "\n",
    "Probabilistic computing on the other hand, relies on p-bits, tunable noise sources that interact via an Ising model to create what are effectively small Boltzmann machines which can be thought of as \"invertible\" logic gates that form invertible logic circuits.\n",
    "\n",
    "The behaviour of a p-bit is described with the following equation:\n",
    "\n",
    "$$m = \\text{sgn}(U(-1,+1)+\\tanh(a))$$\n",
    "\n",
    "Where $m$ is the final state of the $m$, $sgn$ is the \"sign\" function, $U(-1,+1)$ represents the uniform probability between in the interval $(-1,+1)$ and $a$ is an activation term.\n",
    "\n",
    "Below, we'll define a simple p-bit and the change its activation to demonstrate its behaviour clearly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<BarContainer object of 2 artists>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x300 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from random import uniform\n",
    "from math import tanh\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "class pbit():\n",
    "\n",
    "    def __init__(self, clamped=None):\n",
    "\n",
    "        self.activation = 0\n",
    "        self.clamped = None \n",
    "        if clamped != None:\n",
    "            self.clamped = clamped\n",
    "    \n",
    "    def sample(self):\n",
    "        if self.clamped != None:\n",
    "            return self.clamped\n",
    "        return self.__sgn(uniform(-1,1)+tanh(self.activation))\n",
    "\n",
    "    def __sgn(self,i):\n",
    "        if i <= 0:\n",
    "            return -1\n",
    "        return 1\n",
    "\n",
    "fig,axs = plt.subplots(1,4,figsize=(12,3))\n",
    "num_samples = 100\n",
    "\n",
    "# Iterate through a few different activation values\n",
    "for i in range(3):\n",
    "    samples = []\n",
    "\n",
    "    my_first_pbit = pbit()\n",
    "    my_first_pbit.activation = -1 + i\n",
    "\n",
    "    for j in range(num_samples):\n",
    "        samples.append(my_first_pbit.sample())\n",
    "\n",
    "    val = sum([s < 0 for s in samples])\n",
    "\n",
    "    axs[i].set_title(f\"Activation: {-1+i}\")\n",
    "    axs[i].bar([-1,1],[val,num_samples-val])\n",
    "\n",
    "# Just a quick example to explain clamping behaviour\n",
    "samples = []\n",
    "my_first_pbit = pbit(1)\n",
    "print(my_first_pbit.clamped)\n",
    "for j in range(num_samples):\n",
    "    samples.append(my_first_pbit.sample())\n",
    "\n",
    "val = sum([s < 0 for s in samples])\n",
    "\n",
    "axs[3].set_title(f\"Clamped: {1}\")\n",
    "axs[3].bar([-1,1],[val,num_samples-val])\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.10.6"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "e7370f93d1d0cde622a1f8e1c04877d8463912d04d973331ad4851f04de6915a"
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 },
 "nbformat": 4,
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}