vignettes/hopfield_model.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hopfield Networks\n",
    "\n",
    "*Notes by Aditi Pujar*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A Hopfield network is an early neural network model that was inspired by spin glass models. It has a single layer of fully connected neurons and is a very simple example of recurrent neural network (RNN) architecture.\n",
    "\n",
    "Hopfield networks can be used for pattern recognition and storage. \n",
    "Thus, they used to be very popular in neuroscience as a means to model associative memory, a conceptualisation of the idea that \"neurons that fire together, wire together\".  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Components of a Hopfield Network\n",
    "\n",
    "+ A Hopfield network is made up of $N$ fully connected neurons, $\\sigma_1, \\sigma_2,\\ldots, \\sigma_N$ (where $N$ = length of the pattern we want to store), where each neuron can take values $\\sigma_i=\\pm 1$ (analogous to quantum spins) \n",
    "\n",
    "+ The network is specified through the weight matrix, $W$ where $W_{ij}$ captures how neurons $\\sigma_i$ and $\\sigma_j$ interact. We can encode and extract patterns $\\hat{x_p}, p=1,2,\\ldots,P$, where each pattern $\\hat{x_p}$ is just a particular sequence of spins $\\hat{x_p} = (\\sigma_{1,p},\\sigma_{2,p},\\ldots,\\sigma_{N,p})$.\n",
    "\n",
    "+ There exist conditions on the number of patterns $P$ that can be efficiently encoded into a network with number of neurons $N$. As a general rule of thumb, we require $P/N<0.138$\n",
    "\n",
    "## Steps of implementing a Hopfield Network\n",
    "\n",
    "1. We first \"fit\" our model to our data - we encode the patterns we want to store, $\\{\\hat{x_p}:p=1,2,\\ldots,P\\}$ into our weight matrix, $W$. (Note that weight matrix is symmetric, and there are no self interactions, $W_{ii}=0\\forall i$)\n",
    "\n",
    "For a basic implementation, we can simply take:\n",
    "\n",
    "$$ W_{ij} = \\frac{1}{P}\\sum_p\\sigma_{i,p}\\sigma_{j,p}$$\n",
    "\n",
    "$$ \\implies W = \\frac{1}{P}\\sum_p\\ \\hat{x_p}^T\\hat{x_p}$$\n",
    "\n",
    "(simplifies to averaging over outer products of each $\\hat{x_p}$)  \n",
    "\n",
    "2. Then, we can \"transform\" a noisy/partial pattern $\\hat{x_{trial}}$ on our model, and thus retrieve a de-noised/complete pattern from the network. This is by performing an update rule on $\\hat{x_{trial}}$ and hopefully, after multiple passes, it settles onto one of the stored patterns, $\\hat{x_p}$.\n",
    "\n",
    "Our simplified update rule (with no bias) is defined as:\n",
    "$$ \\sigma_{i,new} = sgn\\left(\\sum_j W_{ij}\\sigma_{j,current} \\right) $$\n",
    "$$ \\hat{x_{new}} = sgn\\left( W\\hat{x_{current}}\\right) $$\n",
    "\n",
    "where our signum function,\n",
    "\n",
    "$$ sgn(\\theta) = \\begin{cases}\n",
    "    +1 & \\text{if } \\theta > 0 \\\\ % & is your \"\\tab\"-like command (it's a tab alignment character)\n",
    "    -1 & \\text{otherwise.}\n",
    "\\end{cases}$$\n",
    "\n",
    "3. Finally, as an aside - inspired as this model is from the Sherrington-Kirkpatrick spin glass systems, we can define an energy associated with each pattern:\n",
    "$$ E = -\\frac{1}{2}\\sum_{i,j}W_{ij}\\sigma_i\\sigma_j $$\n",
    "\n",
    "It can be proven that at each update step defined above, the model will seek to decrease this energy. And that it ultimately will settle into an energy minima. (Knowing that spin glasses have complicated energy landscapes already indicate the possible failure modes of these Hopfield networks) \n",
    "\n",
    "$$ *** $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now implement this for the following scenario of digits from 0-9 being stored as a sequences of 0's and 1's of shape $(1 \\times 90)$ using a $(10\\times 9)$ neuron array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If I have sequences of 0's and 1's that represent the 9 digits in the following manner - "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x300 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_patterns = 10\n",
    "patterns = np.zeros((num_patterns,90))\n",
    "\n",
    "patterns[0] = [0,0,0,1,1,1,0,0,0,\\\n",
    "               0,0,1,0,0,0,1,0,0,\\\n",
    "               0,1,0,0,0,0,0,1,0,\\\n",
    "               0,1,0,0,0,0,0,1,0,\\\n",
    "               0,1,0,0,0,0,0,1,0,\\\n",
    "               0,1,0,0,0,0,0,1,0,\\\n",
    "               0,1,0,0,0,0,0,1,0,\\\n",
    "               0,1,0,0,0,0,0,1,0,\\\n",
    "               0,0,1,0,0,0,1,0,0,\\\n",
    "               0,0,0,1,1,1,0,0,0]\n",
    "\n",
    "patterns[1] = [0,0,0,0,0,1,0,0,0,\\\n",
    "               0,0,0,0,1,1,0,0,0,\\\n",
    "               0,0,0,1,0,1,0,0,0,\\\n",
    "               0,0,1,0,0,1,0,0,0,\\\n",
    "               0,0,0,0,0,1,0,0,0,\\\n",
    "               0,0,0,0,0,1,0,0,0,\\\n",
    "               0,0,0,0,0,1,0,0,0,\\\n",
    "               0,0,0,0,0,1,0,0,0,\\\n",
    "               0,0,0,0,0,1,0,0,0,\\\n",
    "               0,0,1,1,1,1,1,1,1]\n",
    "\n",
    "patterns[2] = [0,0,1,1,1,1,1,0,0,\\\n",
    "               0,1,0,0,0,0,0,1,0,\\\n",
    "               1,0,0,0,0,0,0,0,1,\\\n",
    "               0,0,0,0,0,0,0,0,1,\\\n",
    "               0,0,1,1,1,1,1,1,0,\\\n",
    "               0,1,0,0,0,0,0,0,0,\\\n",
    "               1,0,0,0,0,0,0,0,0,\\\n",
    "               1,0,0,0,0,0,0,0,0,\\\n",
    "               1,0,0,0,0,0,0,0,0,\\\n",
    "               1,1,1,1,1,1,1,1,1]\n",
    "\n",
    "patterns[3] = [1,1,1,1,1,1,1,1,0,\\\n",
    "               0,0,0,0,0,0,1,0,0,\\\n",
    "               0,0,0,0,0,1,0,0,0,\\\n",
    "               0,0,0,0,1,0,0,0,0,\\\n",
    "               0,0,0,1,1,1,1,0,0,\\\n",
    "               0,0,0,0,0,0,0,1,0,\\\n",
    "               0,0,0,0,0,0,0,0,1,\\\n",
    "               0,0,0,0,0,0,0,0,1,\\\n",
    "               0,0,0,0,0,0,0,1,0,\\\n",
    "               1,1,1,1,1,1,1,0,0]\n",
    "\n",
    "patterns[4] = [0,0,0,0,0,0,0,1,1,\\\n",
    "               0,0,0,0,0,0,1,0,1,\\\n",
    "               0,0,0,0,0,1,0,0,1,\\\n",
    "               0,0,0,0,1,0,0,0,1,\\\n",
    "               0,0,0,1,0,0,0,0,1,\\\n",
    "               0,0,1,0,0,0,0,0,1,\\\n",
    "               0,1,1,1,1,1,1,1,1,\\\n",
    "               0,0,0,0,0,0,0,0,1,\\\n",
    "               0,0,0,0,0,0,0,0,1,\\\n",
    "               0,0,0,0,0,0,0,0,1]\n",
    "\n",
    "patterns[5] = [1,1,1,1,1,1,1,1,1,\\\n",
    "               1,0,0,0,0,0,0,0,0,\\\n",
    "               1,0,0,0,0,0,0,0,0,\\\n",
    "               1,0,0,0,0,0,0,0,0,\\\n",
    "               1,1,1,1,1,1,1,0,0,\\\n",
    "               0,0,0,0,0,0,0,1,0,\\\n",
    "               0,0,0,0,0,0,0,0,1,\\\n",
    "               0,0,0,0,0,0,0,0,1,\\\n",
    "               0,0,0,0,0,0,0,1,0,\\\n",
    "               1,1,1,1,1,1,1,0,0]\n",
    "\n",
    "patterns[6] = [0,0,1,1,1,1,1,0,0,\\\n",
    "               0,1,0,0,0,0,0,1,0,\\\n",
    "               1,0,0,0,0,0,0,0,1,\\\n",
    "               1,0,0,0,0,0,0,0,0,\\\n",
    "               1,0,1,1,1,1,1,0,0,\\\n",
    "               1,1,0,0,0,0,0,1,0,\\\n",
    "               1,0,0,0,0,0,0,0,1,\\\n",
    "               1,0,0,0,0,0,0,0,1,\\\n",
    "               0,1,0,0,0,0,0,1,0,\\\n",
    "               0,0,1,1,1,1,1,0,0]\n",
    "\n",
    "patterns[7] = [1,1,1,1,1,1,1,1,1,\\\n",
    "               0,0,0,0,0,0,0,0,1,\\\n",
    "               0,0,0,0,0,0,0,1,0,\\\n",
    "               0,0,0,0,0,0,1,0,0,\\\n",
    "               0,0,0,0,0,1,0,0,0,\\\n",
    "               0,0,0,0,1,0,0,0,0,\\\n",
    "               0,0,0,1,0,0,0,0,0,\\\n",
    "               0,0,1,0,0,0,0,0,0,\\\n",
    "               0,1,0,0,0,0,0,0,0,\\\n",
    "               1,0,0,0,0,0,0,0,0]\n",
    "\n",
    "patterns[8] = [0,0,1,1,1,1,1,0,0,\\\n",
    "               0,1,0,0,0,0,0,1,0,\\\n",
    "               1,0,0,0,0,0,0,0,1,\\\n",
    "               0,1,0,0,0,0,0,1,0,\\\n",
    "               0,0,1,1,1,1,1,0,0,\\\n",
    "               0,1,0,0,0,0,0,1,0,\\\n",
    "               1,0,0,0,0,0,0,0,1,\\\n",
    "               1,0,0,0,0,0,0,0,1,\\\n",
    "               0,1,0,0,0,0,0,1,0,\\\n",
    "               0,0,1,1,1,1,1,0,0]\n",
    "\n",
    "patterns[9] = [0,0,1,1,1,1,1,0,0,\\\n",
    "               0,1,0,0,0,0,0,1,0,\\\n",
    "               1,0,0,0,0,0,0,0,1,\\\n",
    "               0,1,0,0,0,0,0,1,1,\\\n",
    "               0,0,1,1,1,1,1,0,1,\\\n",
    "               0,0,0,0,0,0,0,0,1,\\\n",
    "               0,0,0,0,0,0,0,0,1,\\\n",
    "               1,0,0,0,0,0,0,0,1,\\\n",
    "               0,1,0,0,0,0,0,1,0,\\\n",
    "               0,0,1,1,1,1,1,0,0]\n",
    "\n",
    "dim_pattern = (10,9)\n",
    "fig, axs = plt.subplots(nrows = 2, ncols = num_patterns//2, figsize=(6,3))\n",
    "fig.suptitle('Stored Patterns')\n",
    "for i in range(num_patterns):\n",
    "    xi, yi = i//(num_patterns//2), i % (num_patterns//2)\n",
    "    axs[xi, yi].imshow(patterns[i].reshape(dim_pattern),aspect='auto',cmap = 'binary')\n",
    "    axs[xi, yi].set_xticks([])\n",
    "    axs[xi, yi].set_yticks([])\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thus, I have sequences of 0's and 1's of shape $1\\times N$ (here, $N =90$) that can be reshaped into 2D arrays (of shape $dim_{pattern}=(10,9)$) that represent digits from 0-9.\n",
    "\n",
    "These patterns can be stored in and retrieved from a Hopfield network containing $N$ fully connected neurons in the following manner:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "class HopfieldNetwork:\n",
    "\n",
    "    def __init__(self, stored_patterns, noise = 0.05):\n",
    "\n",
    "        self.num_patterns = stored_patterns.shape[0]\n",
    "        self.N = stored_patterns.shape[1] # no of neurons = size of a single pattern\n",
    "\n",
    "        self.stored_patterns = self.bool_to_spins(stored_patterns)\n",
    "        self.noise = noise\n",
    "\n",
    "        self.W = self.W_matrix()\n",
    "        self.energies = []\n",
    "        self.pattern_history = []\n",
    "\n",
    "    def bool_to_spins(self, patterns):\n",
    "        return np.array([(-np.ones_like(patterns[i,:]))**(patterns[i,:]+1) for i in range(patterns.shape[0])])\n",
    "        \n",
    "    def spins_to_bool(self, patterns):\n",
    "        return np.array([(pat+1)//2 for pat in patterns])\n",
    "    \n",
    "    def W_matrix(self, e = 1):\n",
    "        W = np.zeros((self.N, self.N))\n",
    "        for pattern in self.stored_patterns:\n",
    "            W += e*np.outer(pattern,pattern)\n",
    "\n",
    "        W[np.diag_indices(self.N)] = 0\n",
    "        W /= self.num_patterns\n",
    "        return W\n",
    "    \n",
    "    def energy(self, current_pats):\n",
    "        cp_energy = np.zeros(current_pats.shape[0])\n",
    "\n",
    "        for k, pattern in enumerate(current_pats):\n",
    "            cp_energy[k] = -0.5*np.sum(np.multiply(self.W, np.outer(pattern,pattern)))\n",
    "        return cp_energy\n",
    "\n",
    "    def generate_test(self,noise=None):\n",
    "        if noise is None:\n",
    "            noise = self.noise\n",
    "\n",
    "        test_patterns = []\n",
    "        for pat in self.stored_patterns:\n",
    "            test_patterns.append(np.array([-1*pat[i] if np.random.random()<noise\n",
    "                                            else pat[i] for i in range(pat.size)]))\n",
    "        return np.array(test_patterns)\n",
    "    \n",
    "    def run(self, num_cycles=5, test_pats=None, noise = None):\n",
    "        if test_pats is None:\n",
    "            test_pats = self.generate_test(noise) # generates test_patterns in [-1,1]\n",
    "        else:\n",
    "            test_pats = self.bool_to_spins(test_pats)\n",
    "\n",
    "        current_pats = np.copy(test_pats)\n",
    "        self.pattern_history.append(current_pats)\n",
    "        self.energies.append(self.energy(current_pats))\n",
    "\n",
    "        for _ in range(num_cycles):\n",
    "                new_patterns = np.sign(np.matmul(current_pats,(self.W).T))\n",
    "\n",
    "                self.pattern_history.append(new_patterns)\n",
    "                self.energies.append(self.energy(new_patterns))\n",
    "\n",
    "                current_pats = np.copy(new_patterns)\n",
    "\n",
    "        self.energies = np.array(self.energies)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# instantiate the model\n",
    "model = HopfieldNetwork(patterns)\n",
    "\n",
    "# Run the model\n",
    "model.run()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 300x1200 with 30 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(nrows = model.num_patterns, ncols = 3, figsize = (3,12))\n",
    "for i in range(model.num_patterns):\n",
    "    axs[i,0].imshow(model.pattern_history[0][i].reshape(10,9),aspect=\"auto\",cmap='tab10')\n",
    "    axs[i,1].imshow(model.pattern_history[-1][i].reshape(10,9),aspect=\"auto\",cmap='tab20')\n",
    "    axs[i,2].imshow(model.stored_patterns[i].reshape(10,9),aspect=\"auto\",cmap='tab20c')\n",
    "\n",
    "    axs[i,0].set_xticks([]); axs[i,0].set_yticks([])\n",
    "    axs[i,1].set_xticks([]); axs[i,1].set_yticks([])\n",
    "    axs[i,2].set_xticks([]); axs[i,2].set_yticks([])\n",
    "\n",
    "axs[0,0].set_title('Noisy Input')\n",
    "axs[0,1].set_title('Hopfield\\n Prediction')\n",
    "axs[0,2].set_title('Target')\n",
    "\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that unfortunately, we haven't been succesful in extracting de-noised patterns using the Hopfield network. We have already stumbled across the major pitfall of these methods - existence of spurious states. \n",
    "\n",
    "Spurious states are non-stored patterns that are attractors of the network dynamics. If we start near one of these spurious states the dynamics will converge towards them, which is obviously not ideal. These arise due to the complex energy landscape of the Sherrington-Kirkpatrick spin-glass. This is also reflected in the energy plots of each state, over time:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Hopfield Energy')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1,figsize=(4,4))\n",
    "for i in range(num_patterns):\n",
    "    ax.plot(model.energies[:,i],label=f'pattern {i}')\n",
    "ax.legend()\n",
    "ax.set_title('Energy v/s Time'); ax.set_xlabel('No. of cycles'); ax.set_ylabel('Hopfield Energy')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "We are slightly more successful when we take a smaller number of patterns and we try to choose more distinct digits - e.g. 0,1,3,4,7.\n",
    "\n",
    "## Smaller Subset of Stored Patterns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 500x150 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_patterns = 5\n",
    "sd_patterns = np.zeros((num_patterns,90))\n",
    "\n",
    "sd_patterns[0] = [0,0,0,1,1,1,0,0,0,\\\n",
    "               0,0,1,0,0,0,1,0,0,\\\n",
    "               0,1,0,0,0,0,0,1,0,\\\n",
    "               0,1,0,0,0,0,0,1,0,\\\n",
    "               0,1,0,0,0,0,0,1,0,\\\n",
    "               0,1,0,0,0,0,0,1,0,\\\n",
    "               0,1,0,0,0,0,0,1,0,\\\n",
    "               0,1,0,0,0,0,0,1,0,\\\n",
    "               0,0,1,0,0,0,1,0,0,\\\n",
    "               0,0,0,1,1,1,0,0,0]\n",
    "\n",
    "sd_patterns[1] = [0,0,0,0,0,1,0,0,0,\\\n",
    "               0,0,0,0,1,1,0,0,0,\\\n",
    "               0,0,0,1,0,1,0,0,0,\\\n",
    "               0,0,1,0,0,1,0,0,0,\\\n",
    "               0,0,0,0,0,1,0,0,0,\\\n",
    "               0,0,0,0,0,1,0,0,0,\\\n",
    "               0,0,0,0,0,1,0,0,0,\\\n",
    "               0,0,0,0,0,1,0,0,0,\\\n",
    "               0,0,0,0,0,1,0,0,0,\\\n",
    "               0,0,1,1,1,1,1,1,1]\n",
    "\n",
    "sd_patterns[2] = [0,0,1,1,1,1,1,0,0,\\\n",
    "               0,1,0,0,0,0,0,1,0,\\\n",
    "               1,0,0,0,0,0,0,0,1,\\\n",
    "               0,0,0,0,0,0,0,0,1,\\\n",
    "               0,0,1,1,1,1,1,1,0,\\\n",
    "               0,1,0,0,0,0,0,0,0,\\\n",
    "               1,0,0,0,0,0,0,0,0,\\\n",
    "               1,0,0,0,0,0,0,0,0,\\\n",
    "               1,0,0,0,0,0,0,0,0,\\\n",
    "               1,1,1,1,1,1,1,1,1]\n",
    "\n",
    "sd_patterns[3] = [1,1,1,1,1,1,1,1,0,\\\n",
    "               0,0,0,0,0,0,1,0,0,\\\n",
    "               0,0,0,0,0,1,0,0,0,\\\n",
    "               0,0,0,0,1,0,0,0,0,\\\n",
    "               0,0,0,1,1,1,1,0,0,\\\n",
    "               0,0,0,0,0,0,0,1,0,\\\n",
    "               0,0,0,0,0,0,0,0,1,\\\n",
    "               0,0,0,0,0,0,0,0,1,\\\n",
    "               0,0,0,0,0,0,0,1,0,\\\n",
    "               1,1,1,1,1,1,1,0,0]\n",
    "\n",
    "sd_patterns[4] = [0,0,0,0,0,0,0,1,1,\\\n",
    "               0,0,0,0,0,0,1,0,1,\\\n",
    "               0,0,0,0,0,1,0,0,1,\\\n",
    "               0,0,0,0,1,0,0,0,1,\\\n",
    "               0,0,0,1,0,0,0,0,1,\\\n",
    "               0,0,1,0,0,0,0,0,1,\\\n",
    "               0,1,1,1,1,1,1,1,1,\\\n",
    "               0,0,0,0,0,0,0,0,1,\\\n",
    "               0,0,0,0,0,0,0,0,1,\\\n",
    "               0,0,0,0,0,0,0,0,1]\n",
    "\n",
    "dim_pattern = (10,9)\n",
    "fig, axs = plt.subplots(nrows = 1, ncols = num_patterns, figsize=(5,1.5))\n",
    "fig.suptitle('Stored Patterns\\n')\n",
    "for i in range(num_patterns):\n",
    "    axs[i].imshow(patterns[i].reshape(dim_pattern),aspect='auto')\n",
    "    axs[i].set_xticks([])\n",
    "    axs[i].set_yticks([])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "model_sd = HopfieldNetwork(sd_patterns)\n",
    "model_sd.run()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 300x600 with 15 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(nrows = model_sd.num_patterns, ncols = 3, figsize = (3,6))\n",
    "for i in range(model_sd.num_patterns):\n",
    "    axs[i,0].imshow(model_sd.pattern_history[0][i].reshape(10,9),aspect=\"auto\",cmap='tab10')\n",
    "    axs[i,1].imshow(model_sd.pattern_history[-1][i].reshape(10,9),aspect=\"auto\",cmap='tab20')\n",
    "    axs[i,2].imshow(model_sd.stored_patterns[i].reshape(10,9),aspect=\"auto\",cmap='tab20c')\n",
    "\n",
    "    axs[i,0].set_xticks([]); axs[i,0].set_yticks([])\n",
    "    axs[i,1].set_xticks([]); axs[i,1].set_yticks([])\n",
    "    axs[i,2].set_xticks([]); axs[i,2].set_yticks([])\n",
    "\n",
    "axs[0,0].set_title('Noisy Input')\n",
    "axs[0,1].set_title('Hopfield\\n Prediction')\n",
    "axs[0,2].set_title('Target')\n",
    "\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1,figsize=(4,4))\n",
    "for i in range(num_patterns):\n",
    "    ax.plot(model_sd.energies[:,i],label=f'pattern {i}')\n",
    "ax.legend()\n",
    "ax.set_title('Energy v/s Time'); ax.set_xlabel('No. of cycles'); ax.set_ylabel('Hopfield Energy');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Therefore, we could extract denoised states for 0 and 4 when we took a smaller number of patterns. We could thus demonstrate some utility of a basic Hopfield network. \n",
    "\n",
    "### References\n",
    "* [Spin Glass Model Applications and Extensions](https://lewiscoleblog.com/spin-glass-models-5)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "cphy_hw",
   "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": "3.11.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}