study_xor.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# XOR Task"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook contains the main results for the XOR logic function task, presented as Figure 5 in the paper."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "\n",
    "import sys\n",
    "sys.path.append(\"../../neuroptica\")\n",
    "sys.path.append(\"..\")\n",
    "from utils import *\n",
    "\n",
    "import pickle\n",
    "import time\n",
    "import neuroptica as neu\n",
    "import scipy\n",
    "from scipy import interpolate\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "import matplotlib.gridspec as gridspec\n",
    "\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "from utils_xor import *\n",
    "\n",
    "# %matplotlib inline\n",
    "%config InlineBackend.figure_format = 'svg'\n",
    "\n",
    "mpl.rcParams['text.usetex'] = True\n",
    "mpl.rcParams['font.size'] = 9"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define figure function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_xor(model, losses, X, Y, L):\n",
    "    fig = plt.figure(constrained_layout=True, figsize=(3.5, 5.75))\n",
    "    gs = mpl.gridspec.GridSpec(4, 1, figure=fig, height_ratios=[1, 1, 1, 2])\n",
    "    \n",
    "    ax_schem = fig.add_subplot(gs[0])\n",
    "    ax_schem.axis('off')\n",
    "    ax_io    = fig.add_subplot(gs[1])\n",
    "    ax_loss  = fig.add_subplot(gs[2])\n",
    "    ax_extra = fig.add_subplot(gs[3])\n",
    "  \n",
    "    ax_loss.loglog(losses)\n",
    "    ax_loss.set_xlabel(\"Epoch\")\n",
    "    ax_loss.set_ylabel(\"MSE\")\n",
    "    ax_loss.yaxis.set_major_locator(mpl.ticker.LogLocator(numticks=4))\n",
    "\n",
    "    L_actual = len(model.layers)\n",
    "\n",
    "    ticklabels = []\n",
    "    \n",
    "    for i, x in enumerate(X.T):\n",
    "        signal_trace = []\n",
    "        \n",
    "        colori = plt.cm.tab20(i/X.shape[1])\n",
    "        xlabel = np.array2string(np.round(np.abs(x)+0.1), formatter={'float_kind': lambda x: \"%.0f\\n\" % x}, separator=\"\")\n",
    "        ticklabels.append(xlabel[1:-2])\n",
    "        \n",
    "        l0, = ax_io.plot(i, np.abs(Y[0,i]), \"x\", mec=\"k\", mew=1.25, ms=7)\n",
    "        l1, = ax_io.plot(i, np.abs(model.forward_pass(x))[0], \"o\", c=\"#d62728\", mew=1, ms=4)\n",
    "            \n",
    "        signal_trace.append( np.linalg.norm(model.layers[0].input_prev) )\n",
    "        for l, layer in enumerate(model.layers):\n",
    "            if hasattr(layer, \"nonlinearity\"):\n",
    "                if type(layer.nonlinearity) is neu.nonlinearities.ElectroOpticActivation:\n",
    "                    signal_trace.append( np.linalg.norm(layer.output_prev) )\n",
    "            \n",
    "        signal_trace.append(np.linalg.norm(model.forward_pass(x)))\n",
    "\n",
    "    ax_io.set_xticks(np.arange(0,2**N))\n",
    "    ax_io.set_xticklabels(ticklabels)\n",
    "    ax_io.legend(handles=[l0,l1], labels=[\"Desired output\",\"Learned output\"], fontsize=\"smaller\", loc=5)\n",
    "    ax_io.set_xlabel(\"Input $x$\")\n",
    "    ax_io.set_ylabel(r\"Output $\\vert y \\vert$\")\n",
    "\n",
    "\n",
    "    apply_sublabels([ax_schem, ax_io, ax_loss, ax_extra], x=-45, y=3, prefix=\"(\", postfix=\")\", weight=\"normal\")\n",
    "    \n",
    "    fig.align_labels()\n",
    "    \n",
    "    return fig, ax_extra"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Created 2 layer network\n"
     ]
    },
    {
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       "model_id": "7a8b0035302141e391994e9c9c80a5ad",
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       "version_minor": 0
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       "HBox(children=(IntProgress(value=0, max=5000), HTML(value='')))"
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     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "g     = 1.75 * np.pi\n",
    "phi_b = np.pi\n",
    "\n",
    "N_pad = 0\n",
    "L = 2 # Number of layers\n",
    "N = 4 # Number of inputs\n",
    "y_scale = 0.20\n",
    "\n",
    "model = build_network(g=g, g_taper=1, phi_b=phi_b, alpha=0.1, L=L, N=N+N_pad)\n",
    "X, Y = generate_data_XOR(N, y_scale=y_scale, normalize=True)\n",
    "X_padded = np.pad(X, ((0,N_pad),(0,0)), mode='constant', constant_values=1)\n",
    "\n",
    "optimizer = neu.InSituAdam(model, neu.MeanSquaredError, step_size=0.01)\n",
    "losses = optimizer.fit(X_padded, Y, epochs=5000, batch_size=N**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
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   "source": [
    "fig, _ = plot_xor(model, losses, X_padded, Y, L)"
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   "source": [
    "### Visual check of the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
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    "plt.figure()\n",
    "plt.imshow(np.abs(X))\n",
    "plt.title(\"Unpadded\")\n",
    "plt.ylabel(\"x\")\n",
    "plt.xlabel(\"Training data\")\n",
    "plt.xticks(np.arange(0,2**N));\n",
    "\n",
    "plt.figure()\n",
    "plt.imshow(np.abs(X_padded))\n",
    "plt.title(\"Padded\")\n",
    "plt.ylabel(\"x\")\n",
    "plt.xlabel(\"Training data\")\n",
    "plt.xticks(np.arange(0,2**N));"
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sweep the gain"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "L = 2 # Number of layers\n",
    "N = 4 # Number of inputs\n",
    "y_scale = 0.20\n",
    "\n",
    "N_epochs = 5000\n",
    "N_trials = 20\n",
    "\n",
    "g_vec     = np.arange(0.25, 2.25, 0.25) * np.pi\n",
    "phi_b_vec = np.array([-1.0*np.pi, 0.85*np.pi, 0.0*np.pi, 0.5*np.pi])\n",
    "\n",
    "loss_log = np.zeros((N_trials, g_vec.size, phi_b_vec.size, N_epochs))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i, g in enumerate(g_vec):\n",
    "    for j, phi_b in enumerate(phi_b_vec):\n",
    "        for k in range(0, N_trials):\n",
    "            print(k)\n",
    "            model = build_network(g=g, g_taper=1.0, phi_b=phi_b, alpha=0.1, L=L, N=N)\n",
    "            X, Y = generate_data_XOR(N, y_scale=y_scale, normalize=True)\n",
    "            optimizer = neu.InSituAdam(model, neu.MeanSquaredError, step_size=0.01)\n",
    "            loss_log[k, i, j, :] = optimizer.fit(X, Y, epochs=N_epochs, batch_size=N**2)\n",
    "\n",
    "pickle.dump( { \"loss_log\": loss_log, \"g_vec\": g_vec, \"phi_b_vec\": phi_b_vec }, open( \"loss_log.pkl\", \"wb\" ) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pickle.load( open( \"loss_log.pkl\", \"rb\" ) )\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "loss_min  = np.min(loss_log[:,:,:,-1], axis=0)\n",
    "loss_max  = np.max(loss_log[:,:,:,-1], axis=0)\n",
    "loss_mean = np.mean(loss_log[:,:,:,-1], axis=0)\n",
    "loss_std  = np.std(loss_log[:,:,:,-1],  axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<Figure size 252x414 with 4 Axes>"
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   ],
   "source": [
    "fig, ax = plot_xor(model, losses, X, Y, L);\n",
    "for j, phi_b in enumerate(phi_b_vec):\n",
    "    ax.plot(g_vec/np.pi, loss_mean[:,j], \"o-\", label=\"$\\phi_b$ = %.2f$\\pi$\" % (phi_b_vec[j]/np.pi), ms=5)\n",
    "    ax.fill_between(g_vec/np.pi, loss_min[:,j], loss_max[:,j], alpha=0.25)\n",
    "\n",
    "mpl.rcParams['text.usetex'] = True\n",
    "mpl.rcParams['font.size'] = 9\n",
    "\n",
    "ax.legend(fontsize=\"smaller\")\n",
    "ax.set_yscale(\"log\")\n",
    "ax.set_ylabel(\"Final MSE\")\n",
    "ax.set_xlabel(\"Nonlinearity strength $g_\\phi/\\pi$\")\n",
    "ax.yaxis.set_major_locator(mpl.ticker.LogLocator(numticks=5))"
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