06_LSTM_simpleExamples_clean.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simple LSTM examples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Example code for the lecture series \"Machine Learning for Physicists\" by Florian Marquardt\n",
    "\n",
    "Lecture 6\n",
    "\n",
    "See https://machine-learning-for-physicists.org and the current course website linked there!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook shows how to:\n",
    "- train a recurrent (LSTM) network\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import keras library. Also import some of the layers, so we do not need to\n",
    "# write things like \"layers.Dense\", but can just write \"Dense\" instead\n",
    "from tensorflow.keras.models import Sequential\n",
    "from tensorflow.keras.layers import Dense, LSTM\n",
    "\n",
    "# Import the numpy library for matrix manipulations etc.\n",
    "from numpy import *\n",
    "\n",
    "# Set up the graphics by importing the matplotlib plotting library\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib\n",
    "matplotlib.rcParams['figure.dpi']=300 # highres display\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Recall-Net"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A net that can recall a number (that it has been told before), when asked to do so!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def init_memory_net():\n",
    "    global rnn, timesteps\n",
    "    rnn = Sequential()\n",
    "    # note: batch_input_shape is (batchsize,timesteps,data_dim)\n",
    "    rnn.add(LSTM(5, batch_input_shape=(None, timesteps, 3), return_sequences=True))\n",
    "    rnn.add(LSTM(2, return_sequences=True))\n",
    "    rnn.compile(loss='mean_squared_error', optimizer='adam', metrics=['accuracy'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def produce_batch():\n",
    "    global batchsize, timesteps\n",
    "    \n",
    "    observations=zeros([batchsize,timesteps,3])\n",
    "    desired_output=zeros([batchsize,timesteps,2])\n",
    "    \n",
    "    tell_position=random.randint(int(timesteps/2),size=batchsize)\n",
    "    ask_position=int(timesteps/2)+1+random.randint(int(timesteps/2)-1,size=batchsize)\n",
    "    \n",
    "    # mark input-slot 0 with 1 at the tell_position:\n",
    "    observations[range(batchsize),tell_position,0]=1\n",
    "    # write the value to be memorized into input-slot 1\n",
    "    memorize_numbers=random.random(batchsize)\n",
    "    observations[range(batchsize),tell_position,1]=memorize_numbers\n",
    "    # mark input-slot 2 with 1 at the ask_position\n",
    "    observations[range(batchsize),ask_position,2]=1\n",
    "    \n",
    "    desired_output[range(batchsize),ask_position,0]=memorize_numbers\n",
    "    return(observations,desired_output)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch:  299  deviation:  0.303      0.568       26  deviation:  0.566       0.553       0.541       197  deviation:  0.450      240  deviation:  0.395      \r"
     ]
    }
   ],
   "source": [
    "timesteps=20\n",
    "\n",
    "\n",
    "init_memory_net()\n",
    "\n",
    "batchsize=1\n",
    "test_observations,test_target=produce_batch()\n",
    "\n",
    "batchsize=20\n",
    "epochs=300\n",
    "\n",
    "test_output=zeros([timesteps,epochs])\n",
    "\n",
    "for k in range(epochs):\n",
    "    input_observations,output_targets=produce_batch()\n",
    "    rnn.train_on_batch(input_observations,output_targets)\n",
    "    test_output[:,k]=rnn.predict_on_batch(test_observations)[0,:,0]\n",
    "    print(\"epoch: \", k, \" deviation: \", \"{:1.3f}\".format(sum((test_output[:,k]-test_target[0,:,0])**2)), end=\"      \\r\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 2100x1500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig=plt.figure(figsize=(7,5))\n",
    "plt.imshow(test_output,origin='lower',interpolation='nearest',aspect='auto')\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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dmTMV1x87kypJkiS118p9qeqAYrx2qQ9m5vXAlX1Tq4H9KsQ0q0z4zq649kSY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\n",
      "text/plain": [
       "<Figure size 900x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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MA0cDRwD7AKuAu4GbgCuBjdn0P/qLMKmSJElSexVsqT7u7f8i4lTgd4HHLnDI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\nTkSuQmCC\n",
      "text/plain": [
       "<Figure size 900x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Deviation:  5.774731927305701\n"
     ]
    }
   ],
   "source": [
    "batchsize=30\n",
    "test_observations,test_target=produce_batch()\n",
    "test_output=zeros([batchsize,timesteps])\n",
    "\n",
    "test_output[:,:]=rnn.predict_on_batch(test_observations)[:,:,0]\n",
    "\n",
    "fig=plt.figure(figsize=(3,2))\n",
    "plt.imshow(test_target[:,:,0],vmax=1.0,vmin=0.0,origin='lower',interpolation='nearest',aspect='auto')\n",
    "plt.colorbar()\n",
    "plt.show()\n",
    "\n",
    "fig=plt.figure(figsize=(3,2))\n",
    "plt.imshow(test_output,vmax=1.0,vmin=0.0,origin='lower',interpolation='nearest',aspect='auto')\n",
    "plt.colorbar()\n",
    "plt.show()\n",
    "\n",
    "print(\"Deviation: \", sum((test_output-test_target[:,:,0])**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def produce_batch_tell_ask_twice():\n",
    "    global batchsize, timesteps\n",
    "    \n",
    "    observations=zeros([batchsize,timesteps,3])\n",
    "    desired_output=zeros([batchsize,timesteps,2])\n",
    "    \n",
    "    tell_position=random.randint(int(timesteps/2),size=batchsize)\n",
    "    ask_position=int(timesteps/2)+1+random.randint(int(timesteps/4)-2,size=batchsize)\n",
    "    ask_position2=ask_position+1+random.randint(int(timesteps/4)-2,size=batchsize)\n",
    "    \n",
    "    # mark input-slot 0 with 1 at the tell_position:\n",
    "    observations[range(batchsize),tell_position,0]=1\n",
    "    # write the value to be memorized into input-slot 1\n",
    "    memorize_numbers=random.random(batchsize)\n",
    "    observations[range(batchsize),tell_position,1]=memorize_numbers\n",
    "    # mark input-slot 2 with 1 at the ask_position\n",
    "    observations[range(batchsize),ask_position,2]=1\n",
    "    observations[range(batchsize),ask_position2,2]=1\n",
    "    \n",
    "    desired_output[range(batchsize),ask_position,0]=memorize_numbers\n",
    "    desired_output[range(batchsize),ask_position2,0]=memorize_numbers\n",
    "    return(observations,desired_output)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Id399J2Pp7iuq6rJMbubY73pJNnroJgAAwMJbyr4sjfA77DHWZDEs7DdfVbdN8pdJTprq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\n",
      "text/plain": [
       "<Figure size 1200x900 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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nhqzL/nRSbeKpqu9L8gOT7md09x9sdo7uvrK7/+goSYnpu0vd/RMbrHmvJI/b7JoAAADA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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1200x900 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Deviation:  10.010958280487088\n"
     ]
    }
   ],
   "source": [
    "batchsize=30\n",
    "test_observations,test_target=produce_batch_tell_ask_twice()\n",
    "test_output=zeros([batchsize,timesteps])\n",
    "\n",
    "test_output[:,:]=rnn.predict_on_batch(test_observations)[:,:,0]\n",
    "\n",
    "fig=plt.figure(figsize=(4,3))\n",
    "plt.imshow(test_target[:,:,0],vmax=1.0,vmin=0.0,origin='lower',interpolation='nearest',aspect='auto')\n",
    "plt.colorbar()\n",
    "plt.show()\n",
    "\n",
    "fig=plt.figure(figsize=(4,3))\n",
    "plt.imshow(test_output,vmax=1.0,vmin=0.0,origin='lower',interpolation='nearest',aspect='auto')\n",
    "plt.colorbar()\n",
    "plt.show()\n",
    "\n",
    "print(\"Deviation: \", sum((test_output-test_target[:,:,0])**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def init_memory_net_powerful():\n",
    "    global rnn, batchsize, timesteps\n",
    "    rnn = Sequential()\n",
    "    # note: batch_input_shape is (batchsize,timesteps,data_dim)\n",
    "    rnn.add(LSTM(20, batch_input_shape=(None, timesteps, 3), return_sequences=True))\n",
    "    rnn.add(LSTM(2, return_sequences=True))\n",
    "    rnn.compile(loss='mean_squared_error', optimizer='adam', metrics=['accuracy'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " epoch:  299  deviation:  0.05087573666103082588  deviation:  0.008708851943599112 131  deviation:  0.00908358934283952 201  deviation:  0.06849452315618183 290  deviation:  0.04458693106724219"
     ]
    }
   ],
   "source": [
    "init_memory_net_powerful()\n",
    "\n",
    "timesteps=20\n",
    "\n",
    "batchsize=1\n",
    "test_observations,test_target=produce_batch()\n",
    "\n",
    "batchsize=20\n",
    "epochs=300\n",
    "\n",
    "test_output=zeros([timesteps,epochs])\n",
    "\n",
    "for k in range(epochs):\n",
    "    input_observations,output_targets=produce_batch()\n",
    "    rnn.train_on_batch(input_observations,output_targets)\n",
    "    test_output[:,k]=rnn.predict_on_batch(test_observations)[0,:,0]\n",
    "    print(\"\\r epoch: \", k, \" deviation: \", sum((test_output[:,k]-test_target[0,:,0])**2), end=\"\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 3000x2100 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig=plt.figure(figsize=(10,7))\n",
    "plt.imshow(test_output,origin='lower',interpolation='nearest',aspect='auto')\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Gypl7AAAAADNMujLpWnUZOxpDjSyHlXsAAAAAMFLCPQAAAAAYKdtyAQAAAGaY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\noriC5vgDAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1500x1200 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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LBwAAAACbZ2O25U75ZJJfT/LqJH/a3Z8+9kZVHU3yVUmes/PfYx6Y5MVJvmmB+/1xkp9Z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\nAMdU22PqesjIWmzannsAAAAAcMJQ7gE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47i5J3jrns1cn+ZF5N1bVl1pr35/kvyS5zfbp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\nrT0hsyb5yI/Z2Um+Pcnvr+D5VyS5YpF7Fn2DCwAAAAAnnk3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2gU1kuNcJ5c4put8bERdE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\nLfX/D2oWMlWonyoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1500x1200 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Deviation:  1.174358273945748\n"
     ]
    }
   ],
   "source": [
    "batchsize=30\n",
    "test_observations,test_target=produce_batch()\n",
    "test_output=zeros([batchsize,timesteps])\n",
    "\n",
    "test_output[:,:]=rnn.predict_on_batch(test_observations)[:,:,0]\n",
    "\n",
    "fig=plt.figure(figsize=(5,4))\n",
    "plt.imshow(test_target[:,:,0],vmax=1.0,vmin=0.0,origin='lower',interpolation='nearest',aspect='auto')\n",
    "plt.colorbar()\n",
    "plt.show()\n",
    "\n",
    "fig=plt.figure(figsize=(5,4))\n",
    "plt.imshow(test_output,vmax=1.0,vmin=0.0,origin='lower',interpolation='nearest',aspect='auto')\n",
    "plt.colorbar()\n",
    "plt.show()\n",
    "\n",
    "print(\"Deviation: \", sum((test_output-test_target[:,:,0])**2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Countdown-Net"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A net that counts down: At some random time, it is told a number, and then it outputs a 'one' after this number of steps!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "def init_count_net():\n",
    "    global rnn, batchsize, timesteps\n",
    "    global firstLSTMlayer\n",
    "    rnn = Sequential()\n",
    "    # note: batch_input_shape is (batchsize,timesteps,data_dim)\n",
    "    firstLSTMlayer=LSTM(2, batch_input_shape=(None, timesteps, 2), return_sequences=True)\n",
    "    rnn.add(firstLSTMlayer)\n",
    "    rnn.add(LSTM(2, return_sequences=True))\n",
    "    rnn.compile(loss='mean_squared_error', optimizer='adam', metrics=['accuracy'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def produce_batch_counting():\n",
    "    global batchsize, timesteps\n",
    "    \n",
    "    observations=zeros([batchsize,timesteps,2])\n",
    "    desired_output=zeros([batchsize,timesteps,2])\n",
    "    \n",
    "    tell_position=random.randint(int(timesteps/2),size=batchsize)\n",
    "    count_position=random.randint(int(timesteps/2)-1,size=batchsize)\n",
    "    expect_position=tell_position+count_position\n",
    "    \n",
    "    # mark input-slot 0 with 1 at the tell_position:\n",
    "    observations[range(batchsize),tell_position,0]=1\n",
    "    # write the counter value\n",
    "    observations[range(batchsize),tell_position,1]=count_position\n",
    "    \n",
    "    desired_output[range(batchsize),expect_position,0]=1\n",
    "    return(observations,desired_output)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch:  299  deviation:  0.874    81  deviation:  0.944      deviation:  0.936     154  deviation:  0.923     164  deviation:  0.920     0.907     266  deviation:  0.887    \r"
     ]
    }
   ],
   "source": [
    "timesteps=20\n",
    "\n",
    "\n",
    "init_count_net()\n",
    "\n",
    "\n",
    "batchsize=1\n",
    "test_observations,test_target=produce_batch_counting()\n",
    "\n",
    "batchsize=20\n",
    "epochs=300\n",
    "\n",
    "test_output=zeros([timesteps,epochs])\n",
    "\n",
    "for k in range(epochs):\n",
    "    input_observations,output_targets=produce_batch_counting()\n",
    "    rnn.train_on_batch(input_observations,output_targets)\n",
    "    test_output[:,k]=rnn.predict_on_batch(test_observations)[0,:,0]\n",
    "    print(\"epoch: \", k, \" deviation: \", \"{:1.3f}\".format(sum((test_output[:,k]-test_target[0,:,0])**2)), end=\"    \\r\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 2100x1500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig=plt.figure(figsize=(7,5))\n",
    "plt.imshow(test_output,origin='lower',interpolation='nearest',aspect='auto')\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now: try to inspect output of LSTM neurons at intermediate times. This is also a nice example of how to use some smart keras functionality."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "from tensorflow.keras import Model\n",
    "\n",
    "# get a function that represents the mapping from the \n",
    "# network inputs to the neuron output values of the first LSTM layer:\n",
    "neuron_values = Model([rnn.inputs], [firstLSTMlayer.output])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "batchsize=1\n",
    "test_observations,test_target=produce_batch_counting()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[0. 0.]\n",
      "  [0. 0.]\n",
      "  [0. 0.]\n",
      "  [0. 0.]\n",
      "  [0. 0.]\n",
      "  [0. 0.]\n",
      "  [0. 0.]\n",
      "  [1. 7.]\n",
      "  [0. 0.]\n",
      "  [0. 0.]\n",
      "  [0. 0.]\n",
      "  [0. 0.]\n",
      "  [0. 0.]\n",
      "  [0. 0.]\n",
      "  [0. 0.]\n",
      "  [0. 0.]\n",
      "  [0. 0.]\n",
      "  [0. 0.]\n",
      "  [0. 0.]\n",
      "  [0. 0.]]]\n"
     ]
    }
   ],
   "source": [
    "print(test_observations)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "the_values=neuron_values.predict_on_batch([test_observations])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 20, 2)"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shape(the_values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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aMv/l/Uc0x/eK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\n",
      "text/plain": [
       "<Figure size 1800x1200 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(the_values[0,:,:],interpolation='nearest',origin='lower',aspect='auto')\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "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": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}