Helmholtz Machine.ipynb

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  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
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   },
   "outputs": [],
   "source": [
    "%matplotlib notebook\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib\n",
    "\n",
    "matplotlib.rc('image', cmap='coolwarm', interpolation='none')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def sample_from_world():\n",
    "    D = np.zeros((3, 3))\n",
    "    if np.random.rand() < (2 / 3):\n",
    "        idx = np.random.randint(0, 6)\n",
    "        if idx == 0:\n",
    "            D[:, [1, 2]] = 1\n",
    "        elif idx == 1:\n",
    "            D[:, [0, 2]] = 1\n",
    "        elif idx == 2:\n",
    "            D[:, [0, 1]] = 1\n",
    "        elif idx == 3:\n",
    "            D[:, 2] = 1\n",
    "        elif idx == 4:\n",
    "            D[:, 1] = 1\n",
    "        elif idx == 5:\n",
    "            D[:, 0] = 1\n",
    "            \n",
    "    else:\n",
    "        idx = np.random.randint(0, 6)\n",
    "        if idx == 0:\n",
    "            D[[1, 2]] = 1\n",
    "        elif idx == 1:\n",
    "            D[[0, 2]] = 1\n",
    "        elif idx == 2:\n",
    "            D[[0, 1]] = 1\n",
    "        elif idx == 3:\n",
    "            D[2] = 1\n",
    "        elif idx == 4:\n",
    "            D[1] = 1\n",
    "        elif idx == 5:\n",
    "            D[0] = 1\n",
    "        \n",
    "    return D.ravel()[:, None]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  1.,  1.],\n",
       "       [ 1.,  1.,  1.],\n",
       "       [ 0.,  0.,  0.]])"
      ]
     },
     "execution_count": 176,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample_from_world().reshape((3, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "epsilon_b = 0.01 # learning rate for the bias\n",
    "epsilon_W = 0.01 # learning rate for the top layer\n",
    "epsilon_V = 0.15 # learning rate fot he bottom layer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def add_ones(X):\n",
    "    col = np.ones((1, X.shape[1]))\n",
    "    return np.concatenate([X, col], axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def sigmoid(X):\n",
    "    return 1 / (1 + np.exp(-X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def sample(p):\n",
    "    x = np.random.rand(*p.shape) < p\n",
    "    return x.astype(int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def wake(V_G, W_G, b_G, V_R, W_R):\n",
    "    # experience reality\n",
    "    d = sample_from_world()\n",
    "    \n",
    "    # pass sense datum up through recognition network\n",
    "    y = sample(sigmoid(np.dot(V_R, add_ones(d))))\n",
    "    x = sample(sigmoid(np.dot(W_R, add_ones(y))))\n",
    "    \n",
    "    # pass back down through generative network and compute probabilities\n",
    "    xi = sigmoid(b_G)\n",
    "    psi = sigmoid(np.dot(W_G, add_ones(x)))\n",
    "    delta = sigmoid(np.dot(V_G, add_ones(y)))\n",
    "    \n",
    "    # adjust generative weights\n",
    "    b_G += epsilon_b * (x - xi)\n",
    "    W_G += epsilon_W * np.dot(y - psi, add_ones(x).T)\n",
    "    V_G += epsilon_V * np.dot(d - delta, add_ones(y).T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def sleep(V_G, W_G, b_G, V_R, W_R):\n",
    "    # initiate a \"dream\"\n",
    "    x = sample(sigmoid(b_G))\n",
    "    \n",
    "    # pass down through generative network\n",
    "    y = sample(sigmoid(np.dot(W_G, add_ones(x))))\n",
    "    d = sample(sigmoid(np.dot(V_G, add_ones(y))))\n",
    "    \n",
    "    # pass back up through recognition network\n",
    "    psi = sigmoid(np.dot(V_R, add_ones(d)))\n",
    "    xi = sigmoid(np.dot(W_R, add_ones(y)))\n",
    "    \n",
    "    # adjust recognition weights\n",
    "    V_R += epsilon_V * np.dot(y - psi, add_ones(d).T)\n",
    "    W_R += epsilon_W * np.dot(x - xi, add_ones(y).T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# generative weights\n",
    "V_G = np.zeros((9, 7))\n",
    "W_G = np.zeros((6, 2))\n",
    "b_G = np.zeros((1, 1))\n",
    "\n",
    "# recognition weights\n",
    "V_R = np.zeros((6, 10))\n",
    "W_R = np.zeros((1, 7))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 1, 0],\n",
       "       [0, 0, 0],\n",
       "       [0, 1, 0]])"
      ]
     },
     "execution_count": 195,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# initiate a \"dream\"\n",
    "x = sample(sigmoid(b_G))\n",
    "    \n",
    "# pass down through generative network\n",
    "y = sample(sigmoid(np.dot(W_G, add_ones(x))))\n",
    "d = sample(sigmoid(np.dot(V_G, add_ones(y))))\n",
    "\n",
    "d.reshape((3, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
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       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x;\n",
       "    var y = canvas_pos.y;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# set up plotting\n",
    "fig, axes = plt.subplots(3, 2)\n",
    "vmin = -5\n",
    "vmax = 5\n",
    "im_b_G = axes[0, 1].imshow(b_G, vmin=vmin, vmax=vmax)\n",
    "axes[0, 1].set_title(\"$b_G$\")\n",
    "im_W_G = axes[1, 1].imshow(W_G, vmin=vmin, vmax=vmax)\n",
    "axes[1, 1].set_title(\"$W_G$\")\n",
    "im_V_G = axes[2, 1].imshow(V_G, vmin=vmin, vmax=vmax)\n",
    "axes[2, 1].set_title(\"$V_G$\")\n",
    "im_W_R = axes[1, 0].imshow(W_R, vmin=vmin, vmax=vmax)\n",
    "axes[1, 0].set_title(\"$W_R$\")\n",
    "im_V_R = axes[2, 0].imshow(V_R, vmin=vmin, vmax=vmax)\n",
    "axes[2, 0].set_title(\"$V_R$\")\n",
    "fig.set_size_inches(8, 8, forward=True)\n",
    "plt.tight_layout()\n",
    "plt.draw()\n",
    "plt.show()\n",
    "\n",
    "for i in range(60000):\n",
    "    wake(V_G, W_G, b_G, V_R, W_R)\n",
    "    sleep(V_G, W_G, b_G, V_R, W_R)\n",
    "    if (i % 100) == 0:\n",
    "        im_b_G.set_data(b_G)\n",
    "        im_W_G.set_data(W_G)\n",
    "        im_V_G.set_data(V_G)\n",
    "        im_W_R.set_data(W_R)\n",
    "        im_V_R.set_data(V_R)\n",
    "        fig.canvas.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 0, 0],\n",
       "       [1, 1, 1],\n",
       "       [0, 0, 0]])"
      ]
     },
     "execution_count": 208,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# initiate a \"dream\"\n",
    "x = sample(sigmoid(b_G))\n",
    "    \n",
    "# pass down through generative network\n",
    "y = sample(sigmoid(np.dot(W_G, add_ones(x))))\n",
    "d = sample(sigmoid(np.dot(V_G, add_ones(y))))\n",
    "\n",
    "d.reshape((3, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.5.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}