http://git-wip-us.apache.org/repos/asf/incubator-singa/blob/6ef4bbee/doc/notebook/mlp.ipynb
----------------------------------------------------------------------
diff --git a/doc/notebook/mlp.ipynb b/doc/notebook/mlp.ipynb
index 0f0153b..ea21ee6 100755
--- a/doc/notebook/mlp.ipynb
+++ b/doc/notebook/mlp.ipynb
@@ -1,6 +1,15 @@
 {
  "cells": [
   {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Train a multi-layer perceptron (MLP) model \n",
+    "\n",
+    "In this notebook, we are going to use PySINGA to train a MLP model for 
classifying 2-d points into two categories (i.e., positive and negative). We 
use this example to illustrate the usage of PySINGA's modules. Please refer to 
the [documentation page](http://singa.apache.org/en/docs/index.html) for the 
functions of each module."
+   ]
+  },
+  {
    "cell_type": "code",
    "execution_count": 1,
    "metadata": {
@@ -8,43 +17,107 @@
    },
    "outputs": [],
    "source": [
-    "# pls install PySinga before running the code\n",
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "%matplotlib inline"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "To import PySINGA modules"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
     "from singa import tensor\n",
-    "from singa import device\n",
     "from singa import optimizer\n",
     "from singa import loss\n",
     "from singa import layer\n",
-    "from singa import initializer\n",
-    "from singa.proto.model_pb2 import kTrain\n",
-    "import numpy as np\n",
+    "from singa.proto import model_pb2"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Task is to train a MLP model to classify 2-d points into the positive and 
negative categories.\n",
     "\n",
-    "import matplotlib.pyplot as plt\n",
-    "%matplotlib inline\n",
-    "\n"
+    "## Training data generation\n",
+    "\n",
+    "The following thress steps would be conducted to generate the training 
data.\n",
+    "1. draw a boundary line in the 2-d space \n",
+    "2. generate data points in the 2-dspace\n",
+    "3. label the data points above the boundary line as positive points, and 
label other points as negative points."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We draw the boundary line as $y=5x+1$"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "# generate the boundary\n",
+    "f = lambda x: (5 * x + 1)\n",
+    "bd_x = np.linspace(-1., 1, 200)\n",
+    "bd_y = f(bd_x)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We generate the datapoints by adding a random noise to the data points on 
the boundary line"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "# generate the training data\n",
+    "x = np.random.uniform(-1, 1, 400)\n",
+    "y = f(x) + 2 * np.random.randn(len(x))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We label the data points above the boundary line as positive points with 
label 1 and other data points with label 0 (negative)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
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       "text/plain": [
-       "[<matplotlib.lines.Line2D at 0x7f0a6529af90>]"
-      ]
-     },
-     "execution_count": 2,
-     "metadata": {},
-     "output_type": "execute_result"
-    },
-    {
-     "data": {
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-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f0a6842b090>"
+       "<matplotlib.figure.Figure at 0x7fcfcf3b5e50>"
       ]
      },
      "metadata": {},
@@ -52,42 +125,15 @@
     }
    ],
    "source": [
-    "\n",
-    "# generate the boundary\n",
-    "f = lambda x: (5 * x + 1)\n",
-    "x_tr = np.linspace(-1., 1, 200)\n",
-    "y_tr = f(x_tr)\n",
-    "\n",
-    "\n",
-    "# generate the training data\n",
-    "x = np.random.uniform(-1, 1, 400)\n",
-    "y = f(x) + 2 * np.random.randn(len(x))\n",
-    "\n",
-    "\n",
     "# convert training data to 2d space\n",
-    "dat = np.array([[a,b] for (a, b) in zip(x, y)], dtype=np.float32)\n",
-    "label = []\n",
-    "posx, posy = [], []\n",
-    "negx, negy = [], []\n",
-    "for (a, b) in zip(x, y):    \n",
-    "    if 5.0 * a + 1.0 < b:\n",
-    "        l = 0\n",
-    "        negx.append(a)\n",
-    "        negy.append(b)\n",
-    "    else:\n",
-    "        l = 1\n",
-    "        posx.append(a)\n",
-    "        posy.append(b)\n",
-    "    label.append(l)\n",
-    "    \n",
-    "label = np.asarray(label, dtype=np.int32)\n",
+    "label = np.asarray([5 * a + 1 > b for (a, b) in zip(x, y)])\n",
+    "data = np.array([[a,b] for (a, b) in zip(x, y)], dtype=np.float32)\n",
     "\n",
-    "#plot the training data and the boundary\n",
-    "plt.plot(x_tr, y_tr, '--k', label='truth line')\n",
+    "plt.plot(bd_x, bd_y, 'k', label = 'boundary')\n",
+    "plt.plot(x[label], y[label], 'ro', ms=7)\n",
+    "plt.plot(x[~label], y[~label], 'bo', ms=7)\n",
     "plt.legend(loc='best')\n",
-    "plt.plot(posx, posy, 'ro', ms=7)\n",
-    "plt.plot(negx, negy, 'bo', ms=7)\n",
-    "\n"
+    "plt.show()"
    ]
   },
   {
@@ -98,8 +144,23 @@
    "source": []
   },
   {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Create the MLP model\n",
+    "\n",
+    "1. We will create a MLP by with one dense layer (i.e. fully connected 
layer).\n",
+    "2. We use the Softmax function to get compute the probability of each 
category for every data point.\n",
+    "3. We use the cross-entropy as the loss function.\n",
+    "4. We initialize the weight matrix following guassian distribution 
(mean=0, std=0.1), and set the bias to 0.\n",
+    "5. We creat a SGD updater to update the model parameters.\n",
+    "\n",
+    "2 and 3 are combined by the SoftmaxCrossEntropy."
+   ]
+  },
+  {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 6,
    "metadata": {
     "collapsed": false
    },
@@ -108,15 +169,11 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "(2L, 2L) (2L,)\n"
+      "(2, 2) (2,)\n"
      ]
     }
    ],
    "source": [
-    "\n",
-    "\n",
-    "tdat = tensor.from_numpy(dat)\n",
-    "tlbl = tensor.from_numpy(label)\n",
     "# create layers\n",
     "layer.engine = 'singacpp'\n",
     "dense = layer.Dense('dense', 2, input_sample_shape=(2,))\n",
@@ -124,18 +181,37 @@
     "print p[0].shape, p[1].shape\n",
     "\n",
     "# init parameters\n",
-    "p[0].gaussian(0, 0.1)\n",
-    "p[1].set_value(0)\n",
+    "p[0].gaussian(0, 0.1) # weight matrix\n",
+    "p[1].set_value(0) # bias\n",
     "\n",
     "# setup optimizer and loss func\n",
-    "opt = optimizer.SGD(lr=0.03)\n",
-    "lossfunc = loss.SoftmaxCrossEntropy()\n",
-    "\n"
+    "opt = optimizer.SGD(lr=0.05)\n",
+    "lossfunc = loss.SoftmaxCrossEntropy()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "* Each layer is created with a layer name and other meta data, e.g., the 
dimension size for the dense layer. The last argument is the shape of a single 
input sample of this layer.\n",
+    "* **param_values()** returns a list of tensors as the parameter objects 
of this layer\n",
+    "* SGD optimzier is typically created with the weight decay, and momentum 
specified. The learning rate could be specified at creation or passed in when 
the optimizer is applied."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Train the model\n",
+    "\n",
+    "We run 1000 iterations to train the MLP model. \n",
+    "1. For each iteration, we compute the gradient of the models parameters 
and use them to update the model parameters.\n",
+    "2. Periodically, we plot the prediction from the model."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 8,
    "metadata": {
     "collapsed": false
    },
@@ -144,19 +220,33 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "0.704925477505\n",
-      "0.466226756573\n",
-      "0.39766433835\n",
-      "0.352448284626\n",
-      "0.320274919271\n",
-      "0.296036958694\n"
+      "training loss =  0.245654\n",
+      "training loss =  0.236532\n",
+      "training loss =  0.228489\n",
+      "training loss =  0.221329\n",
+      "training loss =  0.214903\n",
+      "training loss =  0.209094\n",
+      "training loss =  0.203810\n",
+      "training loss =  0.198976\n",
+      "training loss =  0.194531\n",
+      "training loss =  0.190426\n"
      ]
     },
     {
      "data": {
-      "image/png": 
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