exercises_1.ipynb

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    "# Neural networks 101\n",
    "In this notebook you will implement a simple neural network. We'll implement the forward-pass, backpropagation and analyse the effects of different loss functions, activation functions, and architectures. We assume that you are already familiar with backpropation. If not, please refer to the section below. Also [Andrej Karpathy] (http://cs.stanford.edu/people/karpathy/) or [Michal Nielsen] (http://neuralnetworksanddeeplearning.com/chap2.html) has written good descriptions of backprob."
   ]
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   "source": [
    "# Backpropagation explained\n",
    "At first backpropagation in a neural network may seem very complicated. However it can be decomposed into smaller self-contained problems by mechanically applying the chain-rule. This is the method used by all major neural network libraries (Torch, Caffe, Theano, deeppy), and the one we will study here.\n",
    "\n",
    "Recall that a neural network (parameterized by weights W) predicts a target given an input x i.e. $y = p(y|x,W)$. Training a neural network then corresponds to changing the weights W such that the error $E$ between the predicted targets $y$ and the true targets $t$ is minimized. Here E is usually defined as either:\n",
    "\n",
    "1. $E = \\frac{1}{2} \\sum^{K}_{k=1}(y_k-t_k)^2$ For regression problems (Mean Squared Error)\n",
    "2. $E = -\\sum^{K}_{k=1}t_k \\log y_k$ For classification problems (Cross Entropy Error)\n",
    "\n",
    "Neural Networks are usually trained using gradient descent. Here we update $W_{ij}$ by going in the negative direction of $\\frac{\\partial E}{\\partial w_{ji}}$ with $\\alpha$ determining the step size. \n",
    "\n",
    "$W_{ij} = W_{ij} - \\alpha\\frac{\\partial E}{\\partial w_{ji}}$.\n",
    "\n",
    "Backpropagation is simply an effective way to calculate the exact gradient of E w.r.t to all the weights in the network.\n",
    "\n",
    "\n",
    "### Backpropagation Notation\n",
    "Let's start with a small toy network to get hold of the notation.\n",
    "\n",
    "<img src=\"./FFNcasper.png\" alt=\"The network that you are to implement.\" width=\"500\">\n",
    "\n",
    "We use the following notation:\n",
    "\n",
    " * $z^{(l)}$ is the input to a layer $l$\n",
    " * $z^{(l+1)}$ is the output of layer $l$\n",
    " * $t_j,...,t_k$  true targets\n",
    " * $y_j,...,y_k$ predicted targets\n",
    " * $h(\\cdot)$ Nonlinear activation function (sigmoid, tanh, ReLU etc)\n",
    " \n",
    "We define $z^{(0)} = x$.\n",
    "\n",
    "\n",
    "#### Forward Pass\n",
    "\n",
    "\n",
    "In the forward pass all the activations $z^{(l)}_k$ are calculated \"bottom up\". Especially note that the output to the $l$'th layer can be calculated using the output of the ($l-1$)'th layer. \n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "z^{(l+1)} &=  f (z^{(l)}, w^l) \\\\\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "Hence a layer is just a simple function parameterized by $w$ performing some transformation on its output. **Note that we define weigths and nonlinearities as separate layers which differ from the conventional textbook approach. However this have the advantage of having an almost one-to-one mapping between theory and implementation.**\n",
    "\n",
    "The forward pass for common neural network layers:\n",
    " * Linear layer: $z^{(l+1)} =  z^{(l)}w^l + b^{l}$ \n",
    " * Sigmoid layer: $z^{(l+1)} =  \\sigma (z^{(l)} )$ \n",
    " * Softmax layer: $z^{(l+1)} =  \\frac{exp(z^{(l)})}{\\sum_j exp(z^{(l)}_j)}$ \n",
    "\n",
    "\n",
    "#### Calculate the Error\n",
    "\n",
    "The goal of backpropation is to calculate $\\frac{\\partial E}{\\partial w}$ and $\\frac{\\partial E}{\\partial b}$ for all parameters in the network. To calculate the loss function well simply plug in the output of the network into the loss function which \"measures\" the difference between the true and predicited targets. Note that this is always just a single number!\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "E = f(z^{(L)},t), \\text{  }   E \\in \\mathbb{R}\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "Where $L$ denotes the last layer of the network and $f(\\cdot)$ can be any differentiable function calculating the difference between true and predicted targets. \n",
    "\n",
    "#### Backpropagate the Error\n",
    "\n",
    "Backpropagations is an algorithm to calculate the gradient error w.r.t. the weights $\\frac{\\partial E}{\\partial w}$. This can be done by calculating the loss/error of the neural network using the activations from the forward pass, and \"backpropagate\" this error through the network going \"top down\". Without further introduction we will make the following usefull defintion:\n",
    "\n",
    "$$ \n",
    "\\delta_k^{(l)} \\equiv \\frac{\\partial E}{\\partial z_k^{l}} \n",
    "$$\n",
    "\n",
    "Intuitively this describes the error at the k'th unit in the l'th layer. This is known as the delta-message or the error-message at the k'th neuron in layer l.\n",
    "\n",
    "#### Error at output layer L\n",
    "\n",
    "At the output layer the delta-message is:\n",
    "$$ \n",
    "\\delta_k^{(L)} = \\frac{\\partial E}{\\partial z_k^{L}} \n",
    "$$\n",
    "which can be computed using the loss funtion. This is simply the error function differentiated w.r.t to the output of the network. As above we will vectorize this equation to calculate the error for all neurons in the L'th layer\n",
    "\n",
    "$$ \n",
    "\\delta^{(L)} = \\bigtriangledown_{z^L} E\n",
    "$$\n",
    "\n",
    "Where $\\bigtriangledown_a E$ means: partial derivative of E w.r.t to all elements in $z^L$.\n",
    "\n",
    "#### Error in the l'th layer\n",
    "\n",
    "The error $\\delta^l$ in each layer can be calculated using the error $\\delta^{l+1}$ in the layer above:\n",
    "\n",
    "$$ \n",
    "\\delta^{(l)} = \\frac{\\partial E}{\\partial z^{l}} = \\frac{\\partial E}{\\partial z^{l+1}}\\frac{\\partial z^{l+1}}{\\partial z^{l}} = \\delta^{l+1}\\frac{\\partial z^{l+1}}{\\partial z^{l}}^T \n",
    "$$\n",
    "\n",
    "In plain english a layers error-message is the error-message from the layer above multiplied with the layers output differentiated w.r.t its input.\n",
    "\n",
    "The backward pass for common neural network layers:\n",
    " * Linear layer: $\\delta^{(l)} =  \\frac{\\partial E}{\\partial z^{l+1}}\\frac{\\partial z^{l+1}}{\\partial z^l} = \\frac{\\partial (z^{(l)}w^{l+1} + b^{l+1})}{\\partial z^l} = \\delta^{(l+1)}w^{l} $\n",
    " \n",
    " * Sigmoid layer: $\\delta^{(l)} =  \\frac{\\partial E}{\\partial z^{l+1}}\\frac{\\partial z^{l+1}}{\\partial z^l} = \\frac{\\partial (\\sigma(z^{l+1}))}{\\partial z^l} = \\delta^{(l+1)}\\odot \\sigma'(z^{l}) $\n",
    "\n",
    "Where $\\odot$ is the hadamard vector product i.e. element wise multiplication. \n",
    "\n",
    "This important results states that we can calculate all the error-messages in the network by starting at the topmost layer and \"backpropagate\" the errors through the network.\n",
    "\n",
    "\n",
    "#### Gradients w.r.t parameters\n",
    "\n",
    "Using these errors calculated at each layer partial derivatives w.r.t the weights are:\n",
    "\n",
    "$$\n",
    "\\frac{\\partial E}{\\partial w^{(l)}_{jk}} = \\frac{\\partial E}{\\partial z^{l+1}} \\frac{\\partial z^{l+1}}{\\partial  w^{l}_{ik}} = \\frac{\\partial z^{l+1}_k}{\\partial  w^{l}_{ik}} \\delta^{l+1}_k \n",
    "$$\n",
    "\n",
    "and for the bias\n",
    "\n",
    "$$\n",
    "\\frac{\\partial E}{\\partial b^{(l)}_{k}} = \\frac{\\partial E}{\\partial z^{l+1}} \\frac{\\partial z^{l+1}}{\\partial  b^{l}_{k}} = \\frac{\\partial z^{l+1}_k}{\\partial  b^{l}_{k}} \\delta^{l+1}_k \n",
    "$$\n",
    "\n",
    "#### Neural networks as layers - key points\n",
    "By viewing neural networks as a number og layers(actually functions) stacked on top of each other allows us to consider each layer as a self-contained building block used to construct neural networks. For each layer we must be able to calculate/implement three things:\n",
    "\n",
    " * **Forward Pass** - Calculate output given the output from the layer below: $z^{(l+1)} =  f (z^{(l)}, w^l)$\n",
    " * **Backward Pass** - Calculate error message given the delta message from the layer above: $\\delta^{(l)} = \\delta^{l+1}\\frac{\\partial z^{l+1}}{\\partial z^{l}}^T$. \n",
    " * **Update parameters**: If the layer has any paramemters we need to define a method to update these i.e. $\\frac{\\partial E}{\\partial w^{(l)}_{jk}}  = \\frac{\\partial z^{l+1}_k}{\\partial  w^{l}_{ik}} \\delta^{l+1}_k$ and $\\frac{\\partial E}{\\partial b^{(l)}_{k}} =\\frac{\\partial z^{l+1}_k}{\\partial  b^{l}_{k}} \\delta^{l+1}_k $\n",
    "\n",
    "\n",
    "<img src=\"./layer.png\" alt=\"Layers as self-contained units\" width=\"200\">\n",
    "\n",
    "\n",
    "# Summary\n",
    "\n",
    "All the steps have been vizualized for a two-hidden-layer network i the figure below:\n",
    "\n",
    "\n",
    "<img src=\"./notation.png\" alt=\"The network that you are to implement.\" width=\"700\">\n",
    "\n",
    "Backprob step-by-step:\n",
    " * ** Forward Pass: ** Recursively calculate the activations of all layer \"bottom up\" using the activations of the layer below: $z^{(l+1)} =  f (z^{(l)}, w^l)$. Initialize with $z^{(0)} = x$\n",
    " * ** Backward Pass: ** Recursively calculate the error-messages of all layers \"top down\" using the delta-messages from the layer above: $\\delta^{(l)} = \\delta^{l+1}\\frac{\\partial z^{l+1}}{\\partial z^{l}}^T$. Initalize with $\\delta_k^{(L)} = \\frac{\\partial E}{\\partial z_k^{L}}$\n",
    " * ** Update Parameters: ** Update the parameters of all layers using the activations and the delta-messages i.e. $\\frac{\\partial E}{\\partial w^{(l)}_{jk}}  = \\frac{\\partial z^{l+1}_k}{\\partial  w^{l}_{ik}} \\delta^{l+1}_k$ and $\\frac{\\partial E}{\\partial b^{(l)}_{k}} =\\frac{\\partial z^{l+1}_k}{\\partial  b^{l}_{k}} \\delta^{l+1}_k $\n",
    "\n",
    " \n",
    "The backprob algorithm is fairly complicated and it might take several tries to fully grasp whats going on. However, using the above equations we can implement a working neural network which is the good way to fully understand whats going on. we have put the proofs of the equations for optional reading below.\n",
    "\n",
    "\n",
    "###Backprob deriviation\n",
    "\n",
    "To prove that $\\delta_k^{(l)}$ can  be calculated using $\\delta_k^{(l+1)}$\n",
    "$$\n",
    "\\begin{eqnarray}\n",
    "  \\delta^l_j & = & \\frac{\\partial E}{\\partial z^l_j} \\\\\n",
    "  & = & \\sum_k \\frac{\\partial E}{\\partial z^{l+1}_k} \\frac{\\partial z^{l+1}_k}{\\partial z^l_j} \\\\ \n",
    "  & = & \\sum_k \\frac{\\partial z^{l+1}_k}{\\partial z^l_j} \\delta^{l+1}_k = \\frac{\\partial z^{l+1}_k}{\\partial z^l_k} \\delta^{l+1}_k \\tiny{\\blacksquare} \n",
    "\\end{eqnarray}\n",
    "$$\n",
    "\n",
    "To calculate the gradients of the weights and bias first note that in any layer of the network we have \n",
    "\n",
    "$$ \\frac{\\partial z^{l}_k}{\\partial w^{l}_{ik}} = \\frac{\\partial \\sum_j w^{(l)}_{ij}z^{(l-1)}_j + b^{(l)}_j }{\\partial w^{(l)}_{ik}} = z^{(l-1)}_k $$\n",
    "\n",
    "$$ \\frac{\\partial z^{l}_k}{\\partial b^{l}_k} = \\frac{\\partial \\sum_j w^{(l)}_{ij}z^{(l-1)}_j + b^{(l)}_j }{\\partial b^{(l)}_k} = 1 $$\n",
    "\n",
    "To calculate the gradient of the cost funtion of a parameter in the l'th layer well use the chain rule:\n",
    "\n",
    "$$ \\frac{\\partial E}{\\partial w^{l}_{ik}} = \\frac{\\partial E}{\\partial z^{l+1}_k} \\frac{\\partial z^{l+1}_k}{\\partial  w^{l}_{ik}} = \\frac{\\partial z^{l}_k}{\\partial  w^{l}_{ik}}\\delta^{l+1}_k\\tiny{\\blacksquare}$$\n",
    "\n",
    "$$ \\frac{\\partial E}{\\partial b^{l}_k} = \\frac{\\partial E}{\\partial z^{l+1}_k} \\frac{\\partial z^{l+1}_k}{\\partial  b^{l}_k} = \\frac{\\partial z^{l+1}_k}{\\partial  b^{l}_k}\\delta^{l+1}_k \\tiny{\\blacksquare}$$\n",
    "\n",
    "Where we used the definition $\\delta^{l}_k \\equiv \\frac{\\partial E}{\\partial z_k^{l}}$"
   ]
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   "source": [
    "# MNIST dataset\n",
    "The MNIST dataset consists of 70,000 images of handwritten digits from 0-9. The dataset is split into a 50,000 images training set, 10,000 images validation set and 10,000 images test set. The images are 28x28 pixels, where each pixel represents a normalised value between 0-255 (0=black and 255=white).\n",
    "\n",
    "First let's load the MNIST dataset and plot a few examples:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np # Scientific library for numerical programming.\n",
    "import matplotlib.pyplot as plt # Plotting library.\n",
    "import matplotlib\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
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   "outputs": [],
   "source": [
    "def onehot(t, num_classes):\n",
    "    out = np.zeros((t.shape[0], num_classes))\n",
    "    for row, col in enumerate(t):\n",
    "        out[row, col] = 1\n",
    "    return out\n",
    "\n",
    "data = np.load('mnist.npz')\n",
    "num_classes = 10\n",
    "x_train = data['X_train'][:2000].astype('float32')\n",
    "targets_train = data['y_train'][:2000]\n",
    "targets_train = onehot(targets_train, num_classes)\n",
    "\n",
    "x_valid = data['X_valid'][:500].astype('float32')\n",
    "targets_valid = data['y_valid'][:500]\n",
    "targets_valid = onehot(targets_valid, num_classes)\n",
    "\n",
    "x_test = data['X_test'][:500].astype('float32')\n",
    "targets_test = data['y_test'][:500]\n",
    "targets_test = onehot(targets_test, num_classes)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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pl8v1yNXJ3T9+IQQREREkJCTcZnYKDAyUExZjYmJITk7GZDLJRTlzc3NxOBxM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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11823a610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "idx = 0\n",
    "canvas = np.zeros((28*10, 10*28))\n",
    "for i in range(10):\n",
    "    for j in range(10):\n",
    "        canvas[i*28:(i+1)*28, j*28:(j+1)*28] = x_train[idx].reshape((28, 28))\n",
    "        idx += 1\n",
    "plt.figure(figsize=(7, 7))\n",
    "plt.imshow(canvas, cmap='gray')\n",
    "plt.title('MNIST handwritten digits')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The input data is a *#samples* by 784 $(28^2)$ matrix and the targets are a *#samples* by 10 matrix. The targets are one-of-k encoded. We represent the correct label for each sample with a #classes dimensional vector with a 1 at the index corresponding to the correct class.\n",
    "\n",
    "As example we plot the label of the 10 first digits from the training set. You can verify that these labels match with the first 10 digits in the first row in the image above. One-of-k encoding should typically be used when you have categorical targets. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "One-of-k                                  | Label\n",
      "--------------------------------------------------\n",
      "[ 0.  0.  0.  0.  0.  1.  0.  0.  0.  0.] | 5\n",
      "[ 1.  0.  0.  0.  0.  0.  0.  0.  0.  0.] | 0\n",
      "[ 0.  0.  0.  0.  1.  0.  0.  0.  0.  0.] | 4\n",
      "[ 0.  1.  0.  0.  0.  0.  0.  0.  0.  0.] | 1\n",
      "[ 0.  0.  0.  0.  0.  0.  0.  0.  0.  1.] | 9\n",
      "[ 0.  0.  1.  0.  0.  0.  0.  0.  0.  0.] | 2\n",
      "[ 0.  1.  0.  0.  0.  0.  0.  0.  0.  0.] | 1\n",
      "[ 0.  0.  0.  1.  0.  0.  0.  0.  0.  0.] | 3\n",
      "[ 0.  1.  0.  0.  0.  0.  0.  0.  0.  0.] | 1\n",
      "[ 0.  0.  0.  0.  1.  0.  0.  0.  0.  0.] | 4\n"
     ]
    }
   ],
   "source": [
    "print \"One-of-k\" + \" \"*34  + \"| Label\"\n",
    "print \"-\"*50\n",
    "for i in range(10):\n",
    "   print targets_train[i], \"|\",  targets_train[i].argmax(axis=-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook we are going to apply two modeling approaches to the MNIST dataset:\n",
    "1. Supervised classifier where the network inputs $x_i,...,x_n$ ($n=28x28=784$) are the image from the training_set and the output $y_j,...,y_k$ ($k=10$) is the multinomial probability an image being part of a class defined by the targets_train set.\n",
    "2. Deep autoencoder where we are finding a good internal representation $y_j,...,y_k$ of an image $x_i,...,x_n$, by comparing it to a reconstruction $\\hat{x}_i,...,\\hat{x}_n$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#Writing a feed-forward neural network\n",
    "\n",
    "In this exercise we will implement a neural network using a layerwise modular approach. For generality we will separate the linear weights and the nonlinearities into separate layers.\n",
    "\n",
    "The key idea is to realize that a layer should be able to \n",
    "  * Calculate its outout given the input from the layer below, \n",
    "  * Calculate a $\\delta$-message given the $\\delta$-message from the layer above\n",
    "  * Update its parameters (if any) using the $\\delta$-message from the layer above\n",
    "\n",
    "We will call the input to all layers for $z^l$ and the output from all layers for $z^{l+1}$. \n",
    "\n",
    "All code should be implemented using the matrix-notation versions of the equations presented above. This makes your code 1) Easier to read, 2) A lot faster since it will use highly optimized linear algebra libraries on the computer.\n",
    "\n",
    "In the code examples we'll use the following notation:\n",
    "\n",
    " * $x$ : batchsize x numInputs   (inputs)\n",
    " * $W^0$ : numInputs x numHiddenUnits (input to hidden weights)\n",
    " * $b^0$ : [1 x numHiddenUnits] (hidden units biases)\n",
    " * $W^2$ : [numHiddenUnits x NumOutputs] (hidden units to output)\n",
    " * $b^2$ : [1 x numOutputUnits]  (output unit biases)\n",
    " \n",
    "In matrix notation the Forward pass can be written as\n",
    "$$\n",
    "\\begin{align}\n",
    "    z^{(0)} &= = x \\\\\n",
    "    z^{(1)} &= z^{(0)}W^{(0)} + b^{(0)}  \\\\\n",
    "    z^{(2)} &= \\tanh(z^{(2)}) \\\\\n",
    "    z^{(3)} &= z^{(2)}W^{(2)} + b^{(2)} \\\\\n",
    "    y &= softmax(z^{(3)})\n",
    "\\end{align}\n",
    "$$\n",
    "We can then define the forward pass in a neural network with tanh activation and softmax output in a few lines of python code \n",
    "\n",
    "```PYTHON\n",
    "import numpy as np\n",
    "z0 = x\n",
    "z1 = np.dot(z0, W_0) + b_0  # b_0 is broadcasted\n",
    "z2 = np.tanh(z2)\n",
    "z3 = np.dot(z2, W_2) + b_2  # b_2 is broadcasted\n",
    "# softmax z2 to get the output (softmax is explained later)\n",
    "exp_z3 = np.exp(z3)\n",
    "y = exp_z3 / exp_z3.sum(axis=1, keepdims=True)\n",
    "\n",
    "```\n",
    "\n",
    "**You should confirm that the shape of** `y` ** is [batchsize x numClasses].** \n",
    "\n",
    "The code snippet uses [numpy broadcasting](http://docs.scipy.org/doc/numpy/user/basics.broadcasting.html) please make sure that you understand numpy broadcasting. If you don't you should solve the exercise below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# fun with broadcasting. Divide each element in row 1 of x with 1, each element in row 2 with 2 etc. This \n",
    "# You may find numpy reshape and numpy arange and x.shape usefull. This should be one or two lines of code and no \n",
    "# for loops\n",
    "x = np.ones((3, 5))\n",
    "\n",
    "\n",
    "# correct output\n",
    "# [[ 1.          1.          1.          1.          1.        ]\n",
    "#  [ 0.5         0.5         0.5         0.5         0.5       ]\n",
    "#  [ 0.33333333  0.33333333  0.33333333  0.33333333  0.33333333]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Writing a linear layer\n",
    "A linear layer takes an input $z$ and makes a linear transformation to calculate the output $z^{l+1}=w^{l} z^{l}+b^{l}$. \n",
    "\n",
    "The $\\delta$-message is\n",
    "\n",
    "$$\n",
    "    \\delta^{l} = \\frac{\\partial E}{\\partial z^{l}} =  \\frac{\\partial E}{\\partial z^{l+1}} \\frac{\\partial z^{l+1}}{\\partial z^{l}} = w^{(l) T} \\delta^{l+1}\n",
    "$$\n",
    "\n",
    "Lastly we note that we also need to implement the the update of the weights. This is simply done by calculating the gradient for all parameters (recall that $\\frac{\\partial E}{\\partial w^{l}} = z^{l} \\delta^{l+1}$ )\n",
    "\n",
    "\n",
    "#####Exercise 1: Continue writing the linear layer, following the template given below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class LinearLayer():\n",
    "    def __init__(self, num_inputs, num_units, scale=0.01):\n",
    "        self.num_units = num_units\n",
    "        self.num_inputs = num_inputs\n",
    "        self.W = np.random.random((num_inputs, num_units)) * scale\n",
    "        self.b = np.zeros(num_units)\n",
    "\n",
    "    def __str__(self): \n",
    "        return \"LinearLayer(%i, %i)\" % (self.num_inputs, self.num_units)\n",
    "\n",
    "    def fprop(self, x, *args):\n",
    "        # TODO: Write the code for a linear forward-pass and return this value.\n",
    "        raise NotImplemented()\n",
    "        self.x = x\n",
    "        self.z = ????\n",
    "        return self.z \n",
    "        \n",
    "    def bprop(self, delta_in):\n",
    "        # TODO: Write the code for calculating delta and return this value.\n",
    "        raise NotImplemented()\n",
    "        x_t = np.transpose(self.x)\n",
    "        self.grad_W = ???\n",
    "        self.grad_b = ???\n",
    "        W_T = np.transpose(self.W)\n",
    "        self.delta_out = ????\n",
    "        return self.delta_out\n",
    "    \n",
    "    def update_params(self, lr):\n",
    "        self.W = self.W - self.grad_W*lr\n",
    "        self.b = self.b - self.grad_b*lr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Writing activation function layers\n",
    "The forward propagation of the activation function layer is applied as a transformation of the output of a subsequent linear layer, $z^{l+1}=h(z^{l})$, where $z=z_j,...,z_k$ is denoted the output vector of the layer. \n",
    "\n",
    "There exists multiple activation functions, where the most common are:\n",
    "- linear function $f(a) = a$,\n",
    "- sigmoid function $\\sigma (a)=\\frac{1}{1+exp(-a)}$,\n",
    "- tanh function $tanh(a)=\\frac{exp(a)-exp(-a)}{exp(a)+exp(-a)}$,\n",
    "- ReLU function $f(a)=max(0,a)$,\n",
    "- softplus function $f(a)=ln(1+exp(a))$.\n",
    "\n",
    "For a feedforward network the ReLU activation function is often a good choice."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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VwJeAKTZvVClbEPQFCQG/AC4N41QuZbn4VgN+J6mtz4tsX1dS30GDkdiE9pHSO0gZm78I\n3GwT63aCVueTpGUBY6sWZLARmSSCXpPvKDenfaS0AskoXQbcZvNWheI1hEZcn5LGAN8nzUH93Pa3\napwzGjibVIrjOdujGy1X0I7ECNLC8O1t/lW1PK1If67RMFBBj8hGaSvajdISpPmky4F/lFxGoHQq\nSnW0MvBX4IO2n5C0qu3nOrQTetMgclHLm4Hf2vywanlalaafgwpak2yURtLuvptPMkiHAP9sgqqz\nrUxPUh0dAlxh+wmAjsYpaDifIZVPP6dqQQYrYaCChcir5LclGaQDgFdJrrv9gbvDKNWNnqQ62hBY\nQtKNJDfqD2xfWJJ8gxqJ9YDTgVED3TvQzISBCtpcGe+j3SjNIY2UdgemhVFqCD35TpcAtiYlyF0W\nuE3S32wvVAk41g/Wl+w5+AnwHZuHqpan1WjJVEc9mRAOyiMnuxxNeyn0WaQ5pV1splco2mChJ6mO\nHicFRrwGvCbpZlLmjYUMVKQ6qjuHkCKPv1e1IK1Iy6U6yhPC51CYEJY0sTghHDSeXAp9F9pLoT9K\nGiltb/NwlbINQnqS6uhq4JysP0uRXIDxp9lAchb97wL7xrq96ilrBNWTCeGgAUgsBexGMkp7kSLH\nLgP+n81jVco2mOlJqiPb0yVdC9xDClA5z/a06qQeFHwd+J3N36sWJCgpzFzSWFKo7LF5+zBgG9sn\nFM6JcNk6IbEMqdrsWFL12XtI7rsrbJ6sUrZWpVmvz2aVqxWR2Ab4HbCJzdyq5RkotEKYeUyyN5hc\nCn13klEaQ3IhXQF80eapKmULgmYnz8meS9KXME5NQlkGqicTwhGN1EskVqC9FPquwG0ko3S8zbNV\nytbqNDqbedB0fAp4kVQlN2gSynLxLU6a+3g/aUL4Hyy6aj5cFT1AYmXSXNJY0h/oX0hzShNtohRD\ng6gq1VE+739INx8H2r6y0XINNiSGAXcDO9nEHF+daXoXX2cTwmX0PRCQeBspqGQsab3SjSSjdES4\nI1qTnka25vO+BVxLVKRuFN8DfhbGqfkobR2U7T8Cfyyrv1ZH4h3AviSjtA1wPXAhcJDNS1XKFtSF\nnka2nkBaCvA/pUo3SJD4IOm3OKpqWYJFiUwSTYTEGrRXnd2KdNd8HrCfzStVyhbUnW5THUlak2S0\ndiEZqAg2qiMSy5ECIz4V5dubkzBQFSMxnGSUDiCVsPgD8APgTzavVSlb0FB6Ymy+D5xq20rF1Gq6\n+CK4qM+MB261+VPVggwk6hlgFOU2KkBiXdozhI8AJpKi7ybb/LdC0YJOaEC5jVHAeNtj8vY4YH4x\nUELSI7QbpVVJiXuPtT2xUXINFiT+B5gEbB4Rr40l6kG1ABLrAx8mGaV1SKXQLwdutHm9StmC7mmA\ngeo2srXD+RcAkyKKr/9ILA38k5RN5ZKq5RnoNH0U32BF4l20Zwhfg7RK/RTgpiiFPrjpSaqjSgUc\n2IwHpgO/rViOoBsaPoLK/vFjYMEwepzta2uc1/J3gjlN/6a0V51dhfZS6H8diKXQBwvNen02q1zN\nisROwMXAu22eqVqewUCzj6AMfM/2gMzCnI3Su2mfU1qGNJ/0ceBvUewsCJoDiaGkpRpHh3FqDcpy\n8Q2oO7xslN5L+0hJpPmkjwK3R4G/IGgucqXoXwJX2rEes1VYrKR+TpB0t6TzJa1cUp91RWIxiW0l\nziLVUboIeItkoNa3OdnmH2Gcgp4iaYyk6ZL+LemUGscPzXpzj6S/StqiCjkHCOOAtwEnVy1I0HPq\nMgclaTKweo1DpwN/o33+6f8Ba9g+ukYbBs4s7Kp8PUcuhb4d7YEOL5JGSpcD94UxGrjUWMtxRp2j\n+IaQovgWpDpi0fyU2wLTbL+Y8/aNtz2qQzsxB9UNEnuRSriPjHIz5dMyYea5eugk25vXONYUipbT\n7u9ACgnfH3ia9lpKkatrkNKAMPNtSUavbR3UqQC2v9nJ+asA99peq5FyDTQk3kPKyLKnzT+qlmcw\n0tRBEpLWsN1Wj2g/4N5G99lbJJYAdiaNkvYjpaC5HNjR5sEqZQsGLN2mOurA0cA1DZVogCGxEWkR\n/CfCOLUmZQRJfEvSu0nRfI8Cnyihz27JpdB3JRmlvYGHSCOlbWwerVK2YFDQY9eFpJ1JyUy37+T4\n+MJm5a7xZkBiA1KC5dNtruzu/KB+RKqjPvfB0ixcCv1+klG60mZmI/sOWpsqUh3l/VuQ1tKNsf1Q\no+UaCEi8m5TT8kybn1Utz2CnqV18VSOxLKkU+gHAHsBdpIWzp9jMqlK2YFBzB7BhnpedBRwEHFw8\nQdLaJON0WC3jFCyKxJ7ABcBxNpdXLU/QPwakgZJYnjRCGgt8gBQhdRnwOZvZVcoWBNDjVEdfIWUj\nOTclM+cN2yOrkrmZycFNXybN1e1n89eKRQrqwIBx8UmsRHsp9J2BW0mBDlfbPFcfKYPBSrO60ppV\nrjKR2JQ0appLqjL9VDdvCUpk0Lr4JFYhBTh8GNgRuIlklI60eaFK2YIgaCy56vSXSK7RL5HKtjfH\nHXdQF1rOQEmsSnsp9G2BG0jJHw+xmVelbEEQNJ5cuuZ44AhgArBxeEkGJnVJdSTpw5Lul/SWpK07\nHBuXU7lMl/SBvrXP6hKfkrgBeJg0r/QLYE2b/W0uqodxyuGRlRNyNJcMjaK7VEf5nB/m43dL2qps\nGXtKo38niXdIHC1xPSk7zZukYoPHF41TM1wvzSADNI8c/aFeufjuJS1wvbm4U9ImpOikTYAxwI8l\n9ahPiWESx0tMAR4gZXf4MbCGzYE2l9q8XCf52xhd5/b6yuiqBciMrloAmkOGupNTHZ1D0otNgIMl\nbdzhnD2ADWxvSMqOf27pgvac0fVqSEIS60jsL/FdiduBB0nf1U+A4TZf7CRtUd3k6AejqxYgM7pq\nAfpLXVx8tqcD5EijIvsAF9t+A5gh6SFgJOkOaBEk1qa9bMXGpJLM3wOus/lPPWQNgiZhJPCQ7RkA\nki4h6Uuxou7ewK8AbP9d0sqSVrPdspGoOav4isBQUhn71UjFPIcD6wEbkHT/VeBO4DbgJOC2qDw9\n+Gj0HNQwFjZGT5BSvHTGnaRS6P8L3BAXZDCA6Umqo1rnrAULL5WQFkqyvNChbl4Xnzu+bnss1uH1\nkMJz4XHMVhKbAUsAS+XH0vmxLLAcsEJ+fhV4Pj9mA0/lzzaZNEJ6wOb5Tj5TMIjosYHqImP5abYn\n9aLPLqJs9DbSOoajU5+9aLVOSDqj/F4XJeRoLhkaQE+jzTpqQY336Sv9FaY+/HyzHp64Qn6s29kJ\n/dH9ZrhemkEGaB45+kqPDZTt3frQ/pOkoXsba+V9tdof1Gs5gkFHR90YThpFdHXOIvoTehMMZBpR\nsLCoMBOBj0haUtJ6wIYQWYWDgEKqI0lLkoKJJnY4ZyKpSnNb7r65rTz/FAS9pS5zUJL2A35ImvT8\ng6Sptne3PU3SpcA0UljocW6W1BVBUCE9SXVk+xpJe+TgoleAIysUOQhKp2lSHQVBEARBkUa4+HpF\nTxYrNqjf4ZJuzAuM75P0mbx/qKTJkh6UdJ2klUuQZYikqZImVSjDypIul/SApGmStqlIjnH5N7lX\n0gRJSzVaDkm/kDRb0r2FfZ32WY/F5/WgCt1pJr3J/YbuUI3e5H4bqjuVGij1YLFiA3kD+JztTYFR\nwKdz36cCk22PIKVROrUEWU4kuUHbhrNVyPAD4BrbGwNbANPLlkOp9MSxwNa2Nye5vj5SghwXkK7B\nIjX7VD8Wn9eTCnWnmfQGQneq1BtotO7YruxByqV3bWH7VODUimS5ilRhdzqwWt63OjC9wf2uRar8\nuTMwKe8rW4aVgEdq7C9bjqHAv0glJhYnLdTerQw5SCHP93b32YFxwCmF864FRjX6+qwhb1PoTlV6\nk/sJ3XG1epPbbpjuVO3iq7UQsauFvA0h34FsBfyd9MW2RUrNJq10byRnA18E5hf2lS3DesCzki6Q\ndKek8yQtV7YctucAZwEzSUX85tqeXLYcmc76HMbC4eCVXLM0ge5UrDcQugM0nd7QRb+91p2qDVTl\nERqSlieVfT/R9kvFY05mvmEySvoQ8IztqSy6ILMUGTKLA1sDP7a9NSlibCF3QBlySFof+CzpjmwY\nsLykw8qWoyM96LOK67hS3alSb3L/oTuZZtWbHvbbpUxVG6ieLFZsGJKWICnZhbavyrtnS1o9H18D\neKaBImwH7C3pUVLJkF0kXViyDJC+8yds3563Lycp3dMly/Fe4Fbbz9t+k1TufNsK5IDOf4MeLz5v\nMJXpThPoDYTuFGkmvYE66k7VBqonixUbgiQB5wPTbH+/cGgiqc4M+fmqju+tF7ZPsz3c9nqkSc0/\n2z68TBmyHE8Dj0sakXftCtxP8mWXJgfJdz1K0jL599mVNAFethzQ+W/QLIvPK9GdZtAbCN3pQDPp\nDdRTdxo1cdeLCbbdSRN8DwHjSuz3fSTf9V3A1PwYQ5pwvJ6U3v86YOWS5NkJmJhfly4DsCVwO3A3\n6Q5spYrkOJmk4PeSMnkv0Wg5SHfgs4DXSfM6R3bVJ3Bavl6nAx8s65qtIXfputNsepNlGvS6U4Xe\n5H4bqjuxUDcIgiBoSqp28QVBEARBTcJABUEQBE1JGKggCIKgKQkDFQRBEDQlYaCCIAiCpiQMVBAE\nQdCUhIEKgiAImpIwUEEQBEFTEgYqCIIgaErCQAVBEARNSRioipA0X9I7K+j3GkmHN6jtl3KNoCDo\nN5KmSDq6YhnWztd1zZIe/Wz7UEl/qne7A4kwUD1E0gxJu1QtR2+QND6XIFiA7T1sX9jZe3rR9iJ/\nHrZXsD2jv20HQab0GkYd9dz2zHxd90uOnHV+frHEue2LbH+wP+0OdMJA9RzTSWG0QUpkGQ76jKTF\nq5ahExqt5/Ef0gvCQPWAPApZG5iUh/sn5f2XSXpK0lxJN0napPCeX0r6kaTfS5on6W81XHq7SXpQ\n0guSzumi/5GSbsvnzZL0f7loXNvxTSVNlvS8pKcljZP0QWAccFCWeWo+d4qkoyUtleXetNDO2yW9\nKmlVSatk2Z+RNEfSJElr5vO+BuwAnJPb/mHev8BtKWklSb/O758h6fQ2N4mkj0n6i6Tv5LYfkTSm\nHz9R0ALk6+BkSfcAL0laTNIoSbfma/suSTt18t6FvAG1RiQdzj9V0kNZ9+6XtG+H48dKmlY4vlUt\nPS/2I+kgSbd3aOdzkq7Or/eUNFXSi5JmSjqjcOrN+Xlu7nNU1oNbCm1tJ+n2rJf/kLRt4dgUSV/N\nejNP0p8kva1HX3wrU1bNllZ/AI8Cu3TY9zFgOVLtlbOBqYVjvwSeI1W7HAL8Bri4cHw+qYDXiqQq\nk8/QSX0UUoXOkaQbinVIxchOzMdWAJ4CPgcsCSwPjMzHzgB+3aGtG4Gj8uvzgf8tHPs0cE1+PRTY\nD1g6t3kp8Lta7XT4TO/Mr38N/C5/P+uQ6hYdVfjeXgeOJt1RfhJ4surfOB6NfQAzgDuBNYGl8vNz\nwJh8fNe8/baO11i+li8stLVuvt4W66SvscDq+fWBwMvAann7w6RKuO/J2+sDa+fXC+l5sR9gWWAe\nsEHh+O3Agfn1TsCm+fXmwNPAPnl7nY7yZj24Jb8eCrwAHJr7+ggwB1glH58C/BvYIOvkjcA3qv5N\nG/2IEVQ/sP1L26/YfgM4E9hS0gpth4Erbd9h+y3gIuDdHZr4pu15th8nXXAdj7f1c6ftf9ieb/sx\n4GckZQD4EDDL9tm2X7f9su22KpWia5fCBJIitHFI3oftObZ/Z/s/tl8Gvl7os42abUsaQqrwOi5/\nP48BZwHF4IzHbJ/vpH2/BtaQ9I4uZA1aHwM/tP2k7f8Ch5FuiK4FsH09qVLwnjXe2yvXmO3Lnard\nYvtS0p/7yHz4GOBbtv+Zjz9se2YP2nwVuBo4GEDShsBG5ErGtm+yfX9+fS9wCe060538ewL/cpqX\nmm/7ElJRv73bugcusP2Q7f+Qbhhr/l8MJMJA9ZE85P9mdiO8SLrzAli1cNrswuvXSCORIk8XXr9a\n43hbXyOyu+2p3NfXgLbh/XDgkT5+jCnAstmFuC6pMujvcp/LSvppdsu8CNwErNTmpst0Ng+1KmlU\n+Vhh30wPQBQOAAAgAElEQVTSHXMbCz57Vnzo5PMHA4rHC6/XAT6c3XsvSHoB2B5Yvb+dSPpodre1\ntbsZ7bq5FvBwH5ueQDZQpBu632WDgaRtJN2Y3dpzgU/QrqfdMYykI0Uey/vbKP5f1Po/GXCEgeo5\nHf+MDyXd3bzf9krAenl/IyZBzyW59TbIfZ1O+283E+gsXH1+V43mkd2lJIU7GJhk+5V8+AvACJK7\ncCXSnWBxRNZVkMRzwBsk90gba5PcKsHgpnjdzCS57VYpPFaw/e0a73uZ5GJro1MjJmkdkpfh08BQ\n26sA99F+7T5OcpV1J18trgfeLmlLkvdhQuHYBOAqYC3bKwM/oV1Pu2v3SZLBLrJO3j9oCQPVc2aT\nfNVtLA/8F5gjaTmSC6xIbw1VV+cvD7wEvCrpXcCnCsf+QHKPnZgDH1aQ1ObKmA2s22HU07GvNjff\nAvdeoc/XgBclDSXNARTp+H0soGD4viZp+fyH8TnSPFwQtPEbYC9JH5A0RNLSkka3BeN04C5gR0nD\nJa1ECgDqjOVIBuE5YDFJR5JGUG38HDhJ0tZKbCBp7Xys0+saILvzLwO+C6wCTC4cXh54wfbrWQcP\nod0wPUu6Yeys7T8CIyQdLGlxSQcB7wJ+Xzhn0EUAhoHqOd8AvpRdBp8nzZs8RrrDuQ+4jYXvkmqt\n4eh4vOOxzu6yTiJd7PNId4aXtJ1r+yVgN2AvUrDEg8Do/L7L8vPzku6o1Xeer3oZWIOkJG18H1iG\npOS35mNF+X4AjM1ReN+vIfMJwCsk9+MtpDm4C7r4rBG2Psiw/QSwD3AaKUhoJmnkvsgfcZ6f+i1w\nDykwYRKdXDO2p5HmPG8jucU2A/5SOH45yU0+gaRTV5KMDSyq59ToZwLwfuAy20UvxXHAVyXNA76c\n5W3r89Xc51+zzmxDQQ9sP0+aT/4CSedOAj5ke07xo3V4PeB1RjlCpO8NSL8gTfA9Y3vzTs75IbA7\naZ7lY7an9qvTIBhA1NKhPGr9LcnNM4MUKTa3MiGDoALqMYK6AOh0DYukPUhzJxsCHyfNpwRB0E4t\nHToVmGx7BHBD3g6CQUW/DZTtW0jx+52xN/CrfO7fgZUlrdbffoNgoNCJDi3Qm/y8L0EwyChjDmpN\nFg4tfYIU5hkEQeesZrttmcJsIG7qgkFHWfmwOk56LjLxJWnAT/gFrY3tSqKobLsz/Qi9CVqBvupO\nGSOoJ0mLSdtYi05i+22rygdwZtUyVCEHeAvwpeC54IvAh4HXb4bvoxlkyHKUzWxJqwNIWoMU5VaT\nqr+bJvudKpejGWQoWw7wsuDvgJ8BHwperCBHnynDQE0EPgogaRQw1+2ui6BCJJaQOJO0+PB2YLjN\nYTYX2X3OThHUh4nAEfn1EaQFoEHQdEjsANxNWpi/hc0Euz4h8P128Um6mJRlYFVJj5MWdC4BYPun\ntq+RtIekh0jrYo7sb59B/5FYjpRX7E3g3TZPVSzSoKWGDn0F+CZwqVLNrRmkhKdB0DRILE9aN3YA\n8Gk7pUmrJ/02ULYP7sE5x/e3n5KYUrUAmSmNbFxiWVIGiseAo2zeqkKOHjKlagEaTRc6tGupgvSP\nKVULkJlStQA0hwzQQDkk3k/KyHETsJnNnG7e0rd+3M+FuvVCkvvrrwx6hsQvSFkiDuvCOAUFmvX6\nbFa5goGJxEqkNE8fBD5hL5R9ppP39P0ajVRHgwyJQ0kZo48N4xQEQU+R2JOU1u0t0qipW+PUX5q1\n7HLQACTeTsqxt5vNy1XLE3SPpHGkuknzgXuBI51qKQVBKUi8jZR7c1vgozY3ltV3jKAGF2cAE2zu\nqlqQoHtyja5jga2dcvQNYeECk0HQUCTGkm6MniVF6JVmnKA+UXxjSHflQ4Cf2/5Wh+OjSdFibWHL\nV9j+3/72G/QOiRGkKrcbVy1L0GPmkepqLSvpLVI9pEFdHygoB4nVgB+RMsGPtbm1Cjn6NYLKpb3P\nISW63AQ4WFKtP8CbbG+VH2GcquEM4Hs2z1UtSNAznEotnEUqQzGLtIbw+mqlCgYyEpI4jFTW5EHS\nEpRKjBP0fwQ1EnjI9gwASZeQ6rs80OG8iDKqEIk1SeVOjqtalqDnSFof+CxpAeSLwGWSDrV9UYfz\nxhc2p9ieUpaMwcBBYi1SFeDhwB42/+xbOxpNe026ftFfA1UrEew2Hc4xsJ2ku0nuiZOcCooF5fEp\n0tzTi1ULEvSK9wK3OhWzQ9KVwHak4o8LsD2+fNGCgYKESHOdXwP+D9jf5vW+tpdvkKa0t6+O1bh7\nTH8NVE8WUd0JDLf9qqTdSSlbRtQ6Me4E64/E0qSLb8eqZWkl6nkX2A+mA1+WtAzwH9LC3X9UK1Iw\nkJBYj7TgdgVgZ5v7KhZpIfproDomgh1OGkUtwKkkedvrP0r6saShXriUcdvx8f2UJ1iUA4C7bP5V\ntSCtRD3vAvshw92Sfg3cQQozvxP4WdlyBAMPicWA40lptb5Nmp9+s1qpFqW/BuoOYMMcDjuLFCW2\nUNqWXJzwGduWNJKUvaIhaTGCmhxGe+G7oMWw/W3SH0gQ1AWJjYDz8+b2zXzz2i8DZftNSccDfyKF\nmZ9v+wFJn8jHfwqMBT4l6U3gVWIdR2nkUNFtSb9BEASDGInFgS8AXwS+CpxjM79aqbomcvENYCQ+\nA7zXTuVOgr5T1fUpaWXSHMGmpDnfo2z/rWq5gtZCYnPgF6Ro0GNtHi2v78jFF9TmMDpEfAUtxw+A\na2xvDGzBoks4gqBTJJaU+ArwZ1II+W5lGqf+EiOoAUqOzvkHsEYzTn62GlVcn5JWAqbafmcX54Te\nBDWReA9p1DQT+KRdTRaSGEEFtdgXuDqMU0uzHvCspAsk3SnpPEnLVi1U0NxILC3xDeAaUoDN3lUZ\np/4SBmrgsj/Uv8JlUCqLA1sDP7a9Naki9anVihQ0MxLbAXcBG5CSu15Ur/LrVRDlNgYgOXpvc+CG\nqmUJ+sUTwBO2b8/bl1PDQMUC90BiOVImiAOBE2yuqE6W5kl11G0283zOD0m54F4FPmZ7an/7Dbpk\nH+CPNv+pWpCg79h+WtLjkkbYfpCUSeL+GueNL124oGmQ2AU4D/grsLnN81XK0zSpjgrZzHclZZW4\nXdJE2w8UztkD2MD2hpK2Ac4FRvWn36Bb9gV+WbUQQV04AbhI0pLAw8CRFcsTNAm5/Pq3gT2AT9n8\nvmKR6k4Z2cz3JmcysP13SStLWs327H72HdRAYnngfcSC6AGB7buB/6lajqC5kNiDFDZ+Lan8+oBM\nBF1GNvNa56wFhIFqDB8EbrOZV7UgQRDUF4mhwNmk5M9H2gN7nrmMbOawaD2omu+Lyd66sDepgnHQ\nD5okm3kQLEBif9KUyuWkuaaXKxap4TQ8m3mNc9aik7LVMdnbP3KurT2BL1UtS6vTDNnMC30PISVm\nfsL2XlXJEVSDxDtIhmlL4ECbv1QsUmn0dx3UgmzmeRL3IGBih3MmQsoFJ2kUqWx1uPcaw3bATHsh\nl2rQ+pwITKPnHotgAJDLrx9KKr/+KKn8+qAxTlBCNnPb10jaQ9JDpIWGEYXUOPYjFYQMBgiS1iJF\naX0N+HzF4gQlIbEmKQhiXWAvm9u7fsfAJHLxDRBy2eYZwJ7NVhVzIFBhNvPLgK8DKwIndXTxhd4M\nLLIeHw18A/gR8PX+lF9vBvpzjUYmiYHDVsDr1FjIGbQmkj5EKvY5NQdtBAMYiXVJC25XAd5vc0+1\nElVPGKiBw/7Ala2cdytYhO2AvfNi96WBFSX92vZC9b0i+rW1yeXXjwPGA98FvtvKSZ7rGQEbLr4B\ngsT9wNE2f+v25KDXVH19StqJcPENOCQ2JJVfH0LS3+kVi1R3otzGICdXy1yRVP8pGLg0x91k0G8k\nhkicBNxGWte040A0Tv0lXHwDg0OBCTbzqxYkaAy2bwJuqlqOoP9IbEoqJPgKMNLmkYpFalr6PIKS\nNFTSZEkPSrpO0sqdnDdD0j2SpkqKO/w6k/3XhwK/qVqWIAg6R2IJiS+TFoD/nBQIEcapC/rj4jsV\nmGx7BKnuUGeF1AyMtr2V7ZH96C+ozY7AHJt7qxYkCILaSGwN3A5sC2xtc14ENHVPfwzUgizl+Xnf\nLs6NSdzGcTgxehqwSBou6UZJ90u6T9JnqpYp6Dm5/PrXgD8CZ5HWKUamlx7S5yg+SS/YXiW/FjCn\nbbvDeY8ALwJvAT+1fV4n7UU0Ui/JmY0fBja2ebpqeQYyFS7UXR1Y3fZdkpYH/gns21ZzLfSmeZEY\nRZpregD49GDV0YYt1JU0GVi9xqHTixu2LakzS7e97ackvR2YLGm67Vs66W98YTPWc3TPMcCkwXrh\nN5JmyWZu+2lIv6/tlyU9AAxj4ZprQRMhsSzwv8DBpPLrl1csUsvSnxHUdNLc0tOS1gButP2ubt5z\nBvCy7bNqHIs7wV6QM5c/DOxv88+q5RnoNMP1KWldUiTfprZfbha5gnYkdiYFQNwGfNbmuYpFqpyq\nUh1NBI4AvpWfF0lSKmlZYIjtlyQtB3wAOLMffQbt7A88HsZpcJDde5cDJ7YZp8Kx8YXN8DxUgMSK\npP/CvYDj7EWqOgwamiKThKShwKXA2qQkpQfanitpGHCe7T0lvRO4Mr9lceAi29/opL24E+whEkuS\ncu4dZzO5ankGA1Ven5KWAH4P/NH295tFriAhMQb4KTAZOMlmbsUiNRX9uUYj1VELInECKRpoTNWy\nDBYqDJIQKUr2edufaxa5ApBYBfgeabTw8bhZrE2kOhpESLydVDH35KplCUphe+AwYOe82H2qpLgx\nqRiJfYH7SNkgNg/j1BhiBNVC5KwRvwfusTtdGB00gGa9PptVroFKvkH8P2BrUnLXmhHJQTsxgho8\nfIFUK+bLVQsSBIOJXH79I8C9wOPAlmGcGk8ki20RJD4FnADsYPNG1fIEwWBBYhhwLrABsLcdVQPK\noj/JYj+c06+8JWnrLs4bI2m6pH9LOqWv/ZVBs1QtLcqRE0yeCZwCjLZ5rAo5qqIZZKiSVtGfZvmd\n6ilHHjUdBdwF3E3KodetcRqI30VV9MfFdy+wH3BzZydIGgKcA4wBNgEOlrRxP/psNKOrFiAzGkBi\nR+CvwChg+woyH48uub9ajK5agKpoMf0ZXbUAmdH1aERiHeBa4HhgN5uv2Py3TBnqwOiqBegvfTZQ\ntqfbfrCb00YCD9meYfsN4BJgn772OdDJd2wjYK9tJP5GyuN1LjDG5smKxQvKJ/SnZCQWy+70O0hl\nMbaxubtaqQYvjZ6DWhMWytz7BLBNZydnX2+FrLZCNzJ0jERRYZ8Kj8UKjyGk73nJ/FgaWI5UAXcV\n4B2k72lDYDPgZVh1Dinf4XU2b/b/cwUtSo/0p3q9gR7oTrPLsTiwA/DJ/Honm2l1FS3oNX1NFnua\n7Uk9aL+XMexqglGCPl+xAEOBteGCPwCo4gDinD9x0MtQET3Un2bQG2gC3cnURY77+6N7zXLNNosc\nfaVLA2V7t362/yQwvLA9nHQXWKuvWMsRBAvTrf6E3gQDmXqtg+pMSe4ANpS0rqQlgYNg8CZRDIJe\nEvoTDGr6E2a+n6THSRFmf5D0x7x/mKQ/ANh+kxQF8ydgGvDbtkJrQRB0TehPMNhpmlRHQRAEQVCk\n8lRHVS1ElDRc0o15sfF9kj6T9w+VNFnSg5Kuk7RyCbIMyUlAJ1Uow8qSLpf0gKRpkrapSI5x+Te5\nV9IESUs1Wg5Jv5A0W9K9hX2d9pll/He+bj9QT1l6QxW600x6k/sN3aEavcn9NlR3KjVQFS9EfAP4\nnO1NSW7KT+e+TwUm2x4B3JC3G82JJBdO23C2Chl+AFxje2NgC2B62XIoVYw9Ftja9uakEP2PlCDH\nBbBI6ZKafUrahDQXtEl+z48lla5HFepOM+kNhO5UqTfQaN2xXdkD2Ba4trB9KnBqRbJcBexKurhW\ny/tWB6Y3uN+1gOuBnYFJeV/ZMqwEPFJjf9lyDAX+RVoftjgwCditDDmAdYF7u/vswDjglMJ51wKj\nGn191pC3KXSnKr3J/YTuuFq9yW03THeqdvHVWoi4ZtlC5DuQrYC/k77Y2fnQbGC1Bnd/NvBFYH5h\nX9kyrAc8K+kCSXdKOk/ScmXLYXsOcBYwE5gFzLU9uWw5Mp31OYyFQ70ruWZpAt2pWG8gdAdoOr2h\ni357rTtVG6jKIzQkLQ9cAZxo+6XiMScz3zAZJX0IeMb2VDoJ1W+0DJnFSfVtfmx7a1IRtoXcAWXI\nIWl94LOkO7JhwPKSDitbjo70oM8qruNKdadKvcn9h+5kmlVvethvlzJVbaB6vJC3EUhagqRkF9q+\nKu+eLWn1fHwN4JkGirAdsLekR4GLgV0kXViyDJC+8yds3563Lycp3dMly/Fe4FbbzzuFWF9JcmWV\nLQd0/ht0vGbXyvvKpjLdaQK9gdCdIs2kN1BH3anaQFW2EFGSgPOBaba/Xzg0ETgivz6C5GNvCLZP\nsz3c9nqkSc0/2z68TBmyHE8Dj0sakXftCtxP8mWXJgfJdz1K0jL599mVNAFethzQ+W8wEfiIpCUl\nrUfKoVhFfaBKdKcZ9AZCdzrQTHoD9dSdRk3c9WKCbXfSBN9DwLgS+30fyXd9FzA1P8aQJhyvBx4E\nrgNWLkmenYCJ+XXpMgBbAreT6t5cSZr8rUKOk0kKfi/wK2CJRstBugOfBbxOmtc5sqs+gdPy9Tod\n+GBZ12wNuUvXnWbTmyzToNedKvQm99tQ3YmFukEQBEFTUrWLLwiCIAhqEgYqCIIgaErCQAVBEARN\nSRioIAiCoCkJAxUEQRA0JWGggiAIgqYkDFQQBEHQlISBCoIgCJqSMFBBEARBUxIGKgiCIGhKwkD1\nEUmfyqWO50ka2of3z5D0/kbIVg+Uynnv2IB215b0Uk5qGQRB0ClhoPpALjdwFvB+2ysCW0h6vJu3\ndaSS+iy1kPRLSf+vuM/2ZrZvrkPbMyTtUmh3pu0VHEkggyDohjBQfWN1YGnggaoFaQFMJwXlgiAI\numLQGyhJp0h6Irvqprfd7UtaStL3JT2ZH2fnOiYjaDdMcyX9GbgGGJZdV/MkrSFpvKTLJV2S9/1T\n0hadyLDQCEbS6OKIrDMZa7Szp6Spkl6UNFPSGR2Ov0/SrZJeyMePkHQscAhwcpb/6nzuDEm7SBom\n6VVJqxTa2UrSs5KGSFpf0p8lPZf3/UbSSvm8C4G1gUm57ZNy/aL5khbL5wyTNFHS85L+LemYQj/j\nJV0q6Vf5s98n6T09/W2DIGhtBrWBkrQR8GngvdlV9wFgRj58OjCSVOtly/z6S7YfBDbN56xkexdS\nXZ5Z2XW1ou2n8vG9gUuBVYAJwFWShtQQpVN3XzcyduRl4DDbKwF7Ap+StE9uZx2SIf0BsCrwbuAu\n2+cBFwHfyvLvU5AJ27OA24ADCv0cAlxm+628/TVgDWBjUsXM8fm9hwMzgQ/ltr9bQ+ZL8jlrAGOB\nr0vauXB8L1LNmZVIBc/O6eSzB0EwwBjUBgp4C1gK2FTSEnl+5JF87BDgq7afs/0ccCZweD7W0WXV\nmQvrDttX5j/y75HcgqM6ObezNrqScSFs32T7/vz6XtKf/06FzzPZ9m9tv2V7ju27e9A/JON6MCyo\nqHpQ3ofth23fYPuN/D2dXeizSyQNJ5XuPsX261menwMfLZx2i+1r85zVb0g3C0EQDAIGtYGy/RDw\nWdId/2xJF0taIx8eBjxWOH1m3tcbnij05bzdqza6kXEhJG0j6UZJz0iaC3wCeFs+PByoadh6wJXA\ntpJWB3YE5tv+S+5ztezGfELSi8CFhT67Yxgwx/YrhX0zgTUL27MLr18Flm5zDwZBMLAZ9Ipu+2Lb\nOwDrkNxa38qHZgHrFk5dO++r2Uwn+4e3vch/qmt10sYrwLKF7dV7KGNHJgBXAWvZXhn4Ce0jo5nA\n+r2Uv63/F0ilmw8ijcQuLhz+OmmUt1l2LR7OwtdVV23PAoZKWr6wb20Khj0IgsHLoDZQkkbkQICl\ngP8C/yH92UL6E/6SpFUlrQp8hTQ6qMVs4G2SVuyw/z2S9pO0OGkU9B/gbzXefxewh6RV8ijlsz2U\nsSPLAy/Yfl3SSJIxaWMCsKukD0taXNLbJLW5y2YD7+ykzeL7jyDNRU3o0OcrwDxJawJf7PC+2XRi\nGG0/DtwKfCMHpWwBHEVy5QVBMMgZ1AaKNLfzDeBZ4ClS8MC4fOx/gTuAe/LjjryvjQUjA9vTSQbt\nEUlzsgvOwNWkUccc4FBg/0JgQZELgbtJwQ/XkuaO2trvSsaOHAd8VdI84MvAbwsyzgT2AL4APA9M\nBdqiCs8HNsnRfVd20vZEYAPgqTy/1caZwNbAi8Ak4AoWHjV9g2ToX5D0+TZxCscPJo1UZ5FciV+x\n/efCeR1HYLF+KggGCarneklJvyBFjz1je/O87zvAh4DXgYeBI22/WLdOm5Qc4r1BjmQLgiAIekm9\nR1AXAGM67LsO2NT2lsCDdH73P9CIxalBEAT9oK4GyvYtwAsd9k22PT9v/p0UKDAYaJpURkEQBK3I\n4iX3dxQLR4ANWGyfWbUMQRAErUxpBkrS6cDrtid0cjxGG0FTYzvctkFQIqUYKEkfI0WQdVleouo/\nAEnjbY+vUoaQo/lkyHLEDVQQlEzDDZSkMaS1MTvZ/k+j+wuCIAgGBnUNkpB0MWnh5UaSHpd0FPB/\npMWck3Om7R/Xs88gCIJgYFLXEZTtg2vs/kU9+2gwU6oWIDOlagEyU6oWgOaQIQiCCihjoe5QUkaD\ndUiZEg60PbfGe131HFQQdEZcn0FQPmUs1D2VVOZhBHBD3g6CIAiCLmn4Ql1S0b5f5de/AvatZ59B\nEATBwKSMZLGr2W6r6TMbWK2EPoOg30gMkdikajmCYLBSaiYJ2+5qPYmk8YXNKbanNFyoIOiAhOCk\nk8BfgFdflH4yKLKfBEGzUdcgCQBJ6wKTCkES04HRtp/OZShutP2uGu+LSeigciS2JhWEXBs4Bbja\nxnF9BkH5lOHim0gqdEd+vqqEPoOgV0isK/Eb4A+kulSb2VxlR8LfIKiKRi/UPRL4JrCbpAeBXfJ2\nEDQFEkMlvgv8k1SvbITNuTZvVCxaEAx66u7i6yvhQgnKRGJp4ATgZFIV4PE2T3d+flyfQVA2pZV8\nlzRO0v2S7pU0QdJSZfUdBG1ILCZxOPAvYHtgR5tPdmWcgiCohlIMVA6cOBbYOgdPDAE+UkbfQdCG\nxG7AncBxwKE2+9o8ULFYQRB0Qllh5vOAN4BlJb0FLAs8WVLfwSBH4t2kyLz1gHHAlRH8EATNTykj\nKNtzgLOAmcAsYK7t68voOxi8SKwj8WvgWuBqYFObK8I4BUFrUFbBwvWBzwLrAi8Cl0k61PZFHc4b\nX9iMhbpBn5BYBTgNOAr4ESkyb17v2tBoYHTdhQuCoMeUEsUn6SBgN9vH5O3DgVG2P104J6Kkgn4h\nsRRwPCkh8e+AM2yeqk/bcX0GQdmUFcU3HRglaRlJAnYFppXUdzDAyZF5h5Ii83YkReZ9vF7GKQiC\naijFxWf7bkm/Bu4A5pMiqX5WRt/BwEZiV+DbwOvA4Ta3VCxSEAR1IhbqBi2JxJakyLwNSJF5lzcy\n+CGuzyAonzIX6q4s6XJJD0iaJmlUWX0HAweJtSV+BfyJlDdvE5vLIjIvCAYeZZbb+AFwje2xkhYH\nliux76DFyZF544CjgXPpQ2ReEAStRVmZJFYCdrD9CwDbb9p+sYy+g9ZGYmmJL5ACIFYBNrf5Uhin\nIBj4lOXiWw94VtIFku6UdJ6kZUvqO2hBCpF504GdgNE2x9rMqli0IAhKoiwDtTiwNfBj21sDr5DW\nqgTBIuSceXeQso1/1GZvO5YlBMFgo6w5qCeAJ2zfnrcvp4aBikwSg5tCzrx3kuabKktLFJkkgqB6\nSgszl3QzcIztB7MhWsb2KYXjEcY7SJFYB/h/wAfy88+arWBgXJ9BUD5lRvGdAFwkaUlS5dIjS+w7\naEIkhpJy5h1JH3PmBUEwcImFukHpSCxDumH5Iqma7ZnNnpYors8gKJ8yF+oOkTRV0qSy+gyaC4kh\nEkcCDwKjgPflarZNbZyCIKiGMl18J5ISxK5QYp9BEyAhYE/gm8ALwIE2t1UrVRAEzU5ZC3XXAvYA\nfg6Em2QQITEKmEKKzjuNlGk8jFMQBN1SlovvbNJ8w/yS+gsqRuJdElcAlwG/Bra0mRg584Ig6CkN\nN1CSPgQ8Y3sqMXoa8EisKXEecAvwd1Jk3vk2b1YsWhAELUYZc1DbAXtL2gNYGlhR0q9tf7TjibFQ\nt3XJIeOnAMcA5wEb2cypVqq+Ewt1g6B6Sg0zl7QTcJLtvWocizDeFkRiOeAzwOeBK4Gv2jxZrVT1\nJ67PICifMqP42og5iAGAxJLAscDpwF+A7W0erFaqIAgGErFQN+gVEosDhwNnAA8Ap9vcWa1UjSeu\nzyAonypGUEELIrEYcCBwJjAbOMzmL9VKFQTBQKYUAyVpOCnU+B0kF9/PbP+wjL6D/pEN0/7AeFKZ\nlOOB6yNcPAiCRlOKi0/S6sDqtu+StDzwT2Bf2w8UzgkXShNRMExfBl4nGahrBqthiuszCMqnlBGU\n7aeBp/PrlyU9AAwjzWEETUSeYzqQlPXhVVIQxB8Gq2EKgqA6Sp+DkrQusBVpEWfQJEgsDXyMlPHj\nSeALwHVhmIIgqIpSDVR2710OnGj75RrHxxc2Y6FuCUi8Hfgk8GngduCICH6IhbpB0AyUWVF3CeD3\nwB9tf7/G8fDxl4jEVqSAh/1JNZm+ZzOtWqmal7g+g6B8yoriE3A+MK2WcQrKQWIF4MPAx0lzgOeS\ncuU9W6lgQRAENSgriu99wM3APbRnkhhn+9rCOXGH2gAklgB2AQ4F9gZuIuXKuzYSuPacuD6DoHwi\nk8QAJOfH25VkkPYBHgEuAi6xmV2lbK1KXJ9BUD5llnwfI2m6pH9LOqWsfntDnhivnN7KIbGMxA4S\npyWbmEAAAATMSURBVEvcQArp/wxwH/Aem5E2P+itcWqG76MZZAiCoBrKmoMaApxDuqt/Erhd0sTi\nQt0mYTSp+mvVjKaGHHnx7JrACGBTYAtga2AjYBrJjfp9YIrNS42So2SaQYYgCCqgrDDzkcBDtmcA\nSLqE5HpqNgNVGhIi1cdaLj9WAFYCVob3byHxWWA1YHWSUVobWAeYCzxIMkh3koJP7rJ5rfQPEQRB\n0EDKMlBrAo8Xtp8Atul4ksSkXrbbmzmBzs4t7D9uQ4lt8j51OK5OHovlx5DCc9tj8fy8BLBk4bF0\nfn6dlK3hZeAlYB7wAqy7Fun7eoZUyuKJ/Jhh80ovPnMQBEHLUlYU3wHAGNvH5u3DgG1sn1A4pzmi\nNYKgEyJIIgjKpawR1JPA8ML2cNKIYAGh/EEQBEGRsqL47gA21P9v735CtKriMI5/H5KJLEgk6I8K\nDpHgRAQSZEEIIVER1qpsEVLUqigjCHXRtlVEGzeVIkIDoWEjBDZUi6BFQQZmRX8oCmKmqAxqNYNP\ni3OmGV/mrRZzz33T57N63zPzch64d+Y3c+/9nSNtlDQGPABMNZo7IiL+h1qtZj4v6QngBOWezKsj\n+ARfRESMkJFp1I2IiFiqWaPuMH018EraIOk9SaclfSrpyTq+VtK0pC8lvS1pTYMsF0k6Kel4jxnW\nSDoi6XNJn0m6uacce+sxOSXpNUkXd51D0gFJs5JOLRkbOmfN+FU9b+9YySwRsajXArWkgfdOYAJ4\nUNLmRtPPAU/bvh7YCjxe594DTNveBLxT33ftKUpf08K/s31keAl4y/ZmSgPwF61z1L3CHgO22L6B\ncjl4Z4McBynn4FLLzilpgnIPdaJ+Zr+k3v/Qizgf9f2D9XcDr+05YKGBt3O2Z2x/Ul//QWkaXkdZ\nv+5Q/bZDwH1d5pC0HrgbeIXFnqvWGS4HbrN9AMo9Q9u/t85B6QObA1ZLWgWsBn7sOoft94HfBoaH\nzXkvMGl7rjaef005jyNihfVdoJZr4F3XOsTALr9X2l5Ys26WsppDl16k7GJ7dslY6wzjwM+SDkr6\nWNLLki5tncP2r8ALwPeUwnTG9nTrHNWwOa/h3BaJXs7ZiAtB3wWq9yc06i6/Rym7/J6zfp3LEySd\nZZR0D/CT7ZMMWemi6wzVKsqafvttbwH+ZOAyWosckq4FdgMbKYXgstrU3TTHoP8wZ+/nccT5qO8C\n9a8NvF2qu/weBQ7bPlaHZyVdVb9+NWW5oa7cCuyQ9C0wCdwu6XDjDFCXUrL9UX1/hFKwZhrnuAn4\nwPYvtueBN4BbesgBw4/B4Dm7vo5FxArru0D11sD7D7v8TgG76utdwLHBz64U2/tsb7A9TnkY4F3b\nD7XMUHPMAD9I2lSHtgOngeMtc1AezNgq6ZJ6fLZTHh5pnQOGH4MpYKekMUnjwHXAhw3yRFxweu+D\nknQXZYuIhQbe5xvNu+wuv5RfNq9TVg//Drjf9pkGebYBz9jeIWlt6wySbqQ8qDEGfAM8TDkmrXM8\nSykIZymrtT9KWem9sxySJoFtwBWU+03PAW8Om1PSPuARYJ5yafjESmWJiEW9F6iIiIjl9H2JLyIi\nYlkpUBERMZJSoCIiYiSlQEVExEhKgYqIiJGUAhURESMpBSoiIkbSX+3wHfPVmTPyAAAAAElFTkSu\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b4b2110>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def linear(x):\n",
    "    return x\n",
    "\n",
    "def sigmoid(x):\n",
    "    return 1 / (1 + np.exp(-x))\n",
    "\n",
    "def tanh(x):\n",
    "    return (np.exp(x)-np.exp(-x)) / (np.exp(x)+np.exp(-x))\n",
    "\n",
    "def relu(x):\n",
    "    return np.maximum(0, x)\n",
    "\n",
    "def softplus(x):\n",
    "    return np.log(np.exp(x) + 1)\n",
    "\n",
    "x = np.linspace(-10,10,100)\n",
    "\n",
    "plt.subplot(321)\n",
    "plt.plot(linear(x))\n",
    "plt.title('linear activation')\n",
    "plt.subplot(322)\n",
    "plt.plot(sigmoid(x))\n",
    "plt.title('sigmoid activation')\n",
    "plt.subplot(323)\n",
    "plt.plot(tanh(x))\n",
    "plt.title('tanh activation')\n",
    "plt.subplot(324)\n",
    "plt.plot(relu(x))\n",
    "plt.title('relu activation')\n",
    "plt.subplot(325)\n",
    "plt.plot(softplus(x))\n",
    "plt.title('softplus activation')\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#####Exercise 2: Continue writing the activation layer, following the template given below.\n",
    "As a starter we'll show you how to solve the sigmoid activation function. The forward pass is already given above:\n",
    "\n",
    "$$f(x) = \\frac{1}{1 + exp(-x)}$$\n",
    "\n",
    "and in Python\n",
    "\n",
    "```PYTHON\n",
    "1.0 / (1.0 + np.exp(-x))\n",
    "```\n",
    "\n",
    "For the backward pass we need to find the derivative of the sigmoid w.r.t to the input:\n",
    "\n",
    "$$\\frac{\\partial f}{\\partial x} = \\frac{\\partial}{\\partial x} (1+exp(-x))^{-1} = (-1)(1+exp(-x))^{-2}(-exp(-x)) = (1+exp(-x))^{-2}exp(-x) = \\frac{1}{1+exp(-x)} \\frac{exp(-x)}{1+exp(-x)} = $$\n",
    "$$ \\frac{1}{1+exp(-x)} \\frac{(1+exp(-x))-1}{1+exp(-x)} = \\frac{1}{1+exp(-x)} \\frac{1+exp(-x)}{1+exp(-x)} \\frac{-1}{1+exp(-x)} = f(x)(1-f(x))$$\n",
    "\n",
    "This shows that the gradient of the sigmoid can be calculated from the output of the sigmoid layer. When implementing the sigmoid we want save the output from the forward pass and use it when doing the backward pass. \n",
    "\n",
    "*When you have implemented the ReLU function you can go to the next section. If you have extra time you can implement the other activation functions*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class SigmoidActivationLayer():\n",
    "    def __str__(self): \n",
    "        return \"Sigmoid()\"\n",
    "    \n",
    "    def fprop(self, x, train=True):\n",
    "        fx = 1.0 / (1.0 + np.exp(-x)) # calculate sigmoid\n",
    "        self.fx = fx  # cache output for use during backward pass \n",
    "        return fx  \n",
    "\n",
    "    def bprop(self, delta_in):\n",
    "        return self.fx*(1-self.fx)\n",
    "\n",
    "    def update_params(self, lr):\n",
    "        pass  # no params to update\n",
    "\n",
    "class ReluActivationLayer():\n",
    "    def __str__(self): \n",
    "        return \"ReLU()\"\n",
    "\n",
    "    def fprop(self, x, train=True):\n",
    "        raise NotImplemented()\n",
    "\n",
    "    def bprop(self, delta_in):\n",
    "        raise NotImplemented()\n",
    "        \n",
    "    def update_params(self, lr):\n",
    "        pass\n",
    "\n",
    "class TanhActivationLayer():\n",
    "    def __str__(self): \n",
    "        return \"Tanh()\"\n",
    "    \n",
    "    def fprop(self, x, train=True):\n",
    "        raise NotImplemented()\n",
    "\n",
    "    def bprop(self, delta_in):\n",
    "        raise NotImplemented()\n",
    "\n",
    "    def update_params(self, lr):\n",
    "        pass\n",
    "    \n",
    "class SoftplusActivationLayer():\n",
    "    def __str__(self):\n",
    "        return \"Softplus()\"\n",
    "    \n",
    "    def fprop(self, x, train=True):\n",
    "        raise NotImplemented()\n",
    "\n",
    "    def bprop(self, delta_in):\n",
    "        raise NotImplemented()\n",
    "        \n",
    "    def update_params(self, lr):\n",
    "        pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Writing the output activation function\n",
    "In a classifier the output of the network must be a $k$-dimensional vector of real values that sums to 1. Here we introduce the softmax activation function, which is a generalization of the logistic sigmoid function:\n",
    "$\\sigma (z_j) = \\frac{exp(z_j)}{\\sum_k exp(z_k)}$.\n",
    "\n",
    "####Exercise 3: Continue writing the softmax activation layer, following the template given below.\n",
    "*Hints*: \n",
    "\n",
    "* The forward pass can be implemented in a few lines of code without for-loops. You'll need to use broadcasting when dividing by the denominator (i.e the normalizing constant)\n",
    "* The backward pass is very simple. Consider what happens to the sum in the denominator when you take the gradient w.r.t $z_j$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class SoftmaxActivationLayer():\n",
    "    def __str__(self): \n",
    "        return \"Softmax()\"\n",
    "    \n",
    "    def fprop(self, x, train=True):\n",
    "        raise NotImplemented()\n",
    "\n",
    "    def bprop(self, delta_in):\n",
    "        # We'll derive the gradient of CrossEntropyLoss(softmax(x))\n",
    "        # in CrossEntropyLoss. softmax backprob should therefore return\n",
    "        # identity. Cf. Bishop p. 241->...\n",
    "        raise NotImplemented()\n",
    "\n",
    "    def update_params(self, lr):\n",
    "        pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Loss layers\n",
    "Loss layers are slightly different because they take both prediction probabilities and true targets as output. Many different loss layers exists. Here we implement squared loss and cross entropy loss. \n",
    "\n",
    "1. For regression problems use a linear output and MeanSquaredError loss, $\\frac{1}{2} \\sum^{K}_{k=1}(y_k-t_k)^2$.\n",
    "2. For classification problems use a SoftmaxLayer as output and CrossEntropyLoss, $-\\sum^{K}_{k=1}t_k \\log y_k$.\n",
    "\n",
    "\n",
    "#####Exercise 4: Continue writing the mean squared loss and cross entropy loss functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class MeanSquaredLoss():\n",
    "    def __str__(self): \n",
    "        return \"MeanSquaredLoss()\"\n",
    "    \n",
    "    def fprop(self, x, t):\n",
    "        # TODO: Write the code for calculating the error and return this value.\n",
    "        raise NotImplemented()\n",
    "\n",
    "    def bprop(self, y, t):\n",
    "        # TODO: Write the code for calculating derivative of the error and return this value.\n",
    "        raise NotImplemented()\n",
    "        \n",
    "    def update_params(self):\n",
    "        pass\n",
    "\n",
    "class CrossEntropyLoss():\n",
    "    def __str__(self): \n",
    "        return \"CrossEntropyLoss()\"\n",
    "    \n",
    "    def fprop(self, x, t):\n",
    "        # TODO: Write the code for calculating the error and return this value.\n",
    "        raise NotImplemented()\n",
    "        \n",
    "    def bprop(self, y, t):\n",
    "        # TODO: Write the code for calculating derivative of the error and return this value.\n",
    "        raise NotImplemented()\n",
    "        \n",
    "    def update_params(self):\n",
    "        pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#Setting up the model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because we have implemented the layers with a forward pass (`fprop`) and a backward pass (`bprop`) we only need to setup the layers and connect them.\n",
    "\n",
    "#####Exercise 5: Write a classifier with one 100 unit linear layers, corresponding relu activation layer,  and a softmax output layer. Use the cross entropy loss as the loss layer.\n",
    "\n",
    "<img src=\"./network.png\" alt=\"The network that you are to implement.\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "num_samples, num_inputs = x_train.shape\n",
    "num_hidden_units = 100\n",
    "num_classes = 10\n",
    "\n",
    "# TODO: Define each layer in the model here.\n",
    "l1 = LinearLayer(num_inputs, num_hidden_units) \n",
    "l2 = ?????\n",
    "l3 = ?????\n",
    "l4 = ?????\n",
    "\n",
    "LossLayer = CrossEntropyLoss()\n",
    "\n",
    "def forward(x):\n",
    "    # TODO: Write the forward pass through each layer. Return the softmax probabilities as the output.\n",
    "    out1 = l1.fprop(x)\n",
    "    out2 = l2.fprop(?????)\n",
    "    ?????\n",
    "    raise NotImplemented()\n",
    "\n",
    "\n",
    "def backward(y_probs, targets):\n",
    "    # TODO: Write the backward propagation of errors.\n",
    "    delta1 = LossLayer.bprop(???, ???)\n",
    "    delta2 = l_hid_act2.bprop(???)\n",
    "    delta3 = ???\n",
    "    ????\n",
    "    raise NotImplemented()\n",
    "\n",
    "def update(learning_rate):\n",
    "    # TODO: Write the update of each linear layer in the model.\n",
    "    l_hid_pre1.update_params(????)\n",
    "    ?????\n",
    "    raise NotImplemented()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Writing the training loop\n",
    "\n",
    "#####Exercise 6: Check whether the above implementations are implemented correctly by running the training loop below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from confusionmatrix import ConfusionMatrix\n",
    "batch_size = 100\n",
    "num_epochs = 100\n",
    "learning_rate = 0.1\n",
    "num_samples = x_train.shape[0]\n",
    "num_batches = num_samples // batch_size\n",
    "\n",
    "\n",
    "train_acc, train_loss = [], []\n",
    "valid_acc, valid_loss = [], []\n",
    "test_acc, test_loss = [], []\n",
    "for epoch in range(num_epochs):\n",
    "    #Forward->Backprob->Update params\n",
    "    for i in range(num_batches):\n",
    "        idx = range(i*batch_size, (i+1)*batch_size)\n",
    "        x_batch = x_train[idx]\n",
    "        target_batch = targets_train[idx]\n",
    "        #FORWARD PASS\n",
    "        y_probs = ?????\n",
    "        batch_loss_cur = LossLayer.fprop(y_probs, target_batch) \n",
    "        #For large models you likely wan't to plot this to monitor the convergence of the model\n",
    "        batch_loss += [batch_loss_cur]\n",
    "        #BACKWARD PASS\n",
    "        ????\n",
    "        \n",
    "        #UPDATE PARAMETERS\n",
    "        ???\n",
    "        \n",
    "    #A lot of bookkeeping to track of performance - \n",
    "    confusion_train = ConfusionMatrix(num_classes)\n",
    "    #confusion_valid = ??\n",
    "    #confusion_test =??\n",
    "    \n",
    "    y_train_probs = forward(x_train)\n",
    "    train_loss_cur = LossLayer.fprop(y_train_probs, targets_train)\n",
    "    confusion_train.batch_add(targets_train.argmax(-1), y_train_probs.argmax(-1))\n",
    "    train_acc_cur = confusion_train.accuracy()\n",
    "    train_acc += [train_acc_cur]\n",
    "    train_loss += [train_loss_cur.mean()]\n",
    "\n",
    "    #Add tracking of validation and test performance below\n",
    "    valid_acc_cur = 0.0\n",
    "    \n",
    "    print \"Epoch %i : Train Loss %e , Train acc %f,  Valid acc %f \" \\\n",
    "    % (epoch+1, np.mean(train_loss_cur), train_acc_cur, valid_acc_cur)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Plot the performance - add the validation and test performacne when you hae implementet these\n",
    "print confusion\n",
    "plt.plot(range(num_epochs), train_acc)\n",
    "plt.title('Training Accuracy on MNIST')\n",
    "plt.xlabel('Epochs')\n",
    "plt.ylabel('Accuracy')\n",
    "plt.show()\n",
    "\n",
    "plt.plot(train_loss)\n",
    "plt.title('Training Losses on MNIST')\n",
    "plt.xlabel('Updates')\n",
    "plt.ylabel('Loss')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To avoid overfitting we introduce the use of test and validation set. These are not trained upon and will thereby provide an impression on the model generalization while training.\n",
    "\n",
    "#####Exercise 7: In the training loop above, only the training set is evaluated. Rewrite the training loop above to include the test and the validation set and plot the acc/losses for train/valid/test data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With low learning rates the improvements will be linear. With higher learning rates the progression will be more exponential. With a higher learning rate, the loss will decay faster, but the model may get stuck at a worse state, since the training is not able to reach near a minima in the error space.\n",
    "\n",
    "#####Exercise 8: Experiment with different learning rates to increase the accuracy of the model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#####Exercise 9: Change the parameters of training. Can you make the model overfit?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "##Writing a dropout layer\n",
    "Dropout is a way of preventing neural networks to overfit, by setting a random number of unit activations to zero in each layer given a probability. So if a random number is greater than the dropout probability, the activation of the unit is zero. For more info, please have a look at this <a href=https://youtu.be/UcKPdAM8cnI>video</a>.\n",
    "\n",
    "#####Excercise 10: Continue writing the dropout layer, following the template given below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class DropoutLayer():\n",
    "    def __str__(self): \n",
    "        return \"Dropout(%f)\" % self.p\n",
    "    \n",
    "    def __init__(self, p=0.5):\n",
    "        self.p = p\n",
    "\n",
    "    def fprop(self, x, train=True):\n",
    "        if train:\n",
    "            # TODO: Write the code in the if-statement.\n",
    "            raise NotImplemented()\n",
    "        else:\n",
    "            return x\n",
    "\n",
    "    def bprop(self, delta_in):\n",
    "        delta_out = delta_in*self.a\n",
    "        return delta_out\n",
    "\n",
    "    def update_params(self, lr):\n",
    "        pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#####Exercise 11: Add dropout layers to the architecture from exercise 11, and evaluate the progression of the training. Is the model overfitting?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Writing a feed-forward neural network in Theano\n",
    "Theano is a Python library enabling the optimization and evaluation of mathematical expressions at decent speeds, especially by utilizing the GPU. One of the most helpful features in Theano is the ability to automatically calculate <a href=\"http://deeplearning.net/software/theano/tutorial/gradients.html\">gradients</a>. This will be obvious in the following example. Please visit the <a href='http://deeplearning.net/software/theano/introduction.html'>Theano tutorial</a> for an in-debt walkthrough. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import theano\n",
    "import theano.tensor as T # Theano subpackage where many useful symbols are included."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href='http://lasagne.readthedocs.org/en/latest/'>Lasagne</a> is a Python library build on Theano to ease the implementation of deep learning. Many of the frequently used layers are already implemented together with the activation functions, loss functions and optimization algorithms. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import lasagne\n",
    "import numpy as np\n",
    "from lasagne.layers import InputLayer, DenseLayer, get_output, get_all_params\n",
    "from lasagne.init import Normal, Constant\n",
    "from lasagne.nonlinearities import rectify, softmax"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In lasagne a basic feed-forward neural network consists of an input layer and a dense layer. The dense layer contains both the linear and the activation layer. Following you will see how simple it is to define a network similar to the one above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "batch_size = 100\n",
    "num_class = 10\n",
    "learning_rate = 0.1\n",
    "\n",
    "data = np.load('mnist.npz')\n",
    "num_classes = 10\n",
    "x_train = data['X_train'].astype('float32')\n",
    "targets_train = data['y_train'].astype('int32')\n",
    "\n",
    "x_valid = data['X_valid'].astype('float32')\n",
    "targets_valid = data['y_valid'].astype('int32')\n",
    "\n",
    "x_test = data['X_test'].astype('float32')\n",
    "targets_test = data['y_test'].astype('int32')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "l_in = InputLayer(shape=(batch_size, x_train.shape[1]))\n",
    "l_hid = DenseLayer(incoming=l_in, num_units=500, nonlinearity=rectify)\n",
    "l_out = DenseLayer(incoming=l_hid, num_units=10, nonlinearity=softmax)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we will import the cross entropy loss and the stochastic gradient descent update function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from lasagne.objectives import categorical_crossentropy\n",
    "from lasagne.updates import sgd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now define the loss and update functions as Theano expressions. In order to do so we must define the <a href='http://deeplearning.net/software/theano/library/tensor/basic.html'>symbolic variables</a> that will take on the values of a batch during training."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sym_x = T.matrix('sym_x') # a symbolic variable taking on the value of a input batch.\n",
    "sym_t = T.ivector('sym_t') # a symbolic variable taking on the value of the target batch.\n",
    "\n",
    "# Get network output\n",
    "train_out = lasagne.layers.get_output(l_out, sym_x, deterministic=False)\n",
    "eval_out = lasagne.layers.get_output(l_out, sym_x, deterministic=True)\n",
    "\n",
    "\n",
    "# Get list of all trainable parameters in the network.\n",
    "all_params = lasagne.layers.get_all_params(l_out, trainable=True)\n",
    "\n",
    "cost = T.nnet.categorical_crossentropy(train_out+1e-8, sym_t).mean()\n",
    "# Let Theano do its magic and get all the gradients we need for training\n",
    "all_grads = T.grad(cost, all_params)\n",
    "\n",
    "\n",
    "# Set the update function for parameters \n",
    "# you might wan't to experiment with more advanded update schemes like rmsprob, adadelta etc.\n",
    "updates = lasagne.updates.sgd(all_grads, all_params, learning_rate=learning_rate)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "f_eval = theano.function([sym_x],\n",
    "                     eval_out, on_unused_input='warn')\n",
    "\n",
    "f_train = theano.function([sym_x, sym_t],\n",
    "                          [cost],\n",
    "                          updates=updates, on_unused_input='warn')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can use the power of Theano to implement the train, validation, and test functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('l_out', (45, 10))\n"
     ]
    }
   ],
   "source": [
    "    #Test the forward pass\n",
    "    x = np.random.normal(0,1, (45, 28*28)).astype('float32') #dummy data\n",
    "    \n",
    "    model = lasagne.layers.get_output(l_out, sym_x)\n",
    "    out = model.eval({sym_x:x}) #this could also include mask etc if used\n",
    "    print(\"l_out\", out.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Implementing the training loop is done simply by the following code snippet."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from confusionmatrix import ConfusionMatrix\n",
    "batch_size = 100\n",
    "num_epochs = 10\n",
    "learning_rate = 0.1\n",
    "num_samples_train = x_train.shape[0]\n",
    "num_batches_train = num_samples_train // batch_size\n",
    "num_samples_valid = x_valid.shape[0]\n",
    "num_batches_valid = num_samples_valid // batch_size\n",
    "\n",
    "train_acc, train_loss = [], []\n",
    "valid_acc, valid_loss = [], []\n",
    "test_acc, test_loss = [], []\n",
    "cur_loss = 0\n",
    "loss = []\n",
    "for epoch in range(num_epochs):\n",
    "    #Forward->Backprob->Update params\n",
    "    cur_loss = 0\n",
    "    for i in range(num_batches_train):\n",
    "        idx = range(i*batch_size, (i+1)*batch_size)\n",
    "        x_batch = x_train[idx]\n",
    "        target_batch = targets_train[idx]    \n",
    "        batch_loss = f_train(x_batch,target_batch) #this will do the complete backprob pass\n",
    "        cur_loss += batch_loss[0]\n",
    "    loss += [cur_loss/batch_size]\n",
    "    \n",
    "    confusion_valid = ConfusionMatrix(num_classes)\n",
    "    confusion_train = ConfusionMatrix(num_classes)\n",
    "\n",
    "    for i in range(num_batches_train):\n",
    "        idx = range(i*batch_size, (i+1)*batch_size)\n",
    "        x_batch = x_train[idx]\n",
    "        targets_batch = targets_train[idx]\n",
    "        net_out = f_eval(x_batch)   \n",
    "        preds = np.argmax(net_out, axis=-1) \n",
    "        confusion_train.batch_add(targets_batch, preds)\n",
    "\n",
    "    confusion_valid = ConfusionMatrix(num_classes)\n",
    "    for i in range(num_batches_valid):\n",
    "        idx = range(i*batch_size, (i+1)*batch_size)\n",
    "        x_batch = x_valid[idx]\n",
    "        targets_batch = targets_valid[idx]\n",
    "        net_out = f_eval(x_batch)   \n",
    "        preds = np.argmax(net_out, axis=-1) \n",
    "        \n",
    "        confusion_valid.batch_add(targets_batch, preds)\n",
    "    \n",
    "    train_acc_cur = confusion_train.accuracy()\n",
    "    valid_acc_cur = confusion_valid.accuracy()\n",
    "\n",
    "    \n",
    "    print \"Epoch %i : Train Loss %e , Train acc %f,  Valid acc %f \" \\\n",
    "    % (epoch+1, loss[-1], train_acc_cur, valid_acc_cur)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#####Exercise 12: Implement the training loop from exercise 7 in Theano and lasagne."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class FeedforwardNetwork():\n",
    "    def __init__(self):\n",
    "        self.layers = []\n",
    "        \n",
    "    def __str__(self):\n",
    "        if len(self.layers) > 0:\n",
    "            s = \"input \"\n",
    "            for l in self.layers:\n",
    "                s += \" --> \" + str(l) \n",
    "            s += \" --> output\"\n",
    "        else:\n",
    "            s = \"No Layers\"\n",
    "        return s\n",
    "        \n",
    "    def add(self, layer):\n",
    "        self.layers += [layer]\n",
    "\n",
    "    def forward(self, x, train=True):\n",
    "        for layer in self.layers:\n",
    "            x = layer.fprop(x, train=train)\n",
    "        return x\n",
    "\n",
    "    def backward(self, delta):\n",
    "        for layer in reversed(self.layers):\n",
    "            delta = layer.bprop(delta)\n",
    "    \n",
    "    def update(self, lr):\n",
    "        for layer in self.layers:\n",
    "            layer.update_params(lr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ffn = FeedforwardNetwork()\n",
    "\n",
    "ffn.add(LinearLayer(num_inputs, num_hidden_units))\n",
    "ffn.add(ReluActivationLayer())\n",
    "ffn.add(LinearLayer(num_hidden_units, num_classes))\n",
    "ffn.add(SoftmaxActivationLayer())\n",
    "losslayer = CrossEntropyLoss()\n",
    "\n",
    "print \"Network\"\n",
    "print ffn\n",
    "print \"Loss\", losslayer\n",
    "print \"\"\n",
    "\n",
    "\n",
    "acc = []\n",
    "for epoch in range(num_epochs):\n",
    "    confusion = ConfusionMatrix(num_classes)\n",
    "    for i in range(num_batches):\n",
    "        idx = range(i*batch_size, (i+1)*batch_size)\n",
    "        x_batch = x_train[idx]\n",
    "        target_batch = targets_train[idx]\n",
    "\n",
    "        y_probs =  ffn.forward(x_batch)\n",
    "        loss = losslayer.fprop(y_probs, target_batch)\n",
    "        delta = losslayer.bprop(y_probs, target_batch)\n",
    "        ffn.backward(delta)\n",
    "        ffn.update(learning_rate)\n",
    "        confusion.batch_add(target_batch.argmax(-1), y_probs.argmax(-1))\n",
    "    curr_acc = confusion.accuracy()\n",
    "    print \"Epoch %i : Loss %f Train acc %f\" % (epoch, loss, curr_acc)\n",
    "    acc += [curr_acc]"
   ]
  }
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