exercise_650.ipynb

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    "# Computing the Activation Functions for a Batch of Data\n",
    "\n",
    "You may want to compute the activations for various values of input data.\n",
    "\n",
    "Let's say we have a batch of output values like this\n",
    "\n",
    "$\\begin{bmatrix}-10.0 \\\\ -1.0 \\\\ 0.0 \\\\ 1.0 \\\\ 10.0 \\end{bmatrix}$\n",
    "\n",
    "We apply different activation functions to these to add a measure of non-linearity."
   ]
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      "sigmoid: tensor([[ 0.0000],\n",
      "        [ 0.0067],\n",
      "        [ 0.2689],\n",
      "        [ 0.5000],\n",
      "        [ 0.7311],\n",
      "        [ 0.9933],\n",
      "        [ 1.0000]])\n",
      "tanh: tensor([[-1.0000],\n",
      "        [-0.9999],\n",
      "        [-0.7616],\n",
      "        [ 0.0000],\n",
      "        [ 0.7616],\n",
      "        [ 0.9999],\n",
      "        [ 1.0000]])\n",
      "ReLU: tensor([[  0.],\n",
      "        [  0.],\n",
      "        [  0.],\n",
      "        [  0.],\n",
      "        [  1.],\n",
      "        [  5.],\n",
      "        [ 10.]])\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "import torch.nn.functional as F\n",
    "\n",
    "data = torch.Tensor([[-10.],[-5.],[-1.],[0],[1.0],[5.0],[10.0]])\n",
    "\n",
    "result = F.sigmoid(data)\n",
    "print(\"sigmoid: \" + str(result))\n",
    "\n",
    "result = F.tanh(torch.autograd.Variable(data))\n",
    "print(\"tanh: \" + str(result))\n",
    "\n",
    "result = F.relu(torch.autograd.Variable(data))\n",
    "print(\"ReLU: \" + str(result))"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "## Sigmoid in Detail\n",
    "\n",
    "You can also see how the sigmoid function transforms the inputs from the space of real numbers to the space of 0 to 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
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     "name": "stdout",
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     "text": [
      "e^a: tensor([[ 4.5400e-05],\n",
      "        [ 6.7379e-03],\n",
      "        [ 3.6788e-01],\n",
      "        [ 1.0000e+00],\n",
      "        [ 2.7183e+00],\n",
      "        [ 1.4841e+02],\n",
      "        [ 2.2026e+04]])\n"
     ]
    }
   ],
   "source": [
    "result = torch.exp(data)   # data is the preactivation 'a'\n",
    "print(\"e^a: \" + str(result))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that $e^{a}$ is positive for all values of $a$.\n",
    "\n",
    "Now, let's see what happens if we compute $1 + e^{a}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
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     "text": [
      "1 + e^a: tensor([[     1.0000],\n",
      "        [     1.0067],\n",
      "        [     1.3679],\n",
      "        [     2.0000],\n",
      "        [     3.7183],\n",
      "        [   149.4132],\n",
      "        [ 22027.4648]])\n"
     ]
    }
   ],
   "source": [
    "result = 1 + torch.exp(data)   # data is the preactivation 'a'\n",
    "print(\"1 + e^a: \" + str(result))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Obviously $1 + e^{a}$ is greater than or equal to 1 for all values of $a$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 / (1 + e^a): tensor([[ 1.0000],\n",
      "        [ 0.9933],\n",
      "        [ 0.7311],\n",
      "        [ 0.5000],\n",
      "        [ 0.2689],\n",
      "        [ 0.0067],\n",
      "        [ 0.0000]])\n"
     ]
    }
   ],
   "source": [
    "result = 1 / (1 + torch.exp(data))   # data is the preactivation 'a'\n",
    "print(\"1 / (1 + e^a): \" + str(result))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Obviously, the multiplicative inverse (reciprocal) of $1 + e^{a}$ has to lie between 0 and 1 (because $1 + e^{a}$ is greater than $1$).\n",
    "\n",
    "The multiplicative inverse (reciprocal) of $1 + e^{a}$ is the sigmoid function."
   ]
  },
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   "execution_count": null,
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