"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/html": [
"\n",
" \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from IPython.display import YouTubeVideo\n",
"YouTubeVideo('9KM9Td6RVgQ')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So far we’ve built a neural network in python, computed a cost function to let us know how well our network is performing, computed the gradient of our cost function so we can train our network, and last time we numerically validated our gradient computations. After all that work, it’s finally time to train our neural network. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Back in part 3, we decided to train our network using gradient descent. While gradient descent is conceptually pretty straight forward, its implementation can actually be quite complex- especially as we increase the size and number of layers in our neural network. If we just march downhill with consistent step sizes, we may get stuck in a local minimum or flat spot, we may move too slowly and never reach our minimum, or we may move to quickly and bounce out of our minimum. And remember, all this must happen in high-dimensional space, making things significantly more complex. Gradient descent is a wonderfully clever method, but provides no guarantees that we will converge to a good solution, that we will converge to a solution in a certain amount of time, or that we will converge to a solution at all. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The good and bad news here is that this problem is not unique to Neural Networks - there’s an entire field dedicated to finding the best combination of inputs to minimize the output of an objective function: the field of Mathematical Optimization. The bad news is that optimization can be a bit overwhelming; there are many different techniques we could apply to our problem. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Part of what makes the optimization challenging is the broad range of approaches covered - from very rigorous, theoretical methods to hands-on, more heuristics-driven methods. Yann Lecun’s 1998 publication Efficient BackProp presents an excellent review of various optimization techniques as applied to neural networks. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here, we’re going to use a more sophisticated variant on gradient descent, the popular Broyden-Fletcher-Goldfarb-Shanno numerical optimization algorithm. The BFGS algorithm overcomes some of the limitations of plain gradient descent by estimating the second derivative, or curvature, of the cost function surface, and using this information to make more informed movements downhill. BFGS will allow us to find solutions more often and more quickly. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We’ll use the BFGS implementation built into the scipy optimize package, specifically within the minimize function. To use BFGS, the minimize function requires us to pass in an objective function that accepts a vector of parameters, input data, and output data, and returns both the cost and gradients. Our neural network implementation doesn’t quite follow these semantics, so we’ll use a wrapper function to give it this behavior. We’ll also pass in initial parameters, set the jacobian parameter to true since we’re computing the gradient within our neural network class, set the method to BFGS, pass in our input and output data, and some options. Finally, we’ll implement a callback function that allows us to track the cost function value as we train the network. Once the network is trained, we’ll replace the original, random parameters, with the trained parameters. "
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
}
],
"source": [
"%pylab inline\n",
"#Import code from previous videos:\n",
"from partFive import *"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"from scipy import optimize"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"class trainer(object):\n",
" def __init__(self, N):\n",
" #Make Local reference to network:\n",
" self.N = N\n",
" \n",
" def callbackF(self, params):\n",
" self.N.setParams(params)\n",
" self.J.append(self.N.costFunction(self.X, self.y)) \n",
" \n",
" def costFunctionWrapper(self, params, X, y):\n",
" self.N.setParams(params)\n",
" cost = self.N.costFunction(X, y)\n",
" grad = self.N.computeGradients(X,y)\n",
" \n",
" return cost, grad\n",
" \n",
" def train(self, X, y):\n",
" #Make an internal variable for the callback function:\n",
" self.X = X\n",
" self.y = y\n",
"\n",
" #Make empty list to store costs:\n",
" self.J = []\n",
" \n",
" params0 = self.N.getParams()\n",
"\n",
" options = {'maxiter': 200, 'disp' : True}\n",
" _res = optimize.minimize(self.costFunctionWrapper, params0, jac=True, method='BFGS', \\\n",
" args=(X, y), options=options, callback=self.callbackF)\n",
"\n",
" self.N.setParams(_res.x)\n",
" self.optimizationResults = _res\n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If we plot the cost against the number of iterations through training, we should see a nice, monotonically decreasing function. Further, we see that the number of function evaluations required to find the solution is less than 100, and far less than the 10^27 function evaluation that would have been required to find a solution by brute force, as shown in part 3. Finally, we can evaluate our gradient at our solution and see very small values – which make sense, as our minimum should be quite flat. "
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"NN = Neural_Network()"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"T = trainer(NN)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Optimization terminated successfully.\n",
" Current function value: 0.000000\n",
" Iterations: 57\n",
" Function evaluations: 63\n",
" Gradient evaluations: 63\n"
]
}
],
"source": [
"T.train(X,y)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0, 0.5, 'Cost')"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
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