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Created May 20, 2016 05:20
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# TensorFlow.jl test - Calculating the real part of a DFT\n",
"\n",
"As an example to learn how to use TensorFlow, we will learn a common linear operator: the Discrete Fourier Transform, or, to be more precise, the real part of the non-negative frequencies of the DFT$^{[1]}$. This transform, defined as:\n",
"\n",
"$$\n",
"X[k] = \\sum_{i=0}^{N} x[i] e^{-j i \\frac{k 2 \\pi}{N}}\n",
"$$\n",
"\n",
"projects an input signal onto complex exponential bases, so as to allow us to decompose the signal in terms of its frequency content. When we take the real part of this output, assuming that $x[i]$ is real, projects the complex exponentials down into sinusoids:\n",
"\n",
"$$\n",
"\\Re \\left(X[k] \\right) = \\sum_{i=0}^{N} x[i] \\cos \\left( i \\frac{k 2 \\pi}{N} \\right)\n",
"$$\n",
"\n",
"This linear relationship, transforming $x[i]$ for $i \\in [0, 1, \\dots, N]$ into $X[k]$ for $k \\in [0, 1, \\dots, N/2 + 1]$ can be learned by a simple neural network. Calling this a neural network is somewhat of an abuse of the term, as for linear operators one does not need any hidden layers. Indeed, we will construct a single weight matrix $W$ and map our input $x$ to our predicted output $\\hat{y}$ as:\n",
"\n",
"$$\n",
"\\hat{y} = W * x \\quad\\quad W \\in \\Re^{33 \\times 64}\n",
"$$\n",
"\n",
"Ideally, the columns of $W$ will learn the sinusoids described above. We will learn this by creating random test vectors, and minimizing a cost function across the predicted output $\\hat{y}$ of each test vector and the \"true\" output $y$, calculated by actually performing a DFT. We will use the $\\ell_2$ norm of the error vector as the cost function to minimize, and the optimization algorithm used will be a Gradient Descent-based solver.\n",
"\n",
"$$\n",
"\\text{argmin}_W\\, \\|y - \\hat{y}\\|_2\n",
"$$\n",
"\n",
"Let's setup the TensorFlow variables and datatypes to perform this calculation:"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"I tensorflow/stream_executor/dso_loader.cc:105] successfully opened CUDA library libcublas.so locally\n",
"I tensorflow/stream_executor/dso_loader.cc:105] successfully opened CUDA library libcudnn.so locally\n",
"I tensorflow/stream_executor/dso_loader.cc:105] successfully opened CUDA library libcufft.so locally\n",
"I tensorflow/stream_executor/dso_loader.cc:105] successfully opened CUDA library libcuda.so.1 locally\n",
"I tensorflow/stream_executor/dso_loader.cc:105] successfully opened CUDA library libcurand.so locally\n"
]
}
],
"source": [
"# Import TensorFlow types\n",
"using TensorFlow\n",
"import TensorFlow: DT_FLOAT32\n",
"import TensorFlow.API: GradientDescentOptimizer, l2_loss\n",
"\n",
"# This is where we'll store our models once we're done generating them\n",
"try mkdir(\"models\") end\n",
"\n",
"# Network Parameters; we'll have 64 input nodes at 33 output\n",
"n_input = 64\n",
"n_output = 33\n",
"\n",
"# Create input and output placeholders (variables that are not optimized\n",
"# but are instead calculated/fed in with a FeedDict)\n",
"x = Placeholder(DT_FLOAT32, [-1, n_input])\n",
"y = Placeholder(DT_FLOAT32, [-1, n_output])\n",
"\n",
"# Construct simple neural network with no hidden layers, we are just learning\n",
"# the linear weights mapping our input neurons to our output neurons\n",
"w = Variable(randn(Tensor, [n_input, n_output]))\n",
"\n",
"# y_hat, the predicted output is simply a linear combination of inputs\n",
"y_hat = (x * w)\n",
"\n",
"# Our cost function will be the L2 loss between y (the placeholder for ground\n",
"# truth) and y_hat (the predicted output). We will optimize that cost with a\n",
"# Gradient Descent optimizer using a learning rate of 1e-5\n",
"cost = l2_loss(y_hat - y)\n",
"optimizer = minimize(GradientDescentOptimizer(1e-5), cost);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Training data\n",
"\n",
"We will create a chunk of training examples in the form of random noise (these will be what we substitute in for the `x` Variable above), and will also calculate our ground truth vectors (which will be substituted in for the `y` Variable above):"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Create our training data, 100k examples of 64-length input vectors\n",
"num_examples = 100_000\n",
"\n",
"training_data = Array{Float32,2}(n_input, num_examples)\n",
"ground_truth = Array{Float32,2}(n_output, num_examples)\n",
"\n",
"# The transformation we are learning; h(x) returns the real part of the positive frequencies in fft(x)\n",
"h = x -> real(fft(x))[1:div(n_input,2)+1]\n",
"\n",
"for idx in 1:num_examples\n",
" # Random noise serves as a nice system identification probe signal\n",
" training_data[:,idx] = randn(n_input)\n",
" \n",
" # Store the ground truth transformation of the training data\n",
" ground_truth[:,idx] = h(training_data[:,idx])\n",
"end"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Model training\n",
"\n",
"TensorFlow operations all happen within the context of a \"session\". Operations include everything from initializing variables to running the optimization algorithms. We start by initializing all variables we will be optimizing over, then build a `FeedDict`, which is a dictionary mapping the `Placeholder` variables we created above in the setup cell to their actual values. If this were a larger dataset (e.g. one that didn't fit into memory all at once) we would feed in small batches (note that nowhere in our TensorFlow setup did we state that we would be providing 100k examples of training data; TensorFlow will happily consume as much data as we send it) and optimize over those small batches one after another.\n",
"\n",
"This training loop runs until either the training error falls below a threshold (here set to the extremely strict `1e-5` as we know the Neural Network should be able to exactly learn the transform) or the number of training epochs exceeds a threshold (here set to the generous value of `100`), at which point the optimization is stopped, the model is saved to disk and the session is closed."
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[Epoch 01] cost: 1.015e+05\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"I tensorflow/core/common_runtime/gpu/gpu_device.cc:755] Creating TensorFlow device (/gpu:0) -> (device: 0, name: GeForce GTX TITAN X, pci bus id: 0000:03:00.0)\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"[Epoch 02] cost: 1.359e+02\n",
"[Epoch 03] cost: 2.318e-01\n",
"[Epoch 04] cost: 4.488e-04\n",
"[Epoch 05] cost: 2.361e-06\n",
"Final cost after 5 epochs: 2.361e-06\n",
"\n",
"Saving model in models/realfft.jls\n"
]
}
],
"source": [
"# Training Parameters\n",
"max_error_threshold = 1e-5\n",
"max_training_epochs = 100\n",
"\n",
"sess = Session()\n",
"try\n",
" # Run the initialization operation. Note that initialize_all_variables() is a function\n",
" # that returns the operation that actually initializes the variables\n",
" run(sess, initialize_all_variables())\n",
"\n",
" # Keep track of our epoch number and average cost\n",
" epoch_idx = 0\n",
" epoch_cost = Inf\n",
" \n",
" # This is where we provide the concrete values for the Placeholder variables defined above,\n",
" # Unfortunately, Python is row-major so they store their observation matrices transposed\n",
" # from what we would typically do in Julia. It's still faster to transpose now, after\n",
" # generating the values than to deal with everything in a non-native storage format.\n",
" batch_vars = FeedDict(x => training_data', y => ground_truth')\n",
" \n",
" # Keep running until we exceed our maximum training epochs, or we satisfy our error threshold\n",
" while epoch_idx < max_training_epochs && epoch_cost >= max_error_threshold\n",
" # Optimize over the data provided by these batch variables\n",
" run(sess, optimizer, batch_vars)\n",
" \n",
" # Compute cost for this epoch\n",
" epoch_cost = run(sess, cost, batch_vars)\n",
" epoch_idx += 1\n",
" println(@sprintf(\"[Epoch %02d] cost: %.3e\", epoch_idx, epoch_cost))\n",
" end\n",
"\n",
" # Display a happy message when we finish!\n",
" println(@sprintf(\"Final cost after %d epochs: %.3e\\n\", epoch_idx, epoch_cost))\n",
"catch e\n",
" # Quietly obey an InterruptException, yell a little louder otherwise\n",
" if !isa(e, InterruptException)\n",
" println(\"Caught exception!\")\n",
" showerror(STDOUT, e, catch_backtrace())\n",
" end\n",
" println(\"Attempting to save model...\")\n",
"finally\n",
" # Save model in a file\n",
" modelpath = \"models/realfft.jls\"\n",
" \n",
" # Recover the weights by simply \"run\"'ing the w object created above in the setup cell\n",
" weights = run(sess, w)\n",
" println(\"Saving model in $modelpath\")\n",
" \n",
" # Serialize it out to a file path\n",
" open(modelpath, \"w\") do file\n",
" serialize(file, weights)\n",
" end\n",
" \n",
" # Always close the session once we're done\n",
" close(sess)\n",
"end"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Model validation\n",
"\n",
"We validate the model in two ways:\n",
"\n",
"* First, we load in the weights matrix learned earlier and plot the weights for a certain output neurons. If the model has indeed learned the transformation listed above, then we should see sinusoids of varying frequency as we look at each output neuron's weights in turn.\n",
"\n",
"\n",
"* Second, we build a sinusoid (a signal type very dissimilar to our training data) and pump it through the model, comparing that output with the ground-truth output of passing the sinusoid through the `h()` function defined in the training data cell above."
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false,
"scrolled": false
},
"outputs": [
{
"data": {
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"text/plain": [
"PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7fe55009d250>)"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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"text/plain": [
"PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7fe5500ed450>)"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# We'll be using PyPlot to visualize our output\n",
"using PyPlot\n",
"PyPlot.plt[:interactive](true)\n",
"\n",
"# Helper function to calculate the l2 norm on Julia arrays\n",
"l2_norm(x::AbstractArray) = sqrt(sum(abs(x).^2))\n",
"\n",
"# Open the last model we learned\n",
"open(\"models/realfft.jls\", \"r\") do file\n",
" weights = deserialize(file)\n",
" \n",
" figure(figsize=(16,5))\n",
" plot(weights[:,1:4])\n",
" xlim([0,63])\n",
" xlabel(\"Time\")\n",
" ylabel(\"Amplitude\")\n",
" legend([\"Basis $idx\" for idx in 0:3])\n",
" title(\"First four Fourier bases\");\n",
" \n",
" figure(figsize=(16,5))\n",
" x = sin(2*π*4*collect(1:64)/64)\n",
" plot(weights'*x)\n",
" plot(h(x))\n",
" xlim([0,32])\n",
" xlabel(\"Wavenumber\")\n",
" ylabel(\"Real part of DFT\")\n",
" legend([\"Learned Transform\", \"FFT\"])\n",
" title(@sprintf(\"Ground-truth comparison - L2 error: %.3e\", l2_norm(h(x) - weights'*x)))\n",
"end;"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Addendum\n",
"\n",
"* Yes, the transform being learned here is essentially an incomplete [Discrete Cosine Transform](https://en.wikipedia.org/wiki/Discrete_cosine_transform). However, I like thinking in terms of Fourier bases, so there.\n",
"\n",
"\n",
"* The model training process is robust against exceptions, so try decreasing the model learning rate to something like `1e-6`, then interrupting the kernel while training to save a model with high error. This will allow you to inspect a noisy estimate of the Fourier basis functions, which is cheap family-friendly-fun for everybody.\n",
"\n",
"\n",
"* There is no cross-validation going on here at all because we are learning an exactly representable transform, and so overfitting is essentially impossible as long as the training data size exceeds the number of parameters being optimized over. In any real use case, that is not the case."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 0.4.5",
"language": "julia",
"name": "julia-0.4"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "0.4.5"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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