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|
{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "vDJ4XzMqodTy"
},
"source": [
"# Eager Execution: Working with Gradients\n",
"\n",
"This notebook demonstrates:\n",
"\n",
"* How to get gradients using TensorFlow's eager execution capabilities\n",
"* How to apply the gradients so you can update your variables"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "GQJysDM__Qb0"
},
"source": [
"# Setup: Import eager and enable eager execution.\n"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
}
},
"colab_type": "code",
"id": "OiMPZStlibBv"
},
"outputs": [],
"source": [
"# Import TensorFlow.\n",
"import tensorflow as tf\n",
"\n",
"# Import TensorFlow eager execution support (subject to future changes).\n",
"import tensorflow.contrib.eager as tfe\n",
"\n",
"# Enable eager execution.\n",
"tfe.enable_eager_execution()"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "1CLWJl0QliB0"
},
"source": [
"# Fitting a Simple Linear Model"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "-39gouo7mtgu"
},
"source": [
"## Step 1: Synthesize some data\n",
"\n",
"To demonstrate fitting a model with TensorFlow's eager execution, we'll fit a linear model to some synthesized data (which includes some noise).\n",
"\n",
"In the code, we use the variable names `w` and `b` to represent the single weight and bias we'll use to fit our model."
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"cellView": "code",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
}
},
"colab_type": "code",
"id": "rQsdCg9PfIL-"
},
"outputs": [],
"source": [
"# The constants we'll try to fit our variables to:\n",
"true_w = 3\n",
"true_b = 2\n",
"\n",
"NUM_EXAMPLES = 1000\n",
"\n",
"# Our inputs:\n",
"inputs = tf.random_normal(shape=[NUM_EXAMPLES, 1])\n",
"\n",
"# Our labels, with noise:\n",
"noise = tf.random_normal(shape=[NUM_EXAMPLES, 1])\n",
"labels = inputs * true_w + true_b + noise"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"cellView": "code",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
},
"height": 360,
"output_extras": [
{
"item_id": 1
}
]
},
"colab_type": "code",
"executionInfo": {
"elapsed": 127,
"status": "ok",
"timestamp": 1505502830690,
"user": {
"displayName": "",
"photoUrl": "",
"userId": ""
},
"user_tz": 240
},
"id": "O4lsC4ckAcar",
"outputId": "2f760690-cafb-4777-b970-91d839f99faf"
},
"outputs": [
{
"data": {
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++y7Hbvewb18ql1/+BCUlz7FtWwuqMxiAhUDAjlH8X3stgaSkROLjm4GvEmnr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\nPyQ+uNKCpR6MAAAAAElFTkSuQmCC\n",
"text/plain": [
"\u003cmatplotlib.figure.Figure at 0xa813090\u003e"
]
},
"metadata": {
"tags": []
},
"output_type": "display_data"
}
],
"source": [
"# Plot the Data (Optional)\n",
"\n",
"import matplotlib.pyplot as plt\n",
"\n",
"plt.scatter(inputs.numpy(), labels.numpy())\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "JaFHyAG9nDET"
},
"source": [
"## Step 2: Define our TensorFlow variables\n",
"\n",
"We'll use Keras's object-oriented [`Dense`](https://www.tensorflow.org/api_docs/python/tf/contrib/keras/layers/Dense) layer to create our variables. In this case, we'll create a `Dense` layer with a single weight and bias.\n",
"\n",
"(**Note**: We're using the implementation of `Dense` found in `tf.layers.Dense` though the documentation link is for `tf.contrib.keras.layers.Dense`. When TensorFlow 1.4 is released, the documentation will also be in `tf.layers.Dense`) "
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"cellView": "code",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
},
"height": 34,
"output_extras": [
{
"item_id": 1
}
]
},
"colab_type": "code",
"executionInfo": {
"elapsed": 22,
"status": "ok",
"timestamp": 1505502830753,
"user": {
"displayName": "",
"photoUrl": "",
"userId": ""
},
"user_tz": 240
},
"id": "z9r-ZeyrXu3A",
"outputId": "6230a7a3-29fe-4d08-f101-da80425bad82"
},
"outputs": [
{
"data": {
"text/plain": [
"[]"
]
},
"execution_count": 4,
"metadata": {
"tags": []
},
"output_type": "execute_result"
}
],
"source": [
"# Create TensorFlow Variables using Keras's Dense layer.\n",
"\n",
"wb = tf.layers.Dense(units=1, use_bias=True)\n",
"\n",
"# We can access the underlying TensorFlow variables using wb.variables.\n",
"# However, the variables won't exist until the dimensions of the input\n",
"# tensors are known. Once the dimensions of the input tensors are known,\n",
"# Keras can create and initialize the variables. Until then, Keras will\n",
"# report the variables as an empty list: [].\n",
"\n",
"wb.variables"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "docKLUaonYG_"
},
"source": [
"## Step 3: Define our loss function\n",
"\n",
"Our loss function is the standard L2 loss (where we reduce the loss to its mean across its inputs)."
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"cellView": "code",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
}
},
"colab_type": "code",
"id": "0_w8ZJSCtuY7"
},
"outputs": [],
"source": [
"def loss_fn(inputs, labels, wb):\n",
" \"\"\"Calculates the mean L2 loss for our linear model.\"\"\"\n",
" predictions = wb(inputs)\n",
" return tf.reduce_mean(tf.square(predictions - labels))"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"cellView": "code",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
},
"height": 34,
"output_extras": [
{
"item_id": 1
}
]
},
"colab_type": "code",
"executionInfo": {
"elapsed": 24,
"status": "ok",
"timestamp": 1505502830875,
"user": {
"displayName": "",
"photoUrl": "",
"userId": ""
},
"user_tz": 240
},
"id": "RkNbXoXkpjVH",
"outputId": "c36fc98d-3a57-4074-901d-c10ae017ae3f"
},
"outputs": [
{
"data": {
"text/plain": [
"\u003ctf.Tensor: id=40, shape=(), dtype=float32, numpy=7.3549819\u003e"
]
},
"execution_count": 6,
"metadata": {
"tags": []
},
"output_type": "execute_result"
}
],
"source": [
"# Test loss function (optional).\n",
"\n",
"loss_fn(inputs, labels, wb)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
},
"height": 51,
"output_extras": [
{
"item_id": 1
}
]
},
"colab_type": "code",
"executionInfo": {
"elapsed": 57,
"status": "ok",
"timestamp": 1505502830981,
"user": {
"displayName": "",
"photoUrl": "",
"userId": ""
},
"user_tz": 240
},
"id": "K_7beXoHOU7t",
"outputId": "1ad0856a-02ec-4117-a6c0-b41030981d87"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"w: tf.Tensor([[ 1.56891453]], shape=(1, 1), dtype=float32)\n",
"b: tf.Tensor([ 0.], shape=(1,), dtype=float32)\n"
]
}
],
"source": [
"# At this point, the variables exist, and can now be queried:\n",
"\n",
"w, b = wb.variables\n",
"print(\"w: \" + str(w.read_value()))\n",
"print(\"b: \" + str(b.read_value()))"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "YIlebeb_qYtC"
},
"source": [
"## Step 4: Create our gradients function using `implicit_value_and_gradients()`\n",
"\n",
"With a loss function defined, we can calculate gradients and apply them to our variables to update them.\n",
"\n",
"To calculate the gradients, we wrap our loss function using the `implicit_value_and_gradients()` function.\n",
"\n",
"`implicit_value_and_gradients()` returns a function that accepts the same inputs as the function passed in, and returns a tuple consisting of:\n",
"\n",
"1. the value returned by the function passed in (in this case, the loss calculated by `loss_fn()`), and\n",
"1. a list of tuples consisting of:\n",
" 1. The value of the gradient (a `tf.Tensor`) with respect to a given variable\n",
" 1. The corresponding variable (`tf.Variable`)\n",
"\n",
"Test it out below to get a feel for what it does. Notice how the first value of the returned tuple (the loss) is the same as the value returned in the cell above that tests our loss function."
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"cellView": "code",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
}
},
"colab_type": "code",
"id": "v1spZQ4NwW1U"
},
"outputs": [],
"source": [
"# Produce our gradients function. See description above for details about\n",
"# the returned function's signature.\n",
"\n",
"value_and_gradients_fn = tfe.implicit_value_and_gradients(loss_fn)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"cellView": "code",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
},
"height": 153,
"output_extras": [
{
"item_id": 1
}
]
},
"colab_type": "code",
"executionInfo": {
"elapsed": 46,
"status": "ok",
"timestamp": 1505502831114,
"user": {
"displayName": "",
"photoUrl": "",
"userId": ""
},
"user_tz": 240
},
"id": "21WMcpsmFFLd",
"outputId": "f51b3171-33f5-4f87-8bf7-0be2dc8edc8a"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Outputs of value_and_gradients_fn:\n",
"Loss: tf.Tensor(7.35498, shape=(), dtype=float32)\n",
"\n",
"Gradient: tf.Tensor([[-3.00773573]], shape=(1, 1), dtype=float32)\n",
"Variable: \u003ctf.Variable 'dense/kernel:0' shape=(1, 1) dtype=float32\u003e\n",
"\n",
"Gradient: tf.Tensor([-4.06519032], shape=(1,), dtype=float32)\n",
"Variable: \u003ctf.Variable 'dense/bias:0' shape=(1,) dtype=float32\u003e\n"
]
}
],
"source": [
"# Show outputs of value_and_gradients_fn.\n",
"\n",
"print(\"Outputs of value_and_gradients_fn:\")\n",
"\n",
"value, grads_and_vars = value_and_gradients_fn(inputs, labels, wb)\n",
"\n",
"print('Loss: {}'.format(value))\n",
"for (grad, var) in grads_and_vars:\n",
" print(\"\")\n",
" print('Gradient: {}\\nVariable: {}'.format(grad, var))"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "JVDWpL9VYWdP"
},
"source": [
"## Step 5: Create an optimizer\n",
"\n",
"We'll use a `GradientDescentOptimizer` to fit our model."
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"cellView": "code",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
}
},
"colab_type": "code",
"id": "DudNEebMKDWN"
},
"outputs": [],
"source": [
"optimizer = tf.train.GradientDescentOptimizer(learning_rate=0.1)"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "YBeJYxY8YaiO"
},
"source": [
"### Step 5a: Test Our Optimizer\n",
"\n",
"Now we have everything needed to start fitting our variables to the data!\n",
"\n",
"In the next cell, we'll demo these capabilities. We'll:\n",
"\n",
"1. Print the current values of `w` and `b`\n",
"1. Calculate the loss and gradients\n",
"1. Apply the gradients\n",
"1. Print out the new values of `w` and `b`\n",
"\n",
"You can run the cell multiple times. Each time, you should see the values of `w` and `b` get closer to their true values of 3 and 2."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"cellView": "code",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
},
"height": 102,
"output_extras": [
{
"item_id": 1
}
]
},
"colab_type": "code",
"executionInfo": {
"elapsed": 103,
"status": "ok",
"timestamp": 1505502831285,
"user": {
"displayName": "",
"photoUrl": "",
"userId": ""
},
"user_tz": 240
},
"id": "diDZfrMJM3OC",
"outputId": "d585fff0-ecb3-4e98-9b33-bbae07a95d8c"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Values of w, b, BEFORE applying gradients:\n",
"(array([[ 1.56891453]], dtype=float32), array([ 0.], dtype=float32))\n",
"()\n",
"Values of w, b, AFTER applying gradients:\n",
"(array([[ 1.86968815]], dtype=float32), array([ 0.40651903], dtype=float32))\n"
]
}
],
"source": [
"# Test the optimizer.\n",
"\n",
"print(\"Values of w, b, BEFORE applying gradients:\")\n",
"w, b = wb.variables\n",
"print(w.read_value().numpy(), b.read_value().numpy())\n",
"print()\n",
"\n",
"# Calculate the gradients:\n",
"empirical_loss, gradients_and_variables = value_and_gradients_fn(\n",
" inputs, labels, wb)\n",
"optimizer.apply_gradients(gradients_and_variables)\n",
"\n",
"print(\"Values of w, b, AFTER applying gradients:\")\n",
"print(w.read_value().numpy(), b.read_value().numpy())"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "61TgeLVlKEQp"
},
"source": [
"## Step 6: Create a training loop\n",
"\n",
"Of course, now we can simply turn all of this code into a self-standing training loop. We'll also capture our loss and approximations of `w` and `b` and plot them over time."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
},
"height": 397,
"output_extras": [
{
"item_id": 1
},
{
"item_id": 2
}
]
},
"colab_type": "code",
"executionInfo": {
"elapsed": 225,
"status": "ok",
"timestamp": 1505502831550,
"user": {
"displayName": "",
"photoUrl": "",
"userId": ""
},
"user_tz": 240
},
"id": "VukGe-huNaJ4",
"outputId": "f0a8d665-1910-477c-d8ab-c94ccdc4afcd"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[2.111051321029663, 2.3047544956207275, 2.4602210521698, 2.5850086212158203, 2.6851789951324463, 2.7655951976776123, 2.830157995223999, 2.8819968700408936, 2.9236228466033936, 2.9570505619049072]\n"
]
},
{
"data": {
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8lHDsTLHDvZo3KPZ1WcerhCI9VGY9XwFwGDkan3++Cr16PY2tW3ejevUaFd9+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\nAAAAAElFTkSuQmCC\n",
"text/plain": [
"\u003cmatplotlib.figure.Figure at 0xc1dc310\u003e"
]
},
"metadata": {
"tags": []
},
"output_type": "display_data"
}
],
"source": [
"# Train our variables.\n",
"\n",
"# numpy is used for its asscalar() function.\n",
"import numpy as np\n",
"\n",
"num_training_steps = 10\n",
"\n",
"def train_model(inputs, labels, wb, optimizer, num_training_steps):\n",
" loss_at_step = []\n",
" w_at_step = []\n",
" b_at_step = []\n",
" for step_num in range(num_training_steps):\n",
" loss, gradients_and_variables = value_and_gradients_fn(inputs, labels, wb)\n",
" loss_at_step.append(np.asscalar(loss.numpy()))\n",
" \n",
" optimizer.apply_gradients(gradients_and_variables)\n",
" w, b = wb.variables\n",
" w_at_step.append(np.asscalar(w.read_value().numpy()))\n",
" b_at_step.append(np.asscalar(b.read_value().numpy()))\n",
"\n",
" print(w_at_step)\n",
" t = range(0, num_training_steps)\n",
" plt.plot(t, loss_at_step, 'k',\n",
" t, w_at_step, 'r',\n",
" t, [true_w] * num_training_steps, 'r--',\n",
" t, b_at_step, 'b',\n",
" t, [true_b] * num_training_steps, 'b--')\n",
" plt.legend(['loss', 'w estimate', 'w true', 'b estimate', 'b true'])\n",
" plt.show()\n",
"\n",
"train_model(inputs, labels, wb, optimizer, num_training_steps)"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "UNurY9VJ-hpH"
},
"source": [
"## Other Ways to Compute Gradients\n",
"\n",
"Using our loss function as an example (`loss_fn()`), there are several other ways we could compute gradients:\n",
"\n",
"1. `tfe.implicit_gradients()`\n",
"1. `tfe.gradients_function()`\n",
"1. `tfe.implicit_value_and_gradients()`\n",
"1. `tfe.value_and_gradients_function()`\n",
"\n",
"Each of these functions does the following:\n",
"* Wraps a function.\n",
"* Returns a function with the same input signature as the wrapped function.\n",
"\n",
"They differ only in what information they return.\n",
"\n",
"### Gradients-only functions\n",
"\n",
"The following two functions return a function that returns only the variables' gradients:\n",
"\n",
"1. `tfe.gradients_function()`: Returns the partial derivatives of the function `f()` with respect to the parameters of `f()`.\n",
"1. `tfe.implicit_gradients()`: Returns the partial derivatives of the function `f()` with respect to the trainable parameters (`tf.Variable`) used by `f()`.\n",
"\n",
"In our example above, the `tf.layers.Dense` object encapsulates the trainable parameters.\n",
"\n",
"### Value and gradients functions\n",
"\n",
"The following two functions are identical to their counterparts above, except that they also return the value of the wrapped function.\n",
"\n",
"1. `tfe.implicit_value_and_gradients()`\n",
"1. `tfe.value_and_gradients_function()`\n",
"\n",
"### Gradient demos\n",
"\n",
"In the demos below, we show examples for the `implicit_*` functions, since our existing loss function works seamlessly with these versions. (The other versions require that your parameters are tensors and tensors only; in our example, we're using a `Dense` layer.)\n"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
},
"height": 85,
"output_extras": [
{
"item_id": 1
}
]
},
"colab_type": "code",
"executionInfo": {
"elapsed": 100,
"status": "ok",
"timestamp": 1505502831671,
"user": {
"displayName": "",
"photoUrl": "",
"userId": ""
},
"user_tz": 240
},
"id": "aEoCftnfAIH5",
"outputId": "72f1c1dc-a574-463f-f860-c4e5f48fcdaa"
},
"outputs": [
{
"data": {
"text/plain": [
"[(\u003ctf.Tensor: id=673, shape=(1, 1), dtype=float32, numpy=array([[-0.26846504]], dtype=float32)\u003e,\n",
" \u003ctf.Variable 'dense/kernel:0' shape=(1, 1) dtype=float32\u003e),\n",
" (\u003ctf.Tensor: id=671, shape=(1,), dtype=float32, numpy=array([-0.32890949], dtype=float32)\u003e,\n",
" \u003ctf.Variable 'dense/bias:0' shape=(1,) dtype=float32\u003e)]"
]
},
"execution_count": 13,
"metadata": {
"tags": []
},
"output_type": "execute_result"
}
],
"source": [
"# tfe.implicit_gradients() demo\n",
"gradients_fn = tfe.implicit_gradients(loss_fn)\n",
"\n",
"# Returns only gradients and variables:\n",
"gradients_fn(inputs, labels, wb)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
},
"height": 102,
"output_extras": [
{
"item_id": 1
}
]
},
"colab_type": "code",
"executionInfo": {
"elapsed": 88,
"status": "ok",
"timestamp": 1505502831785,
"user": {
"displayName": "",
"photoUrl": "",
"userId": ""
},
"user_tz": 240
},
"id": "bbgCUdCzAVhH",
"outputId": "152aa9b6-9e42-4b7e-848a-9423c0b1929c"
},
"outputs": [
{
"data": {
"text/plain": [
"(\u003ctf.Tensor: id=688, shape=(), dtype=float32, numpy=1.0623235\u003e,\n",
" [(\u003ctf.Tensor: id=720, shape=(1, 1), dtype=float32, numpy=array([[-0.26846504]], dtype=float32)\u003e,\n",
" \u003ctf.Variable 'dense/kernel:0' shape=(1, 1) dtype=float32\u003e),\n",
" (\u003ctf.Tensor: id=718, shape=(1,), dtype=float32, numpy=array([-0.32890949], dtype=float32)\u003e,\n",
" \u003ctf.Variable 'dense/bias:0' shape=(1,) dtype=float32\u003e)])"
]
},
"execution_count": 14,
"metadata": {
"tags": []
},
"output_type": "execute_result"
}
],
"source": [
"# tfe.implicit_value_and_gradients() demo\n",
"value_gradients_fn = tfe.implicit_value_and_gradients(loss_fn)\n",
"\n",
"# Returns the value returned by the function passed in, gradients, and variables:\n",
"value_gradients_fn(inputs, labels, wb)"
]
}
],
"metadata": {
"colab": {
"default_view": {},
"last_runtime": {
"build_target": "",
"kind": "local"
},
"name": "Eager Execution Tutorial: Working with Gradients",
"provenance": [],
"version": "0.3.2",
"views": {}
}
},
"nbformat": 4,
"nbformat_minor": 0
}
|
