TensorFlow basics

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This guide provides a quick overview of TensorFlow basics. Each section of this doc is an overview of a larger topic—you can find links to full guides at the end of each section.

TensorFlow is an end-to-end platform for machine learning. It supports the following:

  • Multidimensional-array based numeric computation (similar to NumPy.)
  • GPU and distributed processing
  • Automatic differentiation
  • Model construction, training, and export
  • And more


TensorFlow operates on multidimensional arrays or tensors represented as tf.Tensor objects. Here is a two-dimensional tensor:

import tensorflow as tf

x = tf.constant([[1., 2., 3.],
                 [4., 5., 6.]])

[[1. 2. 3.]
 [4. 5. 6.]], shape=(2, 3), dtype=float32)
(2, 3)
<dtype: 'float32'>

The most important attributes of a tf.Tensor are its shape and dtype:

  • Tensor.shape: tells you the size of the tensor along each of its axes.
  • Tensor.dtype: tells you the type of all the elements in the tensor.

TensorFlow implements standard mathematical operations on tensors, as well as many operations specialized for machine learning.

For example:

x + x
<tf.Tensor: shape=(2, 3), dtype=float32, numpy=
array([[ 2.,  4.,  6.],
       [ 8., 10., 12.]], dtype=float32)>
5 * x
<tf.Tensor: shape=(2, 3), dtype=float32, numpy=
array([[ 5., 10., 15.],
       [20., 25., 30.]], dtype=float32)>
x @ tf.transpose(x)
<tf.Tensor: shape=(2, 2), dtype=float32, numpy=
array([[14., 32.],
       [32., 77.]], dtype=float32)>
tf.concat([x, x, x], axis=0)
<tf.Tensor: shape=(6, 3), dtype=float32, numpy=
array([[1., 2., 3.],
       [4., 5., 6.],
       [1., 2., 3.],
       [4., 5., 6.],
       [1., 2., 3.],
       [4., 5., 6.]], dtype=float32)>
tf.nn.softmax(x, axis=-1)
<tf.Tensor: shape=(2, 3), dtype=float32, numpy=
array([[0.09003057, 0.24472848, 0.6652409 ],
       [0.09003057, 0.24472848, 0.6652409 ]], dtype=float32)>
<tf.Tensor: shape=(), dtype=float32, numpy=21.0>

Running large calculations on CPU can be slow. When properly configured, TensorFlow can use accelerator hardware like GPUs to execute operations very quickly.

if tf.config.list_physical_devices('GPU'):
  print("TensorFlow **IS** using the GPU")
  print("TensorFlow **IS NOT** using the GPU")
TensorFlow **IS** using the GPU

Refer to the Tensor guide for details.


Normal tf.Tensor objects are immutable. To store model weights (or other mutable state) in TensorFlow use a tf.Variable.

var = tf.Variable([0.0, 0.0, 0.0])
var.assign([1, 2, 3])
<tf.Variable 'UnreadVariable' shape=(3,) dtype=float32, numpy=array([1., 2., 3.], dtype=float32)>
var.assign_add([1, 1, 1])
<tf.Variable 'UnreadVariable' shape=(3,) dtype=float32, numpy=array([2., 3., 4.], dtype=float32)>

Refer to the Variables guide for details.

Automatic differentiation

Gradient descent and related algorithms are a cornerstone of modern machine learning.

To enable this, TensorFlow implements automatic differentiation (autodiff), which uses calculus to compute gradients. Typically you'll use this to calculate the gradient of a model's error or loss with respect to its weights.

x = tf.Variable(1.0)

def f(x):
  y = x**2 + 2*x - 5
  return y
<tf.Tensor: shape=(), dtype=float32, numpy=-2.0>

At x = 1.0, y = f(x) = (1**2 + 2*1 - 5) = -2.

The derivative of y is y' = f'(x) = (2*x + 2) = 4. TensorFlow can calculate this automatically:

with tf.GradientTape() as tape:
  y = f(x)

g_x = tape.gradient(y, x)  # g(x) = dy/dx

<tf.Tensor: shape=(), dtype=float32, numpy=4.0>

This simplified example only takes the derivative with respect to a single scalar (x), but TensorFlow can compute the gradient with respect to any number of non-scalar tensors simultaneously.

Refer to the Autodiff guide for details.

Graphs and tf.function

While you can use TensorFlow interactively like any Python library, TensorFlow also provides tools for:

  • Performance optimization: to speed up training and inference.
  • Export: so you can save your model when it's done training.

These require that you use tf.function to separate your pure-TensorFlow code from Python.

def my_func(x):
  return tf.reduce_sum(x)

The first time you run the tf.function, although it executes in Python, it captures a complete, optimized graph representing the TensorFlow computations done within the function.

x = tf.constant([1, 2, 3])
<tf.Tensor: shape=(), dtype=int32, numpy=6>

On subsequent calls TensorFlow only executes the optimized graph, skipping any non-TensorFlow steps. Below, note that my_func doesn't print tracing since print is a Python function, not a TensorFlow function.

x = tf.constant([10, 9, 8])
<tf.Tensor: shape=(), dtype=int32, numpy=27>

A graph may not be reusable for inputs with a different signature (shape and dtype), so a new graph is generated instead:

x = tf.constant([10.0, 9.1, 8.2], dtype=tf.float32)
<tf.Tensor: shape=(), dtype=float32, numpy=27.3>

These captured graphs provide two benefits:

  • In many cases they provide a significant speedup in execution (though not this trivial example).
  • You can export these graphs, using tf.saved_model, to run on other systems like a server or a mobile device, no Python installation required.

Refer to Intro to graphs for more details.

Modules, layers, and models

tf.Module is a class for managing your tf.Variable objects, and the tf.function objects that operate on them. The tf.Module class is necessary to support two significant features:

  1. You can save and restore the values of your variables using tf.train.Checkpoint. This is useful during training as it is quick to save and restore a model's state.
  2. You can import and export the tf.Variable values and the tf.function graphs using tf.saved_model. This allows you to run your model independently of the Python program that created it.

Here is a complete example exporting a simple tf.Module object:

class MyModule(tf.Module):
  def __init__(self, value):
    self.weight = tf.Variable(value)

  def multiply(self, x):
    return x * self.weight
mod = MyModule(3)
mod.multiply(tf.constant([1, 2, 3]))
<tf.Tensor: shape=(3,), dtype=int32, numpy=array([3, 6, 9], dtype=int32)>

Save the Module:

save_path = './saved'
tf.saved_model.save(mod, save_path)
INFO:tensorflow:Assets written to: ./saved/assets

The resulting SavedModel is independent of the code that created it. You can load a SavedModel from Python, other language bindings, or TensorFlow Serving. You can also convert it to run with TensorFlow Lite or TensorFlow JS.

reloaded = tf.saved_model.load(save_path)
reloaded.multiply(tf.constant([1, 2, 3]))
<tf.Tensor: shape=(3,), dtype=int32, numpy=array([3, 6, 9], dtype=int32)>

The tf.keras.layers.Layer and tf.keras.Model classes build on tf.Module providing additional functionality and convenience methods for building, training, and saving models. Some of these are demonstrated in the next section.

Refer to Intro to modules for details.

Training loops

Now put this all together to build a basic model and train it from scratch.

First, create some example data. This generates a cloud of points that loosely follows a quadratic curve:

import matplotlib
from matplotlib import pyplot as plt

matplotlib.rcParams['figure.figsize'] = [9, 6]
x = tf.linspace(-2, 2, 201)
x = tf.cast(x, tf.float32)

def f(x):
  y = x**2 + 2*x - 5
  return y

y = f(x) + tf.random.normal(shape=[201])

plt.plot(x.numpy(), y.numpy(), '.', label='Data')
plt.plot(x, f(x), label='Ground truth')


Create a model:

class Model(tf.keras.Model):
  def __init__(self, units):
    self.dense1 = tf.keras.layers.Dense(units=units,
    self.dense2 = tf.keras.layers.Dense(1)

  def call(self, x, training=True):
    # For Keras layers/models, implement `call` instead of `__call__`.
    x = x[:, tf.newaxis]
    x = self.dense1(x)
    x = self.dense2(x)
    return tf.squeeze(x, axis=1)
model = Model(64)
plt.plot(x.numpy(), y.numpy(), '.', label='data')
plt.plot(x, f(x),  label='Ground truth')
plt.plot(x, model(x), label='Untrained predictions')
plt.title('Before training')


Write a basic training loop:

variables = model.variables

optimizer = tf.keras.optimizers.SGD(learning_rate=0.01)

for step in range(1000):
  with tf.GradientTape() as tape:
    prediction = model(x)
    error = (y-prediction)**2
    mean_error = tf.reduce_mean(error)
  gradient = tape.gradient(mean_error, variables)
  optimizer.apply_gradients(zip(gradient, variables))

  if step % 100 == 0:
    print(f'Mean squared error: {mean_error.numpy():0.3f}')
Mean squared error: 19.766
Mean squared error: 1.063
Mean squared error: 1.037
Mean squared error: 1.023
Mean squared error: 1.013
Mean squared error: 1.005
Mean squared error: 1.000
Mean squared error: 0.996
Mean squared error: 0.993
Mean squared error: 0.991
plt.plot(x.numpy(),y.numpy(), '.', label="data")
plt.plot(x, f(x),  label='Ground truth')
plt.plot(x, model(x), label='Trained predictions')
plt.title('After training')


That's working, but remember that implementations of common training utilities are available in the tf.keras module. So, consider using those before writing your own. To start with, the Model.compile and Model.fit methods implement a training loop for you:

new_model = Model(64)

history = new_model.fit(x, y,

INFO:tensorflow:Assets written to: ./my_model/assets
plt.ylim([0, max(plt.ylim())])
plt.ylabel('Loss [Mean Squared Error]')
plt.title('Keras training progress');


Refer to Basic training loops and the Keras guide for more details.