View on TensorFlow.org | Run in Google Colab | View source on GitHub | Download notebook |

This short introduction uses Keras to:

- Load a prebuilt dataset.
- Build a neural network machine learning model that classifies images.
- Train this neural network.
- Evaluate the accuracy of the model.

This tutorial is a Google Colaboratory notebook. Python programs are run directly in the browser—a great way to learn and use TensorFlow. To follow this tutorial, run the notebook in Google Colab by clicking the button at the top of this page.

- In Colab, connect to a Python runtime: At the top-right of the menu bar, select
*CONNECT*. - To run all the code in the notebook, select
**Runtime**>**Run all**. To run the code cells one at a time, hover over each cell and select the**Run cell**icon.

## Set up TensorFlow

Import TensorFlow into your program to get started:

```
import tensorflow as tf
print("TensorFlow version:", tf.__version__)
```

2024-07-19 04:50:57.594328: E external/local_xla/xla/stream_executor/cuda/cuda_fft.cc:485] Unable to register cuFFT factory: Attempting to register factory for plugin cuFFT when one has already been registered 2024-07-19 04:50:57.615392: E external/local_xla/xla/stream_executor/cuda/cuda_dnn.cc:8454] Unable to register cuDNN factory: Attempting to register factory for plugin cuDNN when one has already been registered 2024-07-19 04:50:57.621818: E external/local_xla/xla/stream_executor/cuda/cuda_blas.cc:1452] Unable to register cuBLAS factory: Attempting to register factory for plugin cuBLAS when one has already been registered TensorFlow version: 2.17.0

If you are following along in your own development environment, rather than Colab, see the install guide for setting up TensorFlow for development.

## Load a dataset

Load and prepare the MNIST dataset. The pixel values of the images range from 0 through 255. Scale these values to a range of 0 to 1 by dividing the values by `255.0`

. This also converts the sample data from integers to floating-point numbers:

```
mnist = tf.keras.datasets.mnist
(x_train, y_train), (x_test, y_test) = mnist.load_data()
x_train, x_test = x_train / 255.0, x_test / 255.0
```

## Build a machine learning model

Build a `tf.keras.Sequential`

model:

```
model = tf.keras.models.Sequential([
tf.keras.layers.Flatten(input_shape=(28, 28)),
tf.keras.layers.Dense(128, activation='relu'),
tf.keras.layers.Dropout(0.2),
tf.keras.layers.Dense(10)
])
```

/tmpfs/src/tf_docs_env/lib/python3.9/site-packages/keras/src/layers/reshaping/flatten.py:37: UserWarning: Do not pass an `input_shape`/`input_dim` argument to a layer. When using Sequential models, prefer using an `Input(shape)` object as the first layer in the model instead. super().__init__(**kwargs) WARNING: All log messages before absl::InitializeLog() is called are written to STDERR I0000 00:00:1721364660.663156 56038 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721364660.666664 56038 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721364660.670358 56038 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721364660.674062 56038 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721364660.685427 56038 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721364660.688589 56038 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721364660.692023 56038 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721364660.695376 56038 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721364660.698673 56038 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721364660.701824 56038 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721364660.705138 56038 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721364660.708441 56038 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721364661.951741 56038 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721364661.953806 56038 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721364661.955856 56038 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721364661.957976 56038 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721364661.960186 56038 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721364661.962086 56038 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721364661.964034 56038 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721364661.966119 56038 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721364661.968233 56038 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721364661.970146 56038 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721364661.972077 56038 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721364661.974062 56038 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721364662.012641 56038 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721364662.014656 56038 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721364662.016627 56038 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721364662.018655 56038 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721364662.020846 56038 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721364662.022757 56038 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721364662.024702 56038 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721364662.026818 56038 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721364662.029083 56038 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721364662.031511 56038 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721364662.033897 56038 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355 I0000 00:00:1721364662.036327 56038 cuda_executor.cc:1015] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero. See more at https://github.com/torvalds/linux/blob/v6.0/Documentation/ABI/testing/sysfs-bus-pci#L344-L355

`Sequential`

is useful for stacking layers where each layer has one input tensor and one output tensor. Layers are functions with a known mathematical structure that can be reused and have trainable variables. Most TensorFlow models are composed of layers. This model uses the `Flatten`

, `Dense`

, and `Dropout`

layers.

For each example, the model returns a vector of logits or log-odds scores, one for each class.

```
predictions = model(x_train[:1]).numpy()
predictions
```

array([[ 0.8345982 , 0.02583528, 0.02325563, -0.13725212, -0.4650353 , -0.04670947, -0.8046191 , -0.91970056, -0.60336345, 0.06968632]], dtype=float32)

The `tf.nn.softmax`

function converts these logits to *probabilities* for each class:

```
tf.nn.softmax(predictions).numpy()
```

array([[0.24845515, 0.1106641 , 0.110379 , 0.09401102, 0.06773675, 0.10292028, 0.04823308, 0.04298984, 0.05898604, 0.1156248 ]], dtype=float32)

Define a loss function for training using `losses.SparseCategoricalCrossentropy`

:

```
loss_fn = tf.keras.losses.SparseCategoricalCrossentropy(from_logits=True)
```

The loss function takes a vector of ground truth values and a vector of logits and returns a scalar loss for each example. This loss is equal to the negative log probability of the true class: The loss is zero if the model is sure of the correct class.

This untrained model gives probabilities close to random (1/10 for each class), so the initial loss should be close to `-tf.math.log(1/10) ~= 2.3`

.

```
loss_fn(y_train[:1], predictions).numpy()
```

2.2738006

Before you start training, configure and compile the model using Keras `Model.compile`

. Set the `optimizer`

class to `adam`

, set the `loss`

to the `loss_fn`

function you defined earlier, and specify a metric to be evaluated for the model by setting the `metrics`

parameter to `accuracy`

.

```
model.compile(optimizer='adam',
loss=loss_fn,
metrics=['accuracy'])
```

## Train and evaluate your model

Use the `Model.fit`

method to adjust your model parameters and minimize the loss:

```
model.fit(x_train, y_train, epochs=5)
```

Epoch 1/5 WARNING: All log messages before absl::InitializeLog() is called are written to STDERR I0000 00:00:1721364663.834708 56203 service.cc:146] XLA service 0x7f11140090d0 initialized for platform CUDA (this does not guarantee that XLA will be used). Devices: I0000 00:00:1721364663.834742 56203 service.cc:154] StreamExecutor device (0): Tesla T4, Compute Capability 7.5 I0000 00:00:1721364663.834748 56203 service.cc:154] StreamExecutor device (1): Tesla T4, Compute Capability 7.5 I0000 00:00:1721364663.834752 56203 service.cc:154] StreamExecutor device (2): Tesla T4, Compute Capability 7.5 I0000 00:00:1721364663.834760 56203 service.cc:154] StreamExecutor device (3): Tesla T4, Compute Capability 7.5 124/1875 ━━━━━━━━━━━━━━━━━━━━ 2s 1ms/step - accuracy: 0.5870 - loss: 1.3581 I0000 00:00:1721364664.935413 56203 device_compiler.h:188] Compiled cluster using XLA! This line is logged at most once for the lifetime of the process. 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 4s 1ms/step - accuracy: 0.8587 - loss: 0.4892 Epoch 2/5 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 2s 1ms/step - accuracy: 0.9564 - loss: 0.1545 Epoch 3/5 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 2s 1ms/step - accuracy: 0.9668 - loss: 0.1108 Epoch 4/5 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 2s 1ms/step - accuracy: 0.9745 - loss: 0.0840 Epoch 5/5 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 2s 1ms/step - accuracy: 0.9769 - loss: 0.0736 <keras.src.callbacks.history.History at 0x7f12e35bbdc0>

The `Model.evaluate`

method checks the model's performance, usually on a validation set or test set.

```
model.evaluate(x_test, y_test, verbose=2)
```

313/313 - 1s - 3ms/step - accuracy: 0.9765 - loss: 0.0736 [0.0735689178109169, 0.9764999747276306]

The image classifier is now trained to ~98% accuracy on this dataset. To learn more, read the TensorFlow tutorials.

If you want your model to return a probability, you can wrap the trained model, and attach the softmax to it:

```
probability_model = tf.keras.Sequential([
model,
tf.keras.layers.Softmax()
])
```

```
probability_model(x_test[:5])
```

<tf.Tensor: shape=(5, 10), dtype=float32, numpy= array([[2.5668689e-06, 2.8617961e-08, 6.7279427e-05, 6.6734367e-04, 6.4502831e-10, 5.8443953e-07, 4.1521453e-11, 9.9919063e-01, 3.2529251e-06, 6.8329733e-05], [1.2201831e-06, 2.6708450e-03, 9.9731594e-01, 8.1051858e-06, 2.4292790e-14, 2.8059355e-06, 9.0277763e-07, 1.9389720e-13, 2.4434263e-07, 2.1835914e-12], [4.8376046e-06, 9.9864870e-01, 3.5636904e-04, 4.7940091e-05, 6.0353945e-05, 7.5621178e-06, 2.2408689e-04, 5.2158791e-04, 1.2816055e-04, 4.0530810e-07], [9.9990797e-01, 1.1300950e-09, 1.1733700e-06, 4.4789645e-06, 5.3895673e-07, 4.3203971e-05, 1.4648891e-05, 4.7963540e-06, 2.9773885e-08, 2.3247434e-05], [1.3722783e-06, 7.6345319e-10, 2.3831459e-05, 1.3882489e-08, 9.9793315e-01, 5.6978706e-06, 1.2278924e-05, 4.9375034e-05, 4.0938976e-06, 1.9701675e-03]], dtype=float32)>

## Conclusion

Congratulations! You have trained a machine learning model using a prebuilt dataset using the Keras API.

For more examples of using Keras, check out the tutorials. To learn more about building models with Keras, read the guides. If you want learn more about loading and preparing data, see the tutorials on image data loading or CSV data loading.