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__)
```

2024-08-16 07:45:15.387747: 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 2024-08-16 07:45:15.408731: 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 2024-08-16 07:45:15.415209: 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 00:00:1723794318.490455 241277 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 00:00:1723794318.494342 241277 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 00:00:1723794318.497584 241277 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 00:00:1723794318.501312 241277 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 00:00:1723794318.512702 241277 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 00:00:1723794318.516197 241277 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 00:00:1723794318.519187 241277 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 00:00:1723794318.522647 241277 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 00:00:1723794318.526047 241277 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 00:00:1723794318.529503 241277 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 00:00:1723794318.532428 241277 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 00:00:1723794318.535893 241277 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 00:00:1723794319.771712 241277 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 00:00:1723794319.773840 241277 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 00:00:1723794319.775826 241277 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 00:00:1723794319.777872 241277 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 00:00:1723794319.779874 241277 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 00:00:1723794319.781821 241277 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 00:00:1723794319.783693 241277 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 00:00:1723794319.785644 241277 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 00:00:1723794319.787540 241277 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 00:00:1723794319.789499 241277 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 00:00:1723794319.791369 241277 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 00:00:1723794319.793317 241277 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 00:00:1723794319.831749 241277 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 00:00:1723794319.833814 241277 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 00:00:1723794319.835738 241277 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 00:00:1723794319.837736 241277 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 00:00:1723794319.839701 241277 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 00:00:1723794319.841655 241277 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 00:00:1723794319.843526 241277 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 00:00:1723794319.845500 241277 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 00:00:1723794319.847443 241277 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 00:00:1723794319.849923 241277 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 00:00:1723794319.852250 241277 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 00:00:1723794319.854736 241277 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([[ 0.68130803, -0.03935227, -0.53304887, 0.22200397, -0.3079031 , -0.6267688 , 0.43393654, 0.5691322 , 0.31098977, 0.32141146]], dtype=float32)

The `tf.nn.softmax`

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

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

array([[0.16339162, 0.07947874, 0.04851112, 0.10321827, 0.06076043, 0.0441712 , 0.12758444, 0.14605366, 0.11282429, 0.11400625]], 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()
```

3.1196823

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 00:00:1723794322.305243 241442 service.cc:146] XLA service 0x7effb8008d30 initialized for platform CUDA (this does not guarantee that XLA will be used). Devices: I0000 00:00:1723794322.305276 241442 service.cc:154] StreamExecutor device (0): Tesla T4, Compute Capability 7.5 I0000 00:00:1723794322.305281 241442 service.cc:154] StreamExecutor device (1): Tesla T4, Compute Capability 7.5 I0000 00:00:1723794322.305284 241442 service.cc:154] StreamExecutor device (2): Tesla T4, Compute Capability 7.5 I0000 00:00:1723794322.305287 241442 service.cc:154] StreamExecutor device (3): Tesla T4, Compute Capability 7.5 112/1875 ━━━━━━━━━━━━━━━━━━━━ 2s 1ms/step - accuracy: 0.6089 - loss: 1.3300 I0000 00:00:1723794323.392324 241442 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: 0.8622 - loss: 0.4811 Epoch 2/5 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 2s 1ms/step - accuracy: 0.9547 - loss: 0.1539 Epoch 3/5 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 2s 1ms/step - accuracy: 0.9676 - loss: 0.1107 Epoch 4/5 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 2s 1ms/step - accuracy: 0.9738 - loss: 0.0843 Epoch 5/5 1875/1875 ━━━━━━━━━━━━━━━━━━━━ 2s 1ms/step - accuracy: 0.9764 - loss: 0.0769 <keras.src.callbacks.history.History at 0x7f0184ec7490>

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: 0.9782 - loss: 0.0729 [0.07293704897165298, 0.9782000184059143]

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([[1.5427084e-07, 7.5027339e-11, 3.1343968e-06, 4.6326011e-05, 8.9990645e-13, 1.5266414e-07, 2.0456495e-13, 9.9994934e-01, 2.1858141e-07, 7.8530559e-07], [1.7771253e-08, 8.4947787e-05, 9.9989736e-01, 1.8331458e-06, 8.3026415e-15, 3.4793761e-08, 6.2480517e-08, 7.9319728e-12, 1.5733674e-05, 3.5440111e-15], [3.3602277e-07, 9.9804592e-01, 5.7737787e-05, 5.8099768e-06, 6.3599517e-05, 2.3768812e-06, 2.3459031e-06, 1.6781164e-03, 1.4260423e-04, 1.0617223e-06], [9.9997318e-01, 8.7561805e-11, 9.8983969e-07, 9.0878149e-10, 1.0803159e-07, 3.3033965e-07, 2.3622524e-05, 6.7567669e-07, 4.7765565e-09, 1.1131582e-06], [1.1404303e-05, 2.4895797e-09, 6.0792736e-06, 4.9114313e-08, 9.9449867e-01, 5.9158310e-06, 2.9842497e-05, 4.8574508e-05, 8.5193824e-06, 5.3910208e-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.