# Training & evaluation with the built-in methods

## Setup

    library(keras3)

## Introduction

This guide covers training, evaluation, and prediction (inference) models when using built-in APIs for training & validation (such as `fit()`, `evaluate()` and `predict()`).

If you are interested in leveraging `fit()` while specifying your own training step function, see the Customizing what happens in `fit()` guide.

If you are interested in writing your own training & evaluation loops from scratch, see the guide Writing a training loop from scratch.

In general, whether you are using built-in loops or writing your own, model training & evaluation works strictly in the same way across every kind of Keras model – Sequential models, models built with the Functional API, and models written from scratch via model subclassing.

## API overview: a first end-to-end example

When passing data to the built-in training loops of a model, you should either use:

- Arrays (if your data is small and fits in memory)
- `tf_dataset` objects
- PyTorch `DataLoader` instances

In the next few paragraphs, we’ll use the MNIST dataset as NumPy arrays, in order to demonstrate how to use optimizers, losses, and metrics. Afterwards, we’ll take a close look at each of the other options.

Let’s consider the following model (here, we build in with the Functional API, but it could be a Sequential model or a subclassed model as well):

    inputs <- keras_input(shape = 784, name="digits")
    outputs <- inputs |>
      layer_dense(units = 64, activation = "relu", name = "dense_1") |>
      layer_dense(units = 64, activation = "relu", name = "dense_2") |>
      layer_dense(units = 10, activation = "softmax", name = "predictions")
    model <- keras_model(inputs = inputs, outputs = outputs)
    summary(model)

    ## [1mModel: "functional"[0m
    ## ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓
    ## ┃[1m [0m[1mLayer (type)                   [0m[1m [0m┃[1m [0m[1mOutput Shape          [0m[1m [0m┃[1m [0m[1m      Param #[0m[1m [0m┃
    ## ┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩
    ## │ digits ([38;5;33mInputLayer[0m)             │ ([38;5;45mNone[0m, [38;5;34m784[0m)            │             [38;5;34m0[0m │
    ## ├─────────────────────────────────┼────────────────────────┼───────────────┤
    ## │ dense_1 ([38;5;33mDense[0m)                 │ ([38;5;45mNone[0m, [38;5;34m64[0m)             │        [38;5;34m50,240[0m │
    ## ├─────────────────────────────────┼────────────────────────┼───────────────┤
    ## │ dense_2 ([38;5;33mDense[0m)                 │ ([38;5;45mNone[0m, [38;5;34m64[0m)             │         [38;5;34m4,160[0m │
    ## ├─────────────────────────────────┼────────────────────────┼───────────────┤
    ## │ predictions ([38;5;33mDense[0m)             │ ([38;5;45mNone[0m, [38;5;34m10[0m)             │           [38;5;34m650[0m │
    ## └─────────────────────────────────┴────────────────────────┴───────────────┘
    ## [1m Total params: [0m[38;5;34m55,050[0m (215.04 KB)
    ## [1m Trainable params: [0m[38;5;34m55,050[0m (215.04 KB)
    ## [1m Non-trainable params: [0m[38;5;34m0[0m (0.00 B)

Here’s what the typical end-to-end workflow looks like, consisting of:

- Training
- Validation on a holdout set generated from the original training data
- Evaluation on the test data

We’ll use MNIST data for this example.

    c(c(x_train, y_train), c(x_test, y_test)) %<-% dataset_mnist()

    # Preprocess the data (these are NumPy arrays)
    x_train <- array_reshape(x_train, c(60000, 784)) / 255
    x_test <- array_reshape(x_test, c(10000, 784)) / 255

    # Reserve 10,000 samples for validation
    x_val <- x_train[1:10000,]
    y_val <- y_train[1:10000]
    x_train <- x_train[-c(1:10000),]
    y_train <- y_train[-c(1:10000)]

We specify the training configuration (optimizer, loss, metrics):

    model |> compile(
      # Optimizer
      optimizer = optimizer_rmsprop(),
      # Loss function to minimize
      loss = loss_sparse_categorical_crossentropy(),
      # List of metrics to monitor
      metrics = list(metric_sparse_categorical_accuracy())
    )

We call `fit()`, which will train the model by slicing the data into “batches” of size `batch_size`, and repeatedly iterating over the entire dataset for a given number of `epochs`.

    history <- model |> fit(
      x_train, y_train,
      batch_size = 64,
      epochs = 2,
      # We pass some validation for
      # monitoring validation loss and metrics
      # at the end of each epoch
      validation_data = list(x_val, y_val)
    )

    ## Epoch 1/2
    ## 782/782 - 2s - 3ms/step - loss: 0.3410 - sparse_categorical_accuracy: 0.9035 - val_loss: 0.1869 - val_sparse_categorical_accuracy: 0.9455
    ## Epoch 2/2
    ## 782/782 - 1s - 1ms/step - loss: 0.1588 - sparse_categorical_accuracy: 0.9532 - val_loss: 0.1303 - val_sparse_categorical_accuracy: 0.9626

The returned `history` object holds a record of the loss values and metric values during training:

    history

    ##
    ## Final epoch (plot to see history):
    ##                            loss: 0.1588
    ##     sparse_categorical_accuracy: 0.9532
    ##                        val_loss: 0.1303
    ## val_sparse_categorical_accuracy: 0.9626

We evaluate the model on the test data via `evaluate()`:

    # Evaluate the model on the test data using `evaluate`
    results <- model |> evaluate(x_test, y_test, batch_size=128)

    ## 79/79 - 0s - 4ms/step - loss: 0.1258 - sparse_categorical_accuracy: 0.9625

    str(results)

    ## List of 2
    ##  $ loss                       : num 0.126
    ##  $ sparse_categorical_accuracy: num 0.962

    # Generate predictions (probabilities -- the output of the last layer)
    # on new data using `predict`
    predictions <- model |> predict(x_test[1:2,])

    ## 1/1 - 0s - 160ms/step

    dim(predictions)

    ## [1]  2 10

Now, let’s review each piece of this workflow in detail.

## The `compile()` method: specifying a loss, metrics, and an optimizer

To train a model with `fit()`, you need to specify a loss function, an optimizer, and optionally, some metrics to monitor.

You pass these to the model as arguments to the `compile()` method:

    model |> compile(
      optimizer = optimizer_rmsprop(learning_rate = 1e-3),
      loss = loss_sparse_categorical_crossentropy(),
      metrics = list(metric_sparse_categorical_accuracy())
    )

The `metrics` argument should be a list – your model can have any number of metrics.

If your model has multiple outputs, you can specify different losses and metrics for each output, and you can modulate the contribution of each output to the total loss of the model. You will find more details about this in the Passing data to multi-input, multi-output models section.

Note that if you’re satisfied with the default settings, in many cases the optimizer, loss, and metrics can be specified via string identifiers as a shortcut:

    model |> compile(
      optimizer = "rmsprop",
      loss = "sparse_categorical_crossentropy",
      metrics = c("sparse_categorical_accuracy")
    )

For later reuse, let’s put our model definition and compile step in functions; we will call them several times across different examples in this guide.

    get_uncompiled_model <- function() {
      inputs <- keras_input(shape = 784, name = "digits")
      outputs <- inputs |>
        layer_dense(units = 64, activation = "relu", name = "dense_1") |>
        layer_dense(units = 64, activation = "relu", name = "dense_2") |>
        layer_dense(units = 10, activation = "softmax", name = "predictions")
      keras_model(inputs = inputs, outputs = outputs)
    }

    get_compiled_model <- function() {
      model <- get_uncompiled_model()
      model |> compile(
        optimizer = "rmsprop",
        loss = "sparse_categorical_crossentropy",
        metrics = c("sparse_categorical_accuracy")
      )
      model
    }

### Many built-in optimizers, losses, and metrics are available

In general, you won’t have to create your own losses, metrics, or optimizers from scratch, because what you need is likely to be already part of the Keras API:

Optimizers:

- [`optimizer_sgd()`] (with or without momentum)
- [`optimizer_rmsprop()`]
- [`optimizer_adam()`]
- etc.

Losses:

- [`loss_mean_squared_error()`]
- [`loss_kl_divergence()`]
- [`loss_cosine_similarity()`]
- etc.

Metrics:

- [`metric_auc()`]
- [`metric_precision()`]
- [`metric_recall()`]
- etc.

### Custom losses

If you need to create a custom loss, Keras provides three ways to do so.

The first method involves creating a function that accepts inputs `y_true` and `y_pred`. The following example shows a loss function that computes the mean squared error between the real data and the predictions:

    custom_mean_squared_error <- function(y_true, y_pred) {
      op_mean(op_square(y_true - y_pred), axis = -1)
    }

    model <- get_uncompiled_model()
    model |> compile(optimizer = "adam",
                     loss = custom_mean_squared_error)

    # We need to one-hot encode the labels to use MSE
    y_train_one_hot <- op_one_hot(y_train, num_classes = 10)
    model |> fit(x_train, y_train_one_hot, batch_size = 64, epochs = 2)

    ## Epoch 1/2
    ## 782/782 - 2s - 2ms/step - loss: 0.0157
    ## Epoch 2/2
    ## 782/782 - 1s - 1ms/step - loss: 0.0074

If you need a loss function that takes in parameters beside `y_true` and `y_pred`, you can subclass the Keras base `Loss` class using [`Loss()`] and implement the following two methods:

- `initialize()`: accept parameters to pass during the call of your loss function
- `call(y_true, y_pred)`: use the targets (y_true) and the model predictions (y_pred) to compute the model’s loss

Let’s say you want to use mean squared error, but with an added term that will de-incentivize prediction values far from 0.5 (we assume that the categorical targets are one-hot encoded and take values between 0 and 1). This creates an incentive for the model not to be too confident, which may help reduce overfitting (we won’t know if it works until we try!).

Here’s how you would do it:

    loss_custom_mse <- Loss(
      classname = "CustomMSE",
      initialize = function(regularization_factor = 0.1, name = "custom_mse") {
        super$initialize(name = name)
        self$regularization_factor <- regularization_factor
      },
      call = function(y_true, y_pred) {
        mse <- op_mean(op_square(y_true - y_pred), axis = -1)
        reg <- op_mean(op_square(0.5 - y_pred), axis = -1)
        mse + reg * self$regularization_factor
      }
    )

    model <- get_uncompiled_model()
    model |> compile(optimizer="adam", loss = loss_custom_mse())

    y_train_one_hot <- op_one_hot(y_train, num_classes=10)
    model |> fit(x_train, y_train_one_hot, batch_size=64, epochs=1)

    ## 782/782 - 2s - 2ms/step - loss: 0.0388

### Custom metrics

If you need a metric that isn’t part of the API, you can easily create custom metrics by subclassing the Keras base `Metric` class using [`Metric()`]. You will need to implement 4 methods:

- `initialize()`, in which you will create state variables for your metric.
- `update_state(y_true, y_pred, sample_weight = NULL)`, which uses the targets y_true and the model predictions y_pred to update the state variables.
- `result()`, which uses the state variables to compute the final results.
- `reset_state()`, which reinitializes the state of the metric.

State update and results computation are kept separate (in `update_state()` and `result()`, respectively) because in some cases, the results computation might be very expensive and would only be done periodically.

Here’s a simple example showing how to implement a `CategoricalTruePositives` metric that counts how many samples were correctly classified as belonging to a given class:

    metric_categorical_true_positives <- Metric(
      "CategoricalTruePositives",

      initialize = function(name = "categorical_true_positives", ...) {
        super$initialize(name = name, ...)
        self$true_positives <- self$add_variable(shape = shape(),
                                                 name = "ctp",
                                                 initializer = "zeros")
      },

      update_state = function(y_true, y_pred, sample_weight = NULL) {
        y_pred <- op_argmax(y_pred, axis = 2) |> op_reshape(c(-1, 1))
        values <- op_cast(y_true, "int32") == op_cast(y_pred, "int32")
        values <- op_cast(values, "float32")
        if (!is.null(sample_weight)) {
          sample_weight <- op_cast(sample_weight, "float32")
          values <- op_multiply(values, sample_weight)
        }
        self$true_positives$assign_add(op_sum(values))
      },

      result = function() {
        self$true_positives$value
      },

      reset_state = function() {
        self$true_positives$assign(0.0)
      }
    )

    model <- get_uncompiled_model()
    model |> compile(
      optimizer = optimizer_rmsprop(learning_rate = 1e-3),
      loss = loss_sparse_categorical_crossentropy(),
      metrics = c(metric_categorical_true_positives())
    )
    history <- model |> fit(x_train, y_train, batch_size = 64, epochs = 3)

    ## Epoch 1/3
    ## 782/782 - 2s - 2ms/step - categorical_true_positives: 284988.0000 - loss: 0.3444
    ## Epoch 2/3
    ## 782/782 - 1s - 1ms/step - categorical_true_positives: 284263.0000 - loss: 0.1656
    ## Epoch 3/3
    ## 782/782 - 1s - 1ms/step - categorical_true_positives: 284165.0000 - loss: 0.1200

### Handling losses and metrics that don’t fit the standard signature

The overwhelming majority of losses and metrics can be computed from `y_true` and `y_pred`, where `y_pred` is an output of your model – but not all of them. For instance, a regularization loss may only require the activation of a layer (there are no targets in this case), and this activation may not be a model output.

In such cases, you can call `self$add_loss(loss_value)` from inside the call method of a custom layer. Losses added in this way get added to the “main” loss during training (the one passed to `compile()`). Here’s a simple example that adds activity regularization (note that activity regularization is built-in in all Keras layers – this layer is just for the sake of providing a concrete example):

    layer_custom_activity_regularizer <- Layer(
      "ActivityRegularization",
      call = function(inputs) {
        self$add_loss(op_sum(inputs) * 0.1)
        inputs  # Pass-through layer.
      }
    )

    inputs <- keras_input(shape = 784, name = "digits")
    outputs <- inputs |>
      layer_dense(units = 32, activation = "relu", name = "dense_1") |>
      layer_custom_activity_regularizer() |>
      layer_dense(units = 64, activation = "relu", name = "dense_2") |>
      layer_dense(units = 10, name = "predictions")

    model <- keras_model(inputs = inputs, outputs = outputs)
    model |> compile(optimizer = optimizer_rmsprop(learning_rate = 1e-3),
                     loss = loss_sparse_categorical_crossentropy(from_logits = TRUE))

    # The displayed loss will be much higher than before
    # due to the regularization component.
    model |> fit(x_train, y_train, batch_size = 64, epochs = 1)

    ## 782/782 - 2s - 2ms/step - loss: 2.3721

Note that when you pass losses via `add_loss()`, it becomes possible to call `compile()` without a loss function, since the model already has a loss to minimize.

Consider the following `LogisticEndpoint` layer: it takes as inputs targets & logits, and it tracks a crossentropy loss via `add_loss()`.

    layer_logistic_endpoint <- Layer(
      "LogisticEndpoint",
      initialize = function(name = NULL) {
        super$initialize(name = name)
        self$loss_fn <- loss_binary_crossentropy(from_logits = TRUE)
      },
      call = function(targets, logits, sample_weights = NULL) {
        # Compute the training-time loss value and add it
        # to the layer using `self.add_loss()`.
        loss <- self$loss_fn(targets, logits, sample_weights)
        self$add_loss(loss)

        # Return the inference-time prediction tensor (for `predict()`).
        op_softmax(logits)
      }
    )

You can use it in a model with two inputs (input data & targets), compiled without a `loss` argument, like this:

    inputs <- keras_input(shape = 3, name = "inputs")
    targets <- keras_input(shape = 10, name = "targets")

    logits <- inputs |> layer_dense(10)
    predictions <- layer_logistic_endpoint(name = "predictions")(targets, logits)

    model <- keras_model(inputs = list(inputs, targets),
                         outputs = predictions)
    model |> compile(optimizer = "adam")  # No loss argument!

    data <- list(
      inputs = random_normal(c(3, 3)),
      targets = random_normal(c(3, 10))
    )
    model |> fit(data, epochs = 1)

    ## 1/1 - 0s - 434ms/step - loss: 0.9638

For more information about training multi-input models, see the section Passing data to multi-input, multi-output models.

### Automatically setting apart a validation holdout set

In the first end-to-end example you saw, we used the `validation_data` argument to pass a list of arrays `list(x_val, y_val)` to the model for evaluating a validation loss and validation metrics at the end of each epoch.

Here’s another option: the argument `validation_split` allows you to automatically reserve part of your training data for validation. The argument value represents the fraction of the data to be reserved for validation, so it should be set to a number higher than 0 and lower than 1. For instance, `validation_split = 0.2` means “use 20% of the data for validation”, and `validation_split = 0.6` means “use 60% of the data for validation”.

The way the validation is computed is by taking the last x% samples of the arrays received by the `fit()` call, before any shuffling.

Note that you can only use `validation_split` when training with NumPy data.

    model <- get_compiled_model()
    model |> fit(x_train, y_train,
                 batch_size = 64,
                 validation_split = 0.2, epochs = 1)

    ## 625/625 - 2s - 3ms/step - loss: 0.3817 - sparse_categorical_accuracy: 0.8919 - val_loss: 0.1953 - val_sparse_categorical_accuracy: 0.9431

## Training & evaluation using TF `Dataset` objects

In the past few paragraphs, you’ve seen how to handle losses, metrics, and optimizers, and you’ve seen how to use the `validation_data` and `validation_split` arguments in `fit()`, when your data is passed as arrays.

Another option is to use an iterator-like, such as a `tf.data.Dataset`, a PyTorch `DataLoader`, or an R generator function. Let’s take look at the former.

The `{tfdatasets}` R package containes a set of utilities for loading and preprocessing data in a way that’s fast and scalable. For a complete guide about creating `Datasets`, see the tf.data documentation.

You can use `tf.data` to train your Keras models regardless of the backend you’re using – whether it’s JAX, PyTorch, or TensorFlow. You can pass a `Dataset` instance directly to the methods `fit()`, `evaluate()`, and `predict()`:

    library(tfdatasets, exclude = "shape")
    model <- get_compiled_model()

    # First, let's create a training Dataset instance.
    # For the sake of our example, we'll use the same MNIST data as before.
    train_dataset <- tensor_slices_dataset(list(x_train, y_train))

    # Shuffle and slice the dataset.
    train_dataset <- train_dataset |>
      dataset_shuffle(buffer_size=1024) |>
      dataset_batch(64)

    # Now we get a test dataset.
    test_dataset <-
      tensor_slices_dataset(list(x_test, y_test)) |>
      dataset_batch(64)

    # Since the dataset already takes care of batching,
    # we don't pass a `batch_size` argument.
    model |> fit(train_dataset, epochs = 3)

    ## Epoch 1/3
    ## 782/782 - 2s - 2ms/step - loss: 0.3365 - sparse_categorical_accuracy: 0.9041
    ## Epoch 2/3
    ## 782/782 - 1s - 1ms/step - loss: 0.1606 - sparse_categorical_accuracy: 0.9521
    ## Epoch 3/3
    ## 782/782 - 1s - 999us/step - loss: 0.1178 - sparse_categorical_accuracy: 0.9646

    # You can also evaluate or predict on a dataset.
    result <- model |> evaluate(test_dataset)

    ## 157/157 - 1s - 4ms/step - loss: 0.1213 - sparse_categorical_accuracy: 0.9596

    result

    ## $loss
    ## [1] 0.1213006
    ##
    ## $sparse_categorical_accuracy
    ## [1] 0.9596

Note that the `Dataset` is reset at the end of each epoch, so it can be reused of the next epoch.

If you want to run training only on a specific number of batches from this Dataset, you can pass the `steps_per_epoch` argument, which specifies how many training steps the model should run using this Dataset before moving on to the next epoch.

    model <- get_compiled_model()

    # Prepare the training dataset
    train_dataset <- tensor_slices_dataset(list(x_train, y_train))
    train_dataset <- train_dataset |>
      dataset_shuffle(buffer_size = 1024) |>
      dataset_batch(64)

    # Only use the 100 batches per epoch (that's 64 * 100 samples)
    model |> fit(train_dataset, epochs = 3, steps_per_epoch = 100)

    ## Epoch 1/3
    ## 100/100 - 1s - 8ms/step - loss: 0.8017 - sparse_categorical_accuracy: 0.7806
    ## Epoch 2/3
    ## 100/100 - 0s - 1ms/step - loss: 0.3661 - sparse_categorical_accuracy: 0.9006
    ## Epoch 3/3
    ## 100/100 - 0s - 1ms/step - loss: 0.3009 - sparse_categorical_accuracy: 0.9106

You can also pass a `Dataset` instance as the `validation_data` argument in `fit()`:

    model <- get_compiled_model()

    # Prepare the training dataset
    train_dataset <- tensor_slices_dataset(list(x_train, y_train))
    train_dataset <- train_dataset |>
      dataset_shuffle(buffer_size=1024) |>
      dataset_batch(64)

    # Prepare the validation dataset
    val_dataset <- tensor_slices_dataset(list(x_val, y_val))
    val_dataset <- val_dataset |> dataset_batch(64)

    model |> fit(train_dataset, epochs = 1, validation_data = val_dataset)

    ## 782/782 - 2s - 3ms/step - loss: 0.3428 - sparse_categorical_accuracy: 0.9022 - val_loss: 0.2337 - val_sparse_categorical_accuracy: 0.9291

At the end of each epoch, the model will iterate over the validation dataset and compute the validation loss and validation metrics.

If you want to run validation only on a specific number of batches from this dataset, you can pass the `validation_steps` argument, which specifies how many validation steps the model should run with the validation dataset before interrupting validation and moving on to the next epoch:

    model  <- get_compiled_model()

    # Prepare the training dataset
    train_dataset <- tensor_slices_dataset(list(x_train, y_train))
    train_dataset <- train_dataset |>
      dataset_shuffle(buffer_size = 1024) |>
      dataset_batch(64)

    # Prepare the validation dataset
    val_dataset <- tensor_slices_dataset(list(x_val, y_val))
    val_dataset <- val_dataset |> dataset_batch(64)

    model %>% fit(
      train_dataset,
      epochs = 1,
      # Only run validation using the first 10 batches of the dataset
      # using the `validation_steps` argument
      validation_data = val_dataset,
      validation_steps = 10,
    )

    ## 782/782 - 2s - 3ms/step - loss: 0.3391 - sparse_categorical_accuracy: 0.9035 - val_loss: 0.1997 - val_sparse_categorical_accuracy: 0.9391

Note that the validation dataset will be reset after each use (so that you will always be evaluating on the same samples from epoch to epoch).

The argument `validation_split` (generating a holdout set from the training data) is not supported when training from `Dataset` objects, since this feature requires the ability to index the samples of the datasets, which is not possible in general with the `Dataset` API.

## Using sample weighting and class weighting

With the default settings the weight of a sample is decided by its frequency in the dataset. There are two methods to weight the data, independent of sample frequency:

- Class weights
- Sample weights

### Class weights

This is set by passing a named list to the `class_weight` argument to `fit()`. This list maps class indices to the weight that should be used for samples belonging to this class.

This can be used to balance classes without resampling, or to train a model that gives more importance to a particular class.

For instance, if class “0” is half as represented as class “1” in your data, you could use `model |> fit(..., class_weight = c("0" = 1, "1" = 0.5))`.

Here’s an R example where we use class weights or sample weights to give more importance to the correct classification of class #5 (which is the digit “5” in the MNIST dataset).

    class_weight <- c(
        "0" = 1.0,
        "1" = 1.0,
        "2" = 1.0,
        "3" = 1.0,
        "4" = 1.0,
        # Set weight "2" for class "5",
        # making this class 2x more important
        "5" = 2.0,
        "6" = 1.0,
        "7" = 1.0,
        "8" = 1.0,
        "9" = 1.0
    )

    model <- get_compiled_model()
    model |> fit(x_train, y_train,
                 class_weight = class_weight,
                 batch_size = 64, epochs = 1)

    ## 782/782 - 2s - 2ms/step - loss: 0.3713 - sparse_categorical_accuracy: 0.9018

### Sample weights

For fine grained control, or if you are not building a classifier, you can use `sample_weights`.

- When training from R arrays: Pass the `sample_weight` argument to `fit()`.
- When training from `tf_dataset` or any other sort of iterator: yield `(input_batch, label_batch, sample_weight_batch)` tuples.

A “sample weights” array is an array of numbers that specify how much weight each sample in a batch should have in computing the total loss. It is commonly used in imbalanced classification problems (the idea being to give more weight to rarely-seen classes).

When the weights used are ones and zeros, the array can be used as a mask for the loss function (entirely discarding the contribution of certain samples to the total loss).

    sample_weight <- rep(1.0, length(y_train))
    sample_weight[y_train == 5] <- 2.0

    model <- get_compiled_model()
    model |> fit(
      x_train, y_train,
      sample_weight = sample_weight,
      batch_size = 64, epochs = 1
    )

    ## 782/782 - 2s - 2ms/step - loss: 0.3740 - sparse_categorical_accuracy: 0.9015

Here’s a matching `Dataset` example:

    sample_weight <- rep(1.0, length(y_train))
    sample_weight[y_train == 5] <- 2.0

    # Create a Dataset that includes sample weights
    # (3rd element in the return tuple).
    train_dataset <- tensor_slices_dataset(list(
        x_train, y_train, sample_weight
    ))

    # Shuffle and slice the dataset.
    train_dataset <- train_dataset |>
      dataset_shuffle(buffer_size = 1024) |>
      dataset_batch(64)

    model <- get_compiled_model()
    model |> fit(train_dataset, epochs = 1)

    ## 782/782 - 2s - 2ms/step - loss: 0.3654 - sparse_categorical_accuracy: 0.9057

## Passing data to multi-input, multi-output models

In the previous examples, we were considering a model with a single input (a tensor of shape `(764)`) and a single output (a prediction tensor of shape `(10)`). But what about models that have multiple inputs or outputs?

Consider the following model, which has an image input of shape `(32, 32, 3)` (that’s `(height, width, channels)`) and a time series input of shape `(NA, 10)` (that’s `(timesteps, features)`). Our model will have two outputs computed from the combination of these inputs: a “score” (of shape `(1)`) and a probability distribution over five classes (of shape `(5)`).

    image_input <- keras_input(c(32, 32, 3), name = "img_input")
    timeseries_input <- keras_input(c(NA, 10), name = "ts_input")

    x1 <- image_input |>
      layer_conv_2d(filters = 3, kernel_size = c(3, 3)) |>
      layer_global_max_pooling_2d()

    x2 <- timeseries_input |>
      layer_conv_1d(filters = 3, kernel_size = 3) |>
      layer_global_max_pooling_1d()

    x <- layer_concatenate(x1, x2)

    score_output <- layer_dense(x, 1, name = "score_output")
    class_output <- layer_dense(x, 5, name = "class_output")

    model <- keras_model(
      inputs = list(image_input, timeseries_input),
      outputs = list(score_output, class_output)
    )

Let’s plot this model, so you can clearly see what we’re doing here (note that the shapes shown in the plot are batch shapes, rather than per-sample shapes).

    plot(model, show_shapes = TRUE)

plot of chunk unnamed-chunk-26

At compilation time, we can specify different losses to different outputs, by passing the loss functions as a list:

    model |> compile(
      optimizer = optimizer_rmsprop(1e-3),
      loss = list(
        loss_mean_squared_error(),
        loss_categorical_crossentropy()
      )
    )

If we only passed a single loss function to the model, the same loss function would be applied to every output (which is not appropriate here).

Likewise for metrics:

    model |> compile(
      optimizer = optimizer_rmsprop(1e-3),
      loss = list(
        loss_mean_squared_error(),
        loss_categorical_crossentropy()
      ),
      metrics = list(
        list(
          metric_mean_absolute_error(),
          metric_mean_absolute_percentage_error()
        ),
        list(metric_categorical_accuracy())
      )
    )

Since we gave names to our output layers, we could also specify per-output losses and metrics via a named list:

    model |> compile(
      optimizer = optimizer_rmsprop(1e-3),
      loss = list(
        score_output = loss_mean_squared_error(),
        class_output = loss_categorical_crossentropy()
      ),
      metrics = list(
        score_output = list(
          metric_mean_absolute_error(),
          metric_mean_absolute_percentage_error()
        ),
        class_output = list(metric_categorical_accuracy())
      )
    )

We recommend the use of names if you have more than 2 outputs.

It’s possible to give different weights to different output-specific losses (for instance, one might wish to privilege the “score” loss in our example, by giving to 2x the importance of the class loss), using the `loss_weights` argument:

    model |> compile(
      optimizer = optimizer_rmsprop(1e-3),
      loss = list(
        score_output = loss_mean_squared_error(),
        class_output = loss_categorical_crossentropy()
      ),
      metrics = list(
        score_output = list(
          metric_mean_absolute_error(),
          metric_mean_absolute_percentage_error()
        ),
        class_output = list(metric_categorical_accuracy())
      ),
      loss_weights = list(score_output = 2.0, class_output = 1.0)
    )

You could also choose not to compute a loss for certain outputs, if these outputs are meant for prediction but not for training:

    # loss list, positional version
    model |> compile(
      optimizer = optimizer_rmsprop(1e-3),
      loss = list(NULL, loss_categorical_crossentropy())
    )

    # Or loss list, named version
    model |> compile(
      optimizer = optimizer_rmsprop(1e-3),
      loss = list(class_output = loss_categorical_crossentropy())
    )

Passing data to a multi-input or multi-output model in `fit()` works in a similar way as specifying a loss function in compile: you can pass lists of arrays (with 1:1 mapping to the outputs that received a loss function) or dicts mapping output names to arrays.

    model |> compile(
      optimizer = optimizer_rmsprop(1e-3),
      loss = list(
        loss_mean_squared_error(),
        loss_binary_crossentropy()
      )
    )

    # Generate dummy data
    img_data <- random_normal(c(100, 32, 32, 3))
    ts_data <- random_normal(c(100, 20, 10))
    score_targets <- random_normal(c(100, 1))
    class_targets <- random_normal(c(100, 5))

    # Fit on unnamed lists (positional matching)
    model |> fit(
        list(img_data, ts_data),
        list(score_targets, class_targets),
        batch_size=32,
        epochs=1
    )

    ## 4/4 - 2s - 535ms/step - class_output_categorical_accuracy: 0.2300 - class_output_loss: 1.8162 - loss: 3.8764 - score_output_loss: 1.6820 - score_output_mean_absolute_error: 0.8826 - score_output_mean_absolute_percentage_error: 1826.5676

    # Alternatively, fit on named lists (names matching)
    model <- keras_model(
      inputs = list(image_input, timeseries_input),
      outputs = list(score_output = score_output,
                     class_output = class_output)
    ) |> compile(
      optimizer = optimizer_rmsprop(1e-3),
      loss = list(
        loss_mean_squared_error(),
        loss_binary_crossentropy()
      )
    )

    model |> fit(
      list(img_input = img_data, ts_input = ts_data),
      list(score_output = score_targets, class_output = class_targets),
      batch_size = 32,
      epochs = 1
    )

    ## 4/4 - 2s - 386ms/step - class_output_loss: 4.1489 - loss: 4.5443 - score_output_loss: -4.1125e-01

Here’s the `Dataset` use case: similarly as what we did for R arrays, the `Dataset` should return a tuple of named lists (dicts).

    train_dataset <- tensor_slices_dataset(list(
      list(img_input = img_data, ts_input = ts_data),
      list(score_output = score_targets, class_output = class_targets)
    ))
    train_dataset <- train_dataset |>
      dataset_shuffle(buffer_size = 1024) |>
      dataset_batch(64)

    model |> fit(train_dataset, epochs = 1)

    ## 2/2 - 1s - 665ms/step - class_output_loss: 3.8547 - loss: 3.5725 - score_output_loss: -1.5209e-01

## Using callbacks

Callbacks in Keras are objects that are called at different points during training (at the start of an epoch, at the end of a batch, at the end of an epoch, etc.). They can be used to implement certain behaviors, such as:

- Doing validation at different points during training (beyond the built-in per-epoch validation)
- Checkpointing the model at regular intervals or when it exceeds a certain accuracy threshold
- Changing the learning rate of the model when training seems to be plateauing
- Doing fine-tuning of the top layers when training seems to be plateauing
- Sending email or instant message notifications when training ends or where a certain performance threshold is exceeded
- Etc.

Callbacks can be passed as a list to your call to `fit()`:

    model <- get_compiled_model()

    callbacks <- list(
      callback_early_stopping(
        # Stop training when `val_loss` is no longer improving
        monitor = "val_loss",
        # "no longer improving" being defined as "no better than 1e-2 less"
        min_delta = 1e-2,
        # "no longer improving" being further defined as "for at least 2 epochs"
        patience = 2,
        verbose = 1
      )
    )
    model |> fit(
      x_train,
      y_train,
      epochs = 20,
      batch_size = 64,
      callbacks = callbacks,
      validation_split = 0.2,
    )

    ## Epoch 1/20
    ## 625/625 - 2s - 3ms/step - loss: 0.3695 - sparse_categorical_accuracy: 0.8961 - val_loss: 0.1873 - val_sparse_categorical_accuracy: 0.9469
    ## Epoch 2/20
    ## 625/625 - 1s - 1ms/step - loss: 0.1751 - sparse_categorical_accuracy: 0.9489 - val_loss: 0.1403 - val_sparse_categorical_accuracy: 0.9579
    ## Epoch 3/20
    ## 625/625 - 1s - 1ms/step - loss: 0.1277 - sparse_categorical_accuracy: 0.9625 - val_loss: 0.1218 - val_sparse_categorical_accuracy: 0.9651
    ## Epoch 4/20
    ## 625/625 - 1s - 1ms/step - loss: 0.1007 - sparse_categorical_accuracy: 0.9700 - val_loss: 0.1153 - val_sparse_categorical_accuracy: 0.9661
    ## Epoch 5/20
    ## 625/625 - 1s - 1ms/step - loss: 0.0822 - sparse_categorical_accuracy: 0.9760 - val_loss: 0.1104 - val_sparse_categorical_accuracy: 0.9670
    ## Epoch 6/20
    ## 625/625 - 1s - 1ms/step - loss: 0.0683 - sparse_categorical_accuracy: 0.9801 - val_loss: 0.1098 - val_sparse_categorical_accuracy: 0.9689
    ## Epoch 7/20
    ## 625/625 - 1s - 1ms/step - loss: 0.0571 - sparse_categorical_accuracy: 0.9838 - val_loss: 0.1116 - val_sparse_categorical_accuracy: 0.9698
    ## Epoch 8/20
    ## 625/625 - 1s - 1ms/step - loss: 0.0485 - sparse_categorical_accuracy: 0.9864 - val_loss: 0.1126 - val_sparse_categorical_accuracy: 0.9702
    ## Epoch 8: early stopping

### Many built-in callbacks are available

There are many built-in callbacks already available in Keras, such as:

- `callback_model_checkpoint()`: Periodically save the model.
- `callback_early_stopping()`: Stop training when training is no longer improving the validation metrics.
- `callback_tensorboard()`: periodically write model logs that can be visualized in TensorBoard (more details in the section “Visualization”).
- `callback_csv_logger()`: streams loss and metrics data to a CSV file.
- etc.

See the callbacks documentation for the complete list.

### Writing your own callback

You can create a custom callback by subclassing the base [`Callback()`] class. A callback has access to its associated model through the class property `self$model`.

Make sure to read the complete guide to writing custom callbacks.

Here’s a simple example saving a list of per-batch loss values during training:

    callback_loss_history <- Callback(
      classname = "LossHistory",
      initialize = function(file = "per_training_batch_losses.txt", ...) {
        super$initialize(...)
        private$file <- file
      },
      on_train_begin = function(logs = NULL) {
        private$per_batch_losses <- fastmap::faststack()
      },
      on_train_batch_begin = function(batch, logs = NULL) {
        private$per_batch_losses$push(logs$loss)
      },
      on_train_end = function(logs = NULL) {
        per_batch_losses <- private$per_batch_losses$as_list() |> as.numeric()
        write(per_batch_losses, private$file)
      }
    )

## Checkpointing models

When you’re training model on relatively large datasets, it’s crucial to save checkpoints of your model at frequent intervals.

The easiest way to achieve this is with [`callback_model_checkpoint()`]:

    model <- get_compiled_model()

    callbacks <- list(
      callback_model_checkpoint(
        # Path where to save the model
        # The two parameters below mean that we will overwrite
        # the current checkpoint if and only if
        # the `val_loss` score has improved.
        # The saved model name will include the current epoch.
        filepath = "mymodel_{epoch}.keras",
        save_best_only = TRUE,
        # Only save a model if `val_loss` has improved.
        monitor = "val_loss",
        verbose = 1
      )
    )
    model |> fit(
      x_train, y_train,
      epochs = 2, batch_size = 64,
      callbacks = callbacks,
      validation_split = 0.2
    )

    ## Epoch 1/2
    ##
    ## Epoch 1: val_loss improved from None to 0.19344, saving model to mymodel_1.keras
    ##
    ## Epoch 1: finished saving model to mymodel_1.keras
    ## 625/625 - 2s - 3ms/step - loss: 0.3787 - sparse_categorical_accuracy: 0.8940 - val_loss: 0.1934 - val_sparse_categorical_accuracy: 0.9441
    ## Epoch 2/2
    ##
    ## Epoch 2: val_loss improved from 0.19344 to 0.14251, saving model to mymodel_2.keras
    ##
    ## Epoch 2: finished saving model to mymodel_2.keras
    ## 625/625 - 1s - 1ms/step - loss: 0.1768 - sparse_categorical_accuracy: 0.9478 - val_loss: 0.1425 - val_sparse_categorical_accuracy: 0.9600

The `ModelCheckpoint` callback can be used to implement fault-tolerance: the ability to restart training from the last saved state of the model in case training gets randomly interrupted. Here’s a basic example:

    # Prepare a directory to store all the checkpoints.
    checkpoint_dir <- "./ckpt"
    fs::dir_create(checkpoint_dir)

    make_or_restore_model <- function() {
      # Either restore the latest (best) model, or create a fresh one
      # if there is no checkpoint available.
      checkpoints <- Sys.glob(file.path(checkpoint_dir, "model-loss=*.keras"))

      if (length(checkpoints) > 0) {
        checkpoint_losses <- sub("^model-loss=([0-9.]+)\\.keras$", "\\1",
                                 basename(checkpoints)) |> as.numeric()
        best_checkpoint <- checkpoints[which.min(checkpoint_losses)]
        load_model(best_checkpoint)
      } else {
        get_compiled_model()
      }
    }

    model <- make_or_restore_model()
    callbacks <- list(
      # This callback saves the model every 100 batches.
      # We include the training loss in the saved model name.
      callback_model_checkpoint(
        filepath = file.path(checkpoint_dir, "model-loss={loss:.2f}.keras"),
        save_freq = 100
      )
    )
    model |> fit(x_train, y_train, epochs = 1, callbacks = callbacks)

    ## 1563/1563 - 3s - 2ms/step - loss: 0.2932 - sparse_categorical_accuracy: 0.9145

You call also write your own callback for saving and restoring models.

For a complete guide on serialization and saving, see the guide to saving and serializing Models.

## Using learning rate schedules

A common pattern when training deep learning models is to gradually reduce the learning as training progresses. This is generally known as “learning rate decay”.

The learning decay schedule could be static (fixed in advance, as a function of the current epoch or the current batch index), or dynamic (responding to the current behavior of the model, in particular the validation loss).

### Passing a schedule to an optimizer

You can easily use a static learning rate decay schedule by passing a schedule object as the `learning_rate` argument in your optimizer:

    initial_learning_rate <- 0.1
    lr_schedule <- learning_rate_schedule_exponential_decay(
        initial_learning_rate, decay_steps=100000, decay_rate=0.96,
        staircase=TRUE
    )

    optimizer <- optimizer_rmsprop(learning_rate = lr_schedule)

Several built-in schedules are available: `ExponentialDecay`, `PiecewiseConstantDecay`, `PolynomialDecay`, and `InverseTimeDecay`.

### Using callbacks to implement a dynamic learning rate schedule

A dynamic learning rate schedule (for instance, decreasing the learning rate when the validation loss is no longer improving) cannot be achieved with these schedule objects, since the optimizer does not have access to validation metrics.

However, callbacks do have access to all metrics, including validation metrics! You can thus achieve this pattern by using a callback that modifies the current learning rate on the optimizer. In fact, this is even built-in as [`callback_reduce_lr_on_plateau()`].

## Visualizing loss and metrics during training with TensorBoard

The best way to keep an eye on your model during training is to use TensorBoard – a browser-based application that you can run locally that provides you with:

- Live plots of the loss and metrics for training and evaluation
- (optionally) Visualizations of the histograms of your layer activations
- (optionally) 3D visualizations of the embedding spaces learned by your `layer_embedding()`

If you have installed TensorFlow with pip, you should be able to launch TensorBoard from the command line:

    tensorboard --logdir=/full_path_to_your_logs

or from R using:

    tensorflow::tensorboard(logdir = "/full_path_to_your_logs")

### Using the TensorBoard callback

The easiest way to use TensorBoard with a Keras model and the `fit()` method is with [`callback_tensorboard()`].

In the simplest case, just specify where you want the callback to write logs, and you’re good to go:

    tb_callback <- callback_tensorboard(
      log_dir = "/full_path_to_your_logs",
      histogram_freq = 0, # How often to log histogram visualizations
      embeddings_freq = 0, # How often to log embedding visualizations
      update_freq = "epoch", # How often to write logs (default: once per epoch)
    )

For more information, see `callback_tensorboard()`.