Multilayer Perceptron#

A multiclass feed-forward neural network classifier with user-defined hidden layers. The Multilayer Perceptron is a deep learning model capable of forming higher-order feature representations through layers of computation. In addition, the MLP features progress monitoring which stops training when it can no longer improve the validation score. It also utilizes network snapshotting to make sure that it always has the best model parameters even if progress began to decline during training.

Note: If there are not enough training samples to build an internal validation set with the user-specified holdout ratio then progress monitoring will be disabled.

Interfaces: Estimator, Learner, Online, Probabilistic, Verbose, Persistable

Data Type Compatibility: Continuous


# Param Default Type Description
1 hidden array An array composing the user-specified hidden layers of the network in order.
2 batch size 128 int The number of training samples to process at a time.
3 optimizer Adam Optimizer The gradient descent optimizer used to update the network parameters.
4 alpha 1e-4 float The amount of L2 regularization applied to the weights of the output layer.
5 epochs 1000 int The maximum number of training epochs. i.e. the number of times to iterate over the entire training set before terminating.
6 min change 1e-4 float The minimum change in the training loss necessary to continue training.
7 window 3 int The number of epochs without improvement in the validation score to wait before considering an early stop.
8 hold out 0.1 float The proportion of training samples to use for progress monitoring.
9 cost fn CrossEntropy ClassificationLoss The function that computes the loss associated with an erroneous activation during training.
10 metric FBeta Metric The validation metric used to score the generalization performance of the model during training.


use Rubix\ML\Classifiers\MultilayerPerceptron;
use Rubix\ML\NeuralNet\Layers\Dense;
use Rubix\ML\NeuralNet\Layers\Dropout;
use Rubix\ML\NeuralNet\Layers\Activation;
use Rubix\ML\NeuralNet\Layers\PReLU;
use Rubix\ML\NeuralNet\ActivationFunctions\LeakyReLU;
use Rubix\ML\NeuralNet\Optimizers\Adam;
use Rubix\ML\NeuralNet\CostFunctions\CrossEntropy;
use Rubix\ML\CrossValidation\Metrics\MCC;

$estimator = new MultilayerPerceptron([
    new Dense(200),
    new Activation(new LeakyReLU()),
    new Dropout(0.3),
    new Dense(100),
    new Activation(new LeakyReLU()),
    new Dropout(0.3),
    new Dense(50),
    new PReLU(),
], 128, new Adam(0.001), 1e-4, 1000, 1e-3, 3, 0.1, new CrossEntropy(), new MCC());

Additional Methods#

Return the loss at each epoch from the last training session:

public steps() : float[]|null

Return the validation score at each epoch from the last training session:

public scores() : float[]|null

Returns the underlying neural network instance or null if untrained:

public network() : Network|null


  • G. E. Hinton. (1989). Connectionist learning procedures.
  • L. Prechelt. (1997). Early Stopping - but when?