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eNeural.net / Dart is an AI Library for efficient Artificial Neural Networks. The library is portable (native, JS/Web, Flutter) and the computation is capable to use SIMD (Single Instruction Multiple Data) to improve performance.


import 'package:eneural_net/eneural_net.dart';
import 'package:eneural_net/eneural_net_extensions.dart';

void main() {
  // Type of scale to use to compute the ANN:
  var scale = ScaleDouble.ZERO_TO_ONE;

  // The samples to learn in Float32x4 data type:
  var samples = SampleFloat32x4.toListFromString(
    true, // Already normalized in the scale.

  // The activation function to use in the ANN:
  var activationFunction = ActivationFunctionSigmoid();

  // The ANN using layers that can compute with Float32x4 (SIMD compatible type).
  var ann = ANN(
    LayerFloat32x4(2, activationFunction), // Input layer: 2 neurons
    [3],                                   // 1 Hidden layer: 3 neurons
    LayerFloat32x4(1, activationFunction), // Output layer: 1 neuron


  // Training algorithm:
  var backpropagation = Backpropagation(ann);

  var chronometer = Chronometer('Backpropagation').start();

  // Train the ANN using Backpropagation until global error 0.01,
  // with max epochs per training session of 1000000 and
  // a max retry of 10 when a training session can't reach
  // the target global error:
  var achievedTargetError = backpropagation.trainUntilGlobalError(samples,
          targetGlobalError: 0.01, maxEpochs: 1000000, maxRetries: 10);

  chronometer.stop(operations: backpropagation.totalTrainingActivations);

  // Compute the current global error of the ANN:
  var globalError = ann.computeSamplesGlobalError(samples);

  for (var i = 0; i < samples.length; ++i) {
    var sample = samples[i];

    var input = sample.input;
    var expected = sample.output;

    // Activate the sample input:

    // The current output of the ANN (after activation):
    var output = ann.output;

    print('- $i> $input -> $output ($expected) > error: ${output - expected}');

  print('globalError: $globalError');
  print('achievedTargetError: $achievedTargetError');


SIMD (Single Instruction Multiple Data)

Dart has support for SIMD when computation is made using Float32x4 and Int32x4.

The basic principle with SIMD is to execute math operations simultaneously in 4 numbers.

Float32x4 is a lane of 4 double (32 bits single precision floating points). Example of multiplication:

  var fs1 = Float32x4( 1.1 , 2.2 , 3.3  , 4.4  );
  var fs2 = Float32x4( 10  , 100 , 1000 , 1000 );
  var fs3 = fs1 * fs2 ;
  // Output:
  // [11.000000, 220.000000, 3300.000000, 4400.000000]

See "dart:typed_data library" and "Using SIMD in Dart".


The class Signal represents the collection of numbers (including its related operations) that will flow through the ANN, representing the actual signal that an Artificial Neural Network should compute.

The main implementation is SignalFloat32x4 and represents an ANN Signal based in Float32x4. All the operations prioritizes the use of SIMD.

The framework of Signal allows the implementation of any kind of data to represent the numbers and operations of an eNeural.net ANN. SignalInt32x4 is an experimental implementation to exercise an ANN based in integers.

Activation Functions

ActivationFunction is the base class for ANN neurons activation functions:

  • ActivationFunctionSigmoid:

    The classic Sigmoid function (return for x a value between 0.0 and 1.0):

    activation(double x) {
      return 1 / (1 + exp(-x)) ;
  • ActivationFunctionSigmoidFast:

    Fast approximation version of Sigmoid function, that is not based in exp(x):

    activation(double x) {
      x *= 3 ;
      return 0.5 + ((x) / (2.5 + x.abs()) / 2) ;

    Function author: Graciliano M. Passos: gmpassos@GitHub.

  • ActivationFunctionSigmoidBoundedFast:

    Fast approximation version of Sigmoid function, that is not based in exp(x), bounded to a lower and upper limit for x.

    activation(double x) {
      if (x < lowerLimit) {
        return 0.0 ;
      } else if (x > upperLimit) {
        return 1.0 ;
      x = x / scale ;
      return 0.5 + (x / (1 + (x * x))) ;

    Function author: Graciliano M. Passos: gmpassos@GitHub.


exp is the function of the natural exponent, e, to the power x.

This is an important ANN function, since is used by the popular Sigmoid function, and usually a high precision version is slow, but a high precision version is actually not necessary for Artificial Neural Networks, opening the opportunity for implementations that are just an approximation.

Fast Math

An internal fast math library is used to compute ActivationFunctionSigmoid.

If you want you can import this library and use it in your projects:

import 'package:eneural_net/eneural_net_fast_math.dart' as fast_math ;

void main() {
  // Fast `exp` function:

  // Fast high precision `exp` function:
  var highPrecision = <double>[0.0 , 0.0];
  fast_math.expHighPrecision(2, 0.0, highPrecision);

The implementation is based in the Dart package Complex:


You can find more at: eneural.net


The official source code is hosted @ GitHub:

Features and bugs

Please file feature requests and bugs at the issue tracker.


Any help from open-source community is always welcome and needed:

  • Found an issue?
    • Fill a bug with details.
  • Wish a feature?
    • Open a feature request.
  • Are you using and liking the project?
    • Promote the project: create an article, post or make a donation.
  • Are you a developer?
    • Fix a bug and send a pull request.
    • Implement a new feature, like other training algorithms and activation functions.
    • Improve unit tests.
  • Have you already helped in any way?
    • Many thanks from me, the contributors and everybody that uses this project!


Graciliano M. Passos: gmpassos@GitHub.


Apache License - Version 2.0


eNeural.net library.
A group of Dart extensions for numbers and collections that can help with data handling and calculation.
Fast math library.