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Flex is a probabilistic deep learning library for data streams. It has the following features:

  • Fast. Flex provides probabilistic deep learning that is fast enough to solve the real-world problems.
  • Typesafe and Functional. Types and pure functions make the code easy to understand and maintain.
  • Easy. You can program with a minimal knowledge of probability theory.

Today, neural networks have been widely used for solving problems in many areas. However, classical neural networks have some limitations when you want to include uncertainties in the model. For example, suppose that input data and training data contain a lot of noise. If you need to detect whether the data contains false-positive or false-negative, the model should represent how reliable the input and the output are. To deal with this issue, probabilistic deep learning, also known as the Bayesian neural network, can be used. It is a way to treat both input and output as a probability distribution and it is one of the best approaches to represent uncertainties. However, the Bayesian neural network is so computationally slow that it cannot be readily applied to the real-world problems. Flex is fast enough to make it possible to apply the Bayesian neural network to the real-world problems.

Getting Started

WIP. Flex is published to Maven Central and built for Scala 2.12, so you can add the following to your build.sbt:

libraryDependencies ++= Seq(
  "com.xxxnell" %% "flex-core",
  "com.xxxnell" %% "flex-chain"
).map(_ % "0.0.5")

Then, you need to import the context of Flex.

import flex.implicits._
import flex.chain.implicits._

Building a Model

We will use 3 hiddel layers with 10 neurons each.

val (kin, kout) = (20, 10)
val (l0, l1, l2, l3) = (784, 10, 10, 1)
val (k0, k1, k2, k3) = (20, 20, 20, 20)
val model0 = Complex
  .empty(kin, kout)
  .addStd(l0 -> k0, l0 * l1 -> k1, l1 * l2 -> k2, l2 * l3 -> k3)
  .map { case x1 :: z1 :: rem => z1.reshape(l1, l0).mmul(x1).tanh :: rem }
  .map { case h1 :: z2 :: rem => z2.reshape(l2, l1).mmul(h1).tanh :: rem }
  .map { case h2 :: z3 :: rem => z3.reshape(l3, l2).mmul(h2) :: rem }

First, construct an empty model using Complex.empty. Second, add the variables to be used for this neural network. Here, a prior probabilities of these variables are standard normal distributions with a mean of zero and a variance of one. Third, define a transformation of each layers using map operation. In this example, tanh was used as the activator.


Contributions are always welcome. Any kind of contribution, such as writing a unit test, documentation, bug fix, or implementing the algorithm of Flex in another language, is helpful. It is also possible to make academic collaboration works. If you need some help, please contact me via email or twitter.

The master branch of this repository contains the latest stable release of Flex. In general, pull requests should be submitted from a separate feature branch starting from the develop branch.

Fo more detail, see the contributing documentation.


All code of Flex is available to you under the MIT license.

Copyright the maintainers.


Probabilistic deep learning for data streams.

Flex Info

⭐ Stars 127
🔗 Source Code github.com
🕒 Last Update a year ago
🕒 Created 4 years ago
🐞 Open Issues 25
➗ Star-Issue Ratio 5
😎 Author xxxnell