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🚧 Ongoing project 🚧 Status: Prototype 🚧

Nexus is a prototypical typesafe deep learning system in Scala.

Nexus is a departure from common deep learning libraries such as TensorFlow, PyTorch, MXNet, etc.

  • Ever been baffled by the axes of tensors? Which axis should I max out?
  • Ever got TypeErrors in Python?
  • Ever spending hours or days getting the tensors' axes and dimensions right?

Nexus' answer to these problems is static types. By specifying tensor axes' semantics in types exploiting Scala's expressive types, compilers can validate the program at compile time, freeing developers' burden of remembering axes by heart, and eliminating nearly all errors above before even running.

Nexus embraces declarative and functional programming: Neural networks are built using small composable components, making code very easy to follow, understand and maintain.

A first glance

A simple neural network for learning the XOR function can be found here.

Building a typesafe XOR network:

  class In extends Dim;     val In = new In          
  class Hidden extends Dim; val Hidden = new Hidden
  class Out extends Dim;    val Out = new Out // tensor axis labels declared as types and singletons

  val x = Input[FloatTensor[In]]()     // input vectors
  val y = Input[FloatTensor[Out]]()    // gold labels

  val ŷ = x                       |>   // type: Symbolic[FloatTensor[In]]
    Affine(In -> 2, Hidden -> 2)  |>   // type: Symbolic[FloatTensor[Hidden]]
    Logistic                      |>   // type: Symbolic[FloatTensor[Hidden]]
    Affine(Hidden -> 2, Out -> 2) |>   // type: Symbolic[FloatTensor[Out]]
    Softmax                            // type: Symbolic[FloatTensor[Out]]
  val loss = CrossEntropy(y, ŷ)        // type: Symbolic[Float]

Design goals

  • Typeful. Each axis of a tensor is statically typed using tuples. For example, an image is typed as FloatTensor[(Width, Height, Channel)], whereas an embedded sentence is typed as FloatTensor[(Word, Embedding)]. This frees programmers from remembering what each axis stands for.
  • Typesafe. Very strong static type checking to eliminate most bugs at compile time.
  • Never, ever specify axis index again. For things like reduce_sum(x, axis=1), write x |> SumAlong(AxisName).
  • Automatic typeclass derivation: Differentiation through any case class (product type).
  • Versatile switching between eager and lazy evaluation.
  • [TODO] Typesafe tensor sizes using literal singleton types (Scala 2.13+).
  • [TODO] Automatic batching over sequences/trees (Neubig, Goldberg, Dyer, NIPS 2017). Free programmers from the pain of manual batching.
  • [TODO] GPU Acceleration. Reuse Torch C++ core through Swig (bindings).
  • [TODO] Multiple backends. Torch / MXNet? / TensorFlow.js for Scala.js? / libtorch for ScalaNative?
  • [TODO] Automatic operator fusion for optimization.
  • [TODO] Typesafe higher-order gradients / Jacobians.


Nexus is modularized. It contains the following modules:

Module Description
nexus-tensor Foundations for typesafe tensors
nexus-diff Typesafe deep learning (differentiable programming)
nexus-prob Typesafe probabilistic programming
nexus-ml High-level machine learning abstractions / models
nexus-jvm-backend JVM reference backend (slow)
nexus-torch Torch native CPU backend
nexus-torch-cuda Torch CUDA GPU backend


Please cite this in academic work as

 author = {Chen, Tongfei},
 title = {Typesafe Abstractions for Tensor Operations (Short Paper)},
 booktitle = {Proceedings of the 8th ACM SIGPLAN International Symposium on Scala},
 series = {SCALA 2017},
 year = {2017},
 pages = {45--50},
 url = {},
 doi = {10.1145/3136000.3136001}