Go
Gorgonia is a library that helps facilitate machine learning in Go.

Gorgonia

Gorgonia is a library that helps facilitate machine learning in Go. Write and evaluate mathematical equations involving multidimensional arrays easily. If this sounds like Theano or TensorFlow, it's because the idea is quite similar. Specifically, the library is pretty low-level, like Theano, but has higher goals like Tensorflow.

Gorgonia:

• Can perform automatic differentiation
• Can perform symbolic differentiation
• Can perform gradient descent optimizations
• Can perform numerical stabilization
• Provides a number of convenience functions to help create neural networks
• Is fairly quick (comparable to Theano and Tensorflow's speed)
• Will support GPU/CUDA
• Will support distributed computing

Why Use Gorgonia?

When the author created the primordial version of Gorgonia, TensorFlow wasn't released yet. And now that TensorFlow has been released, there still isn't a good Go extension. The main reason to use Gorgonia is if you are using Go extensively.

It may sound biased, but this author also thinks that it's easier to reason about the equations with Gorgonia than Theano. This is mainly due to the reduced feature set (for example, Gorgonia has no support for something like Theano's scan).

Installation

The package is go-gettable: go get -u github.com/chewxy/gorgonia.

There are very few dependencies that Gorgonia uses - and they're all pretty stable, so as of now, there isn't a need for vendoring tools. These are the list of external packages that Gorgonia calls, ranked in order of reliance that this package has (subpackages are omitted):

• gonum/graph†
• gonum/blas†
• math32‡
• set‡
• gographviz†
• rng
• errors‡
• gonum/matrix†

Packages marked with a † indicates that the development of Gorgonia is committed to keeping up with the most updated versions of these packages.

Packages marked with a ‡ have generally stable APIs.

Usage

Gorgonia works by creating a computation graph, and then executing it. Think of it as a programming language, but is limited to mathematical functions. In fact this is the dominant paradigm that the user should be used to thinking about. The computation graph is an AST

Here's an example - say you want to define a math expression z = x + y. Here's how you'd do it:

import (
    "fmt"
    "log"

    . "github.com/chewxy/gorgonia"
)

func main() {
    g := NewGraph()

    var x, y, z *Node
    var err error

    // define the expression
    x = NewScalar(g, Float64, WithName("x"))
    y = NewScalar(g, Float64, WithName("y"))
    if z, err = Add(x, y); err != nil {
        log.Fatal(err)
    }

    // compile into a program
    prog, locMap, err := Compile(g)
    if err != nil {
        log.Fatal(err)
    }

    // create a VM to run the program on
    machine := NewTapeMachine(prog, locMap)

    // set initial values then run
    Let(x, 2.0)
    Let(y, 2.5)
    if err = machine.RunAll(); err != nil {
        log.Fatal(err)
    }

    fmt.Printf("%v", z.Value())
    // Output: 4.5
}

You might note that it's a little more verbose than other packages of similar nature. For example, instead of compiling to a callable function, Gorgonia specifically compiles into a *program which requires a *TapeMachine to run. It also requires manual a Let(...) call.

The author would like to contend that this is a Good Thing - to shift one's thinking to a machine-based thinking. It helps a lot in figuring out where things might go wrong.

VMs

There are two VMs in the current version of Gorgonia:

• TapeMachine
• LispMachine

They function differently and take different inputs. The TapeMachine is useful for executing expressions that are generally static (that is to say the computation graph does not change). Due to its static nature, the TapeMachine is good for running expressions that are compiled-once-run-many-times (such as linear regression, SVM and the like).

The LispMachine on the other hand was designed to take a graph as an input, and executes directly on the nodes of the graph. If the graph change, simply create a new lightweight LispMachine to execute it on. The LispMachine is suitable for tasks such as creating recurrent neural networks without a fixed size.

Prior to release of Gorgonia, there was a third VM - a stack based VM that is similar to TapeMachine but deals with artificial gradients better. It may see light of day again, once this author has managed to fix all the kinks.

Differentiation

Gorgonia performs both symbolic and automatic differentiation. There are subtle differences between the two processes. The author has found that it's best to think of it this way - Automatic differentiation is differentiation that happens at runtime, concurrently with the execution of the graph, while symbolic differentiation is differentiation that happens during the compilation phase.

Runtime of course, refers to the execution of the expression graph, not the program's actual runtime.

With the introduction to the two VMs, it's easy to see how Gorgonia can perform both symbolic and automatic differentiation. Using the same example as above, the reader should note that there was no differentiation done. Instead, let's try with a LispMachine:

import (
    "fmt"
    "log"

    . "github.com/chewxy/gorgonia"
)

func main() {
    g := NewGraph()

    var x, y, z *Node
    var err error

    // define the expression
    x = NewScalar(g, Float64, WithName("x"))
    y = NewScalar(g, Float64, WithName("y"))
    if z, err = Add(x, y); err != nil {
        log.Fatal(err)
    }

    // set initial values then run
    Let(x, 2.0)
    Let(y, 2.5)

    // by default, LispMachine performs forward mode and backwards mode execution
    m := NewLispMachine(g)
    if err = m.RunAll(); err != nil {
        log.Fatal(err)
    }

    fmt.Printf("z: %v", z.Value())

    if xgrad, err := x.Grad(); err != nil {
        fmt.Printf("dz/dx: %v", xgrad)
    }

    if ygrad, err := y.Grad(); err != nil {
        fmt.Printf("dz/dy: %v", ygrad)
    }

    // Output:
    // z: 4.5
    // dz/dx: 1
    // dz/dy: 1
}

Of course, Gorgonia also supports the more traditional symbolic differentiation like in Theano:

    g := NewGraph()

    var x, y, z *Node
    var err error

    // define the expression
    x = NewScalar(g, Float64, WithName("x"))
    y = NewScalar(g, Float64, WithName("y"))
    if z, err = Add(x, y); err != nil {
        log.Fatal(err)
    }

    // symbolically differentiate z with regards to x and y
    // this adds the gradient nodes to the graph g
    var Grads Nodes
    if grads, err = Grad(z, x, y); err != nil {
        log.Fatal(err)
    }

    // compile into a program
    prog, locMap, err := Compile(g)
    if err != nil {
        log.Fatal(err)
    }

    // create a VM to run the program on
    machine := NewTapeMachine(prog, locMap)

    // set initial values then run
    Let(x, 2.0)
    Let(y, 2.5)
    if err = machine.RunAll(); err != nil {
        log.Fatal(err)
    }

    fmt.Printf("%v", z.Value())
    if xgrad, err := x.Grad(); err != nil {
        fmt.Printf("dz/dx: %v", xgrad)
    }

    if ygrad, err := y.Grad(); err != nil {
        fmt.Printf("dz/dy: %v", ygrad)
    }

    // Output:
    // z: 4.5
    // dz/dx: 1 | 1
    // dz/dy: 1 | 1

Currently Gorgonia only performs backwards mode automatic differentiation (aka backpropagation), although one may observe the vestiges of an older version which supported forwards mode differentiation in the existence of *dualValue. It may return in the future.

Graph

A lot has been said about a computation graph or an expression graph. But what is it exactly? Think of it as an AST for the math expression that you want. Here's the graph for the examples (but with a vector and a scalar addition instead) above:

By the way, Gorgonia comes with nice-ish graph printing abilities. Here's an example of a graph of the equation y = x² and its derivation:

To read the graph is easy. The expression builds from bottom up, while the derivations build from top down. This way the derivative of each node is roughly on the same level.

Red-outlined nodes indicate that it's a root node. Green outlined nodes indicate that they're a leaf node. Nodes with a yellow background indicate that it's an input node. The dotted arrows indicate which node is the gradient node for the pointed-to node.

Concretely, it says that c42011e840 (dy/dx) is the gradient node of the input c42011e000 (which is x).

Node Rendering

A Node is rendered thusly:

Additional Notes

• If it's an input node, then the Op row will not show up.
• If there are no Values bound to the node, it will show up as NIL. However, when there are values and gradients, it will try to as best as possible display the values bound to the node.

API Stability

Gorgonia's API is as of right now, not considered stable. It will be stable from version 1.0 forwards.

Roadmap

Here are the goals for Gorgonia, sorted by importance

• 90+% test coverage. Current coverage is 50% for Gorgonia and 75% for the Tensor packages
• TravisCI for this package.
• Clean out the tests. The tests were the results of many years of accumulation. It'd be nice to refactor them out nicely.
• More advanced operations (like einsum). The current Tensor operators are pretty primitive.
• Improve Op extensibility by exposing/changing the Op interface to be all exported, and not a mix of exported and unexported methods (Alternatively, create a Compose Op type for extensibility). This way everyone can make their own custom Ops.
• Refactor the CuBLAS package as well as the Blase package.
• Distributed computing. The ability to spread jobs out across multiple machines and communicating with each other has been attempted at least 3 times, but failed each time.
• Re-introduce the VM that deals with artificial/synthetic gradients.
• Improve performance especially re: allocation, minimize impact of type system.
• Better documentation on why certain decisions were made, and the design of Gorgonia in gneral.
• Higher order derivative optimization algorithms (LBFGS comes to mind)
• Derivative-free optimization algorithms

Goals

The primary goal for Gorgonia is to be a highly performant machine learning/graph-based computation library that can scale across multiple machines. It should bring the appeal of Go (simple compilation and deployment process) to the ML world. It's a long way from there currently, however, the baby steps are already there.

The secondary goal for Gorgonia is to provide a platform for exploration for non-standard deep-learning and neural network related things. This includes things like neo-hebbian learning, corner-cutting algorithms, evolutionary algorithms and the like.

Contributing

Obviously since you are most probably reading this on Github, Github will form the major part of the workflow for contributing to this package.

See also: CONTRIBUTING.md

Contributors and Significant Contributors

All contributions are welcome. However, there is a new class of contributor, called Significant Contributors.

A Significant Contributor is one who has shown deep understanding of how the library works and/or its environs. Here are examples of what constitutes a Significant Contribution:

• Wrote significant amounts of documentation pertaining to why/the mechanics of particular functions/methods and how the different parts affect one another
• Wrote code, and tests around the more intricately connected parts of Gorgonia
• Wrote code and tests, and have at least 5 pull requests accepted
• Provided expert analysis on parts of the package (for example, you may be a floating point operations expert who optimized one function)
• Answered at least 10 support questions.

Significant Contributors list will be updated once a month (if anyone even uses Gorgonia that is).

How To Get Support

The best way of support right now is to open a ticket on Github.

Licence

Gorgonia is licenced under a variant of Apache 2.0. It's for all intents and purposes the same as the Apache 2.0 Licence, with the exception of not being able to commercially profit directly from the package unless you're a Significant Contributor (for example, providing commercial support for the package). It's perfectly fine to profit directly from a derivative of Gorgonia (for example, if you use Gorgonia as a library in your product)

Everyone is still allowed to use Gorgonia for commercial purposes (example: using it in a software for your business).