gorgonia

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 Go to latest Published: Sep 10, 2020 License: Apache-2.0 Imports: 37 Imported by: 243

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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)
  • Supports CUDA/GPGPU computation (OpenCL not yet supported, send a pull request)
  • Will support distributed computing

Goals

The primary goal for Gorgonia is to be a highly performant machine learning/graph computation-based 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.

Why Use Gorgonia?

The main reason to use Gorgonia is developer comfort. If you're using a Go stack extensively, now you have access to the ability to create production-ready machine learning systems in an environment that you are already familiar and comfortable with.

ML/AI at large is usually split into two stages: the experimental stage where one builds various models, test and retest; and the deployed state where a model after being tested and played with, is deployed. This necessitate different roles like data scientist and data engineer.

Typically the two phases have different tools: Python (PyTorch, etc) is commonly used for the experimental stage, and then the model is rewritten in some more performant language like C++ (using dlib, mlpack etc). Of course, nowadays the gap is closing and people frequently share the tools between them. Tensorflow is one such tool that bridges the gap.

Gorgonia aims to do the same, but for the Go environment. Gorgonia is currently fairly performant - its speeds are comparable to PyTorch's and Tensorflow's CPU implementations. GPU implementations are a bit finnicky to compare due to the heavy cgo tax, but rest assured that this is an area of active improvement.

Getting started

Installation

The package is go-gettable: go get -u gorgonia.org/gorgonia.

Gorgonia is compatible with go modules.

Documentation

Up-to-date documentation, references and tutorials are present on the official Gorgonia website at https://gorgonia.org.

Keeping Updated

Gorgonia's project has a Slack channel on gopherslack, as well as a Twitter account. Official updates and announcements will be posted to those two sites.

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, and has no branching capability (no if/then or loops). In fact this is the dominant paradigm that the user should be used to thinking about. The computation graph is an AST.

Microsoft's CNTK, with its BrainScript, is perhaps the best at exemplifying the idea that building of a computation graph and running of the computation graphs are different things, and that the user should be in different modes of thoughts when going about them.

Whilst Gorgonia's implementation doesn't enforce the separation of thought as far as CNTK's BrainScript does, the syntax does help a little bit.

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

package gorgonia_test

import (
	"fmt"
	"log"

	. "gorgonia.org/gorgonia"
)

// Basic example of representing mathematical equations as graphs.
//
// In this example, we want to represent the following equation
//		z = x + y
func Example_basic() {
	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)
	}

	// create a VM to run the program on
	machine := NewTapeMachine(g)
	defer machine.Close()

	// 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.

Additionally, there are no support for branching - that is to say there are no conditionals (if/else) or loops. The aim is not to build a Turing-complete computer.

More examples are present in the example subfolder of the project, and step-by-step tutorials are present on the main website

Using CUDA

Gorgonia comes with CUDA support out of the box. Please see the reference documentation about how cuda works on the Gorgonia.org website, or jump to the tutorial.

About Gorgonia's development process

Versioning

We use semver 2.0.0 for our versioning. Before 1.0, Gorgonia's APIs are expected to change quite a bit. API is defined by the exported functions, variables and methods. For the developers' sanity, there are minor differences to semver that we will apply prior to version 1.0. They are enumerated below:

  • The MINOR number will be incremented every time there is a deleterious break in API. This means any deletion, or any change in function signature or interface methods will lead to a change in MINOR number.
  • Additive changes will NOT change the MINOR version number prior to version 1.0. This means that if new functionality were added that does not break the way you use Gorgonia, there will not be an increment in the MINOR version. There will be an increment in the PATCH version.
API Stability

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

Go Version Support

Gorgonia supports 2 versions below the Master branch of Go. This means Gorgonia will support the current released version of Go, and up to 4 previous versions - providing something doesn't break. Where possible a shim will be provided (for things like new sort APIs or math/bits which came out in Go 1.9).

The current version of Go is 1.13.1. The earliest version Gorgonia supports is Go 1.11.x but Gonum supports only 1.12+. Therefore, the minimum Go version to run the master branch is Go > 1.12.

Hardware and OS supported

Gorgonia runs on :

  • linux/AMD64
  • linux/ARM7
  • linux/ARM64
  • win32/AMD64
  • darwin/AMD64
  • freeBSD/AMD64

If you have tested gorgonia on other platform, please update this list.

Hardware acceleration

Gorgonia use some pure assembler instructions to accelerate somes mathematical operations. Unfortunately, only amd64 is supported.

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.

Frequently Asked Questions

Why are there seemingly random runtime.GC() calls in the tests?

The answer to this is simple - the design of the package uses CUDA in a particular way: specifically, a CUDA device and context is tied to a VM, instead of at the package level. This means for every VM created, a different CUDA context is created per device per VM. This way all the operations will play nicely with other applications that may be using CUDA (this needs to be stress-tested, however).

The CUDA contexts are only destroyed when the VM gets garbage collected (with the help of a finalizer function). In the tests, about 100 VMs get created, and garbage collection for the most part can be considered random. This leads to cases where the GPU runs out of memory as there are too many contexts being used.

Therefore at the end of any tests that may use GPU, a runtime.GC() call is made to force garbage collection, freeing GPU memories.

In production, one is unlikely to start that many VMs, therefore it's not really a problem. If there is, open a ticket on Github, and we'll look into adding a Finish() method for the VMs.

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).

Dependencies

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):

Package Used For Vitality Notes Licence
gonum/graph Sorting *ExprGraph Vital. Removal means Gorgonia will not work Development of Gorgonia is committed to keeping up with the most updated version gonum license (MIT/BSD-like)
gonum/blas Tensor subpackage linear algebra operations Vital. Removal means Gorgonial will not work Development of Gorgonia is committed to keeping up with the most updated version gonum license (MIT/BSD-like)
cu CUDA drivers Needed for CUDA operations Same maintainer as Gorgonia MIT/BSD-like
math32 float32 operations Can be replaced by float32(math.XXX(float64(x))) Same maintainer as Gorgonia, same API as the built in math package MIT/BSD-like
hm Type system for Gorgonia Gorgonia's graphs are pretty tightly coupled with the type system Same maintainer as Gorgonia MIT/BSD-like
vecf64 optimized []float64 operations Can be generated in the tensor/genlib package. However, plenty of optimizations have been made/will be made Same maintainer as Gorgonia MIT/BSD-like
vecf32 optimized []float32 operations Can be generated in the tensor/genlib package. However, plenty of optimizations have been made/will be made Same maintainer as Gorgonia MIT/BSD-like
set Various set operations Can be easily replaced Stable API for the past 1 year set licence (MIT/BSD-like)
gographviz Used for printing graphs Graph printing is only vital to debugging. Gorgonia can survive without, but with a major (but arguably nonvital) feature loss Last update 12th April 2017 gographviz licence (Apache 2.0)
rng Used to implement helper functions to generate initial weights Can be replaced fairly easily. Gorgonia can do without the convenience functions too rng licence (Apache 2.0)
errors Error wrapping Gorgonia won't die without it. In fact Gorgonia has also used goerrors/errors in the past. Stable API for the past 6 months errors licence (MIT/BSD-like)
gonum/mat Compatibility between Tensor and Gonum's Matrix Development of Gorgonia is committed to keeping up with the most updated version gonum license (MIT/BSD-like)
testify/assert Testing Can do without but will be a massive pain in the ass to test testify licence (MIT/BSD-like)

These are the packages and libraries which inspired and were adapted from in the process of writing Gorgonia (the Go packages that were used were already declared above):

Source How it's Used Licence
Numpy Inspired large portions. Directly adapted algorithms for a few methods (explicitly labelled in the docs) MIT/BSD-like. Numpy Licence
Theano Inspired large portions. (Unsure: number of directly adapted algorithms) MIT/BSD-like Theano's licence
Caffe im2col and col2im directly taken from Caffe. Convolution algorithms inspired by the original Caffee methods Caffe Licence

Documentation

Overview

Package gorgonia is a library that helps facilitate machine learning in Go. Write and evaluate mathematical equations involving multidimensional arrays easily. Do differentiation with them just as easily.

Example (Autodiff)

Autodiff showcases automatic differentiation 

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)
defer m.Close()
if err = m.RunAll(); err != nil {
	log.Fatal(err)
}

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

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

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

Output:

z: 4.5
dz/dx: 1
dz/dy: 1
Example (Basic)

Basic example of representing mathematical equations as graphs.

In this example, we want to represent the following equation 

z = x + y

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)
}

// create a VM to run the program on
machine := NewTapeMachine(g)
defer machine.Close()

// 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
Example (ConcurrentTraining) 
xV, yV, bs := prep()
concurrentTraining(xV, yV, bs, epochs)

fmt.Printf("x:\n%1.1v", xV)
fmt.Printf("y:\n%1.1v", yV)

// Outputx:
// x:
// ⎡    6      7      8      9  ... 5e+01  5e+01  5e+01  5e+01⎤
// ⎢7e+01  7e+01  7e+01  7e+01  ... 1e+02  1e+02  1e+02  1e+02⎥
// ⎢1e+02  1e+02  1e+02  1e+02  ... 2e+02  2e+02  2e+02  2e+02⎥
// ⎢2e+02  2e+02  2e+02  2e+02  ... 2e+02  2e+02  2e+02  2e+02⎥
// .
// .
// .
// ⎢4e+07  4e+07  4e+07  4e+07  ... 4e+07  4e+07  4e+07  4e+07⎥
// ⎢4e+07  4e+07  4e+07  4e+07  ... 4e+07  4e+07  4e+07  4e+07⎥
// ⎢4e+07  4e+07  4e+07  4e+07  ... 4e+07  4e+07  4e+07  4e+07⎥
// ⎣4e+07  4e+07  4e+07  4e+07  ... 4e+07  4e+07  4e+07  4e+07⎦
// y:
// [-1e+02  -4e+02  -7e+02  -9e+02  ... -2e+08  -2e+08  -2e+08  -2e+08]

Output:
Example (ErrorHandling)

Gorgonia provides an API that is fairly idiomatic - most of the functions in in the API return (T, error). This is useful for many cases, such as an interactive shell for deep learning. However, it must also be acknowledged that this makes composing functions together a bit cumbersome.

To that end, Gorgonia provides two alternative methods. First, the `Lift` based functions; Second the `Must` function 

// Lift
g := NewGraph()
x := NewMatrix(g, Float32, WithShape(2, 3), WithInit(RangedFrom(0)), WithName("a"))
y := NewMatrix(g, Float32, WithShape(3, 2), WithInit(ValuesOf(float32(2))), WithName("b"))
z := NewMatrix(g, Float32, WithShape(2, 1), WithInit(Zeroes()), WithName("bias"))
wrong := NewMatrix(g, Float64, WithShape(2, 3), WithInit(RangedFrom(0)), WithName("wrong"))

// Different LiftXXX functions exist for different API signatures
// A good way to do this is to have some instantiated functions at the top level of the package
mul := Lift2(Mul)
add := Lift2(Add)
addB := Lift2Broadcast(BroadcastAdd)
sq := Lift1(Square)
sm := Lift1Axial(SoftMax)

nn := sm(sq(addB(mul(x, y), z, nil, []byte{1}))) // OK
nnPlusWrong := add(nn, wrong)                    // Wrong types. Will Error
fmt.Printf("nn: %v\nAn error occurs: %v\n", nn, nnPlusWrong.Err())

// Must()
h := NewGraph()
a := NewMatrix(h, Float32, WithShape(2, 3), WithInit(RangedFrom(0)), WithName("a"))
b := NewMatrix(h, Float32, WithShape(3, 2), WithInit(ValuesOf(float32(2))), WithName("b"))
c := NewMatrix(h, Float32, WithShape(2, 1), WithInit(RangedFrom(0)), WithName("c"))
wrong2 := NewMatrix(h, Float64, WithShape(2, 3), WithInit(RangedFrom(0)), WithName("wrong"))

// This is OK
nn2 := Must(SoftMax(
	Must(Square(
		Must(BroadcastAdd(
			Must(Mul(a, b)),
			c,
			nil, []byte{1},
		)),
	)),
))
fmt.Printf("nn2: %v\n", nn2)

defer func() {
	if r := recover(); r != nil {
		fmt.Printf("An error occurs (caught by recover()): %v\n", r)
	}
}()
nn2PlusWrong := Must(Add(nn2, wrong2))
_ = nn2PlusWrong

Output:

nn: ÷ false(%a, %f) :: Matrix float32
An error occurs: Type inference error. Op: + false. Children: [Matrix float32, Matrix float64], OpType:Matrix a → Matrix a → Matrix a: Unable to unify while inferring type of + false: Unification Fail: float64 ~ float32 cannot be unified
nn2: ÷ false(%a, %f) :: Matrix float32
An error occurs (caught by recover()): Type inference error. Op: + false. Children: [Matrix float32, Matrix float64], OpType:Matrix a → Matrix a → Matrix a: Unable to unify while inferring type of + false: Unification Fail: float64 ~ float32 cannot be unified
Example (KeepDims) 
g := NewGraph()
a := NodeFromAny(g, tensor.New(tensor.WithShape(2, 3), tensor.WithBacking([]float64{1, 2, 3, 4, 5, 6})))
m1, _ := Mean(a, 1)
m2, _ := KeepDims(a, false, func(a *Node) (*Node, error) { return Mean(a, 1) })
m3, _ := Mean(a, 0)
m4, _ := KeepDims(a, true, func(a *Node) (*Node, error) { return Mean(a, 0) })
m5, _ := KeepDims(a, true, func(a *Node) (*Node, error) { return Mean(a) })

// these reads are necessary as the VM may feel free to clobber the underlying data.
// e.g. if m1.Value() is used in the print statement below, the answer will be wrong.
// This is because before the VM executes the operations, a check is done to see if unsafe
// operations may be done. Unsafe operations are useful in saving memory.
// In this example, Reshape can be unsafely done if no other node is "using" m1,
// so m1.Value() will have its shape clobbered. Thus if m1.Value() is read after the VM has run,
// there is no guarantee that the data is correct. The only way around this is to "use" m1, by the Read() function.
var m1v, m2v, m3v, m4v Value
Read(m1, &m1v)
Read(m2, &m2v)
Read(m3, &m3v)
Read(m4, &m4v)

vm := NewTapeMachine(g)
if err := vm.RunAll(); err != nil {
	panic(err)
}

fmt.Printf("a:\n%v\n", a.Value())
fmt.Printf("m1 (shape: %v):\n%v\n", m1.Value().Shape(), m1v)
fmt.Printf("m2 (shape: %v):\n%v\n", m2.Value().Shape(), m2v)
fmt.Printf("m3 (shape: %v):\n%v\n", m3.Value().Shape(), m3v)
fmt.Printf("m4 (shape: %v):\n%v\n", m4.Value().Shape(), m4v)
fmt.Printf("m5 (shape: %v):\n%v\n", m5.Value().Shape(), m5.Value())

Output:

a:
⎡1  2  3⎤
⎣4  5  6⎦

m1 (shape: (2)):
[2  5]
m2 (shape: (2, 1)):
C[2  5]
m3 (shape: (3)):
[2.5  3.5  4.5]
m4 (shape: (1, 3)):
R[2.5  3.5  4.5]
m5 (shape: (1, 1)):
⎡3.5⎤
Example (LinearRegression)

Linear Regression Example

The formula for a straight line is 

y = mx + c

We want to find an `m` and a `c` that fits the equation well. We'll do it in both float32 and float64 to showcase the extensibility of Gorgonia 

package main

import (
	"fmt"
	"log"
	"math/rand"
	"runtime"

	. "gorgonia.org/gorgonia"
	"gorgonia.org/tensor"
)

const (
	vecSize = 1000000
)

// manually generate a fake dataset which is y=2x+random
func xy(dt tensor.Dtype) (x tensor.Tensor, y tensor.Tensor) {
	var xBack, yBack interface{}
	switch dt {
	case Float32:
		xBack = tensor.Range(tensor.Float32, 1, vecSize+1).([]float32)
		yBackC := tensor.Range(tensor.Float32, 1, vecSize+1).([]float32)

		for i, v := range yBackC {
			yBackC[i] = v*2 + rand.Float32()
		}
		yBack = yBackC
	case Float64:
		xBack = tensor.Range(tensor.Float64, 1, vecSize+1).([]float64)
		yBackC := tensor.Range(tensor.Float64, 1, vecSize+1).([]float64)

		for i, v := range yBackC {
			yBackC[i] = v*2 + rand.Float64()
		}
		yBack = yBackC
	}

	x = tensor.New(tensor.WithBacking(xBack), tensor.WithShape(vecSize))
	y = tensor.New(tensor.WithBacking(yBack), tensor.WithShape(vecSize))
	return
}

func random(dt tensor.Dtype) interface{} {
	rand.Seed(13370)
	switch dt {
	case tensor.Float32:
		return rand.Float32()
	case tensor.Float64:
		return rand.Float64()
	default:
		panic("Unhandled dtype")
	}
}

func linregSetup(Float tensor.Dtype) (m, c *Node, machine VM) {
	var xT, yT Value
	xT, yT = xy(Float)

	g := NewGraph()
	x := NewVector(g, Float, WithShape(vecSize), WithName("x"), WithValue(xT))
	y := NewVector(g, Float, WithShape(vecSize), WithName("y"), WithValue(yT))
	m = NewScalar(g, Float, WithName("m"), WithValue(random(Float)))
	c = NewScalar(g, Float, WithName("c"), WithValue(random(Float)))

	pred := Must(Add(Must(Mul(x, m)), c))
	se := Must(Square(Must(Sub(pred, y))))
	cost := Must(Mean(se))

	if _, err := Grad(cost, m, c); err != nil {
		log.Fatalf("Failed to backpropagate: %v", err)
	}

	// machine := NewLispMachine(g)  // you can use a LispMachine, but it'll be VERY slow.
	machine = NewTapeMachine(g, BindDualValues(m, c))
	return m, c, machine
}

func linregRun(m, c *Node, machine VM, iter int, autoCleanup bool) (retM, retC Value) {
	if autoCleanup {
		defer machine.Close()
	}
	model := []ValueGrad{m, c}
	solver := NewVanillaSolver(WithLearnRate(0.001), WithClip(5)) // good idea to clip

	if CUDA {
		runtime.LockOSThread()
		defer runtime.UnlockOSThread()
	}
	var err error
	for i := 0; i < iter; i++ {
		if err = machine.RunAll(); err != nil {
			fmt.Printf("Error during iteration: %v: %v\n", i, err)
			break
		}

		if err = solver.Step(model); err != nil {
			log.Fatal(err)
		}

		machine.Reset() // Reset is necessary in a loop like this
	}
	return m.Value(), c.Value()

}

func linearRegression(Float tensor.Dtype, iter int) (retM, retC Value) {
	defer runtime.GC()
	m, c, machine := linregSetup(Float)
	return linregRun(m, c, machine, iter, true)
}

// Linear Regression Example
//
// The formula for a straight line is
//
//	y = mx + c
//
// We want to find an `m` and a `c` that fits the equation well. We'll do it in both float32 and float64 to showcase the extensibility of Gorgonia
func main() {
	var m, c Value
	// Float32
	m, c = linearRegression(Float32, 500)
	fmt.Printf("float32: y = %3.3fx + %3.3f\n", m, c)

	// Float64
	m, c = linearRegression(Float64, 500)
	fmt.Printf("float64: y = %3.3fx + %3.3f\n", m, c)

}

Output:

float32: y = 2.001x + 2.001
float64: y = 2.001x + 2.001
Example (Monad_raison_detre)

This example showcases the reasons for the more confusing functions. 

// The main reason for the following function is to make it easier to create APIs.
// Gorgonia;s APIs are very explicit hence not very user friendly.

const (
	n        = 32
	features = 784
	size     = 100
)

// The following is an example of how to set up a neural network

// First, we set up the components
g := NewGraph()
w1 := NewMatrix(g, Float32, WithShape(features, size), WithName("w"), WithInit(GlorotU(1)))
b1 := NewMatrix(g, Float32, WithShape(1, size), WithName("b"), WithInit(Zeroes()))
x1 := NewMatrix(g, Float32, WithShape(n, features), WithName("x"))

// Then we write the expression:
var xw, xwb, act *Node
var err error
if xw, err = Mul(x1, w1); err != nil {
	fmt.Printf("Err while Mul: %v\n", err)
}
if xwb, err = BroadcastAdd(xw, b1, nil, []byte{0}); err != nil {
	fmt.Printf("Err while Add: %v\n", err)
}
if act, err = Tanh(xwb); err != nil {
	fmt.Printf("Err while Tanh: %v\n", err)
}
fmt.Printf("act is a %T\n", act)

// The following is how to set up the exact same network

// First we set up our environment
//
// These LiftXXX functions transforms Gorgonia's default API into functions that return `Result`
var mul = Lift2(Mul)                   // Lift2 turns a func(*Node, *Node) (*Node, error)
var tanh = Lift1(Tanh)                 // Lift1 turns a func(*Node) (*Node, error)
var add = Lift2Broadcast(BroadcastAdd) // Lift2Broadcast turns a func(*Node, *Node, []byte, []byte) (*Nide, error)

// First we set up the components
h := NewGraph()
w2 := NewMatrix(h, Float32, WithShape(features, size), WithName("w"), WithInit(GlorotU(1)))
b2 := NewMatrix(h, Float32, WithShape(1, size), WithName("b"), WithInit(Zeroes()))
x2 := NewMatrix(h, Float32, WithShape(n, features), WithName("x"))

// Then we write the expression
act2 := tanh(add(mul(x2, w2), b2, nil, []byte{0}))
fmt.Printf("act2 is a %T (note it's wrapped in the `Result` type)\n", act2)
fmt.Println()
// both g and h are the same graph but the expression is easier to write for act2
fmt.Printf("Both g and h are the same graph:\ng: %v\nh: %v\n", g.AllNodes(), h.AllNodes())

Output:

act is a *gorgonia.Node
act2 is a *gorgonia.Node (note it's wrapped in the `Result` type)

Both g and h are the same graph:
g: [w, b, x, A × B(%2, %0), Reshape(1, 100)(%1), SizeOf=32(%3), Repeat0(%4, %5), + false(%3, %6), tanh(%7)]
h: [w, b, x, A × B(%2, %0), Reshape(1, 100)(%1), SizeOf=32(%3), Repeat0(%4, %5), + false(%3, %6), tanh(%7)]
Example (Monad_raison_detre_errors)

This example showcases dealing with errors. This is part 2 of the raison d'être of the more complicated functions - dealing with errors 

// Observe that in a similar example, errors are manually controllable in the original case,
// but automated in the second case
const (
	n        = 32
	features = 784
	size     = 100
)

// The following is an example of how to set up a neural network

// First, we set up the components
g := NewGraph()
w1 := NewMatrix(g, Float32, WithShape(features, size), WithName("w"), WithInit(GlorotU(1)))
b1 := NewMatrix(g, Float32, WithShape(1, size), WithName("b"), WithInit(Zeroes()))
x1 := NewMatrix(g, Float32, WithShape(n, features), WithName("x"))

// Then we write the expression:
var xw, xwb, act *Node
var err error
if xw, err = Mul(x1, w1); err != nil {
	fmt.Printf("Err while Mul: %v\n", err)
}
// we introduce an error here - it should be []byte{0}
if xwb, err = BroadcastAdd(xw, b1, nil, []byte{1}); err != nil {
	fmt.Printf("Err while Add: %v\n", err)
	goto case2
}
if act, err = Tanh(xwb); err != nil {
	fmt.Printf("Err while Tanh: %v\n", err)
}
_ = act // will never happen

case2:

// The following is how to set up the exact same network

// First we set up our environment
//
// Now, remember all these functions no longer return (*Node, error). Instead they return `Result`
var mul = Lift2(Mul)
var tanh = Lift1(Tanh)
var add = Lift2Broadcast(BroadcastAdd)

// First we set up the components
h := NewGraph()
w2 := NewMatrix(h, Float32, WithShape(features, size), WithName("w"), WithInit(GlorotU(1)))
b2 := NewMatrix(h, Float32, WithShape(1, size), WithName("b"), WithInit(Zeroes()))
x2 := NewMatrix(h, Float32, WithShape(n, features), WithName("x"))

// Then we write the expression
act2 := tanh(add(mul(x2, w2), b2, nil, []byte{1}))

// REMEMBER: act2 is not a *Node! It is a Result
fmt.Printf("act2: %v\n", act2)

// To extract error, use CheckOne
fmt.Printf("error: %v\n", CheckOne(act2))

// If you extract the *Node from an error, you get nil
fmt.Printf("Node: %v\n", act2.Node())

Output:

Err while Add: Failed to infer shape. Op: + false: Shape mismatch: (32, 100) and (1, 10000)
act2: Failed to infer shape. Op: + false: Shape mismatch: (32, 100) and (1, 10000)
error: Failed to infer shape. Op: + false: Shape mismatch: (32, 100) and (1, 10000)
Node: <nil>
Example (NonConcurrentTraining) 
xV, yV, _ := prep()
nonConcurrentTraining(xV, yV, epochs)

fmt.Printf("x:\n%1.1v", xV)
fmt.Printf("y:\n%1.1v", yV)

Output:

x:
⎡    6      7      8      9  ... 5e+01  5e+01  5e+01  5e+01⎤
⎢7e+01  7e+01  7e+01  7e+01  ... 1e+02  1e+02  1e+02  1e+02⎥
⎢1e+02  1e+02  1e+02  1e+02  ... 2e+02  2e+02  2e+02  2e+02⎥
⎢2e+02  2e+02  2e+02  2e+02  ... 2e+02  2e+02  2e+02  2e+02⎥
.
.
.
⎢4e+07  4e+07  4e+07  4e+07  ... 4e+07  4e+07  4e+07  4e+07⎥
⎢4e+07  4e+07  4e+07  4e+07  ... 4e+07  4e+07  4e+07  4e+07⎥
⎢4e+07  4e+07  4e+07  4e+07  ... 4e+07  4e+07  4e+07  4e+07⎥
⎣4e+07  4e+07  4e+07  4e+07  ... 4e+07  4e+07  4e+07  4e+07⎦
y:
[-1e+02  -4e+02  -7e+02  -9e+02  ... -2e+08  -2e+08  -2e+08  -2e+08]
Example (SymbolicDiff)

SymbolicDiff showcases symbolic differentiation 

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)
}

// create a VM to run the program on
machine := NewTapeMachine(g)
defer machine.Close()

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

fmt.Printf("z: %v\n", z.Value())
if xgrad, err := x.Grad(); err == nil {
	fmt.Printf("dz/dx: %v | %v\n", xgrad, grads[0].Value())
}

if ygrad, err := y.Grad(); err == nil {
	fmt.Printf("dz/dy: %v | %v\n", ygrad, grads[1].Value())
}

Output:

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

Index

Examples

Constants

View Source 
const CUDA = false

CUDA indicates if this build is using CUDA

View Source 
const DEBUG = false

DEBUG indicates if this build is in debug mode. It is not.

Variables

View Source 
var (

	// Float64 ...
	Float64 = tensor.Float64
	// Float32 ...
	Float32 = tensor.Float32
	// Int ...
	Int = tensor.Int
	// Int64 ...
	Int64 = tensor.Int64
	// Int32 ...
	Int32 = tensor.Int32
	// Byte ...
	Byte = tensor.Uint8
	// Bool ...
	Bool = tensor.Bool

	// Ptr is equivalent to interface{}. Ugh Ugh Ugh
	Ptr = tensor.UnsafePointer
)

Functions

func BatchNorm 

func BatchNorm(x, scale, bias *Node, momentum, epsilon float64) (retVal, γ, β *Node, op *BatchNormOp, err error)

BatchNorm applies a batchnormalization. This operator can be used in forward pass or for training. In an evaluation only, the "op" output can be discared. In training phase, γ, β can be discarded and the op should be used.

func Binomial32 

func Binomial32(trials, prob float64, s ...int) []float32

Binomial32 returns a []float32 drawn from a binomial distribution given the trial and probability parameters.

func Binomial64 

func Binomial64(trials, prob float64, s ...int) []float64

Binomial64 returns a []float64 drawn from a binomial distribution given the trial and probability parameters.

func Broadcast 

func Broadcast(a, b *Node, pattern BroadcastPattern) (*Node, *Node, error)

Broadcast apply the pattern to the input nodes and returns two nodes suitable for a binary operator. Broadcast works somewhat like Numpy's broadcast, except it's now exposed as a function.

func CheckOne 

func CheckOne(in Input) error

CheckOne checks whether an input is an error

func Compile 

func Compile(g *ExprGraph) (prog *program, locMap map[*Node]register, err error)

Compile takes a graph and outputs a program suitable for *tapeMachine to run

func CompileFunction 

func CompileFunction(g *ExprGraph, inputs, outputs Nodes) (prog *program, locMap map[*Node]register, err error)

CompileFunction takes a graph, subsets it based on the input and output nodes provided and outputs a program suitable for *tapeMachine to run. It is analogous to theano.Function(). If some input nodes are not used or is not reachable, this function will return an error

func DebugDerives 

func DebugDerives()

DebugDerives turns on the derivation debug option when printing a graph

func DimSizersToShapes 

func DimSizersToShapes(ds []DimSizer) ([]tensor.Shape, error)

DimSizersToShapes is a convenience function to convert a slice of DimSizer to a slice of tensor.Shape. It will return an error if any of them isn't a tensor.Shape

func DontDebugDerives 

func DontDebugDerives()

DontDebugDerives turns off derivation debug option when printing a graph. It is off by default

func Err 

func Err(e error) gErr

Err is a function that returns a gErr. It wraps errors with stack information. A gErr implements Result, as well as error. This way, the Err() method acts as an unwrapper.

func FmtNodeMap 

func FmtNodeMap(m interface{}) mapFmt

FmtNodeMap is a convenience function to print map[*Node]<T>

The fmt flag that makes it all nicely formatted is "-". Because a map consists of two types (key's type and val's type), and the Go fmt verb doesn't quite allow us to do something like "%ds", a hack is introduced to enable nicer printing of map[*Node]<T>

Here's the hack: The "#" flag is used to indicate if the map will use the Node's ID or Name when formatting the map. 

%-v 	nodeName:%v
%-#v	nodeID:%v
%-d 	nodeName:%x
%-#d 	nodeID: %x
%-p 	nodeName:%p
%-#p	nodeID:%p

If the "-" flag is not found, then the formatter returns the default Go format for map[<T>]<T2>

func Gaussian32 

func Gaussian32(mean, stdev float64, s ...int) []float32

Gaussian32 returns a []float32 drawn from a gaussian distribution as defined by the mean and stdev

func Gaussian64 

func Gaussian64(mean, stdev float64, s ...int) []float64

Gaussian64 returns a []float64 drawn from a gaussian distribution as defined by the mean and stdev

func GlorotEtAlN32 

func GlorotEtAlN32(gain float64, s ...int) []float32

GlorotEtAlN32 returns float32 weights sampled from a normal distribution using the methods specified in Glorot et. al (2010). See also: http://jmlr.org/proceedings/papers/v9/glorot10a/glorot10a.pdf

func GlorotEtAlN64 

func GlorotEtAlN64(gain float64, s ...int) []float64

GlorotEtAlN64 returns float64 weights sampled from a normal distribution using the methods specified in Glorot et. al (2010). See also: http://jmlr.org/proceedings/papers/v9/glorot10a/glorot10a.pdf

func GlorotEtAlU32 

func GlorotEtAlU32(gain float64, s ...int) []float32

GlorotEtAlU32 returns float32 weights sampled from a uniform distribution using the methods specified in Glorot et. al (2010). See also: http://jmlr.org/proceedings/papers/v9/glorot10a/glorot10a.pdf

For best results, use: 

1.0 for gain for weights that will be used in linear and/or sigmoid units
math.Sqrt(2.0) for gain for weights that will be used in ReLU units
math.Sqrt(2.0 / (1+alpha*alpha)) for ReLU that are leaky with alpha

func GlorotEtAlU64 

func GlorotEtAlU64(gain float64, s ...int) []float64

GlorotEtAlU64 returns float64 weights sampled from a uniform distribution using the methods specified in Glorot et. al (2010). See also: http://jmlr.org/proceedings/papers/v9/glorot10a/glorot10a.pdf

For best results, use: 

1.0 for gain for weights that will be used in linear and/or sigmoid units
math.Sqrt(2.0) for gain for weights that will be used in ReLU units
math.Sqrt(2.0 / (1+alpha*alpha)) for ReLU that are leaky with alpha

func GraphCollisionStats 

func GraphCollisionStats() (int, int, int)

GraphCollisionStats returns the collisions in the graph only when built with the debug tag, otherwise it's a noop that returns 0

func HeEtAlN64 

func HeEtAlN64(gain float64, s ...int) []float64

HeEtAlN64 returns float64 weights sampled from a normal distro, using the methods described in He et al (2015). The formula is: 

randn(n) * sqrt(2/n)

See also https://arxiv.org/abs/1502.01852

For best results, use: 

1.0 for gain for weights that will be used in linear and/or sigmoid units
math.Sqrt(2.0) for gain for weights that will be used in ReLU units
math.Sqrt(2.0 / (1+alpha*alpha)) for ReLU that are leaky with alpha

func HeEtAlU64 

func HeEtAlU64(gain float64, s ...int) []float64

HeEtAlU64 returns float64 weights sampled from a uniform distro, using the methods described in He et al (2015). The formula is: 

randn(n) * sqrt(2/n)

See also https://arxiv.org/abs/1502.01852

For best results, use: 

1.0 for gain for weights that will be used in linear and/or sigmoid units
math.Sqrt(2.0) for gain for weights that will be used in ReLU units
math.Sqrt(2.0 / (1+alpha*alpha)) for ReLU that are leaky with alpha

func Let 

func Let(n *Node, be interface{}) error

Let binds a Value to a node that is a variable. A variable is represented as a *Node with no Op. It is equivalent to : 

x = 2

func Lift1 

func Lift1(fn func(a *Node) (*Node, error)) func(a Input) Result

Lift1 decorates a function with a precheck and post function lifting

func Lift1Axial 

func Lift1Axial(fn func(a *Node, axes ...int) (*Node, error)) func(a Input, axes ...int) Result

Lift1Axial decorates a function with a precheck and post function lifting

func Lift2 

func Lift2(fn func(a, b *Node) (*Node, error)) func(a, b Input) Result

Lift2 decorates a function with a precheck and post function lifting

func Lift2Broadcast 

func Lift2Broadcast(fn func(a, b *Node, pat1, pat2 []byte) (*Node, error)) func(a, b Input, pat1, pat2 []byte) Result

Lift2Broadcast decorates a function with a precheck and post function lifting

func NewLispMachine 

func NewLispMachine(g *ExprGraph, opts ...VMOpt) *lispMachine

NewLispMachine creates a VM that executes the graph as it is traversed. Depending on the VMOpts passed in this VM is also capable of performing automatic differentiation.

func NewTapeMachine 

func NewTapeMachine(g *ExprGraph, opts ...VMOpt) *tapeMachine

NewTapeMachine creates a VM that compiles a graph into a prog.

func ReturnNode 

func ReturnNode(n *Node)

ReturnNode returns a node to the pool. It does not check that the *Node has been removed from the graph. USE WITH CAUTION.

func ReturnType 

func ReturnType(t hm.Type)

ReturnType ...

func S 

func S(start int, opt ...int) tensor.Slice

S creates a tensor.Slice. end is optional. It should be passed in as the first param of the optionals. step is optional. It should be passed in as the second param of the optionals.

Default end is start+1. Default step is 1, unless end == step+1, then it defaults to 0

func SetDerivOf 

func SetDerivOf(deriv, of *Node)

SetDerivOf is used to hack around the fundamental limitations of Gorgonia.

Specifically it is used to set a node as the derivative of another node, used in the cuDNN version of batch norm.

The cuDNN BatchNorm operation produces the derivatives for the scale and bias as a side effect of calculating the derivative of the input. Because Gorgonia's Ops are modelled as pure functions (and no tuples) this causes a bit of trouble. With the clever use of scratch space ops multireturn can be simulated. But this causes derivatives to not be set correctly.

func SetOptimizationLevel 

func SetOptimizationLevel(i int)

SetOptimizationLevel sets the fast math optimization level. By default, fast math is turned off, and this function is a no-op.

Use the `fastmath` build tag to use fast math

func TransformResult added in v0.9.7 

func TransformResult(ins ...Input) func(a Input, err error) Result

TransformResult is like LiftResult, but allows for custom data types that fulfil Mker

func TypeOf 

func TypeOf(v Value) hm.Type

TypeOf returns the Type of the value

func Uniform32 

func Uniform32(low, high float64, s ...int) []float32

Uniform32 returns a []float64 drawn from a uniform distribution between [low, high) that is provided

func Uniform64 

func Uniform64(low, high float64, s ...int) []float64

Uniform64 returns a []float64 drawn from a uniform distribution between [low, high) that is provided

func UnsafeLet 

func UnsafeLet(n *Node, be interface{}) error

UnsafeLet binds a Value to any node, not just a variable node. This means that you can use it to change any node's value at the runtime of the graph. UNSAFE!

Additional notes: if `be` is a tensor.Slice, and the node's op is a sliceOp or sliceIncrOp, the op's slice will be replaced with the new slice.

func Use 

func Use(b BLAS)

Use defines which BLAS implementation gorgonia should use. The default is Gonum's Native. These are the other options: 

Use(blase.Implementation())
Use(cubone.Implementation())
Use(cgo.Implementation)

Note the differences in the brackets. The blase and cubone ones are functions.

func UseNonStable 

func UseNonStable()

UseNonStable turns off the stabilization functions when building graphs.

func UseStabilization 

func UseStabilization()

UseStabilization sets the global option to invoke stabilization functions when building the graph. Numerical stabilization is on by default

func ValueClose 

func ValueClose(a, b Value) bool

ValueClose checks whether two values are close to one another. It's predominantly used as an alternative equality test for floats

func ValueEq 

func ValueEq(a, b Value) bool

ValueEq is the equality function for values

func WalkGraph 

func WalkGraph(start *Node) <-chan *Node

WalkGraph walks a graph. It returns a channel of *Nodes, so be sure to consume the channel or there may be a deadlock

func WithGraphName 

func WithGraphName(name string) graphconopt

WithGraphName is a ExprGraph construction option that provides a name.

Types

type ADOp 

type ADOp interface {
	Op

	DoDiff(ctx ExecutionContext, inputs Nodes, output *Node) error
}

An ADOp is an Op that supports automatic differentiation.

type AdaGradSolver 

type AdaGradSolver struct {
	// contains filtered or unexported fields
}

AdaGradSolver is the solver that does adaptive gradient descent. Read the paper: http://jmlr.org/papers/v12/duchi11a.html

func NewAdaGradSolver 

func NewAdaGradSolver(opts ...SolverOpt) *AdaGradSolver

NewAdaGradSolver creates a new AdaGradSolver with sane-ish default values

func (*AdaGradSolver) Step 

func (s *AdaGradSolver) Step(model []ValueGrad) (err error)

Step steps through each node in the model and applies the Adaptive Gradient gradient descent algorithm on the value.

This function will error out if the nodes do not have an associated Grad value.

type AdamSolver 

type AdamSolver struct {
	// contains filtered or unexported fields
}

AdamSolver is the Adaptive Moment Estimation solver (basically RMSProp on steroids). Paper: http://arxiv.org/abs/1412.6980

We overload the purpose of existing data structure of a *dualValue. However, instead of just holding a value and its derivative, the cache's *dualValues hold the Means of gradients (in .Value) and the variances of the gradients (in .d)

func NewAdamSolver 

func NewAdamSolver(opts ...SolverOpt) *AdamSolver

NewAdamSolver creates an Adam solver with these default values: 

eta (learn rate)	  	: 0.001
eps (smoothing factor)		: 1e-8
beta1				: 0.9
beta2 				: 0.999
batch				: 1

func (*AdamSolver) Step 

func (s *AdamSolver) Step(model []ValueGrad) (err error)

Step steps through each node in the model and applies the Adaptive Moment Estimation gradient descent algorithm on the value.

This function will error out if the nodes do not have an associated Grad value.

type Arena 

type Arena interface {
	Get(dev Device, size int64) (tensor.Memory, error)       // Get returns a NoOpError when it cannot get a memory. Please allocate
	GetFromValue(dev Device, v Value) (tensor.Memory, error) // Gets a memory and copies the values into the memory and returns it.
	Put(dev Device, mem tensor.Memory, size int64)           // puts the memory back into the arena
	PutValue(dev Device, v Value)                            // puts the memory back into the arena

	// Transfers memory from device to device
	Transfer(toDev, fromDev Device, v Value, synchronous bool) (retVal Value, err error)
}

Arena is a representation of a pool of tensor.Memory

type AutoDiffError 

type AutoDiffError struct{}

AutoDiffError is an error which should be passed if the function is not differentiable. This is useful for Op implementations

func (AutoDiffError) Error 

func (err AutoDiffError) Error() string

type B 

type B bool

B represents a bool value.

func (*B) Data 

func (v *B) Data() interface{}

Data returns the original representation of the Value

func (*B) Dtype 

func (v *B) Dtype() tensor.Dtype

Dtype returns the Dtype of the value

func (*B) Format 

func (v *B) Format(s fmt.State, c rune)

Format implements fmt.Formatter

func (*B) MemSize 

func (v *B) MemSize() uintptr

MemSize satisfies the tensor.Memory interface

func (*B) Pointer 

func (v *B) Pointer() unsafe.Pointer

Pointer returns the pointer as an unsafe.Pointer. Satisfies the tensor.Memory interface

func (*B) Shape 

func (v *B) Shape() tensor.Shape

Shape returns a scalar shape for all scalar values

func (*B) Size 

func (v *B) Size() int

Size returns 0 for all scalar Values

func (*B) Uintptr 

func (v *B) Uintptr() uintptr

Uintptr satisfies the tensor.Memory interface

type BLAS 

type BLAS interface {
	blas.Float32
	blas.Float64
	blas.Complex64
	blas.Complex128
}

BLAS represents all the possible implementations of BLAS. The default is Gonum's Native

func WhichBLAS 

func WhichBLAS() BLAS

WhichBLAS returns the BLAS that gorgonia uses.

type BarzilaiBorweinSolver 

type BarzilaiBorweinSolver struct {
	// contains filtered or unexported fields
}

BarzilaiBorweinSolver / Barzilai-Borwein performs Gradient Descent in steepest descend direction Solves 0 = F(x), by 

xᵢ₊₁ = xᵢ - eta * Grad(F)(xᵢ)

Where the learn rate eta is calculated by the Barzilai-Borwein method: 

eta(xᵢ) = <(xᵢ - xᵢ₋₁), (Grad(F)(xᵢ) - Grad(F)(xᵢ₋₁))> /
                ∥(Grad(F)(xᵢ) - Grad(F)(xᵢ₋₁))∥²

The input learn rate is used for the first iteration.

TODO: Check out stochastic implementations, e.g. "Barzilai-Borwein Step Size for Stochastic Gradient Descent" https://arxiv.org/abs/1605.04131

func NewBarzilaiBorweinSolver 

func NewBarzilaiBorweinSolver(opts ...SolverOpt) *BarzilaiBorweinSolver

NewBarzilaiBorweinSolver creates a new Barzilai-Borwein solver withs some default values: the learn rate is set to 0.001 and the solver does not use clipping.

func (*BarzilaiBorweinSolver) Step 

func (s *BarzilaiBorweinSolver) Step(model []ValueGrad) (err error)

Step steps through each node in the model and applies the Barzilai-Borwein gradient descent algorithm on the value.

This function will error out if the nodes do not have an associated Grad value.

type BatchNormOp 

type BatchNormOp struct {
	// contains filtered or unexported fields
}

BatchNormOp is a batch normalization process as described by Ioffe and Szegedy (2015) - http://arxiv.org/abs/1502.03167

Normalization is done as: 

γ(x - μ) / σ + β

γ is the scaling factor and β is the offset factor. These are created by BatchNorm()

func (*BatchNormOp) Arity 

func (op *BatchNormOp) Arity() int

Arity returns 1

func (*BatchNormOp) CallsExtern 

func (op *BatchNormOp) CallsExtern() bool

CallsExtern is false

func (*BatchNormOp) DiffWRT 

func (op *BatchNormOp) DiffWRT(inputs int) []bool

DiffWRT ...

func (*BatchNormOp) Do 

func (op *BatchNormOp) Do(values ...Value) (retVal Value, err error)

Do performs the batchnorm computation on the values

func (*BatchNormOp) DoDiff 

func (op *BatchNormOp) DoDiff(ctx ExecutionContext, inputs Nodes, output *Node) error

DoDiff does the gradient computation

func (*BatchNormOp) Hashcode 

func (op *BatchNormOp) Hashcode() uint32

Hashcode ...

func (*BatchNormOp) InferShape 

func (op *BatchNormOp) InferShape(ns ...DimSizer) (tensor.Shape, error)

InferShape from the input values

func (*BatchNormOp) OverwritesInput 

func (op *BatchNormOp) OverwritesInput() int

OverwritesInput is -1 (operator doesn't overwrite any input value)

func (*BatchNormOp) Reset 

func (op *BatchNormOp) Reset() error

Reset the operator by zeroing the internals scratch spaces

func (*BatchNormOp) ReturnsPtr 

func (op *BatchNormOp) ReturnsPtr() bool

ReturnsPtr is true

func (*BatchNormOp) SetTesting 

func (op *BatchNormOp) SetTesting()

SetTesting configure the op for testing mode

func (*BatchNormOp) SetTraining 

func (op *BatchNormOp) SetTraining()

SetTraining configure the op for training mode. A call to this function implicitly calls the Reset() method

func (*BatchNormOp) String 

func (op *BatchNormOp) String() string

func (*BatchNormOp) SymDiff 

func (op *BatchNormOp) SymDiff(inputs Nodes, output *Node, grad *Node) (retVal Nodes, err error)

SymDiff ...

func (*BatchNormOp) Type 

func (op *BatchNormOp) Type() hm.Type

Type ...

func (*BatchNormOp) UsePreallocDo 

func (op *BatchNormOp) UsePreallocDo(prealloc Value, inputs ...Value) (retVal Value, err error)

UsePreallocDo ...

func (*BatchNormOp) WriteHash 

func (op *BatchNormOp) WriteHash(h hash.Hash)

WriteHash ...

type Batched 

type Batched interface {
	WorkAvailable() <-chan struct{}
	DoWork()
}

Batched interface describes any object that can process batch work

type BatchedBLAS 

type BatchedBLAS interface {
	Batched
	BLAS
}

BatchedBLAS interface describes any object that can process BLAS work in batch

type BatchedDevice 

type BatchedDevice interface {
	Batched
	Retval() interface{}
	Errors() error
}

BatchedDevice is the superset of BatchedBLAS and the batched CUDA workflow.

type BinaryOp 

type BinaryOp interface {
	Op

	IsBinary() bool
}

A BinaryOp is an Op that takes only two inputs

type BroadcastPattern 

type BroadcastPattern byte

BroadcastPattern is actually a bit array. It's split into 2 nibbles - the left nibble represents the left operand, the right nibble represents the right operand: 

xxxx|xxxx

The least significant bit of each nibble is elem 0. Concrete examples: 

00000010 (0x02) = broadcast axis 1 of the right operand
00000001 (0x01) = broadcast axis 0 of the right operand
00000101 (0x09) = broadcast axis 0 AND axis 2 of the right operand
00010000 (0x10) = broadcast axis 0 of the left operand
00110000 (0x30) = broadcast axis 0 and axis 1 of the lef operand

You get the drill.

Do note that the current limitation of the BroadcastPattern allows only up to 4 dimensions per operand.

func NewBroadcastPattern 

func NewBroadcastPattern(leftAxes, rightAxes []byte) BroadcastPattern

NewBroadcastPattern is a helper function to create broadcast patterns

type CLDoer 

type CLDoer interface {
	CLDo(inputs ...Value) (Value, error)
}

CLDoer uses OpenCL to perform the Op. As of now, there are NO Ops that support OpenCL

type CUDAADOp 

type CUDAADOp interface {
	ADOp
	CUDADoDiff(extern External, dev Device, inputs Nodes, output *Node) error
}

A CUDAADOp operation have a specific method to run with CUDA

type CUDADoer 

type CUDADoer interface {
	CUDADo(extern External, dev Device, prealloc Value, inputs ...Value) (retVal Value, err error)
}

CUDADoer uses CUDA to perform the Op.

type CloneErrorer 

type CloneErrorer interface {
	Clone() (interface{}, error)
}

CloneErrorer represents any type that can clone itself and return an error if necessary

type Cloner 

type Cloner interface {
	Clone() interface{}
}

Cloner represents any type that can clone itself.

type CopierFrom 

type CopierFrom interface {
	CopyFrom(src interface{}) error
}

CopierFrom represents any type that can copy data from the source provided.

type CopierTo 

type CopierTo interface {
	CopyTo(dest interface{}) error
}

CopierTo represents any type that can copy data to the destination.

type Device 

type Device int

Device represents the device where the code will be executed on. In this build, all code will run on the CPU 

const (
	// CPU the only device the graph will be executed on
	CPU Device = 0
)

func (Device) Alloc 

func (d Device) Alloc(extern External, size int64) (tensor.Memory, error)

Alloc allocates memory on the device. This is currently a NO-OP in this build

func (Device) Free 

func (d Device) Free(extern External, mem tensor.Memory, sie uint) error

Free frees the memory on the device. This is currently a NO-OP in this build

func (Device) IsGPU 

func (d Device) IsGPU() bool

IsGPU will always return false in this build

func (Device) String 

func (d Device) String() string

String implements fmt.Stringer and runtime.Stringer

type DimSizer 

type DimSizer interface {
	DimSize(int) (int, error)
}

DimSizer is any type (typically a tensor.Shape) that allows querying for a dimension size given an input dimension.

func ShapesToDimSizers 

func ShapesToDimSizers(shapes []tensor.Shape) []DimSizer

ShapesToDimSizers is a convenience function to convert a slice of tensor.Shape to a slice of DimSizer

type Dtyper 

type Dtyper interface {
	Dtype() tensor.Dtype
}

Dtyper represents any type (typically a Value) that knows its own Dtype

type Errer 

type Errer interface {
	Err() error
}

Errer is an interface that can return an error.

type ExecutionContext 

type ExecutionContext struct {
	External
	Device
}

ExecutionContext informs how an op should be executed

type ExprGraph 

type ExprGraph struct {
	// contains filtered or unexported fields
}

ExprGraph is a data structure for a directed acyclic graph (of expressions). This structure is the main entry point for Gorgonia.

func NewGraph 

func NewGraph(opts ...graphconopt) *ExprGraph

NewGraph creates a new graph. Duh

func (*ExprGraph) AddNode 

func (g *ExprGraph) AddNode(n *Node) (retVal *Node)

AddNode adds n to the graph. It panics if the added node ID matches an existing node ID.

func (*ExprGraph) AllNodes 

func (g *ExprGraph) AllNodes() Nodes

AllNodes is like Nodes, but returns Nodes instead of []graph.Node. Nodes() has been reserved for the graph.Directed interface, so this one is named AllNodes instead

func (*ExprGraph) ByName 

func (g *ExprGraph) ByName(name string) (retVal Nodes)

ByName returns nodes that have the name provided. Bear in mind that the name that is compared to is the internal name, not the result of calling node.Name(). The reason for doing this is for ease of finding only names that are user-supplied, instead of autogenerated names

func (*ExprGraph) Clone 

func (g *ExprGraph) Clone() interface{}

Clone clones the graph. All nodes gets cloned, and their values are cloned as well.

func (*ExprGraph) Constant 

func (g *ExprGraph) Constant(v Value) *Node

Constant returns a constant that may be found in the graph. If no constant were found, a new one is created instead

func (*ExprGraph) Edge 

func (g *ExprGraph) Edge(u, v int64) graph.Edge

Edge returns the edge from u to v if such an edge exists and nil otherwise. The node v must be directly reachable from u as defined by the From method.

func (*ExprGraph) Edges 

func (g *ExprGraph) Edges() graph.Edges

Edges returns all the edges in the graph.

func (*ExprGraph) ExactSubgraphRoots 

func (g *ExprGraph) ExactSubgraphRoots(ns ...*Node) *ExprGraph

ExactSubgraphRoots creates a subgraph from the roots provided. The difference between SubgraphRoots and ExactSubgraphRoots is that ExactSubGraphRoots will not attempt to discover if any nodes are missing.

Given a function like the following: 

z = x + y
set(x, -x.Grad) // setting the value of x to the negative of the gradient

When SubgraphRoots is used on z, the `-x.Grad` will be included. When using ExactSubgraphRoots, only `x` and `y` are included in the subgraph

func (*ExprGraph) From 

func (g *ExprGraph) From(nodeid int64) graph.Nodes

From returns all nodes in g that can be reached directly from n.

func (*ExprGraph) Has 

func (g *ExprGraph) Has(nodeid int64) bool

Has returns whether the node exists within the graph.

func (*ExprGraph) HasEdgeBetween 

func (g *ExprGraph) HasEdgeBetween(x, y int64) bool

HasEdgeBetween returns whether an edge exists between nodes x and y without considering direction.

func (*ExprGraph) HasEdgeFromTo 

func (g *ExprGraph) HasEdgeFromTo(u, v int64) bool

HasEdgeFromTo returns whether an edge exists in the graph from u to v.

func (*ExprGraph) Inputs 

func (g *ExprGraph) Inputs() (retVal Nodes)

Inputs returns a list of nodes which are inputs (that is to say, the user is required to set a value in it)

func (*ExprGraph) Node 

func (g *ExprGraph) Node(id int64) graph.Node

Node returns the node in the graph with the given ID.

func (*ExprGraph) Nodes 

func (g *ExprGraph) Nodes() graph.Nodes

Nodes returns all the nodes in the graph.

func (*ExprGraph) RemoveNode 

func (g *ExprGraph) RemoveNode(node graph.Node)

RemoveNode removes n from the graph, as well as any edges attached to it. If the node is not in the graph it is a no-op.

func (*ExprGraph) Roots 

func (g *ExprGraph) Roots() (retVal Nodes)

Roots returns a list of nodes that are not children of any other nodes

func (*ExprGraph) SetEdge 

func (g *ExprGraph) SetEdge(e graph.Edge)

SetEdge adds e, an edge from one node to another. If the nodes do not exist, they are added. It will panic if the IDs of the e.From and e.To are equal.

func (*ExprGraph) String 

func (g *ExprGraph) String() string

func (*ExprGraph) Subgraph 

func (g *ExprGraph) Subgraph(ns ...*Node) *ExprGraph

Subgraph subsets a graph. This function has overloaded meanings - If only one node is passed in, it assumes that the one node is the root, otherwise, it treats ns as the subset of nodes to be included in the subgraph

func (*ExprGraph) SubgraphRoots 

func (g *ExprGraph) SubgraphRoots(ns ...*Node) *ExprGraph

SubgraphRoots creates a subgraph, assuming the provided nodes are roots to the new subgraph.

func (*ExprGraph) To 

func (g *ExprGraph) To(nid int64) graph.Nodes

To returns all nodes in g that can reach directly to n.

func (*ExprGraph) ToDot 

func (g *ExprGraph) ToDot() string

ToDot generates the graph in graphviz format. The use of this is to generate for the entire graph which may have multiple trees with different roots TODO: This is getting unwieldy. Perhaps refactor out into a ToDot(...Opt)?

func (*ExprGraph) UnbindAll 

func (g *ExprGraph) UnbindAll()

UnbindAll unbinds all the values from the nodes

func (*ExprGraph) UnbindAllNonInputs 

func (g *ExprGraph) UnbindAllNonInputs()

UnbindAllNonInputs unbinds all the values from nodes that aren't input nodes

type ExternMetadata 

type ExternMetadata struct {
	tensor.Engine
	// contains filtered or unexported fields
}

ExternMetadata is used to hold metadata about external execution devices. In this build, it's an empty struct because the default build doesn't use external devices to execute the graph on

func (*ExternMetadata) Cleanup 

func (m *ExternMetadata) Cleanup()

Cleanup cleans up the ancillary allocations made during the calling of batched external device function.

The reason for this method is due to the fact that there is currently no way to free memory while the context is still running without causing some weirdness to the CUDA calls.

This is a No-op in this build

func (*ExternMetadata) DoWork 

func (m *ExternMetadata) DoWork() error

DoWork flushes any batched cgo calls. In this build it only flushes the batched BLAS calls.

func (*ExternMetadata) Get 

func (m *ExternMetadata) Get(dev Device, size int64) (tensor.Memory, error)

Get allocates a memory of the size. In this build it returns a NoOpError.

func (*ExternMetadata) GetFromValue 

func (m *ExternMetadata) GetFromValue(dev Device, v Value) (tensor.Memory, error)

GetFromValue allocates a memory of the size of v. In this build it returns a NoOpError, and v itself

func (ExternMetadata) HasFunc 

func (m ExternMetadata) HasFunc(name string) bool

HasFunc will always return false in this build

func (*ExternMetadata) Put 

func (m *ExternMetadata) Put(dev Device, mem tensor.Memory, size int64)

Put puts a previously allocated memory slab of the provided size back into the pool. Currently this is a No-op in this build.

func (*ExternMetadata) PutValue 

func (m *ExternMetadata) PutValue(dev Device, v Value)

PutValue puts a previously allocated value into the pool. In this build, it is a noop.

func (*ExternMetadata) Reset 

func (m *ExternMetadata) Reset()

Reset is a noop function for compatibility with the Cuda build

func (*ExternMetadata) Signal 

func (m *ExternMetadata) Signal()

Signal sends a signal down the workavailable channel, telling the VM to call the DoWork method. Signal is a synchronous method

func (*ExternMetadata) Sync 

func (m *ExternMetadata) Sync() chan struct{}

Sync returns the sync channel

func (*ExternMetadata) Transfer 

func (m *ExternMetadata) Transfer(toDev, fromDev Device, v Value, synchronous bool) (retVal Value, err error)

Transfer transfers a value from device to device. In this build, it's a noop, returning the input value, and a nil error

func (*ExternMetadata) WorkAvailable 

func (m *ExternMetadata) WorkAvailable() <-chan bool

WorkAvailable returns a channel of empty struct, which is used to signal to the VM when there is work available. The VM will then call the DoWork method.

type External 

type External interface {
	Arena
	Signal() // signals the machine to do work
	Sync() chan struct{}
}

External is a representation of an external device (cuda/cgo/openCL), conceptually modelled as a machine.

type ExternalOp 

type ExternalOp struct {
	Op
	ExecutionContext

	Prealloc  Value
	Incr      Value // is this a Incr? IncrDoers have higher precedence over PreallocDo
	UseUnsafe bool  // Is this an unsafe op? Lowest of all "special" Dos
}

ExternalOp is an op that contains an external context. This allows for ops to be run without needing a VM

func NewAddOp 

func NewAddOp(a, b *Node, ctx ExecutionContext) *ExternalOp

NewAddOp creates a new *ExternalOp that wraps an add op

func NewExternalOp 

func NewExternalOp(op Op, ctx ExecutionContext, prealloc Value) *ExternalOp

NewExternalOp creates a new *ExternalOp.

func NewHadamardProdOp 

func NewHadamardProdOp(a, b *Node, ctx ExecutionContext) *ExternalOp

NewHadamardProdOp creates a new *ExternalOp that wraps a mul op

func NewSubOp 

func NewSubOp(a, b *Node, ctx ExecutionContext) *ExternalOp

NewSubOp creates a new *ExternalOp that wraps a sub op

func (*ExternalOp) DetermineDevice 

func (op *ExternalOp) DetermineDevice(inputs Nodes, output *Node) error

DetermineDevice ...

func (*ExternalOp) Do 

func (op *ExternalOp) Do(vals ...Value) (Value, error)

Do performs the op,

func (*ExternalOp) String 

func (op *ExternalOp) String() string

type F32 

type F32 float32

F32 represents a float32 value.

func (*F32) Data 

func (v *F32) Data() interface{}

Data returns the original representation of the Value

func (*F32) Dtype 

func (v *F32) Dtype() tensor.Dtype

Dtype returns the Dtype of the value

func (*F32) Format 

func (v *F32) Format(s fmt.State, c rune)

Format implements fmt.Formatter

func (*F32) MemSize 

func (v *F32) MemSize() uintptr

MemSize satisfies the tensor.Memory interface

func (*F32) Pointer 

func (v *F32) Pointer() unsafe.Pointer

Pointer returns the pointer as an unsafe.Pointer. Satisfies the tensor.Memory interface

func (*F32) Shape 

func (v *F32) Shape() tensor.Shape

Shape returns a scalar shape for all scalar values

func (*F32) Size 

func (v *F32) Size() int

Size returns 0 for all scalar Values

func (*F32) Uintptr 

func (v *F32) Uintptr() uintptr

Uintptr satisfies the tensor.Memory interface

type F64 

type F64 float64

F64 represents a float64 value.

func (*F64) Data 

func (v *F64) Data() interface{}

Data returns the original representation of the Value

func (*F64) Dtype 

func (v *F64) Dtype() tensor.Dtype

Dtype returns the Dtype of the value

func (*F64) Format 

func (v *F64) Format(s fmt.State, c rune)

Format implements fmt.Formatter

func (*F64) MemSize 

func (v *F64) MemSize() uintptr

MemSize satisfies the tensor.Memory interface

func (*F64) Pointer 

func (v *F64) Pointer() unsafe.Pointer

Pointer returns the pointer as an unsafe.Pointer. Satisfies the tensor.Memory interface

func (*F64) Shape 

func (v *F64) Shape() tensor.Shape

Shape returns a scalar shape for all scalar values

func (*F64) Size 

func (v *F64) Size() int

Size returns 0 for all scalar Values

func (*F64) Uintptr 

func (v *F64) Uintptr() uintptr

Uintptr satisfies the tensor.Memory interface

type I 

type I int

I represents a int value.

func (*I) Data 

func (v *I) Data() interface{}

Data returns the original representation of the Value

func (*I) Dtype 

func (v *I) Dtype() tensor.Dtype

Dtype returns the Dtype of the value

func (*I) Format 

func (v *I) Format(s fmt.State, c rune)

Format implements fmt.Formatter

func (*I) MemSize 

func (v *I) MemSize() uintptr

MemSize satisfies the tensor.Memory interface

func (*I) Pointer 

func (v *I) Pointer() unsafe.Pointer

Pointer returns the pointer as an unsafe.Pointer. Satisfies the tensor.Memory interface

func (*I) Shape 

func (v *I) Shape() tensor.Shape

Shape returns a scalar shape for all scalar values

func (*I) Size 

func (v *I) Size() int

Size returns 0 for all scalar Values

func (*I) Uintptr 

func (v *I) Uintptr() uintptr

Uintptr satisfies the tensor.Memory interface

type I32 

type I32 int32

I32 represents a int32 value.

func (*I32) Data 

func (v *I32) Data() interface{}

Data returns the original representation of the Value

func (*I32) Dtype 

func (v *I32) Dtype() tensor.Dtype

Dtype returns the Dtype of the value

func (*I32) Format 

func (v *I32) Format(s fmt.State, c rune)

Format implements fmt.Formatter

func (*I32) MemSize 

func (v *I32) MemSize() uintptr

MemSize satisfies the tensor.Memory interface

func (*I32) Pointer 

func (v *I32) Pointer() unsafe.Pointer

Pointer returns the pointer as an unsafe.Pointer. Satisfies the tensor.Memory interface

func (*I32) Shape 

func (v *I32) Shape() tensor.Shape

Shape returns a scalar shape for all scalar values

func (*I32) Size 

func (v *I32) Size() int

Size returns 0 for all scalar Values

func (*I32) Uintptr 

func (v *I32) Uintptr() uintptr

Uintptr satisfies the tensor.Memory interface

type I64 

type I64 int64

I64 represents a int64 value.

func (*I64) Data 

func (v *I64) Data() interface{}

Data returns the original representation of the Value

func (*I64) Dtype 

func (v *I64) Dtype() tensor.Dtype

Dtype returns the Dtype of the value

func (*I64) Format 

func (v *I64) Format(s fmt.State, c rune)

Format implements fmt.Formatter

func (*I64) MemSize 

func (v *I64) MemSize() uintptr

MemSize satisfies the tensor.Memory interface

func (*I64) Pointer 

func (v *I64) Pointer() unsafe.Pointer

Pointer returns the pointer as an unsafe.Pointer. Satisfies the tensor.Memory interface

func (*I64) Shape 

func (v *I64) Shape() tensor.Shape

Shape returns a scalar shape for all scalar values

func (*I64) Size 

func (v *I64) Size() int

Size returns 0 for all scalar Values

func (*I64) Uintptr 

func (v *I64) Uintptr() uintptr

Uintptr satisfies the tensor.Memory interface

type IncrDoer 

type IncrDoer interface {
	IncrDo(toIncr Value, inputs ...Value) error
}

IncrDoer increments the toIncr with the result of doing

type InitWFn 

type InitWFn func(dt tensor.Dtype, s ...int) interface{}

InitWFn is a type of helper function to help initialize weights vector/matrices. It generates the backing required for the tensors.

It's typically used in closures

func Gaussian 

func Gaussian(mean, stdev float64) InitWFn

Gaussian creates a InitWFn with the specified parameters. Example Usage: 

w := NewMatrix(g, Float64, WithName("w"), WithShape(2,2), WithInit(Gaussian(0, 1)))

This will create a backing slice of []float64, with the length of 4, and its values are drawn from a gaussian distro

func GlorotN 

func GlorotN(gain float64) InitWFn

GlorotN creates a InitWFn that populates a Value with weights normally sampled using Glorot et al.'s algorithm

func GlorotU 

func GlorotU(gain float64) InitWFn

GlorotU creates a InitWFn that populates a Value with weights uniformly sampled using Glorot et al.'s algorithm

func HeN 

func HeN(gain float64) InitWFn

func HeU 

func HeU(gain float64) InitWFn

func Ones 

func Ones() InitWFn

Ones creates an InitWfn that populates a Value with ones. See Zeroes() for more explanation.

func RangedFrom 

func RangedFrom(start int) InitWFn

RangedFrom creates an InitWFn that populates a Value starting with the provided start, increamenting the number for each element in the value by 1

func Uniform 

func Uniform(low, high float64) InitWFn

Uniform creates a InitWFn with the specified parameters. Example Usage: 

w := NewMatrix(g, Float64, WithName("w"), WithShape(2,2), WithInit(Uniform(-1, 1)))

This will create a backing slice of []float64, with the length of 4, and its values are drawn from a uniform distro

func ValuesOf 

func ValuesOf(val interface{}) InitWFn

ValuesOf creates an InitWrn that populates a value with val. This function will cause a panic if val's type is incompatible with the values type.

func Zeroes 

func Zeroes() InitWFn

Zeroes creates an InitWfn that populates a Value with... zeroes. I don't know what you expected.

type Input 

type Input interface {
	Node() *Node
	Nodes() Nodes
}

Input is something that can produce both a *Node and Nodes. Returning nil is OK.

type Mker added in v0.9.7 

type Mker interface {
	Mk(...Input) Input
}

Mker is an interface of any Input that can make a new version of itself

type Momentum 

type Momentum struct {
	// contains filtered or unexported fields
}

Momentum is the stochastic gradient descent optimizer with momentum item.

func NewMomentum 

func NewMomentum(opts ...SolverOpt) *Momentum

NewMomentum creates a new Momentum with sane-ish default values

func (*Momentum) Step 

func (s *Momentum) Step(model []ValueGrad) (err error)

Step steps through each node in the model and applies the Momentum stochastic gradient descent algorithm on the value.

This function will error out if the nodes do not have an associated Grad value.

type Namer 

type Namer interface {
	Name() string
}

Namer is anything that has a name

type NoOpError 

type NoOpError interface {
	NoOp() bool
}

NoOpError is an error returned when an operation does nothing.

type NoRetOp 

type NoRetOp interface {
	Op

	ReturnsNothing() bool
}

A NoRetOp is an Op that reads a value, but does not return any value. It's a representation of a not-pure function

type Node 

type Node struct {
	// contains filtered or unexported fields
}

A Node is a node in the computation graph

func Abs 

func Abs(a *Node) (*Node, error)

Abs performs a pointwise abs.

func Add 

func Add(a, b *Node) (*Node, error)

Add performs a pointwise add operation.

func ApplyOp 

func ApplyOp(op Op, children ...*Node) (retVal *Node, err error)

ApplyOp is the generic function application - for when no specialization is required

func ApplyOpWithName 

func ApplyOpWithName(op Op, name string, children ...*Node) (retVal *Node, err error)

ApplyOpWithName applies the op, and then gives the node the given name

func At 

func At(a *Node, coords ...int) (retVal *Node, err error)

At is a symbolic operation for getting a value at the provided coordinates. If the input is a scalar, all the coordinates MUST be 0, or else an error will be returned.

func BatchedMatMul 

func BatchedMatMul(a, b *Node, transes ...bool) (retVal *Node, err error)

BatchedMatMul returns a node representing the batched mat mul operation.

A list of transpose options are allowed. The

Example 
g := NewGraph()
a := NewTensor(g, Float64, 3, WithShape(2, 2, 3), WithInit(RangedFrom(1)), WithName("a"))
b := NewTensor(g, Float64, 3, WithShape(2, 3, 2), WithInit(RangedFrom(13)), WithName("b"))
c, err := BatchedMatMul(a, b)
if err != nil {
	log.Fatal(err)
}
x := NewTensor(g, Float64, 4, WithShape(3, 2, 2, 3), WithInit(RangedFrom(1)), WithName("x"))
y := NewTensor(g, Float64, 4, WithShape(3, 2, 3, 2), WithInit(RangedFrom(37)), WithName("y"))
z, err := BatchedMatMul(x, y)
if err != nil {
	log.Fatal(err)
}

m := NewTapeMachine(g)
if err := m.RunAll(); err != nil {
	log.Fatal(err)
}

fmt.Printf("a: %v\n%v\n", a.Value().Shape(), a.Value().Data())
fmt.Printf("b: %v\n%v\n", b.Value().Shape(), b.Value().Data())
fmt.Printf("c: %v\n%v\n", c.Value().Shape(), c.Value().Data())
fmt.Printf("x: %v\n%v\n", x.Value().Shape(), x.Value().Data())
fmt.Printf("y: %v\n%v\n", y.Value().Shape(), y.Value().Data())
fmt.Printf("z: %v\n%v\n", z.Value().Shape(), z.Value().Data())

Output:

a: (2, 2, 3)
[1 2 3 4 5 6 7 8 9 10 11 12]
b: (2, 3, 2)
[13 14 15 16 17 18 19 20 21 22 23 24]
c: (2, 2, 2)
[94 100 229 244 508 532 697 730]
x: (3, 2, 2, 3)
[1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36]
y: (3, 2, 3, 2)
[37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72]
z: (3, 2, 2, 2)
[238 244 589 604 1084 1108 1489 1522 2146 2188 2605 2656 3424 3484 3937 4006 4918 4996 5485 5572 6628 6724 7249 7354]
Example (WithBackprop) 
g := NewGraph()
a := NewTensor(g, Float64, 4, WithShape(2, 4, 3, 9), WithInit(RangedFrom(1)), WithName("a"))
b := NewTensor(g, Float64, 4, WithShape(2, 4, 3, 9), WithInit(RangedFrom(13)), WithName("b"))
c, err := BatchedMatMul(a, b, false, true)
if err != nil {
	log.Fatal(err)
}
s, err := Sum(c)
if err != nil {
	log.Fatal(err)
}
grads, err := Grad(s, a, b)
if err != nil {
	log.Fatal(err)
}

m := NewTapeMachine(g)
if err := m.RunAll(); err != nil {
	log.Fatal(err)
}

fmt.Printf("a: %v\n%v\n", a.Value().Shape(), a.Value().Data())
fmt.Printf("b: %v\n%v\n", b.Value().Shape(), b.Value().Data())
fmt.Printf("c: %v\n%v\n", c.Value().Shape(), c.Value().Data())
fmt.Printf("grads[0]:%v\n%v\n", grads[0].Shape(), grads[0].Value().Data())

Output:

a: (2, 4, 3, 9)
[1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216]
b: (2, 4, 3, 9)
[13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228]
c: (2, 4, 3, 3)
[825 1230 1635 2202 3336 4470 3579 5442 7305 12732 15324 17916 16296 19617 22938 19860 23910 27960 37761 42540 47319 43512 49020 54528 49263 55500 61737 75912 82878 89844 83850 91545 99240 91788 100212 108636 127185 136338 145491 137310 147192 157074 147435 158046 168657 191580 202920 214260 203892 215961 228030 216204 229002 241800 269097 282624 296151 283596 297852 312108 298095 313080 328065 359736 375450 391164 376422 392865 409308 393108 410280 427452]
grads[0]:(2, 4, 3, 9)
[66 69 72 75 78 81 84 87 90 66 69 72 75 78 81 84 87 90 66 69 72 75 78 81 84 87 90 147 150 153 156 159 162 165 168 171 147 150 153 156 159 162 165 168 171 147 150 153 156 159 162 165 168 171 228 231 234 237 240 243 246 249 252 228 231 234 237 240 243 246 249 252 228 231 234 237 240 243 246 249 252 309 312 315 318 321 324 327 330 333 309 312 315 318 321 324 327 330 333 309 312 315 318 321 324 327 330 333 390 393 396 399 402 405 408 411 414 390 393 396 399 402 405 408 411 414 390 393 396 399 402 405 408 411 414 471 474 477 480 483 486 489 492 495 471 474 477 480 483 486 489 492 495 471 474 477 480 483 486 489 492 495 552 555 558 561 564 567 570 573 576 552 555 558 561 564 567 570 573 576 552 555 558 561 564 567 570 573 576 633 636 639 642 645 648 651 654 657 633 636 639 642 645 648 651 654 657 633 636 639 642 645 648 651 654 657]

func BinaryXent 

func BinaryXent(output, target *Node) (retVal *Node, err error)

BinaryXent is a convenience function for doing binary crossentropy stuff. The formula is as below: 

-(y * logprob) +  (1-y)(1-logprob)

func BinomialRandomNode 

func BinomialRandomNode(g *ExprGraph, dt tensor.Dtype, trials, prob float64, shape ...int) *Node

BinomialRandomNode creates an input node that has a random op so that everytime the node is passed, random values will be plucked from a binomial distribution with the mean and stdev provided. The type of the node depends on the shape passed in. To get a scalar value at run time, don't pass in any shapes

Whilst technically the number of trials of a binomal distribution should be a discrete value (you can't have half a trial), to keep with API uniformity, trials is passed in as a float64, but will be truncated to an int at runtime.

func BroadcastAdd 

func BroadcastAdd(a, b *Node, leftPattern, rightPattern []byte) (*Node, error)

Add performs a add. The operation is precomposed with a broadcast such that the shapes matches before operations commence.

Example

By default, Gorgonia operations do not perform broadcasting. To do broadcasting, you would need to manually specify the operation 

g := NewGraph()
a := NewVector(g, tensor.Float64, WithShape(2), WithName("a"), WithValue(tensor.New(tensor.WithBacking([]float64{100, 100}))))
b := NewMatrix(g, tensor.Float64, WithShape(2, 2), WithName("b"), WithValue(tensor.New(tensor.WithShape(2, 2), tensor.WithBacking([]float64{1, 1, 2, 2}))))

fmt.Printf("a = %v\nb =\n%v\n", a.Value(), b.Value())

_, err := Add(a, b)
fmt.Printf("a + b yields an error: %v\n\n", err)

// Note here the broadcasting of a is on the first axis, not the zeroth axis. Simply put, assume that it's already a (2,1) matrix.
ab, err := BroadcastAdd(a, b, []byte{1}, nil)
if err != nil {
	fmt.Printf("uh oh, something went wrong: %v\n", err)
}

ba, err := BroadcastAdd(b, a, nil, []byte{1})
if err != nil {
	fmt.Printf("uh oh, something went wrong: %v\n", err)
}

// Now, let's run the program
machine := NewTapeMachine(g)
defer machine.Close()
if err = machine.RunAll(); err != nil {
	log.Fatal(err)
}

fmt.Printf("a +⃗ b =\n%v\n", ab.Value())
fmt.Printf("b +⃗ a =\n%v", ba.Value())

Output:

a = [100  100]
b =
⎡1  1⎤
⎣2  2⎦

a + b yields an error: Failed to infer shape. Op: + false: Shape mismatch: (2) and (2, 2)

a +⃗ b =
⎡101  101⎤
⎣102  102⎦

b +⃗ a =
⎡101  101⎤
⎣102  102⎦

func BroadcastEq 

func BroadcastEq(a, b *Node, retSame bool, leftPattern, rightPattern []byte) (*Node, error)

Eq performs a eq. The operation is precomposed with a broadcast such that the shapes matches before operations commence.

func BroadcastGt 

func BroadcastGt(a, b *Node, retSame bool, leftPattern, rightPattern []byte) (*Node, error)

Gt performs a gt. The operation is precomposed with a broadcast such that the shapes matches before operations commence.

func BroadcastGte 

func BroadcastGte(a, b *Node, retSame bool, leftPattern, rightPattern []byte) (*Node, error)

Gte performs a gte. The operation is precomposed with a broadcast such that the shapes matches before operations commence.

Example (CreatingTriangleMatrices) 
// Broadcasting is useful. We can create triangular dense matrices simply

g := NewGraph()
a := NewMatrix(g, tensor.Float64, WithShape(3, 1), WithName("a"), WithInit(RangedFrom(0)))
b := NewMatrix(g, tensor.Float64, WithShape(1, 4), WithName("b"), WithInit(RangedFrom(0)))
tl, err := BroadcastGte(a, b, true, []byte{1}, []byte{0})
if err != nil {
	log.Fatalf("uh oh. Something went wrong %v", err)
}

tu, err := BroadcastLt(a, b, true, []byte{1}, []byte{0})
if err != nil {
	log.Fatalf("uh oh. Something went wrong %v", err)
}

m := NewTapeMachine(g)

// PEDAGOGICAL:
// Uncomment the following code if you want to see what happens behind the scenes
// m.Close()
// logger := log.New(os.Stderr, "",0)
// m = NewTapeMachine(g, WithLogger(logger), WithWatchlist())

defer m.Close()
if err = m.RunAll(); err != nil {
	log.Fatal(err)
}

fmt.Printf("triangular, lower:\n%v\n", tl.Value())
fmt.Printf("triangular, upper:\n%v\n", tu.Value())

Output:

triangular, lower:
⎡1  0  0  0⎤
⎢1  1  0  0⎥
⎣1  1  1  0⎦

triangular, upper:
⎡0  1  1  1⎤
⎢0  0  1  1⎥
⎣0  0  0  1⎦

func BroadcastHadamardDiv 

func BroadcastHadamardDiv(a, b *Node, leftPattern, rightPattern []byte) (*Node, error)

HadamardDiv performs a hadamarddiv. The operation is precomposed with a broadcast such that the shapes matches before operations commence.

func BroadcastHadamardProd 

func BroadcastHadamardProd(a, b *Node, leftPattern, rightPattern []byte) (*Node, error)

HadamardProd performs a hadamardprod. The operation is precomposed with a broadcast such that the shapes matches before operations commence.

func BroadcastLt 

func BroadcastLt(a, b *Node, retSame bool, leftPattern, rightPattern []byte) (*Node, error)

Lt performs a lt. The operation is precomposed with a broadcast such that the shapes matches before operations commence.

func BroadcastLte 

func BroadcastLte(a, b *Node, retSame bool, leftPattern, rightPattern []byte) (*Node, error)

Lte performs a lte. The operation is precomposed with a broadcast such that the shapes matches before operations commence.

func BroadcastNe 

func BroadcastNe(a, b *Node, retSame bool, leftPattern, rightPattern []byte) (*Node, error)

Ne performs a ne. The operation is precomposed with a broadcast such that the shapes matches before operations commence.

func BroadcastPow 

func BroadcastPow(a, b *Node, leftPattern, rightPattern []byte) (*Node, error)

Pow performs a pow. The operation is precomposed with a broadcast such that the shapes matches before operations commence.

func BroadcastSub 

func BroadcastSub(a, b *Node, leftPattern, rightPattern []byte) (*Node, error)

Sub performs a sub. The operation is precomposed with a broadcast such that the shapes matches before operations commence.

func Ceil 

func Ceil(a *Node) (*Node, error)

Ceil performs a pointwise ceil.

func Concat 

func Concat(axis int, ns ...*Node) (retVal *Node, err error)

Concat performs a concatenate on the provided axis and inputs.

Example 
g := NewGraph()
x := NewTensor(g, Float64, 4, WithShape(2, 3, 4, 5), WithInit(RangedFrom(0)), WithName("x"))
y := NewTensor(g, Float64, 4, WithShape(2, 3, 4, 5), WithInit(RangedFrom(120)), WithName("y"))

z, err := Concat(2, x, y)
if err != nil {
	log.Fatal(err)
}

m := NewTapeMachine(g)
if err := m.RunAll(); err != nil {
	log.Fatal(err)
}
tmp := fmt.Sprintf("z %v\n%v", z.Value().Shape(), z.Value())
fmt.Println(strings.Replace(tmp, "\n\n", "\n", -1)) // this is because

Output:

z (2, 3, 8, 5)
⎡  0    1    2    3    4⎤
⎢  5    6    7    8    9⎥
⎢ 10   11   12   13   14⎥
⎢ 15   16   17   18   19⎥
⎢120  121  122  123  124⎥
⎢125  126  127  128  129⎥
⎢130  131  132  133  134⎥
⎣135  136  137  138  139⎦

⎡ 20   21   22   23   24⎤
⎢ 25   26   27   28   29⎥
⎢ 30   31   32   33   34⎥
⎢ 35   36   37   38   39⎥
⎢140  141  142  143  144⎥
⎢145  146  147  148  149⎥
⎢150  151  152  153  154⎥
⎣155  156  157  158  159⎦

⎡ 40   41   42   43   44⎤
⎢ 45   46   47   48   49⎥
⎢ 50   51   52   53   54⎥
⎢ 55   56   57   58   59⎥
⎢160  161  162  163  164⎥
⎢165  166  167  168  169⎥
⎢170  171  172  173  174⎥
⎣175  176  177  178  179⎦

⎡ 60   61   62   63   64⎤
⎢ 65   66   67   68   69⎥
⎢ 70   71   72   73   74⎥
⎢ 75   76   77   78   79⎥
⎢180  181  182  183  184⎥
⎢185  186  187  188  189⎥
⎢190  191  192  193  194⎥
⎣195  196  197  198  199⎦

⎡ 80   81   82   83   84⎤
⎢ 85   86   87   88   89⎥
⎢ 90   91   92   93   94⎥
⎢ 95   96   97   98   99⎥
⎢200  201  202  203  204⎥
⎢205  206  207  208  209⎥
⎢210  211  212  213  214⎥
⎣215  216  217  218  219⎦

⎡100  101  102  103  104⎤
⎢105  106  107  108  109⎥
⎢110  111  112  113  114⎥
⎢115  116  117  118  119⎥
⎢220  221  222  223  224⎥
⎢225  226  227  228  229⎥
⎢230  231  232  233  234⎥
⎣235  236  237  238  239⎦

func Conv1d 

func Conv1d(in, filter *Node, kernel, pad, stride, dilation int) (*Node, error)

Conv1d is a 1D convlution. It relies on Conv2D

func Conv2d 

func Conv2d(im, filter *Node, kernelShape tensor.Shape, pad, stride, dilation []int) (retVal *Node, err error)

Conv2d is a simple 2D convoution, to be used for CPU computation only. If CuDNN is used, use the CUDAConv2D function. These are the properties the inputs must fulfil:

im: must have 4D shape. Expected format is BCHW (batch, channel, height, width) filter: must have 4D shape: (batch, kernel, height, width) kernelShape: shape of the filter kernel pad: len(pad) == 2 stride: len(stride) == 2 dilation: len(dilation) == 2

func Cos 

func Cos(a *Node) (*Node, error)

Cos performs a pointwise cos.

func Cube 

func Cube(a *Node) (*Node, error)

Cube performs a pointwise cube.

func Div 

func Div(a, b *Node) (retVal *Node, err error)

Div is a shortcut function for HadamardDiv for scalar values. For matrix/tensor values, the matrix division operation is not yet handled, and will panic.

func Dropout 

func Dropout(x *Node, dropProb float64) (retVal *Node, err error)

Dropout is a convenience function to implement dropout. It uses randomly zeroes out a *Tensor with a probability drawn from a uniform distribution

func Eq 

func Eq(a, b *Node, retSame bool) (*Node, error)

Eq performs a pointwise eq operation. retSame indicates if the data type of the return value should be the same as the input data type. It defaults to Bool otherwise.

func Exp 

func Exp(a *Node) (*Node, error)

Exp performs a pointwise exp.

func Expm1 

func Expm1(a *Node) (*Node, error)

Expm1 performs a pointwise expm1.

func Floor 

func Floor(a *Node) (*Node, error)

Floor performs a pointwise floor.

func GaussianRandomNode 

func GaussianRandomNode(g *ExprGraph, dt tensor.Dtype, mean, stdev float64, shape ...int) *Node

GaussianRandomNode creates an input node that has a random op so everytime the node is passed, random values will be plucked from a gaussian distribution with the mean and stdev provided. The type of the node depends on the shape passed in. To get a scalar value at run time, don't pass in any shapes

func GlobalAveragePool2D 

func GlobalAveragePool2D(x *Node) (*Node, error)

GlobalAveragePool2D consumes an input tensor X and applies average pooling across the values in the same channel. The expected input shape is BCHW where B is the batch size, C is the number of channels, and H and W are the height and the width of the data.

func Gt 

func Gt(a, b *Node, retSame bool) (*Node, error)

Gt performs a pointwise gt operation. retSame indicates if the data type of the return value should be the same as the input data type. It defaults to Bool otherwise.

func Gte 

func Gte(a, b *Node, retSame bool) (*Node, error)

Gte performs a pointwise gte operation. retSame indicates if the data type of the return value should be the same as the input data type. It defaults to Bool otherwise.

func HadamardDiv 

func HadamardDiv(a, b *Node) (*Node, error)

HadamardDiv performs a pointwise hadamarddiv operation.

func HadamardProd 

func HadamardProd(a, b *Node) (*Node, error)

HadamardProd performs a pointwise hadamardprod operation.

func Im2Col 

func Im2Col(n *Node, kernel, pad, stride, dilation tensor.Shape) (retVal *Node, err error)

Im2Col converts a BCHW image block to columns. The kernel, pad and stride parameter must be shape of size 2, no more no less This poor naming scheme clearly comes from matlab

func Inverse 

func Inverse(a *Node) (*Node, error)

Inverse performs a pointwise inverse.

func InverseSqrt 

func InverseSqrt(a *Node) (*Node, error)

InverseSqrt performs a pointwise inversesqrt.

func KeepDims 

func KeepDims(a *Node, expandLeft bool, fn func(a *Node) (*Node, error)) (*Node, error)

KeepDims is a function that ensures that input and output dimensions are the same though the shape may change.

The expandLeft flag in the function indicates if any shape expansion should be done leftwards or rightwards. For example, if fn() returns a tensor with a shape (3) and the desired dimension is 2, then if `expandLeft` is true the result will be `(1, 3)`. Otherwise the result will be `(3, 1)`.

At the moment, results that turn into scalars cannot have their dimensions kept - the semantics isn't well established yet and is a work in progress.

func LeakyRelu 

func LeakyRelu(x *Node, alpha float64) (*Node, error)

LeakyRelu returns a node whose underlying value is: 

f(x) = alpha * x if x < 0
f(x) = x for x ⩾ 0

applied elementwise.

func Log 

func Log(a *Node) (*Node, error)

Log performs a pointwise log.

func Log1p 

func Log1p(a *Node) (*Node, error)

Log1p performs a pointwise log1p.

func Log2 

func Log2(a *Node) (*Node, error)

Log2 performs a pointwise log2.

func LogSumExp 

func LogSumExp(a *Node, axis int) (retVal *Node, err error)

LogSumExp performs addition in the log domain

func Lt 

func Lt(a, b *Node, retSame bool) (*Node, error)

Lt performs a pointwise lt operation. retSame indicates if the data type of the return value should be the same as the input data type. It defaults to Bool otherwise.

func Lte 

func Lte(a, b *Node, retSame bool) (*Node, error)

Lte performs a pointwise lte operation. retSame indicates if the data type of the return value should be the same as the input data type. It defaults to Bool otherwise.

func Max 

func Max(a *Node, along ...int) (retVal *Node, err error)

Max performs a max() on the input and the provided axes.

func MaxPool1D 

func MaxPool1D(x *Node, kernel, pad, stride int) (*Node, error)

MaxPool1D applies a maxpool on the node x.

func MaxPool2D 

func MaxPool2D(x *Node, kernel tensor.Shape, pad, stride []int) (*Node, error)

MaxPool2D applies the kernel filter to the input node. The pad slice can have two different lengths.

  • if len(pad) == 2, padding is assume to be symetric, and a padding is adding up *and* down to each dimension paddedOutputH = pad[0] + inputH + pad[0] paddedOutputW = pad[1] + inputW + pad[1]
  • if len(pad) == 4, padding is explicit and can be asymmetric. paddedOutputH = pad[0] + inputH + pad[1] paddedOutputW = pad[2] + inputW + pad[3]

func Mean 

func Mean(a *Node, along ...int) (retVal *Node, err error)

Mean performs a mean() on the input and the provided axes.

func Mish added in v0.9.8 

func Mish(a *Node) (retVal *Node, err error)

Mish is a novel activation function that is self regularizing.

https://arxiv.org/abs/1908.08681

func Mul 

func Mul(a, b *Node) (retVal *Node, err error)

Mul is the general handler for multiplication of nodes. It is extremely overloaded. Only use if you know what you're doing

If any of the nodes are ScalarType, then it'll be redirected to HadamardProd() instead If the nodes are both vectors (that is, have a shape of (x, 1) or (1, x)), then the operator used will be a vectorDot If only one of the nodes is a vector, then the operator used will be a matrix-vector multiplication will be used, and most importantly, a transpose will be used (when necessary) If both nodes are matrices, then well, matrix multiplication will be done

func Must 

func Must(n *Node, err error, opts ...NodeConsOpt) *Node

Must indicates a node must be created. If there isn't a node created, or there was an error, it subsumes the error, and immediately panics

func Ne 

func Ne(a, b *Node, retSame bool) (*Node, error)

Ne performs a pointwise ne operation. retSame indicates if the data type of the return value should be the same as the input data type. It defaults to Bool otherwise.

func Neg 

func Neg(a *Node) (*Node, error)

Neg performs a pointwise neg.

func NegNegOptimization 

func NegNegOptimization(a *Node) (retVal *Node, err error)

NegNegOptimization optimizes away -(-x) to just return x place before neg

func NewConstant 

func NewConstant(v interface{}, opts ...NodeConsOpt) *Node

NewConstant takes in any reasonable value and makes it a constant node.

func NewMatrix 

func NewMatrix(g *ExprGraph, t tensor.Dtype, opts ...NodeConsOpt) *Node

NewMatrix creates a Node representing a variable that holds a matrix (nxm)

func NewScalar 

func NewScalar(g *ExprGraph, t tensor.Dtype, opts ...NodeConsOpt) *Node

NewScalar creates a Node representing a variable that holds a scalar value

func NewTensor 

func NewTensor(g *ExprGraph, t tensor.Dtype, dims int, opts ...NodeConsOpt) *Node

NewTensor creates a Node representing a variable that holds a tensor (any n-dimensional array with dimensions greater than 2)

func NewUniqueNode 

func NewUniqueNode(opts ...NodeConsOpt) *Node

NewUniqueNode creates a new unique node in a graph. If no graph was specified in the construction options then it will just return a graphless node.

func NewVector 

func NewVector(g *ExprGraph, t tensor.Dtype, opts ...NodeConsOpt) *Node

NewVector creates a Node representing a variable that holds a vector (nx1 matrix)

func NodeFromAny 

func NodeFromAny(g *ExprGraph, any interface{}, opts ...NodeConsOpt) *Node

NodeFromAny creates a Node from a tensor.Tensor, automatically filling in shape and type info

func Norm 

func Norm(a *Node, axis, p int) (retVal *Node, err error)

Norm returns the p-norm of a Value. Use p=2 if you want to use unordered norms.

This is a simpler version of the norms found in the Tensor package, which specializes and optimizes even more (well, given it's adapted from Numpy, it is clearly way more optimized)

func OneHotVector 

func OneHotVector(id, classes int, t tensor.Dtype, opts ...NodeConsOpt) *Node

OneHotVector creates a node representing a one hot vector

func OuterProd 

func OuterProd(a, b *Node) (retVal *Node, err error)

OuterProd returns a Node representing the outer product of two vectors. This function will return an error if both input nodes are not vectors

func Pow 

func Pow(a, b *Node) (*Node, error)

Pow performs a pointwise pow operation.

func Read 

func Read(n *Node, into *Value) (retVal *Node)

Read allows for extraction of the value of the *Node at runtime into a Value. To achieve this, a pointer to a Value (*Value) is passed into this function, not a Value. The 'into' value remains nil until the execution of the graph (via a call to the Run() methods of the VM)

func Rectify 

func Rectify(x *Node) (retVal *Node, err error)

Rectify is a convenience function for creating rectified linear units activation functions. This function uses ⩾, which is the canonical version. If you want to use >, you can create your own by just following this.

func ReduceAdd 

func ReduceAdd(nodes Nodes, opts ...NodeConsOpt) (retVal *Node, err error)

ReduceAdd takes a slice of *Nodes, and folds them into one by adding

func ReduceMul 

func ReduceMul(nodes Nodes, opts ...NodeConsOpt) (retVal *Node, err error)

ReduceMul is like foldl(*, nodes)

func Reshape 

func Reshape(n *Node, to tensor.Shape) (retVal *Node, err error)

Reshape reshapes a node and returns a new node with the new shape

func Set 

func Set(a, b *Node) (retVal *Node)

Set is the equivalent of doing this: 

a = b

where a and b are both variables

func Sigmoid 

func Sigmoid(a *Node) (*Node, error)

Sigmoid performs a pointwise sigmoid.

func Sign 

func Sign(a *Node) (*Node, error)

Sign performs a pointwise sign.

func Sin 

func Sin(a *Node) (*Node, error)

Sin performs a pointwise sin.

func SizeOf 

func SizeOf(axis int, x *Node) (retVal *Node, err error)

SizeOf returns the size of a value along an axis

func Slice 

func Slice(n *Node, slices ...tensor.Slice) (retVal *Node, err error)

Slice slices a *Node. For T[:] slices, pass in nil. Will error out if node's type is not a Tensor

func SoftMax 

func SoftMax(a *Node, axes ...int) (retVal *Node, err error)

SoftMax performs softmax on the input. Specifically this is used: 

e^(a[i]) / sum((e^(a[i])))

For a more numerically stable SoftMax, use StableSoftMax. TODO: MULTI RANK SOFTMAX

Example 
g := NewGraph()
t := tensor.New(tensor.WithShape(2, 3), tensor.WithBacking([]float64{1, 3, 2, 3, 2, 1}))
u := t.Clone().(*tensor.Dense)
v := tensor.New(tensor.WithShape(2, 2, 3), tensor.WithBacking([]float64{
	1, 3, 2,
	4, 2, 1,

	3, 5, 3,
	2, 1, 5,
}))

a := NodeFromAny(g, t, WithName("a"))
b := NodeFromAny(g, u, WithName("b"))
c := NodeFromAny(g, v, WithName("c"))

sm1 := Must(SoftMax(a))
sm0 := Must(SoftMax(b, 0))
sm := Must(SoftMax(c))
m := NewTapeMachine(g)
if err := m.RunAll(); err != nil {
	log.Fatal(err)
}
fmt.Printf("a:\n%v\nsoftmax(a) - along last axis (default behaviour):\n%1.2f", a.Value(), sm1.Value())
fmt.Printf("b:\n%v\nsoftmax(b) - along axis 0:\n%1.2f", b.Value(), sm0.Value())
tmp := fmt.Sprintf("c %v:\n%v\nsoftmax(c) - along last axis (default behaviour) %v:\n%1.2f", c.Value().Shape(), c.Value(), sm.Value().Shape(), sm.Value())
fmt.Println(strings.Replace(tmp, "\n\n\n", "\n\n", -1))
// the requirement to use tmp and strings.Replace is because when Go runs example tests, it strips excess newlines.

Output:

a:
⎡1  3  2⎤
⎣3  2  1⎦

softmax(a) - along last axis (default behaviour):
⎡0.09  0.67  0.24⎤
⎣0.67  0.24  0.09⎦
b:
⎡1  3  2⎤
⎣3  2  1⎦

softmax(b) - along axis 0:
⎡0.12  0.73  0.73⎤
⎣0.88  0.27  0.27⎦
c (2, 2, 3):
⎡1  3  2⎤
⎣4  2  1⎦

⎡3  5  3⎤
⎣2  1  5⎦

softmax(c) - along last axis (default behaviour) (2, 2, 3):
⎡0.09  0.67  0.24⎤
⎣0.84  0.11  0.04⎦

⎡0.11  0.79  0.11⎤
⎣0.05  0.02  0.94⎦

func Softplus 

func Softplus(a *Node) (*Node, error)

Softplus performs a pointwise softplus.

func Sqrt 

func Sqrt(a *Node) (*Node, error)

Sqrt performs a pointwise sqrt.

func Square 

func Square(a *Node) (*Node, error)

Square performs a pointwise square.

func StableSoftMax 

func StableSoftMax(a *Node) (retVal *Node, err error)

StableSoftMax performs a numerically stable softmax on the input. Specifically this is the formula used: 

e^(a - max(a)) / sum(e^(a - max(a)))

func Sub 

func Sub(a, b *Node) (*Node, error)

Sub performs a pointwise sub operation.

func Sum 

func Sum(a *Node, along ...int) (retVal *Node, err error)

Sum performs a sum() on the input and the provided axes.

func Tanh 

func Tanh(a *Node) (*Node, error)

Tanh performs a pointwise tanh.

func Tensordot 

func Tensordot(aAxes []int, bAxes []int, a, b *Node) (retVal *Node, err error)

Tensordot performs a tensor contraction of a and b along specified axes.

func Transpose 

func Transpose(n *Node, axes ...int) (retVal *Node, err error)

Transpose performs a transpose on the input and provided permutation axes.

func UniformRandomNode 

func UniformRandomNode(g *ExprGraph, dt tensor.Dtype, low, high float64, shape ...int) *Node

UniformRandomNode creates an input node that has a random op so everytime the node is passed, random values will be plucked from a uniform distribution. The type of the node depends on the shape passed in. To get a scalar value at run time, don't pass in any shapes

func Upsample2D added in v0.9.12 

func Upsample2D(x *Node, scale int) (*Node, error)

Upsample2D - simply upscaling Tensor by scale factor. 

1, 2
3, 4
converts to
1,1,2,2
1,1,2,2
3,3,4,4,
3,3,4,4,

func YOLOv3 added in v0.9.14 

func YOLOv3(input *Node, anchors []float32, masks []int, netSize, numClasses int, ignoreTresh float32, targets ...*Node) (*Node, error)

YOLOv3 https://arxiv.org/abs/1804.02767

func (*Node) Clone 

func (n *Node) Clone() (retVal interface{})

Clone clones the node. There are some caveats:

  • the graph is not copied over - the node essentially does not belong to a collection
  • there is no ID
  • the children are not cloned

func (*Node) CloneTo 

func (n *Node) CloneTo(g *ExprGraph) *Node

CloneTo clones the node into a new graph. If CloneTo() is called on the same graph as the n, it will return n. The reason this is done is because at any given time, every node should be unique in the *ExprGraph.

TODO: clone children as well (this means that CloneTo() is only currently suitable fo input nodes)

func (*Node) DataSize 

func (n *Node) DataSize() int

func (*Node) Deriv added in v0.9.11 

func (n *Node) Deriv() *Node

func (*Node) DerivOf added in v0.9.11 

func (n *Node) DerivOf() Nodes

func (*Node) Device 

func (n *Node) Device() Device

Device returns the device the data will be on

func (*Node) Dims 

func (n *Node) Dims() int

Dims indicates how many dimensions the node's result has

func (*Node) Dtype 

func (n *Node) Dtype() tensor.Dtype

Dtype returns the dtype of the node

func (*Node) Err 

func (n *Node) Err() error

Err always returns nil. However, this method is implemented to enable nicer composition of functions

func (*Node) Grad 

func (n *Node) Grad() (Value, error)

Grad returns the gradient if there is one.

func (*Node) GradOnDevice 

func (n *Node) GradOnDevice(dev Device, extern External) (retVal Value, allocOnExtern bool, err error)

GradOnDevice gets the gradient value of the node as a Value but on the desired device. In this build the device is always CPU, so it's equivalent to calling .Grad()

func (*Node) Graph 

func (n *Node) Graph() *ExprGraph

Graph returns the graph of the node

func (*Node) Groups 

func (n *Node) Groups() encoding.Groups

Groups to fulfil the encoding Grouper interface

func (*Node) Hashcode 

func (n *Node) Hashcode() uint32

Hashcode provides the hash for the tree, assuming that the node is the root of the tree. Original implementation was here by Vatine (who's apparently 80 years old and using SO!?!): 

http://stackoverflow.com/questions/1988665/hashing-a-tree-structure

func (*Node) ID 

func (n *Node) ID() int64

ID returns the ID of the node. This satisfies the gonum/graph.Node interface

func (*Node) IsColVec 

func (n *Node) IsColVec() bool

IsColVec indicates if a node represents a Column Vector. This is based on the type of the node, not the actual value associated with the node

func (*Node) IsMatrix 

func (n *Node) IsMatrix() bool

IsMatrix indicates if a node represents a matrix. This is based on the type of the node, not the actual value associated with the node

func (*Node) IsRowVec 

func (n *Node) IsRowVec() bool

IsRowVec indicates if a node represents a Row Vector. This is based on the type of the node, not the actual value associated with the node

func (*Node) IsScalar 

func (n *Node) IsScalar() bool

IsScalar indicates if a node represents a a scalar value. This is based on the type of the node, not the actual value associated with the node

func (*Node) IsVar 

func (n *Node) IsVar() bool

IsVar returns true if the node represents a differentiable variable (i.e. it's an argument to the function that is not a statement)

func (*Node) IsVec 

func (n *Node) IsVec() bool

IsVec returns whether this node is a vector

func (*Node) IsVector 

func (n *Node) IsVector() bool

IsVector indicates if a node represents a vector value. This is based on the type of the node, not the actual value associated with the node

func (*Node) Name 

func (n *Node) Name() string

Name returns the name of the node. If a name was specified and it is too long, the short name will be used instead (except in inputs)

The short name is typically of the form: OpName(%1, %2 ...), making it read more like a function call

func (*Node) Node 

func (n *Node) Node() *Node

Node returns itself. This sorts of monoidal patterns are useful for compositions via interfaces.

func (*Node) Nodes 

func (n *Node) Nodes() Nodes

Nodes returns n as a slice of *Node. Again, this is mostly useful for interfaces

func (*Node) Op 

func (n *Node) Op() Op

Op returns the Op of the node

func (*Node) RestrictedToDot 

func (n *Node) RestrictedToDot(up, down int) string

RestrictedToDot prints the graphviz compatible string but does not print the entire tree up and down indicates how many levels to look up, and how many levels to look down

func (*Node) Shape 

func (n *Node) Shape() tensor.Shape

Shape returns the shape of the node

func (*Node) Strides 

func (n *Node) Strides() []int

Strides returns the strides of the value of the node

func (*Node) String 

func (n *Node) String() string

String() implements the fmt.Stringer interface

func (*Node) ToDot 

func (n *Node) ToDot() string

ToDot returns the graph as a graphviz compatible string. DEPRECATED: This function will be removed in the next release, please use the encoding/dot package

func (*Node) Type 

func (n *Node) Type() hm.Type

Type returns the type of the node

func (*Node) Value 

func (n *Node) Value() Value

Value returns the valuse bound to the node. May return nil

func (*Node) ValueOnDevice 

func (n *Node) ValueOnDevice(dev Device, extern External) (retVal Value, allocOnExtern bool, err error)

ValueOnDevice gets the value of the node as a Value but on the desired device. In this build the device is always CPU, so it's equivalent to calling .Value()

func (*Node) WriteHash 

func (n *Node) WriteHash(h hash.Hash32)

WriteHash writes the hash to the provided Hash32.

type NodeConsOpt 

type NodeConsOpt func(*Node)

NodeConsOpt is a function that provides construction options for any Node.

func In 

func In(g *ExprGraph) NodeConsOpt

In is a node construction option to set a node's graph. A `*Node`'s graph is immutable. If the graph has already been set, a check will be made that the specifiec *Graph and the *Graph set in *Node are the same. If they are not, the function will panic/

func WithChildren 

func WithChildren(children Nodes) NodeConsOpt

WithChildren sets the children of a node to the specified chidren. This construction option does NOT check if existing children exists, and will overwrite the existing children.

func WithGrad 

func WithGrad(any interface{}) NodeConsOpt

WithGrad is a node construction option that binds the value to the *Node. This function may panic if:

  • There isn't already a value associated with the node (.boundTo == nil)
  • The type of the Value does not match the value of the node.

func WithGroupName 

func WithGroupName(name string) NodeConsOpt

WithGroupName is a node construction option to group a *Node within a particular group. This option is useful for debugging with graphs. This function is deprecated and will proabably be remove in the next version.

func WithInit 

func WithInit(fn InitWFn) NodeConsOpt

WithInit is a node construction option to initialize a *Node with the InitWFn provided.

func WithName 

func WithName(name string) NodeConsOpt

WithName is a node construction option that gives the *Node the provided name. This is especially useful in debugging graphs.

func WithOp 

func WithOp(op Op) NodeConsOpt

WithOp is a node construction option to set a node's Op to the specified Op. `Op`s in `*Node`s are immutable once set and cannot be changed. If the node already has an Op specified a check will be made to see if the provided Op and the one already specified in the `*Node` is the same - do note that comparison of Ops is done using the `Hashcode()` method of Ops, and hash collisions MAY occur - If both ops are different, this function will panic.

func WithShape 

func WithShape(shp ...int) NodeConsOpt

WithShape is a node construction option to initialize a *Node with a particular shape. This function panics if the shape's dimensions do not match the specified dimensions of the *Node.

func WithType 

func WithType(t hm.Type) NodeConsOpt

WithType is a node construction option to set a node to the specified type. Types in *Node are immutable once set. If the type has already been specified in the node, a check will be made to see if the both types are the same. If it isn't, it will panic.

func WithValue 

func WithValue(any interface{}) NodeConsOpt

WithValue is a node construction option that binds the value to the *Node. This function may panic if:

  • Gorgonia was unable to convert interface{} into a Value.
  • The type of the Value does not match the type of the nodes.

type NodeSet 

type NodeSet map[*Node]struct{}

NodeSet is the primary type that represents a set

func NewNodeSet 

func NewNodeSet(a ...*Node) NodeSet

NewNodeSet creates and returns a reference to an empty set.

func (NodeSet) Add 

func (set NodeSet) Add(i *Node) bool

Add adds an item to the current set if it doesn't already exist in the set.

func (NodeSet) Cardinality 

func (set NodeSet) Cardinality() int

Cardinality returns how many items are currently in the set.

func (*NodeSet) Clear 

func (set *NodeSet) Clear()

Clear clears the entire set to be the empty set.

func (NodeSet) Clone 

func (set NodeSet) Clone() NodeSet

Clone returns a clone of the set. Does NOT clone the underlying elements.

func (NodeSet) Contains 

func (set NodeSet) Contains(i *Node) bool

Contains determines if a given item is already in the set.

func (NodeSet) ContainsAll 

func (set NodeSet) ContainsAll(i ...*Node) bool

ContainsAll determines if the given items are all in the set

func (NodeSet) Difference 

func (set NodeSet) Difference(other NodeSet) NodeSet

Difference returns a new set with items in the current set but not in the other set

func (NodeSet) Equal 

func (set NodeSet) Equal(other NodeSet) bool

Equal determines if two sets are equal to each other. If they both are the same size and have the same items they are considered equal. Order of items is not relevant for sets to be equal.

func (NodeSet) Intersect 

func (set NodeSet) Intersect(other NodeSet) NodeSet

Intersect returns a new set with items that exist only in both sets.

func (NodeSet) IsSubset 

func (set NodeSet) IsSubset(other NodeSet) bool

IsSubset determines if every item in the other set is in this set.

func (NodeSet) IsSuperset 

func (set NodeSet) IsSuperset(other NodeSet) bool

IsSuperset determines if every item of this set is in the other set.

func (NodeSet) Iter 

func (set NodeSet) Iter() <-chan *Node

Iter returns a channel of type *Node that you can range over.

func (NodeSet) Remove 

func (set NodeSet) Remove(i *Node)

Remove allows the removal of a single item in the set.

func (NodeSet) SymmetricDifference 

func (set NodeSet) SymmetricDifference(other NodeSet) NodeSet

SymmetricDifference returns a new set with items in the current set or the other set but not in both.

func (NodeSet) ToSlice 

func (set NodeSet) ToSlice() Nodes

ToSlice returns the elements of the current set as a slice

func (NodeSet) Union 

func (set NodeSet) Union(other NodeSet) NodeSet

Union returns a new set with all items in both sets.

type Nodes 

type Nodes []*Node

Nodes is a slice of nodes, but it also acts as a set of nodes by implementing the Sort interface

func Backpropagate 

func Backpropagate(outputs, gradOutputs, wrt Nodes) (retVal Nodes, err error)

Backpropagate backpropagates errors by performing reverse-mode symbolic differentiation, starting from the outputs, and working its way towads the inputs.

This is the rough algorithm:

  1. Filter out nodes that are unreachable
  2. Forwards analysis, where a list of nodes affecting the output is added to consideration
  3. Backwards analysis, where a list of nodes affected by differentiating the output are added to the consideration
  4. If there is a difference in both sets, it will cause an error (both sets should be the same)
  5. Traverse the graph from output towards input. On each visit, perform the symbolic differentiation

For most cases, Grad() should be used instead of Backpropagate(), as Grad() performs several checks which would be the general use case, before calling Backpropagate()

func Grad 

func Grad(cost *Node, WRTs ...*Node) (retVal Nodes, err error)

Grad takes a scalar cost node and a list of with-regards-to, and returns the gradient

func NodesFromInputs 

func NodesFromInputs(xs ...Input) (Nodes, error)

NodesFromInputs creates a Nodes from a list of Input.

func Sort 

func Sort(g *ExprGraph) (sorted Nodes, err error)

Sort topologically sorts a ExprGraph: root of graph will be first nodes are sorted using gonum's SortStabilized function.

see https://godoc.org/gonum.org/v1/gonum/graph/topo#SortStabilized for more info

func Unconcat 

func Unconcat(a *Node, along int, n int) (Nodes, error)

Unconcat is the opposite of the built in concat function TODO: port this back to Gorgonia and use Gorgonia's sli instead

Example 
g := NewGraph()
x := NewTensor(g, Float64, 4, WithShape(2, 3, 4, 5), WithInit(RangedFrom(0)), WithName("x"))
y := NewTensor(g, Float64, 4, WithShape(2, 3, 4, 5), WithInit(RangedFrom(120)), WithName("y"))

z, err := Concat(2, x, y)
if err != nil {
	log.Fatal(err)
}

unconcats, err := Unconcat(z, 2, 2)
if err != nil {
	log.Fatal(err)
}
a, b := unconcats[0], unconcats[1]

m := NewTapeMachine(g)
if err := m.RunAll(); err != nil {
	log.Fatal(err)
}
tmp := fmt.Sprintf("a %v\n%v\nb %v\n%v", a.Value().Shape(), a.Value(), b.Value().Shape(), b.Value())
fmt.Println(strings.Replace(tmp, "\n\n", "\n", -1))

Output:

a (2, 3, 4, 5)
⎡  0    1    2    3    4⎤
⎢  5    6    7    8    9⎥
⎢ 10   11   12   13   14⎥
⎣ 15   16   17   18   19⎦

⎡ 20   21   22   23   24⎤
⎢ 25   26   27   28   29⎥
⎢ 30   31   32   33   34⎥
⎣ 35   36   37   38   39⎦

⎡ 40   41   42   43   44⎤
⎢ 45   46   47   48   49⎥
⎢ 50   51   52   53   54⎥
⎣ 55   56   57   58   59⎦

⎡ 60   61   62   63   64⎤
⎢ 65   66   67   68   69⎥
⎢ 70   71   72   73   74⎥
⎣ 75   76   77   78   79⎦

⎡ 80   81   82   83   84⎤
⎢ 85   86   87   88   89⎥
⎢ 90   91   92   93   94⎥
⎣ 95   96   97   98   99⎦

⎡100  101  102  103  104⎤
⎢105  106  107  108  109⎥
⎢110  111  112  113  114⎥
⎣115  116  117  118  119⎦

b (2, 3, 4, 5)
⎡120  121  122  123  124⎤
⎢125  126  127  128  129⎥
⎢130  131  132  133  134⎥
⎣135  136  137  138  139⎦

⎡140  141  142  143  144⎤
⎢145  146  147  148  149⎥
⎢150  151  152  153  154⎥
⎣155  156  157  158  159⎦

⎡160  161  162  163  164⎤
⎢165  166  167  168  169⎥
⎢170  171  172  173  174⎥
⎣175  176  177  178  179⎦

⎡180  181  182  183  184⎤
⎢185  186  187  188  189⎥
⎢190  191  192  193  194⎥
⎣195  196  197  198  199⎦

⎡200  201  202  203  204⎤
⎢205  206  207  208  209⎥
⎢210  211  212  213  214⎥
⎣215  216  217  218  219⎦

⎡220  221  222  223  224⎤
⎢225  226  227  228  229⎥
⎢230  231  232  233  234⎥
⎣235  236  237  238  239⎦

func UnstableSort 

func UnstableSort(g *ExprGraph) (sorted Nodes, err error)

UnstableSort performs a topological sort of the directed graph g returning the 'from' to 'to' sort order. If a topological ordering is not possible, an Unorderable error is returned listing cyclic components in g with each cyclic component's members sorted by ID. When an Unorderable error is returned, each cyclic component's topological position within the sorted nodes is marked with a nil graph.Node.

func (Nodes) Add 

func (ns Nodes) Add(n *Node) Nodes

Add adds to set

func (Nodes) AllSameGraph 

func (ns Nodes) AllSameGraph() bool

AllSameGraph returns true if all the nodes in the slice belong to the same graph. Note that constants do not have to belong to the same graph.

func (Nodes) Contains 

func (ns Nodes) Contains(want *Node) bool

Contains checks if the wanted node is in the set

func (Nodes) Difference 

func (ns Nodes) Difference(other Nodes) Nodes

Difference is ns - other. Bear in mind it is NOT commutative

func (Nodes) Equals 

func (ns Nodes) Equals(other Nodes) bool

Equals returns true if two Nodes are the same

func (Nodes) Err 

func (ns Nodes) Err() error

Err returns nil always

func (Nodes) Format 

func (ns Nodes) Format(s fmt.State, c rune)

Format implements fmt.Formatter, which allows Nodes to be differently formatted depending on the verbs

func (Nodes) Intersect 

func (ns Nodes) Intersect(other Nodes) Nodes

Intersect performs an intersection with other Nodes

func (Nodes) Len 

func (ns Nodes) Len() int

func (Nodes) Less 

func (ns Nodes) Less(i, j int) bool

func (Nodes) Node 

func (ns Nodes) Node() *Node

Node returns nil. Always. This is bound to cause a panic somewhere if an program is not using it correctly. The reason for implementing this is so that it may fulfil common interfaces.

func (Nodes) Nodes 

func (ns Nodes) Nodes() Nodes

Nodes returns itself. This is useful for interfaces

func (Nodes) Set 

func (ns Nodes) Set() Nodes

Set returns a uniquifies slice. It mutates the slice.

func (Nodes) Swap 

func (ns Nodes) Swap(i, j int)

type Op 

type Op interface {

	// Arity returns the number of inputs the Op expects. -1 indicates that it's n-ary and will be determined at runtime
	Arity() int

	// Informs the type of the Op (not the node). This will be used by the type system to infer the final type of the node
	Type() hm.Type

	// returns the output shape as a function of the inputs
	InferShape(...DimSizer) (tensor.Shape, error)

	// executes the op
	Do(...Value) (Value, error)

	// indicates if the Op will return a pointer (allowing possible inplace edits) or by value
	// if it's false, the return value of the Op will be a copy of its input
	ReturnsPtr() bool

	// Does this op potentially call external (cgo or cuda) functions (thereby requiring extra overhead for Go's trampolining thing)
	CallsExtern() bool

	// overwriteInput() is a method which states which input the output will be overwriting.
	// This allows for some efficiency gains as the underlying arrays wouldn't have to be re-allocated.
	// The method returns an int instead of a bool because potentially different operations may be allowed
	// to overwrite certain inputs. For example, consider an operation to increment a value:
	// the IncrementOp would be a unary operator, and assuming we would like to overwrite the input,
	// the retVal of overwriteInput() will be 0 (inputs[0]).
	// -1 is returned if overwriting of input is disallowed
	OverwritesInput() int

	/* Other methods */
	WriteHash(h hash.Hash)
	Hashcode() uint32
	fmt.Stringer
}

An Op is a symbolic representation of an operation Think of them as functions, taking an input (or multiple), and outputting something

All Ops have type signatures that look like this: 

OpName :: (Floats a) ⇒ Tensor a → Tensor a → Tensor a

type RMSPropSolver 

type RMSPropSolver struct {
	// contains filtered or unexported fields
}

RMSPropSolver is a solver that implements Geoffrey Hinton's RMSProp gradient descent optimization algorithm. http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf

func NewRMSPropSolver 

func NewRMSPropSolver(opts ...SolverOpt) *RMSPropSolver

NewRMSPropSolver creates an RMSProp solver with these default values: 

eta (learn rate)	  : 0.001
eps (smoothing factor): 1e-8
rho (decay factor)    : 0.999

func (*RMSPropSolver) Step 

func (s *RMSPropSolver) Step(model []ValueGrad) (err error)

Step steps through each node in the model and applies the RMSProp gradient descent algorithm on the value.

This function will error out if the nodes do not have an associated Grad value.

type ReductionOp 

type ReductionOp interface {
	Op

	IsReduction() bool
}

ReductionOp changes the shape of the node

type Result 

type Result interface {
	Input
	Errer
}

Result is either a Node or Nodes or error. It's a poor man's sum types and it's not sealed for good reason

func LiftResult 

func LiftResult(a Input, err error) Result

LiftResult creates a Result from a Input and error pair. If the error is not nil, the Input is discarded.

The usual use case is in a function that returns a `(*Node, error)`. e.g LiftResult(Add(a, b))

type SDOp 

type SDOp interface {
	Op

	// DiffWRT indicates if the op is differentiable with regards to the given number of inputs
	// returns []bool to indicate which input it is differentiable to
	DiffWRT(inputs int) []bool

	// SymDiff symbolically differentiates the op
	SymDiff(inputs Nodes, output, grad *Node) (retVal Nodes, err error)
}

A SDOp is an Op that supports symbolic differentiation

type Scalar 

type Scalar interface {
	Value
	// contains filtered or unexported methods
}

Scalar represents a scalar(non-array-based) value. Do note that it's the pointers of the scalar types (F64, F32, etc) that implement the Scalar interface. The main reason is primarily due to optimizations with regards to memory allocation and copying for device interoperability.

type Solver 

type Solver interface {
	Step([]ValueGrad) error
}

Solver is anything that does gradient updates. The name solvers is stolen from Caffe. A much shorter name than GradientUpdaters

type SolverOpt 

type SolverOpt func(s Solver)

SolverOpt is a function that provides construction options for a Solver

func WithBatchSize 

func WithBatchSize(batch float64) SolverOpt

WithBatchSize sets the batch size for the solver. Currently only Adam and Vanilla (basic SGD) has batch size support

func WithBeta1 

func WithBeta1(beta1 float64) SolverOpt

WithBeta1 sets the beta1 param of the solver. Only works with Adam

func WithBeta2 

func WithBeta2(beta2 float64) SolverOpt

WithBeta2 sets the beta1 param of the solver. Only works with Adam

func WithClip 

func WithClip(clip float64) SolverOpt

WithClip clips the gradient if it gets too crazy. By default all solvers do not have any clips attached

func WithEps 

func WithEps(eps float64) SolverOpt

WithEps sets the smoothing factor for the solver.

func WithL1Reg 

func WithL1Reg(l1reg float64) SolverOpt

WithL1Reg adds a L1 regularization parameter to the solver. By default, the solvers do not use any regularization param

func WithL2Reg 

func WithL2Reg(l2reg float64) SolverOpt

WithL2Reg adds a L2 regularization parameter to the solver. By default, the solvers do not use any regularization param

func WithLearnRate 

func WithLearnRate(eta float64) SolverOpt

WithLearnRate sets the learn rate or step size for the solver.

func WithMomentum 

func WithMomentum(momentum float64) SolverOpt

WithMomentum sets the momentum of the solver. It is a no-op is the solver's type is not Momentum

func WithRho 

func WithRho(rho float64) SolverOpt

WithRho sets the decay parameter of the RMSProp solver

type StandardEngine 

type StandardEngine struct {
	tensor.StdEng
}

StandardEngine is the default CPU engine for gorgonia

func (StandardEngine) Transpose 

func (e StandardEngine) Transpose(a tensor.Tensor, expStrides []int) error

Transpose tensor a according to expStrides

type SymDiffError 

type SymDiffError struct {
	// contains filtered or unexported fields
}

SymDiffError provides the context at which an error occurred

func (SymDiffError) Error 

func (err SymDiffError) Error() string

func (SymDiffError) Grad 

func (err SymDiffError) Grad() *Node

Grad returns a specific grad involved in the error

func (SymDiffError) Grads 

func (err SymDiffError) Grads() map[*Node]Nodes

Grads returns the grads involved in the error

func (SymDiffError) Node 

func (err SymDiffError) Node() *Node

Node returns a specific node involved in the error

func (SymDiffError) Nodes 

func (err SymDiffError) Nodes() Nodes

Nodes returns the nodes involved in the error

type Tensor 

type Tensor interface {
	// info about the ndarrayN
	Shape() tensor.Shape
	Strides() []int
	Dtype() tensor.Dtype
	Dims() int
	Size() int
	DataSize() int

	// type overloading methods
	IsScalar() bool
	ScalarValue() interface{}

	// engine/memory related stuff
	// all Tensors should be able to be expressed of as a slab of memory
	// Note: the size of each element can be acquired by T.Dtype().Size()
	Engine() tensor.Engine      // Engine can be nil
	MemSize() uintptr           // the size in memory
	Uintptr() uintptr           // the pointer to the first element, as a uintptr
	Pointer() unsafe.Pointer    // the pointer to the first elemment as a unsafe.Ponter
	IsNativelyAccessible() bool // Can Go access the memory
	IsManuallyManaged() bool    // Must Go manage the memory
}

Tensor is an interface that describes an ndarray

type TensorType 

type TensorType struct {
	Dims int // dims

	Of hm.Type
}

TensorType is a type constructor for tensors.

Think of it as something like this: 

data Tensor a = Tensor d a

The shape of the Tensor is not part of TensorType. Shape checking is relegated to the dynamic part of the program run

func (TensorType) Apply 

func (t TensorType) Apply(sub hm.Subs) hm.Substitutable

Apply applies the substitutions on the types. Satisfies the hm.Type interface.

func (TensorType) Eq 

func (t TensorType) Eq(other hm.Type) bool

Eq is the equality function of this type. The type of Tensor has to be the same, and for now, only the dimensions are compared. Shape may be compared in the future for tighter type inference. Satisfies the hm.Type interface.

func (TensorType) Format 

func (t TensorType) Format(state fmt.State, c rune)

Format implements fmt.Formatter. It is also required for the satisfication the hm.Type interface.

func (TensorType) FreeTypeVar 

func (t TensorType) FreeTypeVar() hm.TypeVarSet

FreeTypeVar returns any free (unbound) type variables in this type. Satisfies the hm.Type interface.

func (TensorType) Name 

func (t TensorType) Name() string

Name returns the name of the type, which will always be "Tensor". Satisfies the hm.Type interface.

func (TensorType) Normalize 

func (t TensorType) Normalize(k, v hm.TypeVarSet) (hm.Type, error)

Normalize normalizes the type variable names (if any) in the TensorType. Satisfies the hm.Type interface.

func (TensorType) String 

func (t TensorType) String() string

String implements fmt.Stringer and runtime.Stringer. Satisfies the hm.Type interface.

func (TensorType) Types 

func (t TensorType) Types() hm.Types

Types returns a list of types that TensorType contains - in this case, the type of Tensor (float64, float32, etc). Satisfies the hm.Type interface.

type Typer 

type Typer interface {
	Type() hm.Type
}

Typer represents any type (typically a Op) that knows its own Type

type U8 

type U8 byte

U8 represents a byte value.

func (*U8) Data 

func (v *U8) Data() interface{}

Data returns the original representation of the Value

func (*U8) Dtype 

func (v *U8) Dtype() tensor.Dtype

Dtype returns the Dtype of the value

func (*U8) Format 

func (v *U8) Format(s fmt.State, c rune)

Format implements fmt.Formatter

func (*U8) MemSize 

func (v *U8) MemSize() uintptr

MemSize satisfies the tensor.Memory interface

func (*U8) Pointer 

func (v *U8) Pointer() unsafe.Pointer

Pointer returns the pointer as an unsafe.Pointer. Satisfies the tensor.Memory interface

func (*U8) Shape 

func (v *U8) Shape() tensor.Shape

Shape returns a scalar shape for all scalar values

func (*U8) Size 

func (v *U8) Size() int

Size returns 0 for all scalar Values

func (*U8) Uintptr 

func (v *U8) Uintptr() uintptr

Uintptr satisfies the tensor.Memory interface

type UnaryOp 

type UnaryOp interface {
	Op

	IsUnary() bool
}

A UnaryOp is an Op that takes only one input

type UnsafeDoer 

type UnsafeDoer interface {
	UnsafeDo(inputs ...Value) (Value, error)
}

UnsafeDoer is an op that will overwrite the underlying value.

type UsePreallocDoer 

type UsePreallocDoer interface {
	UsePreallocDo(prealloc Value, inputs ...Value) (Value, error)
}

UsePreallocDoer is an op that works when a preallocated value is provided

type VM 

type VM interface {
	RunAll() error
	Reset()

	// Close closes all the machine resources (CUDA, if any, loggers if any)
	Close() error
}

VM represents a structure that can execute a graph or program. There are two VMs (both unexported):

  • *tapeMachine
  • *lispMachine

The *tapeMachine pre-compiles a graph into a list of instructions, then executes the instructions linearly and sequentially. The main tradeoff is dynamism. Graphs cannot be dynamically created on the fly as a re-compilation process is required (and compilation is relatively expensive). However, graphs executed with the *tapeMachine run much faster as plenty of optimizations has been done in the code generation stage.

The *lispMachine allows for graphs to be dynamically built and executed upon. The tradeoff is that executing a graph on *lispMachine is generally slower than on *tapeMachine, given the same static "image" of a graph.

type VMOpt 

type VMOpt func(m VM)

VMOpt is a VM creation option

func BindDualValues 

func BindDualValues(nodes ...*Node) VMOpt

BindDualValues is an option for *tapeMachine only. This is useful to set when using a Solver

func ExecuteBwdOnly 

func ExecuteBwdOnly() VMOpt

ExecuteBwdOnly creates a VM that will execute a graph by doing back propagation only. The assumption is of course, that the forward graph has already been executed, and there are already values associated with the nodes. This option is only for *lispMachine. Try it on any other VMs and it will panic.

func ExecuteFwdOnly 

func ExecuteFwdOnly() VMOpt

ExecuteFwdOnly creates a VM that will execute a graph forwards only - it will not do back propagation. This option is only for *lispMachine. Try it on any other VMs and it will panic.

func LogBothDir 

func LogBothDir() VMOpt

LogBothDir logs both directions of the execution of the graph. This option is only available for *lispMachine.

func LogBwd 

func LogBwd() VMOpt

LogBwd logs the backwards execution of a graph. This option is only for *lispMachine. Try it on any other VMs and it will panic.

func LogFwd 

func LogFwd() VMOpt

LogFwd logs the forward execution of a graph. This option is only for *lispMachine. Try it on any other VMs and it will panic.

func TraceExec 

func TraceExec() VMOpt

TraceExec is an option for *tapeMachine only. It stores an immutable copy of the executed value into the node, instead of a mutable value, which may be clobbered

func UseCudaFor 

func UseCudaFor(ops ...string) VMOpt

UseCudaFor is an option for *tapeMachine. This function is NO-OP unless the program is built with the `cuda` tag.

func WithEngine 

func WithEngine(e tensor.Engine) VMOpt

WithEngine sets the tensor engine for computation inside the VM.

func WithInfWatch 

func WithInfWatch() VMOpt

WithInfWatch creates a VM that will watch for Infs when executing. It watches for +Inf, -Inf and Inf. No choice there. This slows the execution down.

func WithLogger 

func WithLogger(logger *log.Logger) VMOpt

WithLogger creates a VM with the supplied logger. If the logger is nil, a default logger, writing to os.stderr will be created.

func WithManualGradient 

func WithManualGradient() VMOpt

WithManualGradient allows the user to set the gradient of the root, before backprop. The root gradients should be set using the SetDeriv method

func WithNaNWatch 

func WithNaNWatch() VMOpt

WithNaNWatch creates a VM that will watch for NaNs when executing. This slows the execution down.

func WithPrecompiled 

func WithPrecompiled(prog *program, locMap map[*Node]register) VMOpt

WithPrecompiled is an option to pass in compiled programs. This is useful for users who use the CompileFunction function

func WithValueFmt 

func WithValueFmt(format string) VMOpt

WithValueFmt defines how the logger will output the values. It defaults to "%3.3f"

func WithWatchlist 

func WithWatchlist(list ...interface{}) VMOpt

WithWatchlist creates a VM with a watchlist. When the execution touches the things in the watchlist, the VM's logger will the log it. This allows for watching and finetuning of the algorithm. When nothing is passed in, then the VM will default to watching and logging every single execution object.

The watchlist allows for different things to be watched, depending on VM type: 

*lispMachine will ONLY take *Node
*tapeMachine will take int (for register IDs) or *Node.

type Value 

type Value interface {
	Shape() tensor.Shape // Shape  returns the shape of the Value. Scalar values return ScalarShape()
	Size() int           // Size represents the number of elements in the Value. Note that in cases such as a *tensor.Dense, the underlying slice MAY have more elements than the Size() reports. This is correct.
	Data() interface{}   // Data returns the original representation of the Value
	Dtype() tensor.Dtype // Dtype returns the Dtype of the value

	tensor.Memory
	fmt.Formatter
}

Value represents a value that Gorgonia accepts. At this point it is implemented by:

  • all scalar value types (F64, F32... etc)
  • *tensor.Dense
  • *dualValue

A Value is essentially any thing that knows its own type and shape. Most importantly though, a Value is a pointer - and can be converted into a tensor.Memory. This is done for the sake of interoperability with external devices like cgo or CUDA or OpenCL. This also means for the most part most Values will be allocated on the heap. There are some performance tradeoffs made in this decision, but ultimately this is better than having to manually manage blocks of memory

func CloneValue 

func CloneValue(v Value) (Value, error)

CloneValue clones a value. For scalars, since Go copies scalars, it returns itself

func Copy 

func Copy(dest, src Value) (Value, error)

Copy copies the src values into dest values. For scalars, it just returns itself

func ScalarAsTensor 

func ScalarAsTensor(v Value, dims int, e tensor.Engine) Value

ScalarAsTensor returns the tensor representation of a scalar. It is particularly useful as a "reshape" of tensors of sorts

The Value passed in are either Scalar, tensor.Tensor, or *dualValue. Anything else will panic.

func ZeroValue 

func ZeroValue(v Value) Value

ZeroValue returns the zero value of a type

type ValueCloser 

type ValueCloser interface {
	ValueClose(interface{}) bool
}

ValueCloser represents any type that can perform a close-value check

type ValueEqualer 

type ValueEqualer interface {
	ValueEq(Value) bool
}

ValueEqualer represents any type that can perform a equal value check

type ValueGrad 

type ValueGrad interface {
	Valuer
	Grad() (Value, error)
}

ValueGrad is any type that has a value and a grad. This is used for Solvers

func NodesToValueGrads 

func NodesToValueGrads(in Nodes) (out []ValueGrad)

NodesToValueGrads is a utility function that converts a Nodes to a slice of ValueGrad for the solvers

type Valuer 

type Valuer interface {
	Value() Value
}

Valuer is any type that can return a Value

type VanillaSolver 

type VanillaSolver struct {
	// contains filtered or unexported fields
}

VanillaSolver is your bog standard stochastic gradient descent optimizer. There are no fancy features to this

func NewVanillaSolver 

func NewVanillaSolver(opts ...SolverOpt) *VanillaSolver

NewVanillaSolver creates a new VanillaSolver with sane-ish default values

func (*VanillaSolver) Step 

func (s *VanillaSolver) Step(model []ValueGrad) (err error)

Step steps through each node in the model and applies the most basic gradient descent algorithm on the value.

This function will error out if the nodes do not have an associated Grad value.

type ZeroValuer 

type ZeroValuer interface {
	Value
	ZeroValue() Value
}

ZeroValuer is a a Value that can provide the zero-value of its type

type Zeroer 

type Zeroer interface {
	Value
	Zero()
}

Zeroer is a Value that can zero itself

Source Files

View all Source files

Directories

Path Synopsis
Package blase is a thin wrapper over Gonum's BLAS interface that provides a queue so that cgo calls are batched.
 Package blase is a thin wrapper over Gonum's BLAS interface that provides a queue so that cgo calls are batched.
cmd
cudagen
genapi
gencudaengine
encoding
dot
Package dot creates a graphviz compatible version of the ExprGraph
 Package dot creates a graphviz compatible version of the ExprGraph
examples
286
charRNN
convnet
iris
iris/cmd
logisticregression
mnist
package mnist handles the mnist data set
 package mnist handles the mnist data set
stacked_autoencoder
tiny-yolo-v2-coco
tiny-yolo-v3-coco
internal
encoding
ops
nn
Package nnops implements some operators that have both a pure go implementation and a cuda implementation to use the cuda version, assuming that you have the pre-requisites, simply compile or run the code with the `cuda tag` go run -tags='cuda'
 Package nnops implements some operators that have both a pure go implementation and a cuda implementation to use the cuda version, assuming that you have the pre-requisites, simply compile or run the code with the `cuda tag` go run -tags='cuda'
x
dataviz
vm

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