primitiv Documentation

primitiv is a neural network library developed by National Institute of Information and Communications Technology (NICT) and Nara Institute of Science and Technology (NAIST). primitiv is written in C++11 and supports some other languages such as Python and Rust through bindings. primitiv allows users to write their own networks using a define-by-run style construction methods, and most features in the library is designed device-independent. Users can perform the own network using various computing backends such as Eigen, CUDA and OpenCL with no (or few) modifications of the original code.

Installing primitiv

This section describes how to install primitiv to your computer.

Prerequisites

primitiv is designed based on a device-independent policy, and you can choose dependencies between primitiv and other hardwares using build options.

For the minimal configuration (no other hardwares), primitiv requries below softwares/libraries:

For building unit tests, it requires below libraries:

For using specific hardwares, it requires some hardware-dependent libraries:

Installing primitiv from source (Debian/Ubuntu)

Installing common prerequisites

$ apt install build-essential cmake

Installing Eigen

Although you can install primitiv without any specific hardwares, we recommend to bind at least the Eigen backend to compute your neural networks much faster on CPUs.

$ apt install wget
$ cd /path/to/your/src
$ mkdir -p eigen
$ wget http://bitbucket.org/eigen/eigen/get/3.3.4.tar.bz2
$ tar -xf 3.3.4.tar.bz2 -C eigen --strip-components=1
$ rm 3.3.4.tar.bz2

Installing primitiv

To select primitiv versions to be installed, you can retrieve some archives from official releases.

$ cd /path/to/your/src
$ mkdir -p primitiv
$ wget https://github.com/primitiv/primitiv/archive/v0.3.1.tar.gz
$ tar -xf v0.3.1.tar.gz -C primitiv --strip-components=1
$ rm v0.3.1.tar.gz

Also, you can download a development (or other specific) branch using Git:

$ ce /path/to/your/src
$ apt install git
$ git clone https://github.com/primitiv/primitiv -b develop

Then we build primitiv using a standard process of CMake:

$ cd /path/to/your/src/primitiv
$ mkdir build
$ cd build
$ cmake ..
$ make
$ make install

make install will create libprimitiv.so in the system library directory and primitiv directory in the system include directory.

In some cases, you also need to add the path to the library directory to the ${LD_LIBRARY_PATH} environment variable:

$ export LD_LIBRARY_PATH=/path/to/your/lib:${LD_LIBRARY_PATH}

If we use the Eigen backend, specify both EIGEN3_INCLUDE_DIR and PRIMITIV_USE_EIGEN options to cmake:

$ cmake .. \
  -DEIGEN3_INCLUDE_DIR=/path/to/your/src/eigen \
  -DPRIMITIV_USE_EIGEN=ON

Installing primitiv with CUDA

$ cmake .. -DPRIMITIV_USE_CUDA=ON

The build process tries to find the CUDA Toolkit and the cuDNN library by default. You can also specify the explicit locations of their libraries if searching failed or you want to switch them:

$ cmake .. \
  -DCUDA_TOOLKIT_ROOT_DIR=/path/to/cuda \
  -DCUDNN_ROOT_DIR=/path/to/cuda \
  -DPRIMITIV_USE_CUDA=ON

Installing primitiv with OpenCL

Installing OpenCL C++ Headers

$ git clone https://github.com/KhronosGroup/OpenCL-CLHPP.git
$ cd OpenCL-CLHPP
$ mkdir build
$ cd build
$ cmake .. [OPTIONS]  # See: https://github.com/KhronosGroup/OpenCL-CLHPP
$ make && make install

Installing CLBlast

$ apt install wget
$ wget https://github.com/CNugteren/CLBlast/archive/1.2.0.tar.gz -O ./clblast.tar.gz
$ mkdir clblast
$ cd clblast
$ tar xf ../clblast.tar.gz --strip-components 1
$ mkdir build
$ cd build
$ cmake .. [OPTIONS]  # See: https://github.com/CNugteren/CLBlast
$ make && make install

Configuring primitiv with OpenCL

The following command configures to build the OpenCL backend using system libraries.

$ cmake .. -DPRIMITIV_USE_OPENCL=ON

The build process tries to find the OpenCL library, the OpenCL C++ headers, and the CLBlast library by default. You can also specify the explicit locations of their libraries if searching failed or you want to switch them:

$ cmake .. \
  -DOpenCL_INCLUDE_DIR=/path/to/opencl/include \
  -DOpenCL_LIBRARY=/path/to/libOpenCL.so \
  -DCLHPP_INCLUDE_DIR=/path/to/clhpp/include \
  -DCLBLAST_ROOT=/path/to/clblast/prefix \
  -DPRIMITIV_USE_OPENCL=ON

primitiv C++ Tutorials

This section describes tutorials to learn how to use primitiv in your C++ code..

Step-by-step Example: Solving the XOR Problem

This tutorial introduces a basic and common usage of the primitiv by making and training a simple network for a small classification problem.

Introduction: Problem Formulation

Following lines are the formulation of the problem used in this tutorial:

\[\begin{split}\begin{array}{rrcl} f: & \mathbb{R}^2 & \rightarrow & [-1, 1]; \\ f: & (x_1, x_2) & \mapsto & \left\{ \begin{array}{rl} 1, & \mathrm{if} \ \ x_1 x_2 \geq 0, \\ -1, & \mathrm{otherwise}, \end{array} \right. \end{array}\end{split}\]

where \(x_1, x_2 \in \mathbb{R}\). This is known as the XOR problem; \(f\) detects whether the signs of two arguments are same or not. We know that this problem is linearly non-separatable, i.e., the decision boundary of \(f\) can NOT be represented as a straight line on \(\mathbb{R}\): \(\alpha x_1 + \beta x_2 + \gamma = 0\), where \(\alpha, \beta, \gamma \in \mathbb{R}\).

For example, following code generates random data points \((x_1 + \epsilon_1, x_2 + \epsilon_2, f(x_1, x_2))\) according to this formulation with \(x_1, x_2 \sim \mathcal{N}(x; 0, \sigma_{\mathrm{data}})\) and \(\epsilon_1, \epsilon_2 \sim \mathcal{N}(\epsilon; 0, \sigma_{\mathrm{noise}})\):

#include <random>
#include <tuple>

class DataSource {
  std::mt19937 rng;
  std::normal_distribution<float> data_dist, noise_dist;

public:
  // Initializes the data provider with two SDs.
  DataSource(float data_sd, float noise_sd)
    : rng(std::random_device()())
    , data_dist(0, data_sd)
    , noise_dist(0, noise_sd) {}

  // Generates a data point
  std::tuple<float, float, float> operator()() {
    const float x1 = data_dist(rng);
    const float x2 = data_dist(rng);
    return std::make_tuple(
        x1 + noise_dist(rng),    // x1 + err
        x2 + noise_dist(rng),    // x2 + err
        x1 * x2 >= 0 ? 1 : -1);  // label
  }
};

Following graph is an actual sample generated by above class with data_sd is \(1\) and noise_sd is \(0.1\):

_images/xor_data.png

In this tutorial, we construct a 2-layers (input-hidden-output) perceptron to solve this problem. The whole model formulation is:

\[ \begin{align}\begin{aligned}y := \tanh (W_{hy} \boldsymbol{h} + b_y),\\\boldsymbol{h} := \tanh (W_{xh} \boldsymbol{x} + \boldsymbol{b}_h),\end{aligned}\end{align} \]

where \(y \in \mathbb{R}\) is an output value to be fit to \(f(x_1, x_2)\), \(\boldsymbol{x} := (x_1 \ x_2)^{\top} \in \mathbb{R}^2\) is an input vector, \(\boldsymbol{h} \in \mathbb{R}^N\) represents the \(N\)-dimentional hidden state of the network. There are also 4 free parameters: 2 matrices \(W_{hy} \in \mathbb{R}^{1 \times N}\) and \(W_{xh} \in \mathbb{R}^{N \times 2}\), and 2 bias (column) vectors \(b_y \in \mathbb{R}\) and \(\boldsymbol{b}_h \in \mathbb{R}^N\).

Include and Initialization

primitiv requires you to include primitiv/primitiv.h before using any features in the source code. All features in primitiv is enabled by including this header (available features are depending on specified options while building).

primitiv/primitiv.h basically may not affect the global namespace, and all features in the library is declared in the primitiv namespace. But for brevity, we will omit the primitiv namespace in this tutorial using the using namespace directives. Please pay attention to this point when you reuse these snippets.

#include <iostream>
#include <vector>
#include <primitiv/primitiv.h>

using namespace std;
using namespace primitiv;

int main() {

  // All code will be described here.

  return 0;
}

Before making our network, we need to create at least two objects: Device and Graph. Device objects specifies an actual computing backends (e.g., usual CPUs, CUDA, etc.) and memory usages for these backends. If you installed primitiv with no build options, you can initialize only primitiv::devices::Naive device object. Graph objects describe a temporary computation graph constructed by your code and provides methods to manage their graphs.

devices::Naive dev;
Graph g;

// "Eigen" device can be enabled when -DPRIMITIV_USE_EIGEN=ON
//devices::Eigen dev;

// "CUDA" device can be enabled when -DPRIMITIV_USE_CUDA=ON
//devices::CUDA dev(gpu_id);

Note that Device and Graph is not a singleton; you can also create any number of Device/Graph objects if necessary (even multiple devices share the same backend).

After initializing a Device and a Graph, we set them as the default device/graph used in the library.

Device::set_default(dev);
Graph::set_default(g);

For now, it is enough to know that these are just techniques to reduce coding efforts, and we don’t touch the details of ths function. For more details, please read the document about default objects.

Specifying Parameters and an Optimizer

Our network has 4 parameters described above: \(W_{xh}\), \(\boldsymbol{b}_h\), \(W_{hy}\) and \(b_y\). We first specify these parameters as Parameter objects:

constexpr unsigned N = 8;
Parameter pw_xh({N, 2}, initializers::XavierUniform());
Parameter pb_h({N}, initializers::Constant(0));
Parameter pw_hy({1, N}, initializers::XavierUniform());
Parameter pb_y({}, initializers::Constant(0));

Parameter objects basically take two arguments: shape and initializer. Shapes specify actual volume (and number of free variables) in the parameter, and initializer gives initial values of their variables. Above code uses the Xavier (Glorot) Initializer for matrices, and the constant \(0\) for biases.

Next we initialize an Optimizer object and register all parameters to train their values. We use simple SGD optimizer for now:

constexpr float learning_rate = 0.1;
optimizers::SGD opt(learning_rate);
opt.add(pw_xh, pb_h, pw_hy, pb_y);

Writing the Network

primitiv adopts the define-by-run style for writing neural networks. Users can write their own networks as usual C++ functions. Following code specifies the network described the above formulation using a lambda functor which takes and returns Node objects:

// 2-layers feedforward neural network
// `x` should be with `Shape({2}, B)`
auto feedforward = [&](const Node &x) {
  namespace F = primitiv::functions;
  const Node w_xh = F::parameter<Node>(pw_xh);       // Shape({N, 2})
  const Node b_h = F::parameter<Node>(pb_h);         // Shape({N})
  const Node w_hy = F::parameter<Node>(pw_hy);       // Shape({1, N})
  const Node b_y = F::parameter<Node>(pb_y);         // Shape({})
  const Node h = F::tanh(F::matmul(w_xh, x) + b_h);  // Shape({N}, B)
  return F::tanh(F::matmul(w_hy, h) + b_y);          // Shape({}, B)
};

Node objects represent an virtual results of network calculations which are returned by functions declared in the primitiv::functions namespace and can be used as an argument of their functions. Each Node has a shape, which represents the volume and the size of the minibatch of the Node. primitiv encapsulates the treatment of minibatches according to the minibatch broadcasting rule, and users can concentrate on writing the network structure without considering actual minibatch sizes.

We also describe a loss function about our network:

// Network for the squared loss function.
// `y` is that of returned from `feedforward()`
// `t` should be with `Shape({}, B)`
auto squared_loss = [](const Node &y, const Node &t) {
  namespace F = primitiv::functions;
  const Node diff = y - t;             // Shape({}, B)
  return F::batch::mean(diff * diff);  // Shape({})
};

Also, we write the network to generate input data from above DataSource class:

constexpr float data_sd = 1.0;
constexpr float noise_sd = 0.1;
DataSource data_source(data_sd, noise_sd);

auto next_data = [&](unsigned minibatch_size) {
  std::vector<float> data;
  std::vector<float> labels;
  for (unsigned i = 0; i < minibatch_size; ++i) {
    float x1, x2, t;
    std::tie(x1, x2, t) = data_source();
    data.emplace_back(x1);
    data.emplace_back(x2);
    labels.emplace_back(t);
  }

  namespace F = primitiv::functions;
  return std::make_tuple(
      F::input<Node>(Shape({2}, minibatch_size), data),    // input data `x`
      F::input<Node>(Shape({}, minibatch_size), labels));  // label data `t`
};

primitiv::functions::input takes shape and actual data (as a vector<float>) to make a new Node object. The order of data should be the column-major order, and the minibatch is treated as the last dimension w.r.t. the actual data. For example, the Node with Shape({2, 2}, 3) has 12 values:

\[\begin{split}\left( \begin{array}{cc} a_1 & b_1 \\ c_1 & d_1 \end{array} \right), \left( \begin{array}{cc} a_2 & b_2 \\ c_2 & d_2 \end{array} \right), \left( \begin{array}{cc} a_3 & b_3 \\ c_3 & d_3 \end{array} \right)\end{split}\]

and the actual data should be ordered as:

\[a_1, c_1, b_1, d_1, a_2, c_2, b_2, d_2, a_3, c_3, b_3, d_3.\]

Writing the Training Loop

Now we can perform actual training loop of our network:

for (unsigned epoch = 0; epoch < 100; ++epoch) {
  // Initializes the computation graph
  g.clear();

  // Obtains the next data
  Node x, t;
  std::tie(x, t) = next_data(1000);

  // Calculates the network
  const Node y = feedforward(x);

  // Calculates the loss
  const Node loss = squared_loss(y, t);
  std::cout << epoch << ": train loss=" << loss.to_float() << std::endl;

  // Performs backpropagation and updates parameters
  opt.reset_gradients();
  loss.backward();
  opt.update();
}

Above code uses Node.to_float(), which returns an actual single value stored in the Node (this function can be used only when the Node stores just one value).

You may get following results by running whole code described above (results may change randomly every time you launch the program):

0: loss=1.17221
1: loss=1.07423
2: loss=1.06282
3: loss=1.04641
4: loss=1.00851
5: loss=1.01904
6: loss=0.991312
7: loss=0.983432
8: loss=0.9697
9: loss=0.97692
...

Testing

Additionally, we launch a test process using a fixed data points in every 10 epochs:

  • \((1, 1) \mapsto 1\)
  • \((-1, 1) \mapsto -1\)
  • \((-1, -1) \mapsto 1\)
  • \((1, -1) \mapsto -1\)
for (unsigned epoch = 0; epoch < 100; ++epoch) {
  //
  // Training process written in the previous code block
  //

  if (epoch % 10 == 9) {
    namespace F = primitiv::functions;
    const Node test_x = F::input<Node>(Shape({2}, 4), {1, 1, -1, 1, -1, -1, 1, -1});
    const Node test_t = F::input<Node>(Shape({}, 4), {1, -1, 1, -1});
    const Node test_y = feedforward(test_x);
    const Node test_loss = squared_loss(test_y, test_t);
    std::cout << "test results:";
    for (float val : test_y.to_vector()) {
      std::cout << ' ' << val;
    }
    std::cout << "\ntest loss: " << test_loss.to_float() << std::endl;
  }
}

where Node.to_vector() returns all values stored in the Node.

Finally, you may get like below:

...
8: loss=0.933427
9: loss=0.927205
test results: 0.04619 -0.119208 0.0893511 -0.149148
test loss: 0.809695
10: loss=0.916669
11: loss=0.91744
...
18: loss=0.849496
19: loss=0.845048
test results: 0.156536 -0.229959 0.171106 -0.221599
test loss: 0.649342
20: loss=0.839679
21: loss=0.831217
...

We can see that the test results approaches correct values and the test loss becomes small by proceeding the training process.

Library Designs

This section describes concepts and designs of primitiv.

Header and Library Files

TBD.

Operation Rules with Minibatching

TBD.

Lazy Evaluation

TBD.

Devices

TBD.

Default Device and Graph

TBD.

Training

TBD.

Models

TBD.

Saving and Loading

TBD.

Nodes and Tensors

TBD.

primitiv Reference

This section contains low-level information about primitiv.

primitiv API Reference

Devices

Base Class
class Device : public primitiv::mixins::DefaultSettable<Device>, primitiv::mixins::Nonmovable<Device>

Interface of the Tensor provider.

Subclassed by primitiv::devices::CUDA, primitiv::devices::CUDA16, primitiv::devices::Eigen, primitiv::devices::Naive, primitiv::devices::OpenCL

Public Functions

virtual void dump_description() const = 0

Prints device description to stderr.

virtual DeviceType type() const = 0

Retrieves the type of the device.

Return
A DeviceType value.

Tensor new_tensor_by_constant(const Shape &shape, float k)

Provides a new Tensor object with same-value elements.

Return
A new Tensor object.
Parameters
  • shape: Shape of the tensor.
  • k: Constant to initialize elements.

Tensor new_tensor_by_array(const Shape &shape, const float values[])

Provides a new Tensor object with specific values.

Return
A new Tensor object.
Parameters
  • shape: Shape of the tensor.
  • values: Pointer to array of internal values.

Tensor new_tensor_by_vector(const Shape &shape, const std::vector<float> &values)

Provides a new Tensor object with specific values.

Return
A new Tensor object.
Parameters
  • shape: Shape of the tensor.
  • values: List of internal values.

Tensor copy_tensor(const Tensor &x)

Copies the tensor to this device with allocating a new memory.

Return
Copied tensor.
Remark
The value of x is always duplicated, and the internal memory of the resulting tensor becomes always different from x even if x.device() is same as this.
Parameters
  • x: A tensor to be copied.

void inplace_multiply_const(float k, Tensor &x)

Directly multiplies all elements by a constant.

Parameters
  • k: A constant to multiply.
  • x: A tensor to be updated.

void inplace_add(const Tensor &x, Tensor &y)

Directly adds the first tensor to the second tensor.

Remark
This method keeps the shape of y, and the behavior is conditioned according to the batch size of y and x: y.shape == x.shape: y += x y.shape == 1: y += batch_sum(x) x.shape == 1: y += batch_broadcast(x) otherwise: error.
Parameters
  • x: A tensor to add.
  • y: A tensor to be udpated.

void inplace_subtract(const Tensor &x, Tensor &y)

Directly subtracts the first tensor from the second tensor.

Remark
The batch broadcasting behavior of this method is same as that of inplace_add.
Parameters
  • x: A tensor to subtract.
  • y: A tensor to be updated.

Inherited Classes
class Naive : public primitiv::Device

Device class for the naive function implementations on CPU.

Public Functions

Naive()

Creates a Naive object.

Naive(std::uint32_t seed)

Creates a Naive object.

Parameters
  • seed: The seed value of internal random number generator.

void dump_description() const

Prints device description to stderr.

DeviceType type() const

Retrieves the type of the device.

Return
A DeviceType value.

class Eigen : public primitiv::Device

Device class for the Eigen3 backend.

Public Functions

Eigen()

Creates a Eigen object.

Eigen(std::uint32_t seed)

Creates a Eigen object.

Parameters
  • seed: The seed value of internal random number generator.

void dump_description() const

Prints device description to stderr.

DeviceType type() const

Retrieves the type of the device.

Return
A DeviceType value.

class CUDA : public primitiv::Device

Device class for CUDA.

Public Functions

CUDA(std::uint32_t device_id)

Creates a new CUDA device.

Remark
The random number generator is initialized using std::random_device.
Parameters
  • device_id: ID of the physical GPU.

CUDA(std::uint32_t device_id, std::uint32_t rng_seed)

Creates a new CUDA device.

Parameters
  • device_id: ID of the physical GPU.
  • rng_seed: The seed value of the random number generator.

void dump_description() const

Prints device description to stderr.

DeviceType type() const

Retrieves the type of the device.

Return
A DeviceType value.

Public Static Functions

static std::uint32_t num_devices()

Retrieves the number of active hardwares.

Return
Number of active hardwares.

static void assert_support(std::uint32_t device_id)

Checks whether the device corresponding to the specified ID is supported.

Parameters
  • device_id: Device ID to check.
Exceptions
  • primitiv::Error: This class does not support the specified device.

static bool check_support(std::uint32_t device_id)

Checks whether the device corresponding to the specified ID is supported.

Return
true if this class supports the specified device, false otherwise.
Parameters
  • device_id: Device ID to check.

class OpenCL : public primitiv::Device

Device class for OpenCL.

Public Functions

OpenCL(std::uint32_t platform_id, std::uint32_t device_id)

Creates a new OpenCL device.

Parameters
  • platform_id: Platform ID.
  • device_id: Device ID on the selected platform.

OpenCL(std::uint32_t platform_id, std::uint32_t device_id, std::uint32_t rng_seed)

Creates a new OpenCL device.

Parameters
  • platform_id: Platform ID.
  • device_id: Device ID on the selected platform.
  • rng_seed: Seed value of the random number generator.

void dump_description() const

Prints device description to stderr.

DeviceType type() const

Retrieves the type of the device.

Return
A DeviceType value.

Public Static Functions

static std::uint32_t num_platforms()

Retrieves the number of active platforms.

Return
Number of active platforms.

static std::uint32_t num_devices(std::uint32_t platform_id)

Retrieves the number of active devices on the specified platform.

Return
Number of active devices.
Parameters
  • platform_id: Platform ID. This value should be between 0 to num_platforms() - 1.

static void assert_support(std::uint32_t platform_id, std::uint32_t device_id)

Checks whether the device corresponding to the specified IDs is supported.

Parameters
  • platform_id: Platform ID to check.
  • device_id: Device ID to check.
Exceptions
  • primitiv::Error: This class does not support the specified device.

static bool check_support(std::uint32_t platform_id, std::uint32_t device_id)

Checks whether the device corresponding to the specified ID is supported.

Return
true if this class supports the specified device, false otherwise.
Parameters
  • platform_id: Platform ID to check.
  • device_id: Device ID to check.

Functions

This page describes the basic/composite functions implemented in primitiv. They return a template type Var, and take 0 or more number of references of Var as their arguments. Var becomes either Node or Tensor according to the usage:

primitiv::Node x = ...;
primitiv::Tensor w = ...;
auto y = primitiv::functions::tanh(x);  // `y` becomes a `Node`.
auto u = primitiv::functions::exp(w);  // `u` becomes a `Tensor`.

If the function has no argument with type Var, you must specify the template argument appropriately:

auto x = primitiv::functions::input<Node>(...);  // `x` becomes a `Node`.
auto w = primitiv::functions::parameter<Tensor>(...);  // `w` becomes a `Tensor`.
namespace functions

Functions

template <typename Var>
type_traits::Identity<Var> selu(const Var &x, float a = 1.6732632423543772848170429916717, float s = 1.0507009873554804934193349852946)

Applies an elementwise scaled ELU function:

\[\begin{split} \mathrm{SELU}(x) := s \times \left\{ \begin{array}{ll} x, & \mathrm{if} \ x \geq 0, \\ \alpha (e^x - 1), & \mathrm{otherwise}. \end{array} \right. \end{split}\]
Return
A variable representing \( \mathrm{SELU}(x) \).
Remark
This function is implemented as a composite of some other functions.
Parameters
  • x: A variable representing an argument \( x \).
  • a: A scaling factor \( \alpha \).
  • s: Another scaling factor \( s \).

template <typename Container>
type_traits::Reduce<Container> sum(const Container &xs)

Applies summation along variables in the container.

Return
A new variable.
Remark
This function is implemented as a composite of some other functions.
Parameters
  • xs: Iterable container of variables. xs must have both begin() and end() functions that return the begin/end iterators.

template <typename Container>
type_traits::ReducePtr<Container> sum(const Container &xs)

Same as above, but xs has pointers of variables.

Return
A new variable.
Remark
This function is implemented as a composite of some other functions.
Parameters
  • xs: Iterable container of pointers of variables. xs must have both begin() end end() functions that return the begin/end iterators.

template <typename Var>
type_traits::Identity<Var> mean(const Var &x, std::uint32_t dim)

Calculates means along an axis.

Return
A new variable.
Remark
This function is implemented as a composite of some other functions.
Parameters
  • x: A variable representing values before reduction.
  • dim: Axis to be processed.

template <typename Container>
type_traits::Reduce<Container> mean(const Container &xs)

Calculates means along variables in the container.

Return
A new variable.
Remark
This function is implemented as a composite of some other functions.
Parameters
  • xs: Iterable container of variables. xs must have both begin() and end() functions that return the begin/end iterators.

template <typename Container>
type_traits::ReducePtr<Container> mean(const Container &xs)

Same as above, but xs has pointers of variables.

Return
A new variable.
Remark
This function is implemented as a composite of some other functions.
Parameters
  • xs: Iterable container of pointers of variables. xs must have both begin() end end() functions that return the begin/end iterators.

Tensor zeros_tensor(const Shape &shape, Device *dev)

Creates a new Tensor with all values \( 0 \).

Return
A new Tensor.
Remark
This function is implemented as a composite of some other functions.
Parameters

Node zeros_node(const Shape &shape, Device *dev, Graph *g)

Creates a new Node with all values \( 0 \).

Return
A new Node.
Remark
This function is implemented as a composite of some other functions.
Parameters
  • shape: Shape of the new Node.
  • dev: Device to manage the new Node, or nullptr to use the default device.
  • g: Graph to manage the instance of the Node, or nullptr to use the default graph.

template <typename Var>
type_traits::Identity<Var> zeros(const Shape &shape, Device *dev)

Creates a new variable with all values \( 0 \).

Return
A new variable.
Remark
This function uses the default graph when specifying Node as the template variable.
Remark
This function is implemented as a composite of some other functions.
Parameters
  • shape: Shape of the new variable.
  • dev: Device to manage the new variable, or nullptr to use the default defice.

template <typename Var>
type_traits::Identity<Var> zeros(const Shape &shape, Device &dev)

Creates a new variable with all values \( 0 \).

Return
A new variable.
Remark
This function uses the default graph when specifying Node as the template variable.
Remark
This function is implemented as a composite of some other functions.
Parameters
  • shape: Shape of the new variable.
  • dev: Device to manage the new variable.

template <typename Var>
type_traits::Identity<Var> zeros(const Shape &shape)

Creates a new variable with all values \( 0 \).

Return
A new variable.
Remark
This function always uses the default device, and also uses the default graph when specifying Node as the template variable.
Remark
This function is implemented as a composite of some other functions.
Parameters
  • shape: Shape of the new variable.

Tensor ones_tensor(const Shape &shape, Device *dev)

Creates a new Tensor with all values \( 1 \).

Return
A new Tensor.
Remark
This function is implemented as a composite of some other functions.
Parameters

Node ones_node(const Shape &shape, Device *dev, Graph *g)

Creates a new Node with all values \( 1 \).

Return
A new Node.
Remark
This function is implemented as a composite of some other functions.
Parameters
  • shape: Shape of the new Node.
  • dev: Device to manage the new Node, or nullptr to use the default device.
  • g: Graph to manage the instance of the Node, or nullptr to use the default graph.

template <typename Var>
type_traits::Identity<Var> ones(const Shape &shape, Device *dev)

Creates a new variable with all values \( 1 \).

Return
A new variable.
Remark
This function uses the default graph when specifying Node as the template variable.
Remark
This function is implemented as a composite of some other functions.
Parameters
  • shape: Shape of the new variable.
  • dev: Device to manage the new variable, or nullptr to use the default defice.

template <typename Var>
type_traits::Identity<Var> ones(const Shape &shape, Device &dev)

Creates a new variable with all values \( 1 \).

Return
A new variable.
Remark
This function uses the default graph when specifying Node as the template variable.
Remark
This function is implemented as a composite of some other functions.
Parameters
  • shape: Shape of the new variable.
  • dev: Device to manage the new variable.

template <typename Var>
type_traits::Identity<Var> ones(const Shape &shape)

Creates a new variable with all values \( 1 \).

Return
A new variable.
Remark
This function always uses the default device, and also uses the default graph when specifying Node as the template variable.
Remark
This function is implemented as a composite of some other functions.
Parameters
  • shape: Shape of the new variable.

template <typename Var>
type_traits::Identity<Var> dropout(const Var &x, float rate, bool enabled)

Applies the dropout:

\[\begin{split} \begin{array}{rcl} w & \sim & \mathrm{Bernoulli}(w; 1 - r), \\ \mathrm{dropout}(x) & := & \frac{1}{1 - r} \times w \times x. \end{array} \end{split}\]
Return
A new variable.
Remark
This function is implemented as a composite of some other functions.
Parameters
  • x: A variable representing original values.
  • rate: The dropout probability \( r \). 0 maintains all values and 1 discards all values.
  • enabled: If true, this function applies the operation. Otherwise, this function performs nothing.

template <typename Var>
type_traits::Identity<Var> positive(const Var &x)

Applies a unary \( + \) operation. This function does not change any values of the argument, and returns a copy of it.

Return
A variable representing \( +x \).
Parameters
  • x: A variable representing an argument \( x \).

template <typename Var>
type_traits::Identity<Var> negative(const Var &x)

Applies a unary \( - \) operation.

Return
A variable representing \( -x \).
Parameters
  • x: A variable representing an argument \( x \).

template <typename Var>
type_traits::Identity<Var> add(const Var &x, float k)

Applies an elementwise addition between a variable and a constant.

Return
A variable representing \( x + k \).
Parameters
  • x: A variable representing an argument \( x \).
  • k: A constant \( k \).

template <typename Var>
type_traits::Identity<Var> add(float k, const Var &x)

Applies an elementwise addition between a constant and a variable.

Return
A variable representing \( k + x \).
Parameters
  • k: A constant \( k \).
  • x: A variable representing an argument \( x \).

template <typename Var>
type_traits::Identity<Var> add(const Var &a, const Var &b)

Applies an elementwise addition between two variables.

Return
A variable representing \( a + b \).
Parameters
  • a: A variable representing an argument \( a \).
  • b: A variable representing an argument \( b \).

template <typename Var>
type_traits::Identity<Var> subtract(const Var &x, float k)

Applies an elementwise subtraction between a variable and a constant.

Return
A variable representing \( x - k \).
Parameters
  • x: A variable representing an argument \( x \).
  • k: A constant \( k \).

template <typename Var>
type_traits::Identity<Var> subtract(float k, const Var &x)

Applies an elementwise subtraction between a constant and a variable.

Return
A variable representing \( k - x \).
Parameters
  • k: A constant \( k \).
  • x: A variable representing an argument \( x \).

template <typename Var>
type_traits::Identity<Var> subtract(const Var &a, const Var &b)

Applies an elementwise subtraction between two variables.

Return
A variable representing \( a - b \).
Parameters
  • a: A variable representing an argument \( a \).
  • b: A variable representing an argument \( b \).

template <typename Var>
type_traits::Identity<Var> multiply(const Var &x, float k)

Applies an elementwise multiplication between a variable and a constant.

Return
A variable representing \( x \times k \).
Parameters
  • x: A variable representing an argument \( x \).
  • k: A constant \( k \).

template <typename Var>
type_traits::Identity<Var> multiply(float k, const Var &x)

Applies an elementwise multiplication between a constant and a variable.

Return
A variable representing \( k \times x \).
Parameters
  • k: A constant \( k \).
  • x: A variable representing an argument \( x \).

template <typename Var>
type_traits::Identity<Var> multiply(const Var &a, const Var &b)

Applies an elementwise multiplication between two variables.

Return
A variable representing \( a \times b \).
Parameters
  • a: A variable representing an argument \( a \).
  • b: A variable representing an argument \( b \).

template <typename Var>
type_traits::Identity<Var> divide(const Var &x, float k)

Applies an elementwise division between a variable and a constant.

Return
A variable representing \( x / k \).
Parameters
  • x: A variable representing an argument \( x \).
  • k: A constant \( k \).

template <typename Var>
type_traits::Identity<Var> divide(float k, const Var &x)

Applies an elementwise division between a constant and a variable.

Return
A variable representing \( k / x \).
Parameters
  • k: A constant \( k \).
  • x: A variable representing an argument \( x \).

template <typename Var>
type_traits::Identity<Var> divide(const Var &a, const Var &b)

Applies an elementwise division between two variables.

Return
A variable representing \( a / b \).
Parameters
  • a: A variable representing an argument \( a \).
  • b: A variable representing an argument \( b \).

template <typename Var>
type_traits::Identity<Var> pow(const Var &x, float k)

Applies an elementwise exponentation between a variable and a constant.

Return
A variable representing \( x^k \).
Parameters
  • x: A variable representing an argument \( x \).
  • k: A constant \( k \).

template <typename Var>
type_traits::Identity<Var> pow(float k, const Var &x)

Applies an elementwise exponentation between a constant and a variable.

Return
A variable representing \( k^x \).
Parameters
  • k: A constant \( k \).
  • x: A variable representing an argument \( x \).

template <typename Var>
type_traits::Identity<Var> pow(const Var &a, const Var &b)

Applies an elementwise exponentation between two variables.

Return
A variable representing \( a^b \).
Parameters
  • a: A variable representing an argument \( a \).
  • b: A variable representing an argument \( b \).

template <typename Var>
type_traits::Identity<Var> pown(const Var &x, std::int32_t k)

Applies an elementwise exponentation between a variable and an integer constant. This function can be applied correctly when x has some negative values.

Return
A variable representing \( x^k \).
Parameters
  • x: A variable representing an argument \( x \).
  • k: An integer constant \( k \).

Tensor input_tensor(const Shape &shape, const std::vector<float> &data, Device *dev)

Creates a new Tensor from specific shape and data.

Return
A new Tensor.
Parameters
  • shape: Shape of the new Tensor.
  • data: Inner data of the new Tensor. data.size() should be equal to shape.size() and each data is ordered by the column-major order.
  • dev: Device to manage inner data of the Tensor, or nullptr to use the default device.

Node input_node(const Shape &shape, const std::vector<float> &data, Device *dev, Graph *g)

Creates a new Node from specific shape and data.

Return
A new Node.
Parameters
  • shape: Shape of the new Node.
  • data: Inner data of the new Node. data.size() should be equal to shape.size() and each data is ordered by the column-major order.
  • dev: Device to manage inner data of the Node, or nullptr to use the default device.
  • g: Graph to manage the instance of the Node, or nullptr to use the default graph.

template <typename Var>
type_traits::Identity<Var> input(const Shape &shape, const std::vector<float> &data, Device *dev)

Creates a new variable from specific shape and data.

Return
A new variable.
Remark
This function uses the default graph when specifying Node as the template variable.
Parameters
  • shape: Shape of the new variable.
  • data: Inner data of the new variable. data.size() should be equal to shape.size() and each data is ordered by the column-major order.
  • dev: Device to manage inner data of the variable, or nullptr to use the default device.

template <typename Var>
type_traits::Identity<Var> input(const Shape &shape, const std::vector<float> &data, Device &dev)

Creates a new variable from specific shape and data.

Return
A new variable.
Remark
This function uses the default graph when specifying Node as the template variable.
Parameters
  • shape: Shape of the new variable.
  • data: Inner data of the new variable. data.size() should be equal to shape.size() and each data is ordered by the column-major order.
  • dev: Device to manage inner data of the variable.

template <typename Var>
type_traits::Identity<Var> input(const Shape &shape, const std::vector<float> &data)

Creates a new variable from specific shape and data.

Return
A new variable.
Remark
This function always uses the default device, and also uses the default graph when specifying Node as the template variable.
Parameters
  • shape: Shape of the new variable.
  • data: Inner data of the new variable. data.size() should be equal to shape.size() and each data is ordered by the column-major order.

Tensor parameter_tensor(Parameter &param)

Creates a new Tensor from a specific Parameter.

Return
A new Tensor.
Parameters

Node parameter_node(Parameter &param, Graph *g)

Creates a new Node from a specific Parameter.

Return
A new Node.
Parameters
  • param: Parameter to be associated with the Node.
  • g: Graph to manage the instance of the Node, or nullptr to use the default graph.

template <typename Var>
type_traits::Identity<Var> parameter(Parameter &param)

Creates a new variable from a specific Parameter.

Return
A new variable.
Remark
This function uses the default graph when specifying Node as the template variable.
Parameters
  • param: Parameter to be associated with the variable.

template <typename Var>
type_traits::Identity<Var> copy(const Var &x, Device *dev)

Copies a variable onto a specific device.

Return
A new variable managed on dev.
Parameters
  • x: A variable to be copied.
  • dev: Device to manage the new variable, or nullptr to use the default device.

template <typename Var>
type_traits::Identity<Var> copy(const Var &x, Device &dev)

Copies a variable onto a specific device.

Return
A new variable managed on dev.
Parameters
  • x: A variable to be copied.
  • dev: Device to manage the new variable.

template <typename Var>
type_traits::Identity<Var> copy(const Var &x)

Copies a variable onto the default device.

Return
A new variable managed on the default device.
Parameters
  • x: A variable to be copied.

template <typename Var>
type_traits::Identity<Var> pick(const Var &x, const std::vector<std::uint32_t> &ids, std::uint32_t dim)

Lookups subplanes according to the specific axis and addresses. This function can be used to an embedding lookup associated with a fixed vocabulary. Following examples show how this function work:

\[\begin{split} \begin{array}{lcl} x & := & \left( \begin{array}{ccc} 1 & 4 & 7 \\ 2 & 5 & 8 \\ 3 & 6 & 9 \end{array} \right), \\ \mathrm{pick}(x, [0, 0, 1], 0) & = & \left( \begin{array}{ccc} 1 & 4 & 7 \end{array} \right), \left( \begin{array}{ccc} 1 & 4 & 7 \end{array} \right), \left( \begin{array}{ccc} 2 & 5 & 8 \end{array} \right), \\ \mathrm{pick}(x, [1, 2], 1) & = & \left( \begin{array}{c} 4 \\ 5 \\ 6 \end{array} \right), \left( \begin{array}{c} 7 \\ 8 \\ 9 \end{array} \right), \\ \mathrm{pick}(x, [0], 2) & = & \left( \begin{array}{ccc} 1 & 4 & 7 \\ 2 & 5 & 8 \\ 3 & 6 & 9 \end{array} \right). \end{array} \end{split}\]
The minibatch broadcasting rule is applied between the Shape of x and the number of values in ids:
\[\begin{split} \begin{array}{lcl} x & := & \left( \begin{array}{ccc} 1 & 4 & 7 \\ 2 & 5 & 8 \\ 3 & 6 & 9 \end{array} \right), \left( \begin{array}{ccc} 11 & 14 & 17 \\ 12 & 15 & 18 \\ 13 & 16 & 19 \end{array} \right), \left( \begin{array}{ccc} 21 & 24 & 27 \\ 22 & 25 & 28 \\ 23 & 26 & 29 \end{array} \right), \\ \mathrm{pick}(x, [0], 1) & = & \left( \begin{array}{c} 4 \\ 5 \\ 6 \end{array} \right), \left( \begin{array}{c} 14 \\ 15 \\ 16 \end{array} \right), \left( \begin{array}{c} 24 \\ 25 \\ 26 \end{array} \right), \\ \mathrm{pick}(x, [0, 1, 2], 1) & = & \left( \begin{array}{c} 1 \\ 2 \\ 3 \end{array} \right), \left( \begin{array}{c} 14 \\ 15 \\ 16 \end{array} \right), \left( \begin{array}{c} 27 \\ 28 \\ 29 \end{array} \right). \end{array} \end{split}\]
Return
A new variable.
Parameters
  • x: A variable representing an original data.
  • ids: List of subplane IDs according to the axis dim. Each value must be lower than x.shape()[dim].
  • dim: Axis to be processed.

template <typename Var>
type_traits::Identity<Var> slice(const Var &x, std::uint32_t dim, std::uint32_t lower, std::uint32_t upper)

Extracts a specific range \( [L, U) \) of subplanes along a specific axis. Following examples show how this function work:

\[\begin{split} \begin{array}{lcl} x & := & \left( \begin{array}{ccc} 1 & 4 & 7 \\ 2 & 5 & 8 \\ 3 & 6 & 9 \end{array} \right), \\ \mathrm{slice}(x, 0, 0, 1) & = & \left( \begin{array}{ccc} 1 & 4 & 7 \end{array} \right), \\ \mathrm{slice}(x, 1, 1, 3) & = & \left( \begin{array}{ccc} 4 & 7 \\ 5 & 8 \\ 6 & 9 \end{array} \right), \\ \mathrm{slice}(x, 2, 0, 1) & = & \left( \begin{array}{ccc} 1 & 4 & 7 \\ 2 & 5 & 8 \\ 3 & 6 & 9 \end{array} \right). \end{array} \end{split}\]
Return
A new variable.
Parameters
  • x: A variable representing an original data.
  • dim: Axis to be processed.
  • lower: Lower bound \( L \) of dim.
  • upper: Upper bound \( U \) of dim.

template <typename Var>
std::vector<type_traits::Identity<Var>> split(const Var &x, std::uint32_t dim, std::uint32_t n)

Splits a given variable into specified number of partitions along an axis.

Return
A list of n variables. Each variable is identical with: split(x, dim, n)[i] == slice(x, dim, L(i), U(i)), where L(i) := i * x.shape()[dim] / n and U(i) := (i + 1) * x.shape()[dim] / n.
Parameters
  • x: A variable representing an original data.
  • dim: Axis to be processed.
  • n: The number of resulting partitions. n should be able to divide x.shape()[dim] without residue.
Exceptions
  • primitiv::Error: n can not divide s.shape()[dim] without residue.

template <typename Container>
type_traits::Reduce<Container> concat(const Container &xs, std::uint32_t dim)

Concatenates multiple variables along specific axis. Following examples show how this function work:

\[\begin{split} \begin{array}{lcl} x_1 & := & \left( \begin{array}{ccc} 1 & 4 & 7 \\ 2 & 5 & 8 \\ 3 & 6 & 9 \end{array} \right), \\ x_2 & := & \left( \begin{array}{ccc} 11 & 14 & 17 \\ 12 & 15 & 18 \\ 13 & 16 & 19 \end{array} \right), \\ \mathrm{concat}([x_1, x_2], 0) & = & \left( \begin{array}{ccc} 1 & 4 & 7 \\ 2 & 5 & 8 \\ 3 & 6 & 9 \\ 11 & 14 & 17 \\ 12 & 15 & 18 \\ 13 & 16 & 19 \\ \end{array} \right), \\ \mathrm{concat}([x_1, x_2], 1) & = & \left( \begin{array}{cccccc} 1 & 4 & 7 & 11 & 14 & 17 \\ 2 & 5 & 8 & 12 & 15 & 18 \\ 3 & 6 & 9 & 13 & 16 & 19 \\ \end{array} \right), \\ \mathrm{concat}([x_1, x_2], 2) & = & \left( \left( \begin{array}{ccc} 1 & 4 & 7 \\ 2 & 5 & 8 \\ 3 & 6 & 9 \\ \end{array} \right), \left( \begin{array}{ccc} 11 & 14 & 17 \\ 12 & 15 & 18 \\ 13 & 16 & 19 \\ \end{array} \right) \right). \end{array} \end{split}\]
Return
A new variable.
Parameters
  • xs: Iterable container of variables. xs must have both begin() and end() functions that return the begin/end iterators.
  • dim: Axis to be processed.

template <typename Container>
type_traits::ReducePtr<Container> concat(const Container &xs, std::uint32_t dim)

Same as above, but xs has pointers of variables.

Return
A new variable.
Parameters
  • xs: Iterable container of pointers of variables. xs must have both begin() and end() functions that return the begin/end iterators.
  • dim: Axis to be processed.

template <typename Var>
type_traits::Identity<Var> reshape(const Var &x, const Shape &new_shape)

Changes the Shape of the variable.

Return
A new variable.
Parameters
  • x: A variable with an old Shape.
  • new_shape: A new Shape to be applied to the new variable. The volume and the minibatch size must be same as that of x.shape().

template <typename Var>
type_traits::Identity<Var> flatten(const Var &x)

Changes the Shape of the variable to the column vector.

Return
A new variable.
Parameters
  • x: A variable with an old Shape.

template <typename Var>
type_traits::Identity<Var> transpose(const Var &x)

Applies a matrix transposition.

Return
A new variable representing \( X^\top \).
Parameters
  • x: A variable representing an argument \( X \). The shape of x must be either a scalar, a column vector or a matrix.

template <typename Var>
type_traits::Identity<Var> flip(const Var &x, std::uint32_t dim)

Flips elements along an axis. Following examples show how this function work:

\[\begin{split} \begin{array}{lcl} x & := & \left( \begin{array}{ccc} 1 & 4 & 7 \\ 2 & 5 & 8 \\ 3 & 6 & 9 \end{array} \right), \\ \mathrm{flip}(x, 0) & = & \left( \begin{array}{ccc} 3 & 6 & 9 \\ 2 & 5 & 8 \\ 1 & 4 & 7 \end{array} \right), \\ \mathrm{flip}(x, 1) & = & \left( \begin{array}{c} 7 & 4 & 1 \\ 8 & 5 & 2 \\ 9 & 6 & 3 \end{array} \right), \\ \mathrm{flip}(x, 2) & = & \left( \begin{array}{ccc} 1 & 4 & 7 \\ 2 & 5 & 8 \\ 3 & 6 & 9 \end{array} \right). \end{array} \end{split}\]
Return
A new variable representing \( \mathrm{flip} (x) \).
Parameters
  • x: A variable representing an argument \( x \). The shape of x must be either a scalar, a column vector or a matrix.

template <typename Var>
type_traits::Identity<Var> permute_dims(const Var &x, const std::vector<std::uint32_t> &perm)

Permutes dimensions of a tensor.

\[\begin{split} \begin{array}{lcl} x & := & \left( \left( \begin{array}{cc} 1 & 4 \\ 2 & 5 \\ 3 & 6 \end{array} \right), \left( \begin{array}{cc} 11 & 14 \\ 12 & 15 \\ 13 & 16 \end{array} \right), \left( \begin{array}{cc} 21 & 24 \\ 22 & 25 \\ 23 & 26 \end{array} \right), \left( \begin{array}{cc} 31 & 34 \\ 32 & 35 \\ 33 & 36 \end{array} \right) \right), \\ \mathrm{permute\_dims}(x, [1, 2, 0]) & = & \left( \left( \begin{array}{cccc} 1 & 11 & 21 & 31 \\ 4 & 14 & 24 & 34 \end{array} \right), \left( \begin{array}{cccc} 2 & 12 & 22 & 32 \\ 5 & 15 & 25 & 35 \end{array} \right), \left( \begin{array}{cccc} 3 & 13 & 23 & 33 \\ 6 & 16 & 26 & 36 \end{array} \right) \right), \\ \mathrm{permute\_dims}(x, [2, 0, 1]) & = & \left( \left( \begin{array}{ccc} 1 & 2 & 3 \\ 11 & 12 & 13 \\ 21 & 22 & 23 \\ 31 & 32 & 33 \end{array} \right), \left( \begin{array}{ccc} 4 & 5 & 6 \\ 14 & 15 & 16 \\ 24 & 35 & 36 \\ 34 & 35 & 36 \end{array} \right) \right), \\ \mathrm{permute\_dims}(x, [0, 1, 2]) & = & x. \\ \end{array} \end{split}\]
Return
A new variable.
Parameters
  • x: A variable representing an original data.
  • perm: A list of dimensions for specifying permutation.

template <typename Var>
type_traits::Identity<Var> permute_dims(const Var &x, const std::initializer_list<std::uint32_t> perm)

Permutes dimensions of a tensor.

Return
A new variable.
Parameters
  • x: A variable representing an original data.
  • perm: A list of dimensions for specifying permutation.

template <typename Var>
type_traits::Identity<Var> matmul(const Var &a, const Var &b)

Applies a matrix multiplication between two matrices.

Return
A new variable representing \( AB \).
Parameters
  • a: A variable representing an argument \( A \). The shape of a must be either a scalar, a column vector or a matrix.
  • b: A variable representing an argument \( B \). The shape of b must be either a scalar, a column vector or a matrix, and b.shape()[0] must be equal to a.shape()[1].

template <typename Var>
type_traits::Identity<Var> abs(const Var &x)

Applies an elementwise absolute function.

Return
A variable representing \( \vert x \vert \).
Parameters
  • x: A variable representing an argument \( x \).

template <typename Var>
type_traits::Identity<Var> sqrt(const Var &x)

Applies an elementwise square root function.

Return
A variable representing \( \sqrt{x} \).
Parameters
  • x: A variable representing an argument \( x \).

template <typename Var>
type_traits::Identity<Var> exp(const Var &x)

Applies an elementwise exponential function.

Return
A variable representing \( e^x \).
Parameters
  • x: A variable representing an argument \( x \).

template <typename Var>
type_traits::Identity<Var> log(const Var &x)

Applies an elementwise natural logarithm function.

Return
A variable representing \( \ln (x) \).
Parameters
  • x: A variable representing an argument \( x \).

template <typename Var>
type_traits::Identity<Var> tanh(const Var &x)

Applies an elementwise hyperbolic tangent function.

Return
A variable representing \( \tanh (x) \).
Parameters
  • x: A variable representing an argument \( x \).

template <typename Var>
type_traits::Identity<Var> sigmoid(const Var &x)

Applies an elementwise logistic sigmoid function:

\[ \mathrm{sigmoid}(x) := \frac{1}{1 + e^{-x}}. \]
Return
A variable representing \( \mathrm{sigmoid}(x) \).
Parameters
  • x: A variable representing an argument \( x \).

template <typename Var>
type_traits::Identity<Var> softplus(const Var &x)

Applies an elementwise softplus function:

\[ \mathrm{softplus}(x) := \ln (1 + e^x). \]
Return
A variable representing \( \mathrm{softplus}(x) \).
Parameters
  • x: A variable representing an argument \( x \).

template <typename Var>
type_traits::Identity<Var> sin(const Var &x)

Applies an elementwise sin function.

Return
A variable representing \( \sin (x) \).
Parameters
  • x: A variable representing an argument \( x \).

template <typename Var>
type_traits::Identity<Var> cos(const Var &x)

Applies an elementwise cos function.

Return
A variable representing \( \cos (x) \).
Parameters
  • x: A variable representing an argument \( x \).

template <typename Var>
type_traits::Identity<Var> tan(const Var &x)

Applies an elementwise tangent function.

Return
A variable representing \( \tan (x) \).
Parameters
  • x: A variable representing an argument \( x \).

template <typename Var>
type_traits::Identity<Var> relu(const Var &x)

Applies an elementwise rectified linear unit (ReLU) function:

\[ \mathrm{ReLU}(x) := \max (x, 0). \]
Return
A variable representing \( \mathrm{ReLU}(x) \).
Parameters
  • x: A variable representing an argument \( x \).

template <typename Var>
type_traits::Identity<Var> lrelu(const Var &x)

Applies an elementwise leaky ReLU function:

\[ \mathrm{LReLU}(x) := \max (x, 0.01x). \]
Return
A variable representing \( \mathrm{LReLU}(x) \).
Parameters
  • x: A variable representing an argument \( x \).

template <typename Var>
type_traits::Identity<Var> prelu(const Var &x, float a)

Applies an elementwise parameterized ReLU function:

\[\begin{split} \mathrm{PReLU}(x) := \left\{ \begin{array}{ll} x, & \mathrm{if} \ x \geq 0, \\ \alpha x, & \mathrm{otherwise}. \end{array} \right. \end{split}\]
Return
A variable representing \( \mathrm{PReLU}(x) \).
Parameters
  • x: A variable representing an argument \( x \).
  • a: A scaling factor \( \alpha \).

template <typename Var>
type_traits::Identity<Var> elu(const Var &x, float a)

Applies an elementwise exponential linear unit (ELU) function:

\[\begin{split} \mathrm{ELU}(x) := \left\{ \begin{array}{ll} x, & \mathrm{if} \ x \geq 0, \\ \alpha (e^x - 1), & \mathrm{otherwise}. \end{array} \right. \end{split}\]
Return
A variable representing \( \mathrm{ELU}(x) \).
Parameters
  • x: A variable representing an argument \( x \).
  • a: A scaling factor \( \alpha \).

template <typename Var>
type_traits::Identity<Var> max(const Var &x, std::uint32_t dim)

Retrieves maximum values along an axis. Following examples show how this function work:

\[\begin{split} \begin{array}{lcl} x & := & \left( \begin{array}{ccc} 1 & 6 & 7 \\ 2 & 5 & 9 \\ 3 & 4 & 8 \end{array} \right), \\ \mathrm{max}(x, 0) & = & \left( \begin{array}{ccc} 3 & 6 & 9 \end{array} \right), \\ \mathrm{max}(x, 1) & = & \left( \begin{array}{c} 7 \\ 9 \\ 8 \end{array} \right), \\ \mathrm{max}(x, 2) & = & \left( \begin{array}{ccc} 1 & 6 & 7 \\ 2 & 5 & 9 \\ 3 & 4 & 8 \end{array} \right). \end{array} \end{split}\]
Return
A new variable.
Parameters
  • x: A variable representing values before reduction.
  • dim: Axis to be processed.

template <typename Var>
type_traits::Identity<Var> min(const Var &x, std::uint32_t dim)

Retrieves minimum values along an axis. Following examples show how this function work:

\[\begin{split} \begin{array}{lcl} x & := & \left( \begin{array}{ccc} 1 & 6 & 7 \\ 2 & 5 & 9 \\ 3 & 4 & 8 \end{array} \right), \\ \mathrm{min}(x, 0) & = & \left( \begin{array}{ccc} 1 & 4 & 7 \end{array} \right), \\ \mathrm{min}(x, 1) & = & \left( \begin{array}{c} 1 \\ 2 \\ 3 \end{array} \right), \\ \mathrm{min}(x, 2) & = & \left( \begin{array}{ccc} 1 & 6 & 7 \\ 2 & 5 & 9 \\ 3 & 4 & 8 \end{array} \right). \end{array} \end{split}\]
Return
A new variable.
Parameters
  • x: A variable representing values before reduction.
  • dim: Axis to be processed.

template <typename Var>
type_traits::Identity<Var> sum(const Var &x, std::uint32_t dim)

Applies summation along an axis. Following examples show how this function work:

\[\begin{split} \begin{array}{lcl} x & := & \left( \begin{array}{ccc} 1 & 4 & 7 \\ 2 & 5 & 8 \\ 3 & 6 & 9 \end{array} \right), \\ \mathrm{sum}(x, 0) & = & \left( \begin{array}{ccc} 6 & 15 & 24 \end{array} \right), \\ \mathrm{sum}(x, 1) & = & \left( \begin{array}{c} 12 \\ 15 \\ 18 \end{array} \right), \\ \mathrm{sum}(x, 2) & = & \left( \begin{array}{ccc} 1 & 4 & 7 \\ 2 & 5 & 8 \\ 3 & 6 & 9 \end{array} \right). \end{array} \end{split}\]
Return
A new variable.
Parameters
  • x: A variable representing values before reduction.
  • dim: Axis to be processed.

template <typename Var>
type_traits::Identity<Var> broadcast(const Var &x, std::uint32_t dim, std::uint32_t size)

Applies broadcasting along an axis. Following examples show how this function work:

\[\begin{split} \begin{array}{lcl} x_1 & := & \left( \begin{array}{ccc} 1 & 2 & 3 \end{array} \right), \\ \mathrm{broadcast}(x_1, 0, 3) & = & \left( \begin{array}{ccc} 1 & 2 & 3 \\ 1 & 2 & 3 \\ 1 & 2 & 3 \end{array} \right), \\ x_2 & := & \left( \begin{array}{c} 1 \\ 2 \\ 3 \end{array} \right), \\ \mathrm{broadcast}(x_2, 1, 3) & = & \left( \begin{array}{ccc} 1 & 1 & 1 \\ 2 & 2 & 2 \\ 3 & 3 & 3 \end{array} \right), \\ \mathrm{broadcast}(x_2, 2, 3) & = & \left( \left( \begin{array}{c} 1 \\ 2 \\ 3 \end{array} \right), \left( \begin{array}{c} 1 \\ 2 \\ 3 \end{array} \right), \left( \begin{array}{c} 1 \\ 2 \\ 3 \end{array} \right) \right). \end{array} \end{split}\]
Return
A new variable.
Parameters
  • x: A variable representing values before reduction.
  • dim: Axis to be processed.
  • size: New size of the axis dim.

template <typename Var>
type_traits::Identity<Var> logsumexp(const Var &x, std::uint32_t dim)

Applies a logsumexp reduction along an axis. This function performs similarly to primitiv::functions::sum w.r.t. the axis.

Return
A new variable.
Parameters
  • x: A variable representing values before expansion.
  • dim: Axis to be processed.

template <typename Var>
type_traits::Identity<Var> log_softmax(const Var &x, std::uint32_t dim)

Applies a softmax operation along an axis, and returns the natural logarithm of resulting values.

Return
A new variable.
Parameters
  • x: A variable representing original values.
  • dim: Axis to be processed.

template <typename Var>
type_traits::Identity<Var> softmax(const Var &x, std::uint32_t dim)

Applies a softmax operation along an axis.

Return
A new variable.
Parameters
  • x: A variable representing original values.
  • dim: Axis to be processed.

template <typename Var>
type_traits::Identity<Var> softmax_cross_entropy(const Var &x, const Var &t, std::uint32_t dim)

Applies a softmax cross entropy function between two variables along an axis.

Return
A new variable.
Parameters
  • x: A variable representing logit values.
  • t: A variable representing ground-truth distribution along the axis dim.
  • dim: Axis to be processed.

template <typename Var>
type_traits::Identity<Var> softmax_cross_entropy(const Var &x, const std::vector<std::uint32_t> &ids, std::uint32_t dim)

Applies a softmax cross entropy function between logits and one-hot distributions along an axis.

Return
A new variable.
Parameters
  • x: A variable representing logit values.
  • ids: List of one-hot IDs along the axis dim. Each value must be lower than x.shape()[dim].
  • dim: Axis to be processed.

template <typename Var>
type_traits::Identity<Var> stop_gradient(const Var &x)

Blocks the gradient propagation beyond this function. This function does not modify any values in the input variable, and force to make all gradients \( 0 \).

Return
A new variable.
Parameters
  • x: A variable representing original values.

template <typename Var>
type_traits::Identity<Var> conv2d(const Var &x, const Var &w, std::uint32_t padding0, std::uint32_t padding1, std::uint32_t stride0, std::uint32_t stride1, std::uint32_t dilation0, std::uint32_t dilation1)

Applies a 2D convolution between two variables.

Return
A new variable with Shape \( [d'_0, d'_1, c_2] \). The first and second dimension are calculated as following:
\[ d'_i := \frac{d_i + 2 \times \mathrm{padding}_i - (u_i - 1) \times \mathrm{dilation}_i + 1}{\mathrm{stride}_i} + 1. \]
Parameters
  • x: A variable with Shape \( [d_0, d_1, c_1] \).
  • w: A variable with Shape \( [u_0, u_1, c_1, c_2] \).
  • padding0: Width of zero-padding along the first axis.
  • padding1: Width of zero-padding along the second axis.
  • stride0: Stride along the first axis.
  • stride1: Stride along the second axis.
  • dilation0: Dilation factor along the first axis.
  • dilation1: Dilation factor along the second axis.

template <typename Var>
type_traits::Identity<Var> max_pool2d(const Var &x, std::uint32_t window0, std::uint32_t window1, std::uint32_t padding0, std::uint32_t padding1, std::uint32_t stride0, std::uint32_t stride1)

Applies a 2D max-pooling operation.

Return
A new variable with Shape \( [d'_0, d'_1, c] \). The first and second dimension are calculated as following:
\[ d'_i := \frac{d_i + 2 \times \mathrm{padding}_i - \mathrm{window}_i}{\mathrm{stride}_i} + 1. \]
Parameters
  • x: A variable with Shape \( [d_0, d_1, c] \).
  • window0: Window size along the first axis.
  • window1: Window size along the second axis.
  • padding0: Width of \( -\infty \) padding along the first axis.
  • padding1: Width of \( -\infty \) padding along the second axis.
  • stride0: Stride along the first axis.
  • stride1: Stride along the second axis.

Tensor constant_tensor(const Shape &shape, float k, Device *dev)

Creates a new Tensor with all values the constant \( k \).

Return
A new Tensor.
Parameters
  • shape: Shape of the new Tensor.
  • k: The constant \( k \) of values in the Tensor.
  • dev: Device to manage the new Tensor, or nullptr to use the default device.

Node constant_node(const Shape &shape, float k, Device *dev, Graph *g)

Creates a new Node with all values the constant \( k \).

Return
A new Node.
Parameters
  • shape: Shape of the new Node.
  • k: The constant \( k \) of values in the Node.
  • dev: Device to manage the new Node, or nullptr to use the default device.
  • g: Graph to manage the instance of the Node, or nullptr to use the default graph.

template <typename Var>
type_traits::Identity<Var> constant(const Shape &shape, float k, Device *dev)

Creates a new variable with all values the constant \( k \).

Return
A new variable.
Remark
This function uses the default graph when specifying Node as the template variable.
Parameters
  • shape: Shape of the new variable.
  • k: The constant \( k \) of values in the variable.
  • dev: Device to manage the new variable, or nullptr to use the default device.

template <typename Var>
type_traits::Identity<Var> constant(const Shape &shape, float k, Device &dev)

Creates a new variable with all values the constant \( k \).

Remark
This function uses the default graph when specifying Node as the template variable.
Parameters
  • shape: Shape of the new variable.
  • k: The constant \( k \) of values in the variable.
  • dev: Device to manage the new variable.

template <typename Var>
type_traits::Identity<Var> constant(const Shape &shape, float k)

Creates a new variable with all values the constant \( k \).

Remark
This function always uses the default device, and also uses the default graph when specifying Node as the template variable.
Parameters
  • shape: Shape of the new variable.
  • k: The constant \( k \) of values in the variable.

Tensor identity_tensor(std::uint32_t size, Device *dev)

Creates a new Tensor with an \( N \)-dimensional identity matrix.

Return
A new Tensor.
Parameters
  • size: Size \( N \) of the matrix in the new Tensor.
  • dev: Device to manage the new Tensor, or nullptr to use the default device.

Node identity_node(std::uint32_t size, Device *dev, Graph *g)

Creates a new Node with an \( N \)-dimensional identity matrix.

Return
A new Node.
Parameters
  • size: Size \( N \) of the matrix in the new Node.
  • dev: Device to manage the new Node, or nullptr to use the default device.
  • g: Graph to manage the instance of the Node, or nullptr to use the default graph.

template <typename Var>
type_traits::Identity<Var> identity(std::uint32_t size, Device *dev)

Creates a new variable with an \( N \)-dimensional identity matrix.

Return
A new variable.
Remark
This function uses the default graph when specifying Node as the template variable.
Parameters
  • size: Size \( N \) of the matrix in the new Node.
  • dev: Device to manage the new variable, or nullptr to use the default device.

template <typename Var>
type_traits::Identity<Var> identity(std::uint32_t size, Device &dev)

Creates a new variable with an \( N \)-dimensional identity matrix.

Return
A new variable.
Remark
This function uses the default graph when specifying Node as the template variable.
Parameters
  • size: Size \( N \) of the matrix in the new Node.
  • dev: Device to manage the new variable.

template <typename Var>
type_traits::Identity<Var> identity(std::uint32_t size)

Creates a new variable with an \( N \)-dimensional identity matrix.

Return
A new variable.
Remark
This function always uses the default device, and also uses the default graph when specifying Node as the template variable.
Parameters
  • size: Size \( N \) of the matrix in the new Node.

namespace batch

Functions

template <typename Var>
type_traits::Identity<Var> mean(const Var &x)

Calculates means along the minibatch.

Return
A new variable.
Remark
This function is implemented as a composite of some other functions.
Parameters
  • x: A variable representing values before reduction.

template <typename Var>
type_traits::Identity<Var> normalize(const Var &x)

Applies the batch normalization:

\[\begin{split} \begin{array}{rcl} m_x & := & \frac{1}{B} \sum_{i=1}^{B} x_i, \\ v_x & := & \frac{B}{B - 1} \left( \frac{1}{B} \sum_{i=0}^{B} x_i^2 - m_x^2 \right), \\ \mathrm{batch::normalize}(x) & := & \frac{x - m_x}{\sqrt{v_x + \epsilon}}, \end{array} \end{split}\]
where \( B \) is the minibatch size of \( x \).
Return
A new variable.
Remark
This function is implemented as a composite of some other functions.
Parameters
  • x: A variable representing values before normalization.

template <typename Var>
type_traits::Identity<Var> pick(const Var &x, const std::vector<std::uint32_t> &ids)

Selects items from the batch by IDs.

Return
A new variable.
Parameters
  • x: A variable representing an original data.
  • ids: List of batch IDs. Each value must be lower than x.shape().batch().

template <typename Var>
type_traits::Identity<Var> slice(const Var &x, std::uint32_t lower, std::uint32_t upper)

Extracts a specific range \( [L, U) \) of items along the batch axis.

Return
A new variable.
Parameters
  • x: A variable representing an original data.
  • lower: Lower bound \( L \) of the batch.
  • upper: Upper bound \( U \) of the batch.

template <typename Var>
std::vector<type_traits::Identity<Var>> split(const Var &x, std::uint32_t n)

Splits a given variable into specified number of partitions along the batch.

Return
A list of n variables. Each variable is identical with: batch::split(x, n)[i] == batch::slice(x, L(i), U(i)), where L(i) := i * x.shape().batch() / n and U(i) := (i + 1) * x.shape().batch() / n.
Parameters
  • x: A variable representing an original data.
  • n: The number of resulting partitions. n should be able to divide x.shape().batch() without residue.
Exceptions
  • primitiv::Error: n can not divide s.shape().batch() without residue.

template <typename Container>
type_traits::Reduce<Container> concat(const Container &xs)

Concatenates multiple variables along the batch axis.

Return
A new variable.
Parameters
  • xs: Iterable container of variables. xs must have both begin() and end() functions that return the begin/end iterators.

template <typename Container>
type_traits::ReducePtr<Container> concat(const Container &xs)

Same as above, but xs has pointers of variables.

Return
A new variable.
Parameters
  • xs: Iterable container of pointers of variables. xs must have both begin() and end() functions that return the begin/end iterators.

template <typename Var>
type_traits::Identity<Var> sum(const Var &x)

Applies summation along the minibatch. Following example shows how this function work:

\[\begin{split} \begin{array}{lcl} x & := & \left( \begin{array}{ccc} 1 & 4 & 7 \\ 2 & 5 & 8 \\ 3 & 6 & 9 \end{array} \right), \left( \begin{array}{ccc} 11 & 14 & 17 \\ 12 & 15 & 18 \\ 13 & 16 & 19 \end{array} \right), \\ \mathrm{batch::sum}(x) & = & \left( \begin{array}{ccc} 12 & 18 & 24 \\ 14 & 20 & 26 \\ 16 & 22 & 28 \end{array} \right). \end{array} \end{split}\]
Return
A new variable.
Parameters
  • x: A variable representing values before reduction.

namespace random

Functions

Tensor bernoulli_tensor(const Shape &shape, float p, Device *dev)

Creates a new Tensor with values sampled from the Bernoulli distribution.

Return
A new Tensor.
Parameters
  • shape: Shape of the new Tensor.
  • p: The parameter \( p \) of the Bernoulli distribution.
  • dev: Device to manage the new Tensor, or nullptr to use the default device.

Node bernoulli_node(const Shape &shape, float p, Device *dev, Graph *g)

Creates a new Node with values sampled from the Bernoulli distribution.

Return
A new Node.
Parameters
  • shape: Shape of the new Node.
  • p: The parameter \( p \) of the Bernoulli distribution.
  • dev: Device to manage the new Node, or nullptr to use the default device.
  • g: Graph to manage the instance of the Node, or nullptr to use the default graph.

template <typename Var>
type_traits::Identity<Var> bernoulli(const Shape &shape, float p, Device *dev)

Creates a new variable with values sampled from the Bernoulli distribution.

Return
A new variable.
Remark
This function uses the default graph when specifying Node as the template variable.
Parameters
  • shape: Shape of the new variable.
  • p: The parameter \( p \) of the Bernoulli distribution.
  • dev: Device to manage the new variable, or nullptr to use the default device.

template <typename Var>
type_traits::Identity<Var> bernoulli(const Shape &shape, float p, Device &dev)

Creates a new variable with values sampled from the Bernoulli distribution.

Return
A new variable.
Remark
This function uses the default graph when specifying Node as the template variable.
Parameters
  • shape: Shape of the new variable.
  • p: The parameter \( p \) of the Bernoulli distribution.
  • dev: Device to manage the new variable.

template <typename Var>
type_traits::Identity<Var> bernoulli(const Shape &shape, float p)

Creates a new variable with values sampled from the Bernoulli distribution.

Return
A new variable.
Remark
This function always uses the default device, and also uses the default graph when specifying Node as the template variable.
Parameters
  • shape: Shape of the new variable.
  • p: The parameter \( p \) of the Bernoulli distribution.

Tensor uniform_tensor(const Shape &shape, float lower, float upper, Device *dev)

Creates a new Tensor with values sampled from the uniform distribution.

Return
A new Tensor.
Parameters
  • shape: Shape of the new Tensor.
  • lower: The lower bound \( L \) of the uniform distribution.
  • upper: The upper bound \( U \) of the uniform distribution.
  • dev: Device to manage the new Tensor, or nullptr to use the default device.

Node uniform_node(const Shape &shape, float lower, float upper, Device *dev, Graph *g)

Creates a new Node with values sampled from the uniform distribution.

Return
A new Node.
Parameters
  • shape: Shape of the new Node.
  • lower: The lower bound \( L \) of the uniform distribution.
  • upper: The upper bound \( U \) of the uniform distribution.
  • dev: Device to manage the new Node, or nullptr to use the default device.
  • g: Graph to manage the instance of the Node, or nullptr to use the default graph.

template <typename Var>
type_traits::Identity<Var> uniform(const Shape &shape, float lower, float upper, Device *dev)

Creates a new variable with values sampled from the uniform distribution.

Return
A new variable.
Remark
This function uses the default graph when specifying Node as the template variable.
Parameters
  • shape: Shape of the new variable.
  • lower: The lower bound \( L \) of the uniform distribution.
  • upper: The upper bound \( U \) of the uniform distribution.
  • dev: Device to manage the new variable, or nullptr to use the default device.

template <typename Var>
type_traits::Identity<Var> uniform(const Shape &shape, float lower, float upper, Device &dev)

Creates a new variable with values sampled from the uniform distribution.

Return
A new variable.
Remark
This function uses the default graph when specifying Node as the template variable.
Parameters
  • shape: Shape of the new variable.
  • lower: The lower bound \( L \) of the uniform distribution.
  • upper: The upper bound \( U \) of the uniform distribution.
  • dev: Device to manage the new variable.

template <typename Var>
type_traits::Identity<Var> uniform(const Shape &shape, float lower, float upper)

Creates a new variable with values sampled from the uniform distribution.

Return
A new variable.
Remark
This function always uses the default device, and also uses the default graph when specifying Node as the template variable.
Parameters
  • shape: Shape of the new variable.
  • lower: The lower bound \( L \) of the uniform distribution.
  • upper: The upper bound \( U \) of the uniform distribution.

Tensor normal_tensor(const Shape &shape, float mean, float sd, Device *dev)

Creates a new Tensor with values sampled from the normal distribution.

Return
A new Tensor.
Parameters
  • shape: Shape of the new Tensor.
  • mean: The mean \( \mu \) of the normal distribution.
  • sd: The standard deviation \( \sigma \) of the normal distribution.
  • dev: Device to manage the new Tensor, or nullptr to use the default device.

Node normal_node(const Shape &shape, float mean, float sd, Device *dev, Graph *g)

Creates a new Node with values sampled from the normal distribution.

Return
A new Node.
Parameters
  • shape: Shape of the new Node.
  • mean: The mean \( \mu \) of the normal distribution.
  • sd: The standard deviation \( \sigma \) of the normal distribution.
  • dev: Device to manage the new Node, or nullptr to use the default device.
  • g: Graph to manage the instance of the Node, or nullptr to use the default graph.

template <typename Var>
type_traits::Identity<Var> normal(const Shape &shape, float mean, float sd, Device *dev)

Creates a new variable with values sampled from the normal distribution.

Return
A new variable.
Remark
This function uses the default graph when specifying Node as the template variable.
Parameters
  • shape: Shape of the new variable.
  • mean: The mean \( \mu \) of the normal distribution.
  • sd: The standard deviation \( \sigma \) of the normal distribution.
  • dev: Device to manage the new variable, or nullptr to use the default device.

template <typename Var>
type_traits::Identity<Var> normal(const Shape &shape, float mean, float sd, Device &dev)

Creates a new variable with values sampled from the normal distribution.

Return
A new variable.
Remark
This function uses the default graph when specifying Node as the template variable.
Parameters
  • shape: Shape of the new variable.
  • mean: The mean \( \mu \) of the normal distribution.
  • sd: The standard deviation \( \sigma \) of the normal distribution.
  • dev: Device to manage the new variable.

template <typename Var>
type_traits::Identity<Var> normal(const Shape &shape, float mean, float sd)

Creates a new variable with values sampled from the normal distribution.

Return
A new variable.
Remark
This function always uses the default device, and also uses the default graph when specifying Node as the template variable.
Parameters
  • shape: Shape of the new variable.
  • mean: The mean \( \mu \) of the normal distribution.
  • sd: The standard deviation \( \sigma \) of the normal distribution.

Tensor log_normal_tensor(const Shape &shape, float mean, float sd, Device *dev)

Creates a new Tensor with values sampled from the log-normal distribution.

Return
A new Tensor.
Parameters
  • shape: Shape of the new Tensor.
  • mean: The parameter \( \mu \) of the log-normal distribution.
  • sd: The parameter \( \sigma \) of the log-normal distribution.
  • dev: Device to manage the new Tensor, or nullptr to use the default device.

Node log_normal_node(const Shape &shape, float mean, float sd, Device *dev, Graph *g)

Creates a new Node with values sampled from the log-normal distribution.

Return
A new Node.
Parameters
  • shape: Shape of the new Node.
  • mean: The parameter \( \mu \) of the log-normal distribution.
  • sd: The parameter \( \sigma \) of the log-normal distribution.
  • dev: Device to manage the new Node, or nullptr to use the default device.
  • g: Graph to manage the instance of the Node, or nullptr to use the default graph.

template <typename Var>
type_traits::Identity<Var> log_normal(const Shape &shape, float mean, float sd, Device &dev)

Creates a new variable with values sampled from the log-normal distribution.

Creates a new variable with values sampled from the log-normal distribution.

Return
A new variable.
Remark
This function uses the default graph when specifying Node as the template variable.
Return
A new variable.
Remark
This function uses the default graph when specifying Node as the template variable.
Parameters
  • shape: Shape of the new variable.
  • mean: The parameter \( \mu \) of the log-normal distribution.
  • sd: The parameter \( \sigma \) of the log-normal distribution.
  • dev: Device to manage the new variable, or nullptr to use the default device.
Parameters
  • shape: Shape of the new variable.
  • mean: The parameter \( \mu \) of the log-normal distribution.
  • sd: The parameter \( \sigma \) of the log-normal distribution.
  • dev: Device to manage the new variable.

template <typename Var>
type_traits::Identity<Var> log_normal(const Shape &shape, float mean, float sd)

Creates a new variable with values sampled from the log-normal distribution.

Return
A new variable.
Remark
This function always uses the default device, and also uses the default graph when specifying Node as the template variable.
Parameters
  • shape: Shape of the new variable.
  • mean: The parameter \( \mu \) of the log-normal distribution.
  • sd: The parameter \( \sigma \) of the log-normal distribution.

Tensor gumbel_tensor(const Shape &shape, float mu, float beta, Device *dev)

Creates a new Tensor with values sampled from the Gumbel distribution.

Return
A new Tensor.
Parameters
  • shape: Shape of the new Tensor.
  • mu: The location parameter \( \mu \) of the Gumbel distribution.
  • beta: The scale parameter \( \beta \) of the Gumbel distribution.
  • dev: Device to manage the new Tensor, or nullptr to use the default device.

Node gumbel_node(const Shape &shape, float mu, float beta, Device *dev, Graph *g)

Creates a new Node with values sampled from the Gumbel distribution.

Return
A new Node.
Parameters
  • shape: Shape of the new Node.
  • mu: The location parameter \( \mu \) of the Gumbel distribution.
  • beta: The scale parameter \( \beta \) of the Gumbel distribution.
  • dev: Device to manage the new Node, or nullptr to use the default device.
  • g: Graph to manage the instance of the Node, or nullptr to use the default graph.

template <typename Var>
type_traits::Identity<Var> gumbel(const Shape &shape, float mu, float beta, Device *dev)

Creates a new variable with values sampled from the Gumbel distribution.

Return
A new variable.
Remark
This function uses the default graph when specifying Node as the template variable.
Parameters
  • shape: Shape of the new variable.
  • mu: The location parameter \( \mu \) of the Gumbel distribution.
  • beta: The scale parameter \( \beta \) of the Gumbel distribution.
  • dev: Device to manage the new variable, or nullptr to use the default device.

template <typename Var>
type_traits::Identity<Var> gumbel(const Shape &shape, float mu, float beta, Device &dev)

Creates a new variable with values sampled from the Gumbel distribution.

Return
A new variable.
Remark
This function uses the default graph when specifying Node as the template variable.
Parameters
  • shape: Shape of the new variable.
  • mu: The location parameter \( \mu \) of the Gumbel distribution.
  • beta: The scale parameter \( \beta \) of the Gumbel distribution.
  • dev: Device to manage the new variable.

template <typename Var>
type_traits::Identity<Var> gumbel(const Shape &shape, float mu, float beta)

Creates a new variable with values sampled from the Gumbel distribution.

Return
A new variable.
Remark
This function always uses the default device, and also uses the default graph when specifying Node as the template variable.
Parameters
  • shape: Shape of the new variable.
  • mu: The location parameter \( \mu \) of the Gumbel distribution.
  • beta: The scale parameter \( \beta \) of the Gumbel distribution.

Graph

class Graph : public primitiv::mixins::DefaultSettable<Graph>, primitiv::mixins::Nonmovable<Graph>

Computation graph.

Public Functions

void clear()

Clear all operators in the graph.

Remark
After calling this method, all Node objects supplied by the graph itself is invalidated.

std::vector<Node> add_operator(std::unique_ptr<Operator> &&op, const std::vector<Node> &args)

Adds an operator into the graph.

Return
New Node objects of resulting values.
Parameters
  • op: Interface of the new operator.
  • args: List of arguments. Each node should point a node in the same computation graph.

const Tensor &forward(const Node &node)

Calculates the value of given node.

Return
Calculated value.
Remark
This function calculates only the subgraph which is required to calculate the target node. Each intermediate result is stored to the corresponding node in the subgraph and they are re-used for future calculation. I.e., each node is calculated only once while the lifetime of the Graph object.
Parameters
  • node: Node object specifying the target node.

void backward(const Node &node)

Calculates the backpropagation.

Remark
If node is not yet forwarded, this function implicitly calls forward(node).
Parameters
  • node: Node object specifying the output node.

Shape get_shape(const Node &node) const

Retrieves the shape of the node.

Return
The shape of the node.
Parameters
  • node: Node object specifying the target node.

Device &get_device(const Node &node) const

Retrieves the device of the node.

Return
Device of the node.
Parameters
  • node: Node object specifying the target node.

std::string dump(const std::string &format) const

Dump internal graph structure.

Return
A string that represents the internal graph using given format.
Parameters
  • format: Name of the format. Available options: “dot” … Graphviz’s dot format.

std::uint32_t num_operators() const

Returns the number of operators in the computation graph.

Return
Number of nodes.

Initializers

Base Class
class Initializer : primitiv::mixins::Nonmovable<Initializer>

Abstract class to provide parameter initialization algorithms.

Subclassed by primitiv::initializers::Constant, primitiv::initializers::Identity, primitiv::initializers::Normal, primitiv::initializers::Uniform, primitiv::initializers::XavierNormal, primitiv::initializers::XavierNormalConv2D, primitiv::initializers::XavierUniform, primitiv::initializers::XavierUniformConv2D

Public Functions

virtual void apply(Tensor &x) const = 0

Provides an initialized tensor.

Parameters
  • x: Tensor object to be initialized.

Inherited Classes
class Constant : public primitiv::Initializer

Initializer to generate a same-value tensor.

Public Functions

Constant(float k)

Crates a new Constant initializer.

Parameters
  • k: Initial value of all variables in the parameter.

void apply(Tensor &x) const

Provides an initialized tensor.

Parameters
  • x: Tensor object to be initialized.

class Uniform : public primitiv::Initializer

Initializer using a parameterized uniform distribution with the range \( (L, U] \).

Public Functions

Uniform(float lower, float upper)

Creates a new Uniform initializer.

Parameters
  • lower: Lower bound \( L \) of the uniform distribution.
  • upper: Upper bound \( U \) of the uniform distribution.

void apply(Tensor &x) const

Provides an initialized tensor.

Parameters
  • x: Tensor object to be initialized.

class Normal : public primitiv::Initializer

Initializer using a parameterized normal distribution \( \mathcal{N}(\mu, \sigma) \).

Public Functions

Normal(float mean, float sd)

Creates a new Normal initializer.

Parameters
  • mean: Mean \( \mu \) of the normal distribution.
  • sd: Standard deviation \( \sigma \) of the normal distribution.

void apply(Tensor &x) const

Provides an initialized tensor.

Parameters
  • x: Tensor object to be initialized.

class Identity : public primitiv::Initializer

Identity matrix initializer.

Public Functions

Identity()

Creates a new Identity initializer.

void apply(Tensor &x) const

Provides an initialized tensor.

Parameters
  • x: Tensor object to be initialized.

class XavierUniform : public primitiv::Initializer

The Xavier matrix initialization with the uniform distribution.

Public Functions

XavierUniform(float scale = 1.0f)

Creates a new XavierUniform initializer.

Parameters
  • scale: Additional scaling factor of the uniform distribution.

void apply(Tensor &x) const

Provides an initialized tensor.

Parameters
  • x: Tensor object to be initialized.

class XavierNormal : public primitiv::Initializer

The Xavier matrix initialization with the normal distribution.

Public Functions

XavierNormal(float scale = 1.0f)

Creates a new XavierNormal initializer.

Parameters
  • scale: Additional scaling factor of the normal distribution.

void apply(Tensor &x) const

Provides an initialized tensor.

Parameters
  • x: Tensor object to be initialized.

class XavierUniformConv2D : public primitiv::Initializer

The Xavier initialization with the uniform distribution for conv2d filters.

Public Functions

XavierUniformConv2D(float scale = 1.0f)

Creates a new XavierUniformConv2D initializer.

Parameters
  • scale: Additional scaling factor of the uniform distribution.

void apply(Tensor &x) const

Provides an initialized tensor.

Parameters
  • x: Tensor object to be initialized.

class XavierNormalConv2D : public primitiv::Initializer

The Xavier initialization with the normal distribution for conv2d filters.

Public Functions

XavierNormalConv2D(float scale = 1.0f)

Creates a new XavierNormalConv2D initializer.

Parameters
  • scale: Additional scaling factor of the normal distribution.

void apply(Tensor &x) const

Provides an initialized tensor.

Parameters
  • x: Tensor object to be initialized.

Model

class Model : primitiv::mixins::Nonmovable<Model>

Set of parameters and specific algorithms.

Public Functions

void load(const std::string &path, bool with_stats, Device *device)

Loads all parameters from a file.

Parameters
  • path: Path of the file.
  • with_stats: Whether or not to load all additional statistics.
  • device: Device object to manage parameters.

void load(const std::string &path, bool with_stats, Device &device)

Loads all parameters from a file.

Parameters
  • path: Path of the file.
  • with_stats: Whether or not to load all additional statistics.
  • device: Device object to manage parameters.

void load(const std::string &path, bool with_stats)

Loads all parameters from a file.

Parameters
  • path: Path of the file.
  • with_stats: Whether or not to load all additional statistics.

void load(const std::string &path)

Loads all parameters from a file.

Parameters
  • path: Path of the file.

void save(const std::string &path, bool with_stats) const

Saves all parameters to a file.

Parameters
  • path: Path of the file.
  • with_stats: Whether or not to save all additional statistics.

void save(const std::string &path) const

Saves all parameters to a file.

Parameters
  • path: Path of the file.

void add(const std::string &name, Parameter &param)

Registers a new parameter.

Remark
name should not be overlapped with all registered parameters and submodels.
Parameters
  • name: Name of the parameter.
  • param: Reference to the parameter.

void add(const std::string &name, Model &model)

Registers a new submodel.

Remark
name should not be overlapped with all registered parameters and submodels.
Parameters
  • name: Name of the submodel.
  • model: Reference to the submodel.

const Parameter &get_parameter(const std::string &name) const

Retrieves a parameter with specified name.

Return
Const-reference of the corresponding Parameter object.
Parameters
  • name: Name of the parameter.
Exceptions
  • primitiv::Error: Parameter with name not found.

Parameter &get_parameter(const std::string &name)

Retrieves a parameter with specified name.

Return
Reference of the corresponding Parameter object.
Parameters
  • name: Name of the parameter.
Exceptions
  • primitiv::Error: Parameter with name not found.

const Parameter &get_parameter(const std::vector<std::string> &names) const

Recursively searches a parameter with specified name hierarchy.

Return
Const-reference of the corresponding Parameter object.
Parameters
  • names: Name hierarchy of the parameter.
Exceptions
  • primitiv::Error: Parameter with names not found.

Parameter &get_parameter(const std::vector<std::string> &names)

Recursively searches a parameter with specified name hierarchy.

Return
Const-reference of the corresponding Parameter object.
Parameters
  • names: Name hierarchy of the parameter.
Exceptions
  • primitiv::Error: Parameter with names not found.

const Parameter &get_parameter(const std::initializer_list<std::string> names) const

Recursively searches a parameter with specified name hierarchy.

Return
Const-reference of the corresponding Parameter object.
Parameters
  • names: Name hierarchy of the parameter.
Exceptions
  • primitiv::Error: Parameter with names not found.

Parameter &get_parameter(const std::initializer_list<std::string> names)

Recursively searches a parameter with specified name hierarchy.

Return
Const-reference of the corresponding Parameter object.
Parameters
  • names: Name hierarchy of the parameter.
Exceptions
  • primitiv::Error: Parameter with names not found.

const Model &get_submodel(const std::string &name) const

Retrieves a submodel with specified name.

Return
Const-reference of the corresponding Model object.
Parameters
  • name: Name of the submodel.
Exceptions
  • primitiv::Error: Submodel with name not found.

Model &get_submodel(const std::string &name)

Retrieves a submodel with specified name.

Return
Reference of the corresponding Model object.
Parameters
  • name: Name of the submodel.
Exceptions
  • primitiv::Error: Submodel with name not found.

const Model &get_submodel(const std::vector<std::string> &names) const

Recursively searches a submodel with specified name hierarchy.

Return
Const-reference of the corresponding Model object.
Parameters
  • names: Name hierarchy of the submodel.
Exceptions
  • primitiv::Error: Submodel with names not found.

Model &get_submodel(const std::vector<std::string> &names)

Recursively searches a submodel with specified name hierarchy.

Return
Const-reference of the corresponding Model object.
Parameters
  • names: Name hierarchy of the submodel.
Exceptions
  • primitiv::Error: Submodel with names not found.

const Model &get_submodel(const std::initializer_list<std::string> names) const

Recursively searches a submodel with specified name hierarchy.

Return
Const-reference of the corresponding Model object.
Parameters
  • names: Name hierarchy of the submodel.
Exceptions
  • primitiv::Error: Submodel with names not found.

Model &get_submodel(const std::initializer_list<std::string> names)

Recursively searches a submodel with specified name hierarchy.

Return
Const-reference of the corresponding Model object.
Parameters
  • names: Name hierarchy of the submodel.
Exceptions
  • primitiv::Error: Submodel with names not found.

std::map<std::vector<std::string>, Parameter *> get_all_parameters() const

Retrieves all parameters in the model.

Return
Dictionary of parameters.

std::map<std::vector<std::string>, Parameter *> get_trainable_parameters() const

Retrieves trainable parameters in the model.

Return
Dictionary of parameters.

Node

class Node

Pointer of a node in the computation graph.

Public Functions

bool valid() const

Returns whether the node is valid or not.

Return
true or false w.r.t. the node is valid or not.

Graph &graph() const

Returns corresponding Graph object.

Return
Graph object.

std::uint32_t operator_id() const

Returns the operator ID.

Return
Operator ID.

std::uint32_t value_id() const

Returns the value ID of the operator.

Return
Value ID.

Shape shape() const

Returns shape of the node.

Return
A Shape object.

Device &device() const

Returns device of the node.

Return
Device object.

float to_float() const

Calculates the value of this node and returns a float.

Return
A calculated float value.
Remark
This function calls Graph::forward() internally. This function can be used only when the Node has a scalar and non-minibatched shape (i.e., shape() == Shape())

std::vector<float> to_vector() const

Calculates the value of this node and returns a list of float.

Return
A list of calculated values.
Remark
This function calls Graph::forward() internally.

std::vector<std::uint32_t> argmax(std::uint32_t dim) const

Returns argmax indices along an axis of this node.

Return
A list of integers that indicates positions of the maximum values.
Parameters
  • dim: A specified axis.

std::vector<std::uint32_t> argmin(std::uint32_t dim) const

Returns argmin indices along an axis of this node.

Return
A list of integers that indicates positions of the minimum values.
Parameters
  • dim: A specified axis.

void backward() const

Executes the backward operation from this node.

Optimizers

Base Class
class Optimizer : primitiv::mixins::Nonmovable<Optimizer>

Abstract class for parameter optimizers.

Subclassed by primitiv::optimizers::AdaDelta, primitiv::optimizers::AdaGrad, primitiv::optimizers::Adam, primitiv::optimizers::MomentumSGD, primitiv::optimizers::RMSProp, primitiv::optimizers::SGD

Public Functions

void load(const std::string &path)

Loads configurations from a file.

Parameters
  • path: Path of the optimizer parameter file.

void save(const std::string &path) const

Saves current configurations to a file.

Parameters
  • path: Path of the file that will store optimizer parameters.

std::uint32_t get_epoch() const

Retrieves current epoch.

Return
Current epoch.

void set_epoch(std::uint32_t epoch)

Sets current epoch.

Parameters
  • epoch: New epoch.

float get_learning_rate_scaling() const

Retrieves current learning rate scaling factor.

Return
The scaling factor.

void set_learning_rate_scaling(float scale)

Sets learning rate scaling factor.

Remark
Could not set negative values.
Parameters
  • scale: New scaling factor.

float get_weight_decay() const

Retrieves current L2 decay strength.

Return
Current L2 decay strength.

void set_weight_decay(float strength)

Sets L2 decay strength.

Remark
Could not set negative values.
Parameters
  • strength: New L2 decay strength, or 0 to disable L2 decay.

float get_gradient_clipping() const

Retrieves current gradient clipping threshold.

Return
Current gradient clipping threshold.

void set_gradient_clipping(float threshold)

Sets gradient clipping threshold.

Remark
Could not set negative values.
Parameters
  • threshold: New clipping threshold, or 0 to disable gradient clipping.

void add()

Do nothing. This function is used as the sentinel of other specialized functions.

template <typename T, typename... Args>
void add(T &model_or_param, Args&... args)

Registers multiple parameters and models.

This function behaves similar to multiple

add() calls with the same order of arguments. E.g., below lines should behave similarly (except the case of exceptions): 
add(a, b, c, d);
add(a, b); add(c, d);
add(a); add(b); add(c); add(d);
Parameters

void reset_gradients()

Resets all gradients of registered parameters.

void update()

Updates parameter values.

virtual void get_configs(std::unordered_map<std::string, std::uint32_t> &uint_configs, std::unordered_map<std::string, float> &float_configs) const

Gathers configuration values.

Parameters
  • uint_configs: Configurations with std::uint32_t type.
  • float_configs: Configurations with float type.

virtual void set_configs(const std::unordered_map<std::string, std::uint32_t> &uint_configs, const std::unordered_map<std::string, float> &float_configs)

Sets configuration values.

Parameters
  • uint_configs: Configurations with std::uint32_t type.
  • float_configs: Configurations with float type.

Inherited Classes
class SGD : public primitiv::Optimizer

Simple stochastic gradient descent.

Public Functions

SGD(float eta = 0.1)

Creates a new SGD object.

Parameters
  • eta: Learning rate.

float eta() const

Returns the learning rate.

Return
Learning rate.

class MomentumSGD : public primitiv::Optimizer

Stochastic gradient descent with momentum.

Public Functions

MomentumSGD(float eta = 0.01, float momentum = 0.9)

Creates a new MomentumSGD object.

Parameters
  • eta: Learning rate.
  • momentum: Decay factor of the momentum.

float eta() const

Returns the hyperparameter eta.

Return
The value of eta.

float momentum() const

Returns the hyperparameter momentum.

Return
The value of momentum.

class AdaGrad : public primitiv::Optimizer

AdaGrad optimizer.

Public Functions

primitiv::optimizers::AdaGrad::AdaGrad(float eta = 0.001, float eps = 1e-8)

Creates a new AdaGrad object.

Parameters
  • eta: Learning rate.
  • eps: Bias of power.

float eta() const

Returns the hyperparameter eta.

Return
The value of eta.

float eps() const

Returns the hyperparameter eps.

Return
The value of eps.

class RMSProp : public primitiv::Optimizer

RMSProp Optimizer.

Public Functions

primitiv::optimizers::RMSProp::RMSProp(float eta = 0.01, float alpha = 0.9, float eps = 1e-8)

Creates a new RMSProp object.

Parameters
  • eta: Learning rate.
  • alpha: Decay factor of moment.
  • eps: Bias of power.

float eta() const

Returns the hyperparameter eta.

Return
The value of eta.

float alpha() const

Returns the hyperparameter alpha.

Return
The value of alpha.

float eps() const

Returns the hyperparameter eps.

Return
The value of eps.

class AdaDelta : public primitiv::Optimizer

AdaDelta optimizer. https://arxiv.org/abs/1212.5701

Public Functions

primitiv::optimizers::AdaDelta::AdaDelta(float rho = 0.95, float eps = 1e-6)

Creates a new AdaDelta object.

Parameters
  • rho: Decay factor of RMS operation.
  • eps: Bias of RMS values.

float rho() const

Returns the hyperparameter rho.

Return
The value of rho.

float eps() const

Returns the hyperparameter eps.

Return
The value of eps.

class Adam : public primitiv::Optimizer

Adam optimizer. https://arxiv.org/abs/1412.6980

Public Functions

primitiv::optimizers::Adam::Adam(float alpha = 0.001, float beta1 = 0.9, float beta2 = 0.999, float eps = 1e-8)

Creates a new Adam object.

Parameters
  • alpha: Learning rate.
  • beta1: Decay factor of momentum history.
  • beta2: Decay factor of power history.
  • eps: Bias of power.

float alpha() const

Returns the hyperparameter alpha.

Return
The value of alpha.

float beta1() const

Returns the hyperparameter beta1.

Return
The value of beta1.

float beta2() const

Returns the hyperparameter beta2.

Return
The value of beta2.

float eps() const

Returns the hyperparameter eps.

Return
The value of eps.

Parameter

class Parameter : primitiv::mixins::Nonmovable<Parameter>

Class to manage a trainable tensor parameter.

Public Functions

Parameter()

Creates an invalid parameter object.

Parameter(const Shape &shape, const std::vector<float> &value, Device *device)

Creates a new Parameter object.

Parameters
  • shape: The shape of the parameter. The batch size should be 1.
  • value: List of initial values. Order of elements should be the column-major (Fortran) order.
  • device: The device object to manage internal memory.

Parameter(const Shape &shape, const std::vector<float> &value, Device &device)

Creates a new Parameter object.

Parameters
  • shape: The shape of the parameter. The batch size should be 1.
  • value: List of initial values. Order of elements should be the column-major (Fortran) order.
  • device: The device object to manage internal memory.

Parameter(const Shape &shape, const std::vector<float> &value)

Creates a new Parameter object.

Parameters
  • shape: The shape of the parameter. The batch size should be 1.
  • value: List of initial values. Order of elements should be the column-major (Fortran) order.

Parameter(const Shape &shape, const Initializer &initializer, Device *device)

Creates a new Parameter object.

Parameters
  • shape: The shape of the parameter. The batch size should be 1.
  • initializer: An Initializer object.
  • device: The device object to manage internal memory.

Parameter(const Shape &shape, const Initializer &initializer, Device &device)

Creates a new Parameter object.

Parameters
  • shape: The shape of the parameter. The batch size should be 1.
  • initializer: An Initializer object.
  • device: The device object to manage internal memory.

Parameter(const Shape &shape, const Initializer &initializer)

Creates a new Parameter object.

Parameters
  • shape: The shape of the parameter. The batch size should be 1.
  • initializer: An Initializer object.

void init(const Shape &shape, const std::vector<float> &value, Device *device)

Initializes the Parameter object.

Parameters
  • shape: The shape of the parameter. The batch size should be 1.
  • value: List of initial values. Order of elements should be the column-major (Fortran) order.
  • device: The device object to manage internal memory.

void init(const Shape &shape, const std::vector<float> &value, Device &device)

Initializes the Parameter object.

Parameters
  • shape: The shape of the parameter. The batch size should be 1.
  • value: List of initial values. Order of elements should be the column-major (Fortran) order.
  • device: The device object to manage internal memory.

void init(const Shape &shape, const std::vector<float> &value)

Initializes the Parameter object.

Parameters
  • shape: The shape of the parameter. The batch size should be 1.
  • value: List of initial values. Order of elements should be the column-major (Fortran) order.

void init(const Shape &shape, const Initializer &initializer, Device *device)

Initializes the Parameter object.

Parameters
  • shape: The shape of the parameter. The batch size should be 1.
  • initializer: An Initializer object.
  • device: The device object to manage internal memory.

void init(const Shape &shape, const Initializer &initializer, Device &device)

Initializes the Parameter object.

Parameters
  • shape: The shape of the parameter. The batch size should be 1.
  • initializer: An Initializer object.
  • device: The device object to manage internal memory.

void init(const Shape &shape, const Initializer &initializer)

Initializes the Parameter object.

Parameters
  • shape: The shape of the parameter. The batch size should be 1.
  • initializer: An Initializer object.

void load(const std::string &path, bool with_stats, Device *device)

Loads parameters from specified file.

Parameters
  • path: File path to load parameters.
  • with_stats: Whether or not to load all additional statistics as well as parameter values if the file has them.
  • device: The device object to manage internal memory.

void load(const std::string &path, bool with_stats, Device &device)

Loads parameters from specified file.

Parameters
  • path: File path to load parameters.
  • with_stats: Whether or not to load all additional statistics as well as parameter values if the file has them.
  • device: The device object to manage internal memory.

void load(const std::string &path, bool with_stats)

Loads parameters from specified file.

Parameters
  • path: File path to load parameters.
  • with_stats: Whether or not to load all additional statistics as well as parameter values if the file has them.

void load(const std::string &path)

Loads parameters from specified file.

Parameters
  • path: File path to load parameters.

void save(const std::string &path, bool with_stats) const

Saves current parameters into specified file.

Parameters
  • path: File path to save parameters.
  • with_stats: Whether or not to save all additional statistics as well as parameter values if the parameter object has them.

void save(const std::string &path) const

Saves current parameters into specified file.

Parameters
  • path: File path to save parameters.

bool valid() const

Returns whether the parameter is valid or not.

Return
true or false w.r.t. the parameter is valid or not.

void reset_gradient()

Set all gradients to 0.

void add_stats(const std::string &name, const Shape &shape)

Adds a new optional statistics tensor.

Remark
All elements in the new statistics tensor is initialized by 0.
Parameters
  • name: Name of the statistics.
  • shape: Shape of the tensor.

bool has_stats(const std::string &name) const

Checks whether the statistics with name name exists or not.

Return
true if the entry exists, false otherwise.
Parameters
  • name: Name of the statistics.

Shape shape() const

Returns the shape of the parameter.

Return
Shape object.

Device &device() const

Returns the Device object to manage the internal memory.

Return
Pointer of the Device object.

const Tensor &value() const

Returns the values of the parameter.

Return
A tensor representing the parameter tensor.

Tensor &value()

Returns the values of the parameter.

Return
A tensor representing the parameter tensor.

const Tensor &gradient() const

Returns the current gradient of the parameter.

Return
A tensor representing the gradient of the value.

Tensor &gradient()

Returns the current gradient of the parameter.

Return
A tensor representing the gradient of the value.

const Tensor &stats(const std::string &name) const

Returns the current opotional statistics tensor specified by given name.

Return
A tensor.
Parameters
  • name: Name of the statistics.

Tensor &stats(const std::string &name)

Returns the current opotional statistics tensor specified by given name.

Return
A tensor.
Parameters
  • name: Name of the statistics.

Shape

class Shape

Data structure to represent the shape of the node.

Examples: Shape() == Shape({1, 1, 1, …}, 1): scalar Shape({}) == Shape({1, 1, 1, …}, 1): scalar Shape({n}) == Shape({n, 1, 1, …}, 1): column vector Shape({n, m}) == Shape({n, m, 1, …}, 1): matrix Shape({…}, k): k-parallelized data (mini-batch)

Public Functions

Shape()

Creates a new scalar Shape object.

Shape(std::initializer_list<std::uint32_t> dims, std::uint32_t batch = 1)

Creates a new Shape object.

Parameters
  • dims: List of the dimension sizes.
  • batch: Batch size.

Shape(const std::vector<std::uint32_t> &dims, std::uint32_t batch = 1)

Creates a new Shape object.

Parameters
  • dims: List of the dimension sizes.
  • batch: Batch size.

std::uint32_t operator[](std::uint32_t i) const

Returns the size of the i-th dimension.

Return
Size of the i-th dimension.
Parameters
  • i: Dimension number to check.

const std::vector<std::uint32_t> dims() const

Returns the dimension array.

Return
Copy of the dimension array.

std::uint32_t depth() const

Returns the depth (length of non-1 dimensions) of the shape.

Return
The depth of the shape.

std::uint32_t batch() const

Returns the batch size.

Return
Batch size.

std::uint32_t volume() const

Returns the number of elements in each sample. This value is equal to the product of all dimensions.

Return
Number of elements.

std::uint32_t lower_volume(std::uint32_t dim) const

Returns the number of elements in 1 to specified dim.

Return
dims[0] * dims[1] * ... * dims[dim-1]
Parameters
  • dim: Upper bound of the dimension.

std::uint32_t size() const

Returns the number of elements in all samples of the mini-batch. This value is equal to batch() * volume().

Return
Number of elements.

std::string to_string() const

Returns a string representation of the shape. The format is: “[n,m,…]xk”

Return
Encoded string.

bool operator==(const Shape &rhs) const

Compares this and other shape.

Return
true if this and rhs are same, false otherwise.
Parameters
  • rhs: Shape object to compare.

bool operator!=(const Shape &rhs) const

Compares this and other shape.

Return
true if this and rhs are not same, false otherwise.
Parameters
  • rhs: Shape object to compare.

bool has_batch() const

Checks whether the shape has minibatch or not.

Return
true if the shape has minibatch, false otherwise.

bool has_compatible_batch(const Shape &rhs) const

Checks whether two batch size is compatible (broadcastable) or not.

Return
true if both batch size is compatible, false otherwise.
Parameters
  • rhs: Shape object to compare.

bool is_scalar() const

Checks whether the shape is a scalar or not.

Return
true if the shape is a scalar, false otherwise.

bool is_column_vector() const

Checks whether the shape is a column vector or not.

Return
true if the shape is a column vector, false otherwise.

bool is_matrix() const

Checks whether the shape is a vector or a matrix, or not.

Return
true if the shape is a vector or a matrix, false otherwise.

bool has_same_dims(const Shape &rhs) const

Checks whether two shapes have completely same dimensions.

Return
true if both shape have same dimensions, false otherwise.
Parameters
  • rhs: Shape object to compare.

bool has_same_loo_dims(const Shape &rhs, std::uint32_t dim) const

Checks whether two shapes have same dimensions without an axis. (LOO: leave one out)

Return
true if both shape have same dimensions regardless the dimension dim, false otherwise.
Parameters
  • rhs: Shape object to compare.
  • dim: Dimension to be ignored.

Shape resize_dim(std::uint32_t dim, std::uint32_t m) const

Creates a new shape which have one different dimension.

Return
New shape.
Parameters
  • dim: Dimension to be changed.
  • m: New size of the dimension dim.

Shape resize_batch(std::uint32_t batch) const

Creates a new shape which have specified batch size.

Return
New shape.
Parameters
  • batch: New batch size.

void update_dim(std::uint32_t dim, std::uint32_t m)

Directly updates a specified dimension.

Parameters
  • dim: Dimension to be updated.
  • m: New size of the dimension dim.

void update_batch(std::uint32_t batch)

Directly updates the batch size.

Parameters
  • batch: New batch size.

Tensor

class Tensor

Value with any dimensions.

Public Functions

Tensor()

Creates an invalid Tensor.

bool valid() const

Check whether the object is valid or not.

Return
true if the object is valid, false otherwise.
Remark
This returns false when the object is created through the default constructor or the object had been moved.

void check_valid() const

Check whether the object is valid or not.

Exceptions
  • primitiv::Error: This object is invalid.

Shape shape() const

Returns the shape of the Tensor.

Return
Shape of the Tensor.

Device &device() const

Returns the Device object related to the internal memory.

Return
Device object.

float to_float() const

Retrieves one internal value in the tensor.

Return
An internal float value.
Remark
This function can be used only when the tensor is a scalar and non-minibatched (i.e., shape() == Shape()).

std::vector<float> to_vector() const

Retrieves internal values in the tensor as a vector.

Return
A list of the internal values.
Remark
Each resulting values a re ordered by the column-major order, and the batch size is assumed as the last dimension of the tensor.

std::vector<std::uint32_t> argmax(std::uint32_t dim) const

Retrieves argmax indices along an axis.

Return
A list of integers that indicates positions of the maximum values.
Parameters
  • dim: A specified axis.

std::vector<std::uint32_t> argmin(std::uint32_t dim) const

Retrieves argmin indices along an axis.

Return
A list of integers that indicates positions of the minimum values.
Parameters
  • dim: A specified axis.

void invalidate()

Invalidates this object.

void reset(float k)

Reset internal values using a constant.

Parameters
  • k: A value to be used to initialize each element.

void reset_by_array(const float *values)

Reset internal values using a vector.

Remark
Length of values should be equal to shape().size(). Each element should be ordered by the column-major order, and the batch size is assumed as the last dimension.
Parameters
  • values: Array of values to be used to initialize each element.

void reset_by_vector(const std::vector<float> &values)

Reset internal values using a vector.

Remark
values.size() should be equal to shape().size(). Each element should be ordered by the column-major order, and the batch size is assumed as the last dimension.
Parameters
  • values: List of values to be used to initialize each element.

Tensor reshape(const Shape &new_shape) const

Returns a tensor which have the same values and different shape.

Return
A new tensor.
Parameters
  • new_shape: New shape with batch size 1.

Tensor flatten() const

Returns a flattened tensor.

Return
A new tensor.

Tensor &inplace_multiply_const(float k)

Directly multiplies a constant.

Return
*this
Parameters
  • k: A constant to multiply.

Tensor &inplace_add(const Tensor &x)

Directly adds a value.

Return
*this
Parameters
  • x: A tensor to add.

Tensor &inplace_subtract(const Tensor &x)

Directly subtracts a value.

Return
*this
Parameters
  • x: A tensor to subtract.

Build Options

Standard Options

Users basically can use CMake 3.1.0 standard options (e.g., -DCMAKE_INSTALL_PREFIX) together with the unique options.

Unique Options

PRIMITIV_BUILD_C_API

Default value: OFF

Builds C APIs. libprimitiv_c library file and headers in the primitiv/c directory will also be installed.

PRIMITIV_BUILD_STATIC_LIBRARY

Default value: OFF

Builds static libraries instead of shared objects.

PRIMITIV_BUILD_TESTS

Default value: OFF

Builds test binaries and generates make test command. This option introduces a dependency to the Google Test. FindGTest options can also be used.

PRIMITIV_BUILD_TESTS_PROBABILISTIC

Default value: OFF

Builds test cases that probabilistically fails.

PRIMITIV_GTEST_SOURCE_DIR

Default value: ""

Specifies the source directory of Google Test. If you want to use Google Test provided from Debian/Ubuntu repository, add -DPRIMITIV_GTEST_SOURCE_DIR=/usr/src/googletest/googletest together with -PRIMITIV_BUILD_TESTS=ON option.

PRIMITIV_USE_CACHE

Default value: OFF

Whether or not to use cached values to prevent increasing computation amount. Libraries built with this flag will tend to consume more memory.

PRIMITIV_USE_EIGEN

Default value: OFF

Enables Eigen backend (primitiv::devices::Eigen class). This option introduces a dependency to the Eigen3 library, and FindEigen3 options can also be used.

PRIMITIV_USE_CUDA

Default value: OFF

Enables CUDA backend (primitiv::devices::CUDA class). This option introduces a dependency to the NVIDIA CUDA Toolkit v8.0 or later. FindCuda options can also be used.

PRIMITIV_USE_CUDNN

Default value: OFF

Enables cuDNN as the backend of few CUDA functions. This option introduces a dependency to the cuDNN library v5.0 or later. FindCuDNN options can also be used.

PRIMITIV_USE_OPENCL

Default value: OFF

Enables OpenCL backend(primitiv::devices::OpenCL class). This option introduces dependencies to an OpenCL v1.2 implementation and OpenCL C++ Bindings v2. FindOpenCL options can also be used, and cl2.hpp should be found in /path/to/include/CL.

primitiv File Format v0.1

primitiv File Format is a common binary format to store/load data used in primitiv. It uses the MessagePack wire format as the inner binary representation.

Legend

+------+     +---------------+---------------+...
| Type |  =  | Member Type 1 | Member Type 2 |
|      |     | Member Name 1 | Member Name 2 |
+------+     +---------------+---------------+...

Types

+-------+     +---------------+--------+
| Shape |  =  | array<uint32> | uint32 |
|       |     | dims          | batch  |
+-------+     +---------------+--------+

In the current version, the batch member is always 1 for all Shape objects.

+--------+     +-------+------+
| Tensor |  =  | Shape | bin  |
|        |     | shape | data |
+--------+     +-------+------+

data member has an array of single-precision floating number with the following format:

  • Byte order: Little-endian (differ than MessagePack’s float)
  • Array order: Column-major (Fortran)
  • Batch is treated as the last dimension of the shape (if shape.batch > 1). I.e., The next data begins just after the previous data according to the column-major array order.
+-----------+     +--------+--------+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~+.........
| Parameter |  =  | Tensor | uint32 | str         | Tensor        |
|           |     | value  | N      | stat_key[1] | stat_value[1] | N times
+-----------+     +--------+--------+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~+.........

+-------+     +--------+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~+.........
| Model |  =  | uint32 | array<str>   | Parameter      |
|       |     | N      | param_key[1] | param_value[1] | N times
+-------+     +--------+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~+.........

The key of each parameter represents the address of the parameter from the root model. E.g.:

  • param_key == ["foo"]: Parameter has the name "foo", and is directly owned by the root model.
  • param_key == ["foo", "bar"]: Parameter has the name "bar", and is owned by the submodel "foo".
+-----------+     +------------------+-----------------+
| Optimizer |  =  | map<str, uint32> | map<str, float> |
|           |     | uint_configs     | float_configs   |
+-----------+     +------------------+-----------------+

File Format

+-----------+-----------+-----------+----------------------------------------+
| uint32    | uint32    | uint32    | Shape|Tensor|Parameter|Model|Optimizer |
| ver_major | ver_minor | data_type | data                                   |
+-----------+-----------+-----------+----------------------------------------+

Version numbers are typically equal to following:

  • ver_major == 0
  • ver_minor == 1

Following table shows the correspondence between data_type and data:

data_type data
0x0 Shape
0x100 Tensor
0x200 Parameter
0x300 Model
0x400 Optimizer