Tensor · Apache SINGA

Each Tensor instance is a multi-dimensional array allocated on a specific Device instance. Tensor instances store variables and provide linear algebra operations over different types of hardware devices without user awareness. Note that users need to make sure the tensor operands are allocated on the same device except copy functions.

Tensor Usage

Create Tensor

>>> import numpy as np
>>> from singa import tensor
>>> tensor.from_numpy( np.asarray([[1, 0, 0], [0, 1, 0]], dtype=np.float32) )
[[1. 0. 0.]
 [0. 1. 0.]]

Convert to numpy

>>> a = np.asarray([[1, 0, 0], [0, 1, 0]], dtype=np.float32)
>>> tensor.from_numpy(a)
[[1. 0. 0.]
 [0. 1. 0.]]
>>> tensor.to_numpy(tensor.from_numpy(a))
array([[1., 0., 0.],
       [0., 1., 0.]], dtype=float32)

Tensor Methods

>>> t = tensor.from_numpy(a)
>>> t.transpose([1,0])
[[1. 0.]
 [0. 1.]
 [0. 0.]]

tensor transformation up to 6 dims

>>> a = tensor.random((2,3,4,5,6,7))
>>> a.shape
(2, 3, 4, 5, 6, 7)
>>> a.reshape((2,3,4,5,7,6)).transpose((3,2,1,0,4,5)).shape
(5, 4, 3, 2, 7, 6)

Tensor Arithmetic Methods

tensor is evaluated in real time.

>>> t + 1
[[2. 1. 1.]
 [1. 2. 1.]]
>>> t / 5
[[0.2 0.  0. ]
 [0.  0.2 0. ]]

tensor broadcasting arithmetic:

>>> a
[[1. 2. 3.]
 [4. 5. 6.]]
>>> b
[[1. 2. 3.]]
>>> a + b
[[2. 4. 6.]
 [5. 7. 9.]]
>>> a * b
[[ 1.  4.  9.]
 [ 4. 10. 18.]]
>>> a / b
[[1.  1.  1. ]
 [4.  2.5 2. ]]
>>> a/=b # inplace operation
>>> a
[[1.  1.  1. ]
 [4.  2.5 2. ]]

tensor broadcasting on matrix multiplication (GEMM)

>>> from singa import tensor
>>> a = tensor.random((2,2,2,3))
>>> b = tensor.random((2,3,4))
>>> tensor.mult(a,b).shape
(2, 2, 2, 4)

Tensor Functions

Functions in module singa.tensor return new tensor object after applying the transformation defined in the function.

>>> tensor.log(t+1)
[[0.6931472 0.        0.       ]
 [0.        0.6931472 0.       ]]

Tensor on Different Devices

tensor is created on host (CPU) by default; it can also be created on different hardware devices by specifying the device. A tensor could be moved between devices via to_device() function.

>>> from singa import device
>>> x = tensor.Tensor((2, 3), device.create_cuda_gpu())
>>> x.gaussian(1,1)
>>> x
[[1.531889   1.0128608  0.12691343]
 [2.1674204  3.083676   2.7421203 ]]
>>> # move to host
>>> x.to_device(device.get_default_device())

use Tensor to train MLP


"""
  code snipet from examples/mlp/module.py
"""

label = get_label()
data = get_data()

dev = device.create_cuda_gpu_on(0)
sgd = opt.SGD(0.05)

# define tensor for input data and label
tx = tensor.Tensor((400, 2), dev, tensor.float32)
ty = tensor.Tensor((400,), dev, tensor.int32)
model = MLP(data_size=2, perceptron_size=3, num_classes=2)

# attached model to graph
model.set_optimizer(sgd)
model.compile([tx], is_train=True, use_graph=True, sequential=False)
model.train()

for i in range(1001):
    tx.copy_from_numpy(data)
    ty.copy_from_numpy(label)
    out, loss = model(tx, ty, 'fp32', spars=None)

    if i % 100 == 0:
        print("training loss = ", tensor.to_numpy(loss)[0])

Output:

$ python3 examples/mlp/module.py
training loss =  0.6158037
training loss =  0.52852553
training loss =  0.4571422
training loss =  0.37274635
training loss =  0.30146334
training loss =  0.24906921
training loss =  0.21128304
training loss =  0.18390492
training loss =  0.16362564
training loss =  0.148164
training loss =  0.13589878

Tensor Implementation

The previous section shows the general usage of Tensor, the implementation under the hood will be covered below. First, the design of Python and C++ tensors will be introduced. Later part will talk about how the frontend (Python) and backend (C++) are connected and how to extend them.

Python Tensor

Python class Tensor, defined in python/singa/tensor.py, provides high level tensor manipulations for implementing deep learning operations (via autograd), as well as data management by end users.

It primarily works by simply wrapping around C++ tensor methods, both arithmetic (e.g. sum) and non arithmetic methods (e.g. reshape). Some advanced arithmetic operations are later introduced and implemented using pure Python tensor API, e.g. tensordot. Python Tensor APIs could be used to implement complex neural network operations easily with the flexible methods available.

C++ Tensor

C++ class Tensor, defined in include/singa/core/tensor.h, primarily manages the memory that holds the data, and provides low level APIs for tensor manipulation. Also, it provides various arithmetic methods (e.g. matmul) by wrapping different backends (CUDA, BLAS, cuBLAS, etc.).

Execution Context and Memory Block

Two important concepts or data structures for Tensor are the execution context device, and the memory block Block.

Each Tensor is physically stored on and managed by a hardware device, representing the execution context (CPU, GPU). Tensor math calculations are executed on the device.

Tensor data in a Block instance, defined in include/singa/core/common.h. Block owns the underlying data, while tensors take ownership on the metadata describing the tensor, like shape, strides.

Tensor Math Backends

To leverage on the efficient math libraries provided by different backend hardware devices, SINGA has one set of implementations of Tensor functions for each supported backend.

'tensor_math_cpp.h' implements operations using Cpp (with CBLAS) for CppCPU devices.
'tensor_math_cuda.h' implements operations using Cuda (with cuBLAS) for CudaGPU devices.
'tensor_math_opencl.h' implements operations using OpenCL for OpenclGPU devices.

Exposing C++ APIs to Python

SWIG(http://www.swig.org/) is a tool that can automatically convert C++ APIs into Python APIs. SINGA uses SWIG to expose the C++ APIs to Python. Several files are generated by SWIG, including python/singa/singa_wrap.py. The Python modules (e.g., tensor, device and autograd) imports this module to call the C++ APIs for implementing the Python classes and functions.

import tensor

t = tensor.Tensor(shape=(2, 3))

For example, when a Python Tensor instance is created as above, the Tensor class implementation creates an instance of the Tensor class defined in singa_wrap.py, which corresponds to the C++ Tensor class. For clarity, the Tensor class in singa_wrap.py is referred as CTensor in tensor.py.

# in tensor.py
from . import singa_wrap as singa

CTensor = singa.Tensor

Create New Tensor Functions

With the groundwork set by the previous description, extending tensor functions could be done easily in a bottom up manner. For math operations, the steps are:

Declare the new API to tensor.h
Generate code using the predefined macro in tensor.cc, refer to GenUnaryTensorFn(Abs); as an example.
Declare the template method/function in tensor_math.h
Do the real implementation at least for CPU (tensor_math_cpp.h) and GPU(tensor_math_cuda.h)
Expose the API via SWIG by adding it into src/api/core_tensor.i
Define the Python Tensor API in tensor.py by calling the automatically generated function in singa_wrap.py
Write unit tests where appropriate

Python API

work in progress

CPP API

work in progress