Welcome to plaidml’s documentation!¶

Installation Instructions¶

PlaidML supports Ubuntu, macOS , and Microsoft Windows operating systems.

If necessary, install Python’s pip tool. OpenCL 1.2 or greater is alsorequired.

sudo add-apt-repository universe && sudo apt update
sudo apt install python3-pip
sudo apt install clinfo

Run clinfo, and if it reports "Number of platforms" == 0, you can install a driver (GPU) or enable a CPU via one of these options:

Nvidia – For Nvidia GPUs, run:

sudo add-apt-repository ppa:graphics-drivers/ppa && sudo apt update
sudo apt install nvidia-modprobe nvidia-384 nvidia-opencl-icd-384 libcuda1-384

AMD – For AMD graphics cards, download the AMDGPU PRO driver and follow the instructions provided by AMD for the chip.
Intel® Xeon® Processors OR Intel® Core™ Processors – In lieu of installing specific drivers, you can install ngraph with pip, or you can build the nGraph Library with the cmake flag -DNGRAPH*PLAIDML*ENABLE=TRUE.

Python

Although PlaidML can be run with Python2, we recommend Python3, as well as judicious use of a Virtualenv. To create one just for using PlaidML:

python3 -m venv plaidml-venv
source plaidml-venv/bin/activate

Keras

There are two ways to get Keras working on your system:

Isolate it to your venv as follows:

pip install -U plaidml-keras

Alternatively, install the PlaidML wheels system-wide with:

sudo -H pip install -U plaidml-keras

Finally, set up PlaidML to use a preferred computing device:

plaidml-setup

You can test the installation by running MobileNet in plaidbench. Remember to use sudo -H if you’re working outside of a virtual environment.

pip install plaidml-keras plaidbench
plaidbench keras mobilenet

You can adapt any Keras code by using the PlaidML backend instead of the TensorFlow, CNTK, or Theano backend that you’d normally use; simply change the Keras backend to plaidml.keras.backend. You can do this by modifying

~/.keras/keras.json so that the backend line reads "backend": "plaidml.keras.backend" If this file does not exist, see the [Backend instructions for Keras]. If you don’t need anything special in your Keras settings, you can set the ~/.keras/keras.json as follows:

{
    "epsilon": 1e-07,
    "floatx": "float32",
    "image*data*format": "channels_last",
    "backend": "plaidml.keras.backend"
}

Another option is to globally set the KERAS_BACKEND environment variable to plaidml.keras.backend. A monkey-patch technique involving plaidml.keras.install_backend() may still work, but should be considered deprecated in favor of the above methods.

A computer listed on Apple’s compatibility list with support for OpenCL 1.2 is required; those from 2011 and later usually fit this requirement.

Python

Although PlaidML can be run with Python2, we recommend Python3, as well as judicious use of a Virtualenv. To create one just for using PlaidML:

python3 -m venv plaidml-venv
source plaidml-venv/bin/activate

Keras

To install PlaidML with Keras, run the following:

pip install -U plaidml-keras

Finally, set up PlaidML to use a preferred computing device:

plaidml-setup

PlaidML should now be installed! You can test the installation by running MobileNet in plaidbench.

pip install plaidml-keras plaidbench
plaidbench keras mobilenet

These instructions assume Windows 10 without Python installed; adapt accordingly.

First install Chocolatey by starting an Administrator PowerShell and running:

Set-ExecutionPolicy Bypass -Scope Process -Force; iex ((New-Object System.Net.WebClient).DownloadString('https://chocolatey.org/install.ps1'))

You’ll likely need to reboot your shell at this point.

Install Python:

choco install -y python git vcredist2015

Switch to an unprivileged PowerShell to install and set up PlaidML with Keras

pip install -U plaidml-keras
plaidml-setup

PlaidML should now be installed! You can test the installation by running MobileNet in plaidbench.

pip install plaidml-keras plaidbench
plaidbench keras mobilenet

Intel® SDK for OpenCL™ Applications

Building from source¶

Install Anaconda¶

Install Anaconda. You’ll want to use a Python 3 version. After installing Anaconda, you’ll need to restart your shell, to pick up its environment variable modifications (i.e. the path to the conda tool and shell integrations). For Microsoft Windows, you’ll also need the Visual C++ compiler (2017+) and the Windows SDK, following the Bazel-on-Windows instructions.

Install bazelisk¶

The Bazelisk tool is a wrapper for Bazel which provides the ability to enfore a particular version of Bazel. Download the latest version for your platform and place the executable somewhere in your PATH (e.g. /usr/local/bin). You will also need to mark it as executable. Example:

wget https://github.com/bazelbuild/bazelisk/releases/download/v0.0.8/bazelisk-darwin-amd64
mv bazelisk-darwin-amd64 /usr/local/bin
chmod +x /usr/local/bin/bazelisk

https://github.com/bazelbuild/bazelisk/releases

Configure the build¶

Use the configure script to configure your build. Note: the configure script requires Python 3. By default, running the configure script will: * Create and/or update your conda environment * Configure pre-commit hooks for development purposes * Configure bazelisk based on your host OS

./configure

On Windows, use:

python configure

Here’s an example session:

$ ./configure
Configuring PlaidML build environment
conda found at: /usr/local/miniconda3/bin/conda
Creating conda environment from: $HOME/src/plaidml/environment.yml
Searching for pre-commit in: $HOME/src/plaidml/.cenv/bin
pre-commit installed at .git/hooks/pre-commit
bazelisk version
Bazelisk version: v0.0.8
Starting local Bazel server and connecting to it...
Build label: 0.28.1
Build target: bazel-out/darwin-opt/bin/src/main/java/com/google/devtools/build/lib/bazel/BazelServer_deploy.jar
Build time: Fri Jul 19 15:22:50 2019 (1563549770)
Build timestamp: 1563549770
Build timestamp as int: 1563549770
Using variant: macos*x86*64
Your build is configured.
Use the following to run all unit tests:
bazelisk test //...

Build the PlaidML Python wheel¶

bazelisk build //plaidml:wheel

Install the PlaidML Python wheel¶

pip install -U bazel-bin/plaidml/wheel.pkg/dist/*.whl
plaidml-setup

PlaidML with Keras¶

The PlaidML-Keras Python Wheel contains the code needed for integration with Keras. You can get the latest release of the PlaidML-Keras Python Wheel by running:

pip install plaidml-keras

You can also build and install the wheel from source.

Set up a build environment¶

Follow the setup instructions for Build the PlaidML Python wheel, above.

Build the PlaidML-Keras wheel¶

bazelisk build //plaidml/keras:wheel

Install the PlaidML-Keras Python wheel¶

pip install -U bazel-bin/plaidml/keras/wheel.pkg/dist/*.whl

Testing PlaidML¶

Unit tests are executed through bazel:

bazelisk test //...

Unit tests for frontends are marked manual and must be executed individually (requires running plaidml-setup prior to execution)

bazelisk run //plaidml/keras:backend_test

Contributing to PlaidML¶

We welcome contributions to PlaidML from anyone. This document contains: * Guidelines for creating successful PRs * Outlines the contribution process * Lists general areas for contribution * Provides resources and context to ease development, where relevant and available Before starting any work, please ensure you are able to build and test PlaidML. Guidelines ****** * Create unit tests for new features and bug fixes. Integration tests are required for larger features.

C++ code conforms to the Google Style Guide for CPP.

Python code conforms to the Google Python Style Guide.

Process¶

Ensure there is an open issue assigned to you before doing (too much) work: * If you’re tackling an open issue that isn’t assigned, please assign it to yourself. * If you’d like to solve an issue that is already assigned, please comment on the issue to ensure you’re not duplicating effort. * If you’d like to provide a new feature, open a new issue. Please provide a reasonably-detailed description of what you’d like to do, and clearly indicate that you’re willing to do the work.
Work on a fork as usual in GitHub. Please ensure the same tests travis runs will pass before creating a PR.
Review the License file in the plaidml repo and the Guidelines on this page.

4. Once tests have passed, a maintainer will assign the issue to themselves and run the PR through the (currently private) performance test suite. If there are issues, we will attempt to resolve them, but we may provide details and ask the author to address. 5. Once the performance regression suite has passed, we will accept and merge the PR. Areas for Contribution ****************** * Ops for Frontends

PlaidML welcomes implementations for currently unimplemented operations as well as Tile code for novel operations supported by research.

Please read Adding Tile Ops and How to Write Tile Code tutorials.

ML Framework Frontends (e.g., Keras, Pytorch, etc) * PlaidML welcomes integrations with any established ML framework or interop (NNVM, ONNX, etc). * You can find commonly used operations in the [plaidml.op](api/plaidml.op.rst) module. * Please read building a frontend tutorial.
HALs for Backend Targets (OpenCL, Vulkan, SPIR-V, HVX, etc) * There is no documentation for the HAL currently. The interface is fairly straightforward and the OpenCL HAL <../tile/hal/opencl> provides a good example of a complete HAL.

Please follow the process above before embarking on anything major (like integrating a new frontend or backend).

Troubleshooting¶

Having trouble getting PlaidML to work? Well, you’re in the right place! Before you open a new issue on GitHub, please take a look at the Common Issues, Enable Verbose Logging in PlaidML, and Run Backend Tests. These steps will help enable us to provide you with better support on your issue.

Common Issues¶

PlaidML Setup Errors¶

Memory Errors¶

OSError: exception: access violation reading 0x0000000000000030

This error might be caused by a memory allocation failure, and it fails silently. You can fix this error by decreasing your batch size and trying again.

plaidml.exceptions.ResourceExhausted: Out of memory

This error is caused by incorrect Tile syntax.

Bazel Issues¶

For any Bazel-specific issues you’re encountering, we recommend that you first visit Bazel’s installation documentation which has a comprehensive overview of Bazel on various platforms. Any issues commonly encountered by PlaidML users are documented below.

Encountered error while reading extension file 'workspace.bzl': no such package '@toolchain//'

On MacOS devices, toolchain errors often indicate that the user does not have Xcode properly installed. Even if you have Xcode Command Line Tools installed, you may not have a proper installation of Xcode itself. To check your installation of Xcode, first print the path of the active developer directory:

xcode-select -p

The resulting path should be /Applications/Xcode.app/Contents/Developer. If that is not the path you are seeing when you run xcode-select -p, please go to the App Store and download Xcode. After verifying that Xcode is properly installed, you will need to reset your Bazel instance before running Bazel again:

bazelisk clean --expunge

PlaidML Exceptions¶

Applying function, tensor with mismatching dimensionality

This error may be caused by a known issue with the BatchDot operation, where results are inconsistent across backends. The Keras documentation for BatchDot matches the Theano backend’s implemented behavior and the default behavior within PlaidML. The TensorFlow backend implements BatchDot in a different way, and this causes a mismatch in the expected output shape (there is an open issue against TensorFlow to get this fixed). If you have existing Keras code that was written for the TensorFlow backend, and it is running into this issue, you can enable experimental support for TensorFlow-like BatchDot behavior by setting the environment variable PLAIDML*BATCHDOT*TF_BEHAVIOR to True.

ERROR:plaidml:syntax error, unexpected -, expecting "," or )

This error may be caused by special characters, such as -, that are used in variable names within your code. Please try removing and/or replacing special characters in your variable names, and try running again.

Run Backend Tests¶

Backend Tests provide us with useful information that we can use to help solve your issue. To run backend tests on PlaidML, follow these steps:

Verify that you have the PlaidML Python Wheel built as specified in Building from source
Run the backend tests through Bazel

bazel test --config macos*x86*64 @com*intel*plaidml//plaidml/keras:backend_test

Enable Verbose Logging¶

You can enable verbose logging through the environment variable PLAIDML_VERBOSE. PLAIDML_VERBOSE should be set to an integer specifying the level of verbosity (valid levels are 0-4 inclusive, where 0 is not verbose and 4 is the most verbose).

For instance, the following command would set a verbosity level of 1.

export PLAIDML_VERBOSE=1

Tile eDSL¶

The C++ Tile eDSL (Embedded Domain Specific Language) provides developers with a way of describing a neural network so that the Stripe-based PlaidML compiler can construct an efficient implementation. This tutorial is intended to help machine learning practitioners (or anyone with a background in software engineering and mathematics) get started using the C++ Tile eDSL.

Scope and Warning¶

This tutorial provides an introduction to the C++ Tile eDSL. It is intended to help machine learning practitioners get started writing Tile code as quickly as possible, and as such covers core features, not every language detail. This is a tutorial, not a spec, and as such will consist of a series of examples, with a summary reference section at the end. This tutorial covers how to use the C++ Tile eDSL, not how Tile code is constructed and manipulated by PlaidML. It does not cover the workings of PlaidML utilities such as the pmlc compiler. Tile and PlaidML are still being developed and the APIs discussed here are subject to change.

How to Write Tile Code¶

Sum Over Axis¶

We’re ready to look at some C++ Tile code! Here’s an operation that takes the sum over axis 0 of a 2D tensor (in Keras this would be K.sum(I, axis=0)):

Tensor sum_over_axis(const Tensor& I) {
  TensorDim M, N;
  TensorIndex m, n;
  I.bind_dims(M, N);
  auto O = TensorOutput(N);
  O(n) += I(m, n); // contraction
  return O;
}

def sum_over_axis(I):
  M, N = TensorDims(2)
  m, n = TensorIndexes(2)
  I.bind_dims(M, N)
  O = TensorOutput(N)
  # contraction
  O[n] += I[m, n]
  return O

An operation such as this which merges together values across one or more indices is called a contraction. The syntax may look a bit odd at first, but it’s related to summation notation. Below we show how this C++ Tile code is related to the mathematical formula for the operation by using colors to highlight corresponding pieces:

\[\color{red}O[n] \color{default}= \color{green}\sum_{m} \color{blue}I[m, n]\]

\[\color{red}\verb|O(n)| \color{green}\verb| += | \color{blue}\verb|I(m, n)|\color{default}\verb|;|\]

In green, notice that the summation symbol is represented as += in C++ Tile code. Some portions of the notation do not perfectly correspond. Here’s why:

Summation notation includes a m subscript to indicate that m is the variable being summed over. Tile code implicitly sums over all valid indices (valid means not out of range for any tensor, and not failing any additional user-specified constraints as discussed in later examples).
Tile must be explicitly given the shape of any new tensor created, done in this code by TensorOutput(N). In this case we want N to match the size of the last dimension of I, which is specified by using I.bind_dims(M, N). It is possible, however, to make this dimension of O larger or smaller, which would zero-pad or truncate O respectively. For example,
C++

Python
auto O = TensorOutput(N + 1);
O = TensorOutput(N+1)
would result in a 0 as the last element of O if we’re still assuming N is the size of the last dimension of I.
As is the case for all C++ statements, they must end with a semicolon.

Max Over Axis¶

Taking the maximum over axis 0 looks very similar to taking the sum over axis 0. Just like a sum is represented in Tile with +=, a max is represented by >=. Thus, the Tile code for max over axis 0 is just a single character change from sum over axis 0. Let’s look at it as a Tile function:

Tensor max_over_axis(const Tensor& I) {
  TensorDim M, N;
  TensorIndex m, n;
  I.bind_dims(M, N);
  auto O = TensorOutput(N);
  O(n) >= I(m, n);
  return O;
}

def max_over_axis(I):
  M, N = TensorDims(2)
  m, n = TensorIndexes(2)
  I.bind_dims(M, N)
  O = TensorOutput(N)
  O[n] >= I[m, n]
  return O

Again, this corresponds closely to mathematical notation:

\[\color{red}O[n] \color{default}= \color{green}\max_m \color{blue}I[m, n]\]

\[\color{red}\verb|O(n)| \color{green}\verb| >= | \color{blue}\verb|I(m, n)|\color{default}\verb|;|\]

Matrix Multiply¶

Next we’ll consider matrix multiplication. Let’s look at the mathematical expression for the matrix multiplication C = AB written out in element-level detail:

\[C[i, j] = \sum_{k} (A[i, k] \cdot B[k, j])\]

We can convert this to C++ Tile code using the same correspondence as the previous example: The summation sign becomes plus-assignment, the summation index is omitted, dimensions are given for the output tensor, and the statement ends in a semicolon. Here’s the result:

C(i, j) += A(i, k) * B(k, j);

C[i, j] += A[i, k] * B[k, j];

To have correct dimensions, we need I to be the first dimension of A and J the last dimension of B. Here’s how this looks as part of a full Tile function:

Tensor matmul(const Tensor& A, const Tensor& B) {
  TensorDim I, J, K;
  TensorIndex i, j, k;
  A.bind_dims(I, K);
  B.bind_dims(K, J);
  auto C = TensorOutput(I, J);
  C(i, j) += A(i, k) * B(k, j);
  return C;
}

def matmul(A, B):
  I, J, K = TensorDims(3)
  i, j, k = TensorIndexes(3)
  A.bind_dims(I, K)
  B.bind_dims(K, J)
  C = TensorOutput(I, J)
  C[i, j] += A[i, k] * B[k, j]
  return C

Notice that we use bind_dims on inputs and we use TensorOutput on outputs. Input dimensions can be repeated, which results in an error if the Tile function is passed inputs whose corresponding dimensions don’t all have the specified size (for example A.bind_dims(K, K) would be constrained to a square).

Global Min¶

There is a min contraction <= analogous to the max contraction >=. For the purposes of this example, however, let’s use the formula min(X) = -max(-X), to compute the min. We do this by combining a max computation with elementwise operations that perform the same operation (in this case negation) on every element of a tensor. Elementwise operations generally cannot be performed on the same line as contractions, so we write the global min function (for a 3D tensor) as follows:

Tensor global_min(const Tensor& I) {
  TensorIndex i, j, k;
  auto Neg = -I;
  auto O_Neg = TensorOutput();
  O_Neg() >= Neg(i, j, k);
  auto O = -O_Neg;
  return O;
}

def global_min(I):
  i, j, k = TensorIndexes(3)
  Neg = -I
  O_Neg = TensorOutput()
  O_Neg[()] >= Neg[i, j, k]
  O = -O_Neg
  return O

There are several novel pieces in this example. First, note that the elementwise operations do not include dimensions. Dimensions are inferred from the inputs in elementwise operations, and so are never specified in elementwise ops. Neg has the same shape as I, and O has the same shape as O_Neg. When an elementwise binary operation is performed, the output shape is determined using broadcasting semantics. Which brings us to the next novelty: we have our first example of a 0D tensor, O_Neg. Tensors in Tile are allowed to have zero dimensions. In such a case the tensor represents a scalar, i.e., a single value. In places where dimensions are specified, you can indicate a 0-dimensional tensor by using () for the dimensions, as in this example. Notice that we are taking the max over all axes in a single operation. Contractions implicitly aggregate over all indices that write to the same output location (in this case we aggregate over all values of i, j, and k).

Average¶

To compute the mean of a tensor, we need to sum the elements and divide by the total number of elements summed. We can do this by taking advantage of the fact that we can divide by a constant (including an input TensorDim) as an elementwise operation. Thus, to take the mean over axis 0 of a 2D tensor, we write:

Tensor avg(const Tensor& I) {
  TensorDim X, Y;
  TensorIndex x, y;
  I.bind_dims(X, Y);
  auto Sum = TensorOutput();
  Sum(y) += I(x, y);
  return Sum / X;
}

def avg(I):
  X, Y = TensorDims(2)
  x, y = TensorIndexes(2)
  I.bind_dims(X, Y)
  Sum = TensorOutput()
  Sum[y] += I[x, y]
  return Sum / X

We can perform multiple elementwise operations on the same line, including operations on constants and input dimensions. So, while it would be possible to take a global mean of a 2D tensor in stages as so:

Tensor avg(const Tensor& I) {
  TensorDim X, Y;
  TensorIndex x, y;
  I.bind_dims(X, Y);
  auto Sum = TensorOutput();
  Sum() += I(x, y);
  PartialMean = Sum / X;
  return PartialMean / Y;
}

def avg_stages(I):
  X, Y = TensorDims(2)
  x, y = TensorIndexes(2)
  I.bind_dims(X, Y)
  Sum = TensorOutput()
  Sum[()] += I[x, y]
  PartialMean = Sum / X
  return PartialMean / Y

it is more straightforward to merge the elementwise operations:

Tensor avg(const Tensor& I) {
  TensorDim X, Y;
  TensorIndex x, y;
  I.bind_dims(X, Y);
  auto Sum = TensorOutput();
  Sum() += I(x, y);
  return Sum / (X * Y);
}

def avg_merge(I):
  X, Y = TensorDims(2)
  x, y = TensorIndexes(2)
  I.bind_dims(X, Y)
  Sum = TensorOutput()
  Sum[()] += I[x, y]
  return Sum / (X * Y)

Max Pool 1D¶

Next let’s implement a size 2 stride 2 maxpool in Tile. This is the operation that splits a tensor into groups of 2 and takes the larger element from each group, yielding a tensor of half the original size. This is straightforward to implement in straight C++:

float I[N], O[N / 2];
for (int i = 0; i < N/2; ++i) {
  float curr_max = FLT_MIN;
  for (int j = 0; j < 2; ++j) {
    if (I[2 * i + j] > curr_max) {
      curr_max = I[2 * i + j];
    }
  }
  O[i] = curr_max;
}

for i in range (1 , N//2):
  curr_max = numpy.finfo(float).eps
  for j in range (1 , 2):
    if I[2*i*j] > curr_max:
      curr_max = I[2*i+j]
  O[i] = curr_max

for loops over tensor indices get translated into contractions when written in Tile. The most direct (and, sadly, wrong) implementation in Tile is:

Tensor wrong_max_pool_1d(const Tensor& I) {
  TensorDim N;
  TensorIndex i, j;
  I.bind_dims(N);
  auto O = TensorOutput(N / 2);
  O(i) >= I(2 * i + j);
  return O;
}

def wrong_max_pool_1d(I):
   N = TensorDim()
   i, j = TensorIndexes(2)
   I.bind_dims(N)
   O = TensorOutput(N // 2)
   O[i] >= I[2 * i + j]
   return O

If you were to run this code, every entry of O would equal the global max of I. We correctly determined that this was a maximization operation, and the indices for O and I match those used in the straight C++ code, so what went wrong? The problem with this Tile code is that there are too many “valid” indices. For example, the case i = 1 , j = 3 means that O[1] checks I[5] as one of the potential maximum values, even though O[1] is intended to be max(I[2], I[3]). When we wrote the code with for loops, the inner loop restricted j to 0 or 1; in the Tile code, the compiler figured out the allowed values of j by looking at the shapes of the tensors, and the only restriction that imposes on j is that j must be an integer satisfying 0 <= 2 * i + j < N. When can use add_constraint in Tile to handle such situations:

Something important to note here is that while we wrote j < 2, this constraint actually means 0<= j < 2. Constraints are always bounded below by 0. (Without a constraint, however, index variables may still be negative: the original code included e.g. i = 1, j = -1 as valid index pair.) We determined the Tile code for this example by starting from imperative code, but this Tile code is still very similar to mathematical notation, and we could have started there instead:

\[\color{red}O[i] \color{default}= \color{green}\max_{\color{magenta}0 \leq j < 2} \color{blue}I[2i + j]\]

\[\begin{aligned} & \color{red}\verb|O(i)| \color{green}\verb| >= | \color{blue}\verb|I(2 * i + j)|\color{default}\verb|;| \cr & \color{default}\verb|O.add_constraint(| \color{magenta}\verb|j < 2|\color{default}\verb|);| \end{aligned}\]

This Tile code handles odd values of N by rounding down the output tensor size. You may instead want to round up the output tensor size and use a smaller pool at the edge. This can be accomplished by simply adjusting the size of O:

Tensor max_pool_1d(const Tensor& I) {
  TensorDim N;
  TensorIndex i, j;
  I.bind_dims(N);
  auto O = TensorOutput((N + 1) / 2);
  O(i) >= I(2 * i + j);
  O.add_constraint(j < 2);
  return O;
}

def max_pool_1d(I):
  N = TensorDim()
  i, j = TensorIndexes(2)
  I.bind_dims(N)
  O = TensorOutput((N + 1) // 2)
  O[i] >= I[2 * i + j]
  O.add_constraint(j < 2)
  return O

No special handling is needed for the case i = (N - 1) / 2, j = 1; this is out of range for I and so is ignored by Tile, which is exactly the intended behavior.

Valid Indices¶

When discussing contractions, we’ve mentioned that they accumulate over “all valid indices”. Hopefully the significance of this has been clear for the specific examples we’ve looked at, but to write complex or novel code it helps to have a precise understanding of what is meant by “valid indices”. First, index validity is determined for a full set of index variables: j = 1 is not valid or invalid as a standalone index value, but may be part of a valid or invalid set of index variables. For example, in the code:

I.bind_dims(N);
auto O = TensorOutput((N + 1) / 2);
O(i) >= I(2 * i + j);
O.add_constraint(j < 2);

I.bind_dims(N)
O = TensorOutput[(N + 1) // 2];
O[i] >= I[2 * i + j];
O.add_constraint(j < 2);

with N = 5, the indices i = 1, j = 1 are valid indices. However, i = 2, j = 1 are not valid indices for this operation, nor are i = -1000, j = 1. A set of indices are valid if and only if:

All the index variables are integers.
All the index expressions for every tensor are in range. Specifically, if the index variable values are plugged into every index expression, all the resulting indices are non-negative integers less than the appropriate dimension.
All the constraints are satisfied. Constraints always take the form [index expression] < [constant expression] (where [index expression] is a linear polynomial in the index variables and [constant expression] is a linear polynomial in the input dimensions), and they always implicitly include 0 <= [index expression]. Therefore we could also state this requirement as “every constraint’s index expression is non-negative and less than its specified upper bound”.

Skipping¶

The rule that all index variables must be integers allows us to “skip” certain otherwise valid entries. For example, consider the Tile function:

Tensor skip(const Tensor& I) {
  TensorDim M, N;
  TensorIndex i, j;
  I.bind_dims(M, N);
  auto O = TensorOutput(N);
  O(2 * i) += I(2 * i, j);
  return O;
}

def skip(I):
  M, N = TensorDims(2)
  i, j = TensorIndexes(2)
  I.bind_dims(M, N)
  O = TensorOutput(N)
  O[2 * i] += I[2 * i, j]
  return O

This operation only writes to even entries of O; while i = 1/2, j = 1 does yield valid index expressions (O[1] and I[1, 1]), using a fractional index variable i makes these indices invalid. Note that some elements of O are never written to. Any unwritten elements in the output of a contraction are initialized to 0.

Cumulative Sum¶

Suppose we want to take the cumulative sum of a 1D tensor. That is, we want O[i] to be the sum of all input entries I[k] where k <= i. In summation notation, this is:

\[O[i] = \sum_{k \leq i} I[k]\]

However, we can’t use k <= i as a constraint in Tile; all the index variables must be gathered into a single index expression on one side of the inequality. Thus, we rewrite this as 0 <= i - k. Since the 0 bound is implicitly included in all constraints, we just need to choose an upper bound large enough to never be hit. From the dimensions of the tensors, we already know i < N and 0 <= k, and so N is an appropriate upper bound. The resulting Tile code is:

Tensor csum(const Tensor& I) {
  TensorDim N;
  TensorIndex i, k;
  I.bind_dims(N);
  auto O = TensorOutput(N);
  O(i) += I(k);
  O.add_constraint(i - k < N);
  return O;
}

def csum(I):
  N = TensorDim()
  i, k = TensorIndexes(2)
  I.bind_dims(N)
  O = TensorOutput(N)
  O[i] += I[k]
  O.add_constraint(i - k < N)
  return O

Convolution¶

Let’s implement a 1D convolution with output size equal to input size. This is implementing the Keras backend operation:

K.conv1d(x, kernel, padding='valid')

Let’s start with the mathematical formula for this operation:

\[O[n, x, c_o] = \sum_k \sum_{c_i}(I[n, x + k, c_i] \cdot K[k, c_i, c_o])\]

This is rather complicated, so let’s walk through why this is the same convolution formula we’re used to in machine learning. A convolution produces output for a specific batch element at a specific location in a specific channel by taking a weighted sum of the input for that same batch element at that same location and a surrounding region over all input channels. The weights are given by K, which depends on the output channel, the input channel, and the displacement within the input region relative to the reference location. This generally matches the given formula: The output O is given as a sum of elements from the input I, weighted by K. Looking at the meaning of the index variables, we see that it matches exactly:

n represents which element of the batch we’re on.
ci represents which input channel we’re on.
co represents which output channel we’re on.
x represents our spatial location, giving the location being written to in O and the smallest element read from in I.
Finally, k represents the kernel offset, that is, how far (in the spatial dimension) the input element we’re reading is from the lower bound of the kernel.

This formula directly translates to Tile, although note that padding='valid' means that the spatial dimension of the output will be reduced by one less than the kernel size relative to the spatial dimension of the input:

\[\color{red}O[n, x, c_o] \color{default}= \color{green}\sum_k \sum_{c_i} \color{blue}I[n, x + k, c_i] \color{orange}\cdot \color{lightblue}K[k, c_i, c_o]\]

\[\color{red}\verb|O(n, x, co)| \color{green}\verb| += | \color{blue}\verb|I(n, x + k, ci)| \color{orange}\verb| * | \color{lightblue}\verb|K(k, ci, co)|\color{default}\verb|;|\]

Tensor conv_1d(const Tensor& I, const Tensor& K) {
  TensorDim N, X, KX, CI, CO;
  TensorIndex n, x, k, ci, co;
  I.bind_dims(N, X, CI);
  K.bind_dims(KX, CI, CO);
  auto O = TensorOutput(N, X - KX + 1, CO);
  O(n, x, co) += I(n, x + k, ci) * K(k, ci, co);
  return O;
}

def conv_1d(I, K):
  N, X, KX, CI, CO = TensorDims(5)
  n, x, k, ci, co = TensorIndexes(5)
  I.bind_dims(N, X, CI)
  K.bind_dims(KX, CI, CO)
  O = TensorOutput(N, X - KX + 1, CO)
  O[n, x, co] += I[n, x + k, ci] * K[k, ci, co]
  return O

Dilated 2D Convolution¶

We can tweak this general formula for a convolution to add various features, such as different strides, changing the padding, performing the convolution depthwise, etc. For this example, we will implement a dilated 2D convolution with dilation rate (2, 3). Specfically, we’ll implement the Keras backend function:

K.conv2d(x, kernel, padding='valid', dilation_rate=(2, 3))

The formula for this is very similar to the previous convolution; we just have an additional spatial dimension for each tensor, and the kernel offset index variables are multiplied by dilation scaling factors when used to determine indices for I:

\[O[n, x, y, c_o] = \sum_{k_x} \sum_{k_y} \sum_{c_i} I[n, x + 2k_x, y + 3k_y, c_i] * K[k_x, k_y, c_i, c_o]\]

The effective size for a dilated kernel with kernel size K and dilation rate d is d * (K - 1) + 1, and so to achieve ‘valid’ padding for this convolution, the x dimension must be reduced by 2 * (KX - 1) and the y dimension must be reduced by 3 * (KY - 1), where KX and KY are the x and y dimensions of the kernel respectively. The rest of the Tile code corresponds directly to the formula, and so we get:

Tensor conv_2d(const Tensor& I, const Tensor& K) {
  TensorDim N, X, Y, KX, KY, CI, CO;
  TensorIndex n, x, y, kx, ky, ci, co;
  I.bind_dims(N, X, Y, CI);
  K.bind_dims(KX, KY, CI, CO);
  auto O = TensorOutput(N, X - 2 * (KX - 1), Y - 3 * (KY - 1), CO);
  O(n, x, y, co) += I(n, x + 2 * kx, y + 3 * ky, ci) * K(kx, ky, ci, co);
  return O;
}

def conv_2d_dilated(I, K):
  N, X, Y, KX, KY, CI, CO = TensorDims(7)
  n, x, y, kx, ky, ci, co = TensorIndexes(7)
  I.bind_dims(N, X, Y, CI)
  K.bind_dims(KX, KY, CI, CO)
  O = TensorOutput(N, X - 2 * (KX - 1), Y - 3 * (KY - 1), CO)
  O[n, x, y, co] += I[n, x + 2 * kx, y + 3 * ky, ci] * K[kx, ky, ci, co]
  return O

Complex Convolution¶

This final example demonstrates a strided dilated padded grouped convolution.

\[\begin{aligned} O&[n, x_0, x_1, g, c_{o, g}] \cr &=\sum_{k_0, k_1, c_{i, g}} ( I[n, s_0 x_0 + d_0 k_0 - P_0, s_1 x_1 + d_1 k_1 - P_1, c_{i, g}] * K[k_0, k_1, g, c_{i, g}, c_{o, g}] ) \end{aligned}\]

where `s` gives the stride coefficients, `d` gives the dilation coefficients, and `P` gives the padding offsets.

Tensor complex_conv_2d(
  const Tensor& I,
  const Tensor& K,
  const std::vector<size\_t>& s,  // stride coeffs
  const std::vector<size\_t>& d   // dilation coeffs
) {
    // "same-lower" autopadding will be applied
    TensorDim N, G, GCI, GCO;
    std::vector<TensorDim> X(2);
    std::vector<TensorDim> K(2);
    TensorIndex n, g, gci, gco;
    std::vector<TensorIndex> x(2);
    std::vector<TensorIndex> k(2);
    I.bind_dims(N, X[0], X[1], G, GCI);
    K.bind_dims(K[0], K[1], G, GCI, GCO);
    // Compute output spatial dimensions
    std::vector<TensorDim> Y(2);
    for (size_t i = 0; i < Y.size(); ++i) {
      Y[i] = (X[i] + s[i] \- 1) / s[i];
    }
    // Compute the effective kernel size after dilation
    std::vector<TensorDim> EK(2);
    for (size_t i = 0; i < EK.size(); ++i) {
      EK[i] = d[i] \* (K[i] \- 1) + 1;
    }
    // Compute the padding offset
    std::vector<TensorDim> P(2);
    for (size_t i = 0; i < P.size(); ++i) {
      P[i] = ((Y[i] \- 1) \* s[i] + EK[i] \- X[i]) / 2;
    }
    // Specify the output size
    auto O = TensorOutput(N, Y0, Y1, G, GCO);
    // Compute the convolution
    O(n, x[0], x[1], g, gco) +=
      I(n, s[0]\*x[0] + d[0]\*k[0] \- P[0], s[1]\*x[1] + d[1]\*k[1] \- P[1], g, gci) \*
      K(k0, k1, g, gci, gco);
    return O;
}

def complex_conv_2d(
    I,
    K,
    s0,
    s1,  # stride coeffs
    d0,
    d1  # dilation coeffs
    ):
        # "same-lower" autopadding will be applied
        N, G, GCI, GCO = TensorDims(4)
        X0, X1 = TensorDims(2)
        K0, K1 = TensorDims(2)
        n, g, gci, gco = TensorIndexes(4)
        x0, x1 = TensorIndexes(2)
        k0, k1 = TensorIndexes(2)
        I.bind_dims(N, X0, X1, G, GCI)
        K.bind_dims(K0, K1, G, GCI, GCO)

        # Compute output spatial dimensions
        Y0, Y1 = TensorDims(2)
        Y0 = (X0 + s0 - 1) // s0
        Y1 = (X1 + s1 - 1) // s1

        #Compute the effective kernel size after dilation
        EK0, EK1 = TensorDims(2)
        EK0 = d0 * (K0 - 1) + 1
        EK1 = d1 * (K1 - 1) + 1

        #Compute the padding offset
        P0, P1 = TensorDims(2)
        P0 = ((Y0 - 1) * s0 + EK0 - X0) // 2
        P1 = ((Y1 - 1) * s1 + EK1 - X1) // 2

        # Specify the output size
        O = TensorOutput(N, Y0, Y1, G, GCO)

        # Compute the convolution
        O[n, x0, x1, g, gco] += I[n, s0 * x1 + d0 * k0 - P0, s1 * x1 + d1 * k1 -
                                  P1, g, gci] * K[k0, k1, g, gci, gco]
        return O

Reference¶

Contractions¶

There are five aggregation operations:

operator += or sum: When multiple values are computed for the same output location, they are added together.
operator *= or product: when multiple values are computed for the same output location, they are multiplied together.
operator >= or max: when multiple values are computed for the same output location, the largest one is used.
operator <= or min: when multiple values are computed for the same output location, the smallest one is used.
operator = or assign: when multiple values are computed for the same output location, an error is raised. Note that the compiler errs on the side of caution and may raise an error even when no output location is assigned to multiple times. If the programmer manually confirms that there is at most one value computed for each output location, then any of the other aggregation operations will have equivalent behavior and can be used to bypass this error checking.

There are limited operations available inside a contraction. Principally, contractions allow the use of complex index expressions to determine which elements are read from a tensor. If there is only one tensor used in the contraction, such index manipulations are the only legal options. If there are two tensors used inside the contraction, you also choose a combination operation to determine how their values are combined. The only combination operations that are currently well-supported are multiplication (*) and addition (+). Contractions aggregate over all sets of valid indices. A set of indices is valid for a contraction if and only if:

All index variables are integers
All index expressions used in tensors are within bounds
All user-specified constraints are satisfied

Elementwise Operations¶

Elementwise operations never specify indices or dimensions. The shape of the output tensor is inferred from the shape of the input tensor(s). In most binary operations, if the input tensors have different shapes, the output shape is determined by broadcasting together the input shapes. If this is impossible or ambiguous, it is an error. Common operations (not comprehensive; example tensor variable names provided to illustrate syntax):

Addition: O = A + B;
Subtraction: O = A - B;
Multiplication: O = A * B;
Division: O = A / B;
Equality: O = A == B;
Inequality: O = A != B;
Less: O = A < B;
Square Root: O = sqrt(A);
Exponential: O = exp(A);
Power: O = pow(A, B);
Sine: O = sin(A);
Hyperbolic Tangent: O = tanh(A);
Natural Log: O = log(A);
Sigmoid: O = sigmoid(A);
Conditional: O = select(C, T, F); (C may be a single value or a higher dimensional tensor to be evaluated elementwise. T and F must have the same shape, and unless C is known to be a constant at compile time, both will be evaluated.)

Types¶

Tensor: Multidimensional arrays of a fixed shape. The scope of a tensor is the entire function. By convention, tensors begin with a capital letter.
TensorDim: Positive integers initially passed to a function as sizes of input tensors. The scope of a dimension is the entire function. By convention, dimensions begin with a capital letter.
TensorIndex: Symbolic integers used in contractions to directly index a tensor or as part of a formula to compute a tensor index. The scope of an index is a single operation. By convention, indices begin with a lower case letter.

API¶

Core ¶

PlaidML Core

Contents

Core
- Initialization
- Objects

Initialization ¶

void plaidml::init()¶: Initializes PlaidML’s Core API.

Note

Initialization of PlaidML’s Core Python API happens automatically wherever the module plaidml.core is imported.

Objects ¶

enum core_objects::DType¶

Enumerates all of the data types in PlaidML.

Values:

INVALID = PLAIDML_DATA_INVALID¶

BOOLEAN = PLAIDML_DATA_BOOLEAN¶

INT8 = PLAIDML_DATA_INT8¶

UINT8 = PLAIDML_DATA_UINT8¶

INT16 = PLAIDML_DATA_INT16¶

UINT16 = PLAIDML_DATA_UINT16¶

INT32 = PLAIDML_DATA_INT32¶

UINT32 = PLAIDML_DATA_UINT32¶

INT64 = PLAIDML_DATA_INT64¶

UINT64 = PLAIDML_DATA_UINT64¶

BFLOAT16 = PLAIDML_DATA_BFLOAT16¶

FLOAT16 = PLAIDML_DATA_FLOAT16¶

FLOAT32 = PLAIDML_DATA_FLOAT32¶

FLOAT64 = PLAIDML_DATA_FLOAT64¶

class TensorShape¶

This is a TensorShape.

Public Functions

TensorShape()¶: TensorShape constructor

TensorShape(DType dtype, const std::vector<int64_t> &sizes)¶

TensorShape constructor

Parameters

dtype: DType

TensorShape(DType dtype, const std::vector<int64_t> &sizes, const std::vector<int64_t> &strides)¶

TensorShape constructor

Parameters

dtype: DType
sizes: const vector<int64_t>
strides: const vector<int64_t>

TensorShape(const std::shared_ptr<plaidml_shape> &ptr)¶

TensorShape constructor

Parameters

ptr: const shared_ptr<plaidml_shape>

DType dtype() const¶

dtype

Return: DType

size_t ndims() const¶

Returns the number of dimensions in the TensorShape

Return: size_t

uint64_t nbytes() const¶

nbytes

Return: uint64_t

class View¶

This is a View.

Public Functions

char *data()¶: data

size_t size()¶: size

void writeback()¶: writeback

class Buffer¶

This is a Buffer.

Public Functions

Buffer()¶: Buffer constructor

Buffer(const std::string &device, const TensorShape &shape)¶

Buffer constructor

Parameters

device: string
shape: TensorShape

Buffer(plaidml_buffer *ptr, const TensorShape &shape)¶

Buffer constructor

Parameters

ptr: plaidml_buffer*
shape: TensorShape

plaidml_buffer *as_ptr() const¶

Returns a pointer to the Buffer.

Return: plaidml_buffer*

View mmap_current()¶

mmap_current

Return: View

View mmap_discard()¶

mmap_discard

Return: View

struct Settings¶

These are the Settings.

Public Static Functions

static std::string get(const std::string &key)¶

Gets the setting specified by key

Return

string

Parameters

key: string

static void set(const std::string &key, const std::string &value)¶

Sets the setting specified by key to the value specified.

Parameters

key: string
value: string

EDSL ¶

Embedded Domain Specific Language

Contents

EDSL

Initialization ¶

void plaidml::edsl::init()¶: Initializes PlaidML’s EDSL API.

Note

Initialization of PlaidML’s EDSL Python API happens automatically wherever the module plaidml.edsl is imported.

Objects ¶

class Program¶

This is a program.

Public Functions

Program(const std::string &name, const std::vector<Tensor> &outputs, const std::vector<std::tuple<Tensor, Tensor>> &updates = {})¶: Program constructor

std::string str() const¶: Return the Program as a string.

const std::vector<ProgramArgument> &args() const¶: args

const std::vector<ProgramArgument> &inputs() const¶: inputs

const std::vector<ProgramArgument> &outputs() const¶: outputs

class TensorDim¶

A symbolic object used to specify the dimensions of a Tensor

Public Functions

TensorDim()¶: TensorDim constructor

TensorDim(const std::shared_ptr<plaidml_dim_expr> &ptr)¶: TensorDim constructor

TensorDim(int64_t value)¶: TensorDim constructor

TensorDim operator-() const¶: Represents a subtraction operator overload.

std::string str() const¶: Returns the TensorDim as a string.

int64_t as_int() const¶: Returns the TensorDim as an int.

class TensorIndex¶

A symbolic object used to directly index a Tensor or to compute a Tensor’s index as part of a formula.

Public Functions

TensorIndex()¶: TensorIndex constructor

TensorIndex(int64_t value)¶: TensorIndex constructor

TensorIndex(const std::string &name)¶: TensorIndex constructor

TensorIndex operator-() const¶: Represents an subtraction operator overload on a TensorIndex

Constraint operator<(int64_t rhs) const¶: TODO

Constraint operator<(const TensorDim &rhs) const¶: TODO

std::string str() const¶: Returns the TensorIndex as a string.

struct Constraint¶

This is a constraint.

Public Members

TensorIndex lhs¶: lhs

TensorDim rhs¶: rhs

class IndexedTensor¶

This is an IndexedTensor

Public Functions

IndexedTensor &operator+=(const IndexedTensor &rhs)¶: Represents an aggregation_op of SUM in a contraction

IndexedTensor &operator*=(const IndexedTensor &rhs)¶: Represents an aggregation_op of PROD in a contraction

IndexedTensor &operator>=(const IndexedTensor &rhs)¶: Represents an aggregation_op of MAX in a contraction

IndexedTensor &operator<=(const IndexedTensor &rhs)¶: Represents an aggregation_op of MIN in a contraction

IndexedTensor &operator=(const IndexedTensor &rhs)¶: Represents an aggregation_op of ASSIGN in a contraction

IndexedTensor operator+(const IndexedTensor &rhs) const¶: Represents a combo_op of PLUS in a contraction

IndexedTensor operator*(const IndexedTensor &rhs) const¶: Represents a combo_op of MULTIPLY in a contraction

IndexedTensor operator==(const IndexedTensor &rhs) const¶: Represents a combo_op of EQ in a contraction

class LogicalShape¶

This is a LogicalShape.

Public Functions

LogicalShape(DType dtype, const std::vector<int64_t> &dims)¶: LogicalShape constructor

std::string str() const¶: Returns a LogicalShape as a string

DType dtype() const¶: Returns the datatype of the LogicalShape

size_t ndims() const¶: Returns the number of dimensions of the LogicalShape

std::vector<int64_t> int_dims() const¶: Returns the dimensions of the LogicalShape as a vector of integers.

bool operator==(const LogicalShape &rhs) const¶: TODO

class Tensor¶

A multidimensional array of a fixed shape.

Public Functions

Tensor()¶: Tensor constructor

Tensor(int value)¶

Tensor constructor

Return

Welcome to plaidml’s documentation!¶

Installation Instructions¶

Building from source¶

Install Anaconda¶

Install bazelisk¶

Configure the build¶

Build the PlaidML Python wheel¶

Install the PlaidML Python wheel¶

PlaidML with Keras¶

Set up a build environment¶

Build the PlaidML-Keras wheel¶

Install the PlaidML-Keras Python wheel¶

Testing PlaidML¶

Contributing to PlaidML¶

Process¶

Troubleshooting¶

Common Issues¶

PlaidML Setup Errors¶

Memory Errors¶

Bazel Issues¶

PlaidML Exceptions¶

Run Backend Tests¶

Enable Verbose Logging¶

Tile eDSL¶

Scope and Warning¶

How to Write Tile Code¶

Sum Over Axis¶

Max Over Axis¶

Matrix Multiply¶

Global Min¶

Average¶

Max Pool 1D¶

Valid Indices¶

Skipping¶

Cumulative Sum¶

Convolution¶

Dilated 2D Convolution¶

Complex Convolution¶

Reference¶

Contractions¶

Elementwise Operations¶

Types¶

API¶

Configuration¶