Hypercomplex Ops

This project contains utility functions for manipulating vectors of hypercomplex numbers (think quaternions, octonions, sedenions, etc). Currently only multiplication and conjugation are supported.

Compiled with 64-bit Ubuntu 16.04, GCC 5.4, NVIDIA Driver 387, CUDA Toolkit 9.1, cuDNN 7.0.5, NVIDIA GTX 1050 Ti.

Setup

If you have the same specs as above

1. Download and install tensorflow with GPU support.
2. Download the hypercomplex.so file and place in a known folder.

If you have different specs

1. Download the tensorflow source, compile tensorflow with GPU support, and install the pip package.
2. Download the hypercomplex source and place in tensorflow/tensorflow/core/user_ops.
3. Compile the hypercomplex op library, and place in a known folder.

Usage

To use this library, you must first import tensorflow, and then import the operator library using load_op_library. This method returns a handle to the custom operations in our library.

import tensorflow as tf
HCX = tf.load_op_library("path/to/hypercomplex.so")

You may then use hypercomplex operations in your tensorflow graphs. For efficiency, the final axis of the input tensors is always considered the hypercomplex axis, and must be a power of 2.

a = tf.Variable([0.1, -2.3, 7.2, 1.0])
b = tf.Variable([-5.2, 2.0, 1.2, -1.0])
c = HCX.hypercomplex_multiply(a, b)
d = HCX.hypercomplex_conjugate(c)

For tensorflow to recognize the gradients of these operations, you must add the following lines after load_op_library. Tensorflow currently only supports gradients defined in python.

from tensorflow.python.framework import ops

@ops.RegisterGradient("HypercomplexConjugate")
def _hypercomplex_conjugate_grad(op, grad):
    return [HCX.hypercomplex_conjugate(grad)]

@ops.RegisterGradient("HypercomplexMultiply")
def _hypercomplex_multiply_grad(op, grad):
    return [
        HCX.hypercomplex_multiply(
            grad,
            HCX.hypercomplex_conjugate(op.inputs[1])),
        HCX.hypercomplex_multiply(
            HCX.hypercomplex_conjugate(op.inputs[0]),
            grad)]