pytorch-nd-semiconv 0.1.0

N-dimensional convolutional operators for various semifields

Pytorch N-Dimensional Semifield Convolutions

Documentation

PyTorch provides efficient implementations of linear convolution operators, as well as max-pooling operators. Both of these operators can be considered a kind of semifield convolution, where the semifield defines what 'addition' and 'multiplication' mean.

However, there are other semifields that we may wish to use than the linear. As such, this package aims to simplify the process of implementing new semifield convolutions, as well as providing definitions for standard semifields.

These new semifields can be defined using PyTorch broadcasting operators using BroadcastSemifield, or using SelectSemifield / SubtractSemifield in the cases where no appropriate PyTorch operator exists.

The implementations, while not as optimised as the base PyTorch versions, have decent performance. BroadcastSemifield relies on chaining optimised PyTorch operators but suffers from higher memory usage, while SelectSemifield / SubtractSemifield are custom CUDA operators, optionally JIT compiled into PyTorch extensions using my other library pytorch-numba-extension-jit.

Finally, all three implementations work in arbitrary dimensionality: they support 1D, 2D or any dimensionality of inputs and kernels (though the example kernels provided are only 2D).