convd: D-dimensional Convolution Layers (D>3)

High-dimensional convolution layers for TensorFlow/Keras.

from convd import FFTConvD, SeparableConv4D, SeparableConv6D

Minimal example of 4D convolution

import tensorflow as tf
from convd import FFTConvD

# Shape: [batch, x1, x2, x3, x4, channels]
x = tf.random.normal([1, 8, 8, 8, 8, 1])
y = FFTConvD(filters=4, kernel_size=3)(x)

print(y.shape)  # (1, 8, 8, 8, 8, 4)

Minimal example of 6D convolution

import tensorflow as tf
from convd import FFTConvD

# Shape: [batch, x1, x2, x3, x4, x5, x6, channels]
x = tf.random.normal([1, 4, 4, 4, 4, 4, 4, 1])
y = FFTConvD(filters=4, kernel_size=3)(x)

print(y.shape)  # (1, 4, 4, 4, 4, 4, 4, 4)

Capabilities

• FFTConvD: circular convolution for square 1D-6D inputs.
• SeparableConv4D: separable 4D convolution using 2D kernels.
• SeparableConv6D: separable 6D convolution using 3D kernels.

Limitations

• FFTConvD requires equal spatial sizes, for example N x N or N x N x N.
• FFTConvD supports up to 6 spatial dimensions.
• 7D+ is not currently supported because TensorFlow tf.pad does not support the required tensor rank.
• FFTConvD requires kernel_size <= N.
• FFTConvD is circular convolution, not zero-padded linear convolution.

Citation

This software is released for broad research, educational, and engineering use. If this package helps your work, please cite the following paper:

@misc{tarafdar2026interpretablefrugallearningsystems,
      title={Interpretable and Frugal Learning Systems Employing Multiresolution Pyramids and Volterra Kernels},
      author={Kishore Kumar Tarafdar},
      year={2026},
      eprint={2606.15011},
      archivePrefix={arXiv},
      primaryClass={eess.SP},
      url={https://arxiv.org/abs/2606.15011},
}

License

Apache License 2.0. See LICENSE.