ConvIIR: Separable IIR Layers for Deep Convolutional Networks

ConvIIR provides TensorFlow/Keras separable IIR convolution layers for 2D and 3D inputs.

Copyright 2025 Kishore Kumar Tarafdar. Acknowledgement: 2D layer development support with credit to Ayush Raisoni. Licensed under the Apache License, Version 2.0. See LICENSE.

Capabilities

• Stable direct-form I separable IIR convolution: IIRConv2DStable, IIRConv3DStable.
• Direct-form II separable IIR convolution: IIRConv2DDFII, IIRConv3DDFII.
• Keras-compatible layers for channel-last 2D and 3D tensors.
• Optional UNet-style 2D network blocks built from ConvIIR layers.

Limitations

• The core public API is the DF-I and DF-II 2D/3D IIR convolution layers.
• Experimental Wave+ViT helpers are not documented as public API in this package.
• Inputs are expected to use TensorFlow/Keras channel-last layout.

Installation

pip install ConvIIR

Minimal Example

import tensorflow as tf
from ConvIIR.SeparableIIRDFI2D import IIRConv2DStable
from ConvIIR.SeparableIIRDFI3D import IIRConv3DStable

x2 = tf.random.normal([1, 32, 32, 1])
y2 = IIRConv2DStable(filters=4, kernel_size=(3, 3), ar_order=2, ma_order=2)(x2)

x3 = tf.random.normal([1, 16, 16, 16, 1])
y3 = IIRConv3DStable(filters=2, kernel_size=(3, 3, 3), ar_order=2, ma_order=2)(x3)

print(y2.shape, y3.shape)

Module Imports

from ConvIIR.SeparableIIRDFI2D import IIRConv2DStable
from ConvIIR.SeparableIIRDFI3D import IIRConv3DStable
from ConvIIR.SeparableIIRDFII2D import IIRConv2DDFII
from ConvIIR.SeparableIIRDFII3D import IIRConv3DDFII

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.