VolterraSys 0.0.1

Linear and nonlinear Volterra kernels in natural and multiresolution bases

VolterraSys: Linear and nonlinear Volterra kernels in natural and multiresolution bases

VolterraSys provides TensorFlow/Keras layers for trainable linear and quadratic Volterra kernels in natural and multiresolution bases.

Copyright 2025 Kishore Kumar Tarafdar. Licensed under the Apache License, Version 2.0. See LICENSE.

Capabilities

• Shift-variant 1D linear Volterra kernel: LSVariantVolterra1D.
• Shift-invariant linear Volterra kernels: LSIVolterra1D, LSIVolterra2D, LSIVolterra3D.
• Shift-invariant quadratic Volterra kernels: QSIVolterra1D, QSIVolterra2D, QSIVolterra3D.
• Natural-domain kernels with wave=None.
• Multiresolution kernels with wavelets such as wave="haar".

Limitations

• Inputs are TensorFlow tensors with channel-last layout.
• Multiresolution mode depends on TFDWT.
• Natural-domain computation uses wave=None; wavelet-domain computation uses a supported wavelet name.

Installation

pip install VolterraSys

Minimal Example

import tensorflow as tf
from VolterraSys.LSIVolterra1D import LSIVolterra1D
from VolterraSys.LSIVolterra2D import LSIVolterra2D
from VolterraSys.LSIVolterra3D import LSIVolterra3D
from VolterraSys.QSIVolterra1D import QSIVolterra1D
from VolterraSys.QSIVolterra2D import QSIVolterra2D
from VolterraSys.QSIVolterra3D import QSIVolterra3D

# Natural-domain kernels
x1 = tf.random.normal([1, 32, 1])
y1 = LSIVolterra1D(filters=2, kernel_size=3, wave=None)(x1)

x2 = tf.random.normal([1, 8, 8, 1])
y2 = QSIVolterra2D(filters=2, kernel_size=2, wave=None)(x2)

x3 = tf.random.normal([1, 6, 6, 6, 1])
y3 = QSIVolterra3D(filters=2, kernel_size=2, wave=None)(x3)

print(y1.shape, y2.shape, y3.shape)

Wavelet Mode

layer = LSIVolterra2D(filters=1, kernel_size=4, wave="haar")

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.