# Fast Trainable Multilinear Bases for Image Compression

arXiv: https://arxiv.org/abs/2608.00053 · HTML: https://mlsanity.com/paper/2608.00053/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 55 references that are in the map.
- First posted on arXiv 26 Jul 2026.

## Builds on (most cited first, 13 of 13)

- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [End-to-end Optimized Image Compression](https://mlsanity.com/paper/1611.01704/) (2016)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [A Neural Representation of Sketch Drawings](https://mlsanity.com/paper/1704.03477/) (2017)
- [Lossy Image Compression with Compressive Autoencoders](https://mlsanity.com/paper/1703.00395/) (2017)
- [Riemannian Adaptive Optimization Methods](https://mlsanity.com/paper/1810.00760/) (2018)
- [Unsupervised Generative Modeling Using Matrix Product States](https://mlsanity.com/paper/1709.01662/) (2017)
- [Reparameterizable Subset Sampling via Continuous Relaxations](https://mlsanity.com/paper/1901.10517/) (2019)
- [Probabilistic Inference in the Era of Tensor Networks and Differential Programming](https://mlsanity.com/paper/2405.14060/) (2024)
- [Improved Wavelets for Image Compression from Unitary Circuits](https://mlsanity.com/paper/2203.02556/) (2022)

## Built on by (most cited first, 1 of 1)

- [Quantum-Inspired Trainable and Parameter-Efficient Tensor Networks for Image Inpainting](https://mlsanity.com/paper/2609.17298/) (2026)

## Abstract (arXiv)

The Discrete Fourier Transform (DFT), the Discrete Cosine Transform (DCT), and their block-wise variants underpin most deployed image and video codecs. Their effectiveness rests on three properties: their runtime is near-linear (up to a polylogarithmic factor) in the image size, they are exactly invertible, and they carry few to no parameters. We generalize these transforms to dataset-adaptive isometric multilinear bases that keep all three properties at the cost of a polylogarithmic number of parameters, by parameterizing each basis as an isometric tensor network, inspired by quantum many-body theory, and training one shared basis per image dataset with Riemannian optimization. Because the family contains the DFT and the DCT-IV (a variant of the DCT) as exact points, training can start from these transforms, and it improves on its starting point at the compression level it is trained for. We evaluate the bases on natural photographs and line drawings. On photographs, which the cosine basis already fits well, the best trained basis leads the DCT only under aggressive truncation. On Quick Draw line drawings, under a common codec at matched quality, the best trained basis stores each image in about 20% fewer bytes than the 8x8 block cosine transform of the Joint Photographic Experts Group (JPEG) format, not counting the one-off storage of the basis.