# Automatically Differentiable Nonlinear Tensor Networks (ADNTNs) for Exponential Parameter Compression of Deep Neural Networks

arXiv: https://arxiv.org/abs/2606.00130 · HTML: https://mlsanity.com/paper/2606.00130/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 55 references that are in the map.
- First posted on arXiv 28 May 2026.

## Builds on (most cited first, 25 of 25)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems](https://mlsanity.com/paper/1603.04467/) (2016)
- [What is the State of Neural Network Pruning?](https://mlsanity.com/paper/2003.03033/) (2020)
- [Exploiting Linear Structure Within Convolutional Networks for Efficient Evaluation](https://mlsanity.com/paper/1404.0736/) (2014)
- [Speeding-up Convolutional Neural Networks Using Fine-tuned CP-Decomposition](https://mlsanity.com/paper/1412.6553/) (2014)
- [Compression of Deep Convolutional Neural Networks for Fast and Low Power Mobile Applications](https://mlsanity.com/paper/1511.06530/) (2015)
- [Tensor Ring Decomposition](https://mlsanity.com/paper/1606.05535/) (2016)
- [Rational neural networks](https://mlsanity.com/paper/2004.01902/) (2020)
- [Stable Low-rank Tensor Decomposition for Compression of Convolutional Neural Network](https://mlsanity.com/paper/2008.05441/) (2020)
- [Compression of Deep Learning Models for Text: A Survey](https://mlsanity.com/paper/2008.05221/) (2020)
- [Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives](https://mlsanity.com/paper/1708.09165/) (2017)
- [Tensor Networks Meet Neural Networks: A Survey and Future Perspectives](https://mlsanity.com/paper/2302.09019/) (2023)
- [Automatic Differentiation is Essential in Training Neural Networks for Solving Differential Equations](https://mlsanity.com/paper/2405.14099/) (2024)
- [Compressing Transformer Language Models via Matrix Product Operator Decomposition: A Case Study on PicoGPT](https://mlsanity.com/paper/2603.28534/) (2026)
- [Differentiable Programming of Isometric Tensor Networks](https://mlsanity.com/paper/2110.03898/) (2021)

## Abstract (arXiv)

Large deep neural networks are costly to store and deploy because inference must move and evaluate many parameters. This paper studies Automatically Differentiable Nonlinear Tensor Networks (ADNTNs), compact differentiable weight generators for replacing selected dense, convolutional, and attention layers. An ADNTN maps a small set of trainable tensor cores to a full weight tensor through hierarchical contractions and learnable nonlinearities; the generated layer is then used as an ordinary linear or convolutional operator. We investigate three multilayered topologies: Tree Tensor Networks, augmented Tree Tensor Networks with boundary disentanglers, and MERA-style multi-scale decoders. Compared with flat brick-wall automatically differentiable tensor networks, these hierarchies provide logarithmic-depth communication between tensorised modes and optional lateral mixing, which can improve long-range structure without large increases in stored parameters. We give a unified forward--adjoint formulation showing how reverse-mode automatic differentiation computes pre-activation adjoints and contracted-environment gradients for all trainable cores. The formulation supports task losses, reconstruction losses, distillation, quantisation-aware terms, batching, and modern optimisers. Proof-of-concept experiments on selected AlexNet and VGG-16 layers on CIFAR-10 datasets achieve per-layer parameter-compression ratios from about 2,000× to 430,000×. Several VGG-16 compressed models match or slightly exceed the dense baseline, whereas AlexNet shows moderate degradation under more restrictive redundancy. These results indicate that nonlinear tensor-network generators are a promising structured route to compact pattern-recognition models, while also showing that contraction schedules and hardware-aware implementations remain essential for practical speedups.