# Deep Neural Networks as the Semi-classical Limit of Topological Quantum Neural Networks: The problem of generalisation

arXiv: https://arxiv.org/abs/2210.13741 · HTML: https://mlsanity.com/paper/2210.13741/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 87 references that are in the map.
- First posted on arXiv 25 Oct 2022.

## Builds on (most cited first, 22 of 22)

- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [A Closer Look at Memorization in Deep Networks](https://mlsanity.com/paper/1706.05394/) (2017)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [Exploring Generalization in Deep Learning](https://mlsanity.com/paper/1706.08947/) (2017)
- [Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data](https://mlsanity.com/paper/1703.11008/) (2017)
- [Opening the Black Box of Deep Neural Networks via Information](https://mlsanity.com/paper/1703.00810/) (2017)
- [Sharp Minima Can Generalize For Deep Nets](https://mlsanity.com/paper/1703.04933/) (2017)
- [In Search of the Real Inductive Bias: On the Role of Implicit Regularization in Deep Learning](https://mlsanity.com/paper/1412.6614/) (2014)
- [A PAC-Bayesian Approach to Spectrally-Normalized Margin Bounds for Neural Networks](https://mlsanity.com/paper/1707.09564/) (2017)
- [Train longer, generalize better: closing the generalization gap in large batch training of neural networks](https://mlsanity.com/paper/1705.08741/) (2017)
- [Deep learning: a statistical viewpoint](https://mlsanity.com/paper/2103.09177/) (2021)
- [To understand deep learning we need to understand kernel learning](https://mlsanity.com/paper/1802.01396/) (2018)
- [Generalization and Equilibrium in Generative Adversarial Nets (GANs)](https://mlsanity.com/paper/1703.00573/) (2017)
- [Efficient Learning for Deep Quantum Neural Networks](https://mlsanity.com/paper/1902.10445/) (2019)
- [Why does deep and cheap learning work so well?](https://mlsanity.com/paper/1608.08225/) (2016)
- [Towards Understanding Generalization of Deep Learning: Perspective of Loss Landscapes](https://mlsanity.com/paper/1706.10239/) (2017)
- [Theory of Deep Learning III: explaining the non-overfitting puzzle](https://mlsanity.com/paper/1801.00173/) (2017)
- [Understanding Generalization in Deep Learning via Tensor Methods](https://mlsanity.com/paper/2001.05070/) (2020)
- [A free energy principle for generic quantum systems](https://mlsanity.com/paper/2112.15242/) (2021)
- [Deep Neural Network Capacity](https://mlsanity.com/paper/1708.05029/) (2017)

## Abstract (arXiv)

Deep Neural Networks miss a principled model of their operation. A novel framework for supervised learning based on Topological Quantum Field Theory that looks particularly well suited for implementation on quantum processors has been recently explored. We propose using this framework to understand the problem of generalisation in Deep Neural Networks. More specifically, in this approach, Deep Neural Networks are viewed as the semi-classical limit of Topological Quantum Neural Networks. A framework of this kind explains the overfitting behavior of Deep Neural Networks during the training step and the corresponding generalisation capabilities. We explore the paradigmatic case of the perceptron, which we implement as the semiclassical limit of Topological Quantum Neural Networks. We apply a novel algorithm we developed, showing that it obtains similar results to standard neural networks, but without the need for training (optimisation).