# Data-Dependent Path Normalization in Neural Networks

arXiv: https://arxiv.org/abs/1511.06747 · HTML: https://mlsanity.com/paper/1511.06747/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Nov 2015.

## Built on by (most cited first, 6 of 6)

- [Rethinking Normalization Methods in Federated Learning](https://mlsanity.com/paper/2210.03277/) (2022)
- [Batch Layer Normalization, A new normalization layer for CNNs and RNN](https://mlsanity.com/paper/2209.08898/) (2022)
- [Information-Theoretic Framework for Understanding Modern Machine-Learning](https://mlsanity.com/paper/2506.07661/) (2025)
- [A Theory of Synaptic Neural Balance: From Local to Global Order](https://mlsanity.com/paper/2405.09688/) (2024)
- [Path Regularization: A Near-Complete and Optimal Nonasymptotic Generalization Theory for Multilayer Neural Networks and Double Descent Phenomenon](https://mlsanity.com/paper/2503.02129/) (2025)
- [Demystifying Lipschitz verification: positive matrices, negative results](https://mlsanity.com/paper/2603.28113/) (2026)

## Abstract (arXiv)

We propose a unified framework for neural net normalization, regularization and optimization, which includes Path-SGD and Batch-Normalization and interpolates between them across two different dimensions. Through this framework we investigate issue of invariance of the optimization, data dependence and the connection with natural gradients.