# Criticality & Deep Learning II: Momentum Renormalisation Group

arXiv: https://arxiv.org/abs/1705.11023 · HTML: https://mlsanity.com/paper/1705.11023/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 May 2017.

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

- [Categorical Representation Learning and RG flow operators for algorithmic classifiers](https://mlsanity.com/paper/2203.07975/) (2022)

## Abstract (arXiv)

Guided by critical systems found in nature we develop a novel mechanism consisting of inhomogeneous polynomial regularisation via which we can induce scale invariance in deep learning systems. Technically, we map our deep learning (DL) setup to a genuine field theory, on which we act with the Renormalisation Group (RG) in momentum space and produce the flow equations of the couplings; those are translated to constraints and consequently interpreted as "critical regularisation" conditions in the optimiser; the resulting equations hence prove to be sufficient conditions for - and serve as an elegant and simple mechanism to induce scale invariance in any deep learning setup.