# Inferring relevant features: from QFT to PCA

arXiv: https://arxiv.org/abs/1802.05756 · HTML: https://mlsanity.com/paper/1802.05756/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Feb 2018.

## Built on by (most cited first, 2 of 2)

- [Nonperturbative renormalization for the neural network-QFT correspondence](https://mlsanity.com/paper/2108.01403/) (2021)
- [Renormalization in the neural network-quantum field theory correspondence](https://mlsanity.com/paper/2212.11811/) (2022)

## Abstract (arXiv)

In many-body physics, renormalization techniques are used to extract aspects of a statistical or quantum state that are relevant at large scale, or for low energy experiments. Recent works have proposed that these features can be formally identified as those perturbations of the states whose distinguishability most resist coarse-graining. Here, we examine whether this same strategy can be used to identify important features of an unlabeled dataset. This approach indeed results in a technique very similar to kernel PCA (principal component analysis), but with a kernel function that is automatically adapted to the data, or "learned". We test this approach on handwritten digits, and find that the most relevant features are significantly better for classification than those obtained from a simple gaussian kernel.