# Comment on "Why does deep and cheap learning work so well?" [arXiv:1608.08225]

arXiv: https://arxiv.org/abs/1609.03541 · HTML: https://mlsanity.com/paper/1609.03541/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Sep 2016.

## Built on by (most cited first, 3 of 3)

- [Universality of Winning Tickets: A Renormalization Group Perspective](https://mlsanity.com/paper/2110.03210/) (2021)
- [Towards Worst-Case Guarantees with Scale-Aware Interpretability](https://mlsanity.com/paper/2602.05184/) (2026)
- [Pre-registered tests of solid-state-physics-inspired LLM compression: a cluster-level negative result at small-language-model scale](https://mlsanity.com/paper/2609.34292/) (2026)

## Abstract (arXiv)

In a recent paper, "Why does deep and cheap learning work so well?", Lin and Tegmark claim to show that the mapping between deep belief networks and the variational renormalization group derived in [arXiv:1410.3831] is invalid, and present a "counterexample" that claims to show that this mapping does not hold. In this comment, we show that these claims are incorrect and stem from a misunderstanding of the variational RG procedure proposed by Kadanoff. We also explain why the "counterexample" of Lin and Tegmark is compatible with the mapping proposed in [arXiv:1410.3831].