# High--Dimensional Brain in a High-Dimensional World: Blessing of Dimensionality

arXiv: https://arxiv.org/abs/2001.04959 · HTML: https://mlsanity.com/paper/2001.04959/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jan 2020.

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

- [High-dimensional separability for one- and few-shot learning](https://mlsanity.com/paper/2106.15416/) (2021)
- [Demystification of Few-shot and One-shot Learning](https://mlsanity.com/paper/2104.12174/) (2021)
- [Improving VAE-based Representation Learning](https://mlsanity.com/paper/2205.14539/) (2022)
- [A Mathematical Framework for the Problem of Security for Cognition in Neurotechnology](https://mlsanity.com/paper/2403.07945/) (2024)
- [Mutual Information Learned Regressor: an Information-theoretic Viewpoint of Training Regression Systems](https://mlsanity.com/paper/2211.12685/) (2022)
- [The Crowded Embedding Space: A Mean-Field Mechanism for Emergent Marginalization in Retrieval-Augmented Agents](https://mlsanity.com/paper/2606.28343/) (2026)

## Abstract (arXiv)

High-dimensional data and high-dimensional representations of reality are inherent features of modern Artificial Intelligence systems and applications of machine learning. The well-known phenomenon of the "curse of dimensionality" states: many problems become exponentially difficult in high dimensions. Recently, the other side of the coin, the "blessing of dimensionality", has attracted much attention. It turns out that generic high-dimensional datasets exhibit fairly simple geometric properties. Thus, there is a fundamental tradeoff between complexity and simplicity in high dimensional spaces. Here we present a brief explanatory review of recent ideas, results and hypotheses about the blessing of dimensionality and related simplifying effects relevant to machine learning and neuroscience.