The unreasonable effectiveness of small neural ensembles in high-dimensional brain

TL;DR

This paper explores how small neural ensembles leverage high-dimensional data geometry and measure concentration to enable reliable, fast learning and error correction in brain and artificial systems, revealing fundamental principles behind their effectiveness.

Contribution

It introduces new stochastic separation theorems explaining the power of small neural ensembles in high-dimensional spaces, bridging neuroscience, physics, and mathematics.

Findings

Small neural ensembles can reliably separate data in high-dimensional spaces.

Measure concentration explains the effectiveness of simple units in complex data.

Applications include error correction and memory formation in neural systems.

Abstract

Despite the widely-spread consensus on the brain complexity, sprouts of the single neuron revolution emerged in neuroscience in the 1970s. They brought many unexpected discoveries, including grandmother or concept cells and sparse coding of information in the brain. In machine learning for a long time, the famous curse of dimensionality seemed to be an unsolvable problem. Nevertheless, the idea of the blessing of dimensionality becomes gradually more and more popular. Ensembles of non-interacting or weakly interacting simple units prove to be an effective tool for solving essentially multidimensional problems. This approach is especially useful for one-shot (non-iterative) correction of errors in large legacy artificial intelligence systems. These simplicity revolutions in the era of complexity have deep fundamental reasons grounded in geometry of multidimensional data spaces. To explore and understand these reasons we revisit the background ideas of statistical physics. In the course of the 20th century they were developed into the concentration of measure theory. New stochastic separation theorems reveal the fine structure of the data clouds. We review and analyse biological, physical, and mathematical problems at the core of the fundamental question: how can high-dimensional brain organise reliable and fast learning in high-dimensional world of data by simple tools? Two critical applications are reviewed to exemplify the approach: one-shot correction of errors in intellectual systems and emergence of static and associative memories in ensembles of single neurons.