The unreasonable effectiveness of small neural ensembles in highdimensional brain
Abstract
Complexity is an indisputable, wellknown, and broadly accepted feature of the brain. Despite the apparently obvious and widelyspread 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 noninteracting or weakly interacting simple units prove to be an effective tool for solving essentially multidimensional and apparently incomprehensible problems. This approach is especially useful for oneshot (noniterative) correction of errors in large legacy artificial intelligence systems and when the complete retraining is impossible or too expensive.
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. The Gibbs equivalence of ensembles with further generalizations shows that the data in highdimensional spaces are concentrated near shells of smaller dimension. 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 highdimensional brain organise reliable and fast learning in highdimensional world of data by simple tools? To meet this challenge, we outline and setup a framework based on statistical physics of data.
Two critical applications are reviewed to exemplify the approach: oneshot correction of errors in intellectual systems and emergence of static and associative memories in ensembles of single neurons. Error correctors should be simple; not damage the existing skills of the system; allow fast noniterative learning and correction of new mistakes without destroying the previous fixes. All these demands can be satisfied by new tools based on the concentration of measure phenomena and stochastic separation theory.
We show how a simple enough functional neuronal model is capable of explaining: i) the extreme selectivity of single neurons to the information content of highdimensional data, ii) simultaneous separation of several uncorrelated informational items from a large set of stimuli, and iii) dynamic learning of new items by associating them with already "known" ones. These results constitute a basis for organisation of complex memories in ensembles of single neurons.
 Publication:

Physics of Life Reviews
 Pub Date:
 July 2019
 DOI:
 10.1016/j.plrev.2018.09.005
 arXiv:
 arXiv:1809.07656
 Bibcode:
 2019PhLRv..29...55G
 Keywords:

 Big data;
 Noniterative learning;
 Error correction;
 Measure concentration;
 Blessing of dimensionality;
 Linear discriminant;
 Computer Science  Artificial Intelligence;
 Quantitative Biology  Neurons and Cognition
 EPrint:
 Review paper, accepted in Physics of Life Reviews