English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

To make sense of the world our brains must analyze high-dimensional datasetsstreamed by our sensory organs. Because such analysis begins withdimensionality reduction, modelling early sensory processing requiresbiologically plausible online dimensionality reduction algorithms. Recently, wederived such an algorithm, termed similarity matching, from a MultidimensionalScaling (MDS) objective function. However, in the existing algorithm, thenumber of output dimensions is set a priori by the number of output neurons andcannot be changed. Because the number of informative dimensions in sensoryinputs is variable there is a need for adaptive dimensionality reduction. Here,we derive biologically plausible dimensionality reduction algorithms whichadapt the number of output dimensions to the eigenspectrum of the inputcovariance matrix. We formulate three objective functions which, in the offlinesetting, are optimized by the projections of the input dataset onto itsprincipal subspace scaled by the eigenvalues of the output covariance matrix.In turn, the output eigenvalues are computed as i) soft-thresholded, ii)hard-thresholded, iii) equalized thresholded eigenvalues of the inputcovariance matrix. In the online setting, we derive the three correspondingadaptive algorithms and map them onto the dynamics of neuronal activity innetworks with biologically plausible local learning rules. Remarkably, in thelast two networks, neurons are divided into two classes which we identify withprincipal neurons and interneurons in biological circuits.

A Normative Theory of Adaptive Dimensionality Reduction in Neural Networks