A biological model of nonlinear dimensionality reduction

Obtaining appropriate low-dimensional representations from high-dimensional sensory inputs in an unsupervised manner is essential for straightforward downstream processing. Although nonlinear dimensionality reduction methods such as <i>t</i>-distributed stochastic neighbor embedding (<i>t</i>-SNE) have been developed, their implementation in simple biological circuits remains unclear. Here, we develop a biologically plausible dimensionality reduction algorithm compatible with <i>t</i>-SNE, which uses a simple three-layer feedforward network mimicking the <i>Drosophila</i> olfactory circuit. The proposed learning rule, described as three-factor Hebbian plasticity, is effective for datasets such as entangled rings and MNIST, comparable to <i>t</i>-SNE. We further show that the algorithm could be working in olfactory circuits in Drosophila by analyzing the multiple experimental data in previous studies. We lastly suggest that the algorithm is also beneficial for association learning between inputs and rewards, allowing the generalization of these associations to other inputs not yet associated with rewards.