A clustering neural network model of insect olfaction

Abstract

Abstract-A key step in insect olfaction is the transformation of a dense representation of odors in a small population of neurons -projection neurons (PNs) of the antennal lobe -into a sparse representation in a much larger population of neuronsKenyon cells (KCs) of the mushroom body. What computational purpose does this transformation serve? We propose that the PN-KC network implements an online clustering algorithm which we derive from the k-means cost function. The vector of PN-KC synaptic weights converging onto a given KC represents the corresponding cluster centroid. KC activities represent attribution indices, i.e. the degree to which a given odor presentation is attributed to each cluster. Remarkably, such clustering view of the PN-KC circuit naturally accounts for several of its salient features. First, attribution indices are nonnegative thus rationalizing rectification in KCs. Second, the constraint on the total sum of attribution indices for each presentation is enforced by a Lagrange multiplier identified with the activity of a single inhibitory interneuron reciprocally connected with KCs. Third, the soft-clustering version of our algorithm reproduces observed sparsity and overcompleteness of the KC representation which may optimize supervised classification downstream.

Manifold-tiling Localized Receptive Fields are Optimal in Similarity-preserving Neural Networks

“…The equivalence of (13) to (12) can be seen by performing the W, b, and V t optimizations explicitly and plugging the optimal values back. (13) suggests a two-step online algorithm (see Appendix A.8 for full derivation).…”

“…Relaxations of this optimization problem have been the subject of extensive research to solve clustering and manifold learning problems [25,26,27,28]. A biologically plausible neural network solving this problem was proposed in [12]. For the optimization of NSM-2 we use an augmented Lagrangian method [23,24,28,29].…”

“…Optimization functions considered here belong to the family of similarity-preserving objectives which dictate that similar inputs to the network elicit similar outputs [8,9,10,11,12]. In the absence of sign constraints, such objectives are provably optimized by projecting inputs onto the principal subspace [13,14,15], which can be done online by networks of linear neurons [8,9,10].…”

“…In the absence of sign constraints, such objectives are provably optimized by projecting inputs onto the principal subspace [13,14,15], which can be done online by networks of linear neurons [8,9,10]. Constraining the sign of the output leads to networks of rectifying neurons [11] which have been simulated numerically in the context of clustering and feature learning [11,12,16,17], and analyzed in the context of blind source extraction [18]. In the context of manifold learning, optimal solutions of Nonnegative Similarity-preserving Mapping objectives have been missing because optimization of existing NSM objectives is challenging.…”

A Hybrid Compact Neural Architecture for Visual Place Recognition

“…The fruit fly Drosophila olfactory neural circuit solves a similarity search problem by assigning similar neural activity patterns to similar odors [50], [51]. The fly algorithm performs a three-step procedure as the input odor goes through a threelayer neural circuit [50].…”