Flies and mice are species separated by 600 million years of evolution, yet have evolved olfactory systems that share many similarities in their anatomic and functional organization. What functions do these shared anatomical and functional features serve, and are they optimal for odor sensing? In this study, we address the optimality of evolutionary design in olfactory circuits by studying artificial neural networks trained to sense odors. We found that artificial neural networks quantitatively recapitulate structures inherent in the olfactory system, including the formation of glomeruli onto a compression layer and sparse and random connectivity onto an expansion layer. Finally, we offer theoretical justifications for each result. Our work offers a framework to explain the evolutionary convergence of olfactory circuits, and gives insight and logic into the anatomic and functional structure of the olfactory system. Over the last two decades, both the anatomic and functional organization of the fly and mouse olfactory systems have been mapped to excruciating detail, affording knowledge of how odors are processed along the entirety of olfactory pathway. In both model organisms, the layout of the olfactory system is two layers deep and comprises of a compression layer and an expansion layer. Olfactory perception is initiated by the recognition of odorants by a large repertoire of receptors in the sensory epithelium (Buck & Axel, 1991) . In fruit flies, individual olfactory receptor neurons (ORNs) express only one of 50 different olfactory receptors (ORs), and all neurons (10 on average) that express the same receptor converge with precision onto a unique set of 2-4 projection neurons (PNs) through a specialized structure known as an olfactory glomerulus (Vosshall, Wong, & Axel, 2000) . This layout establishes a one-to-one mapping between ORs and PNs. Information is then conveyed to an expansion layer of 2,500 Kenyon Cells (KCs) through sparse and random connectivity to support a high dimensional representation of odor information before it is classified by 20 read-out neurons, the mushroom body output neurons (MBONs). Experiments reveal that synaptic plasticity at the KC-MBON synapse is necessary and causal in odor learning. The only major differences between the circuits of mice and flies appear to be numerical. Whereas the fly olfactory system consists of 50 ORs, 50 glomeruli, and 2500 KCs, the mouse olfactory system consists of 1500 ORs, 1500 glomeruli, and 1 million piriform neurons. The fact that evolution has evolved to hardwire the same architecture in flies, mice, and multiple other organisms suggests that such an architecture is optimal for the general task of odor sensing. Although we have a detailed anatomy of the olfactory system in both flies and mice, it is unclear why certain features are optimal for odor sensing. In particular, 1) why does every ORN express a single OR, 2) why is information preserved through a one-to-one mapping between ORs and PNs, and 3) why is connectivity onto the expansion layer sparse and random (Litwin-Kumar, Harris, Axel, Sompolinsky, & Abbott, 2017)? To study optimal circuit design, we use a goal-driven approach to train an artificial neural network to classify odors and then analyze the anatomical and functional structures that emerge after training. This approach has recently been used to study the functional profiles of the ventral stream in visual object processing (Yamins & DiCarlo, 2016) . The simplicity of the fly olfactory circuit and the exhaustive knowledge that we have of its anatomy provides constraints that can be used to gain insight into evolutionary design. We trained artificial neural networks using stochastic gradient descent to classify odors. We found that glomeruli emerged in PN layer, and sparse random connectivity emerges in the PN to KC connections. We then explored the sufficient conditions that enabled these features to emerge. We found that the formation of glomeruli did not depend on input noise but rather on the existence of an expansion layer downstream. In addition, we found that an expansion layer with a synaptic degree of 7 endows the olfactory system with robustness by allowing for large tolerances in synaptic efficacies without affecting task performance. Our work offers a framework to explain the Optimal K predicted by maximal weight robustness (red) and direct training (plus signs). The line is a power-law fit of the red dots.
Artificial neural networks evolved the same structures present in the olfactory systems of flies and mice after being trained to classify odors
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