A Robust Feedforward Model of the Olfactory System

Most natural odors have sparse molecular composition. This makes the principles of compressed sensing potentially relevant to the structure of the olfactory code. Yet, the largely feedforward organization of the olfactory system precludes reconstruction using standard compressed sensing algorithms. To resolve this problem, recent theoretical work has shown that signal reconstruction could take place as a result of a low dimensional dynamical system converging to one of its attractor states. However, the dynamical aspects of optimization slowed down odor recognition and were also found to be susceptible to noise. Here we describe a feedforward model of the olfactory system that achieves both strong compression and fast reconstruction that is also robust to noise. A key feature of the proposed model is a specific relationship between how odors are represented at the glomeruli stage, which corresponds to a compression, and the connections from glomeruli to third-order neurons (neurons in the olfactory cortex of vertebrates or Kenyon cells in the mushroom body of insects), which in the model corresponds to reconstruction. We show that should this specific relationship hold true, the reconstruction will be both fast and robust to noise, and in particular to the false activation of glomeruli. The predicted connectivity rate from glomeruli to third-order neurons can be tested experimentally.Author Summary: Many olfactory systems are capable of accurately sensing a minimum of thousands of different odorants using as few as hundreds of different receptors. This compression raises the possibility that the mathematical properties of compressed sensing might be relevant to olfaction, similar to how these properties were found relevant to other sensory systems. In olfaction, previous applications of compressed sensing algorithms relied on the dynamics of neural circuits to reconstruct high dimensional signals. Such approaches are relatively temporally inefficient and sensitive to noise. To overcome these problems, we propose a purely feedforward compressed sensing model of the olfactory system where high dimensional signals can be recovered with a single feedforward layer of neural processing. The reconstructions are shown to be robust to noise, account for a number of experimental observations, and because of the feedforward structure are temporally efficient. Using the model, we make predictions that can be tested in future experiments with respect to optimal connectivity within the olfactory system. Our results indicate that feedforward neural architectures can provide an efficient way to implement compressed sensing in neural systems.