The visual system is highly structured. At subsequent stages of the visual pathway, there exist retinotopic maps that preserve the spatial features of the visual input. One might expect that such maps provide a universally useful way of preserving external structure (the structure of the environment) within internal neural representations. Yet, when scientists have gone to look for similar maps in other sensory pathways, they have, at times, come up short. One such example is found in the olfactory pathway.
Here, odor molecules are first processed by olfactory receptor neurons (ORNs) in the epithelium. Each ORN genetically expresses one of ~100 olfactory receptor genes, and ORNs expressing a given type of receptor gene are expressed within broad spatial zones in the epithelium. All ORNs expressing a given receptor gene then project to a single localized structure, the glomerulus, in the next stage of processing. This leads to a highly organized representation in the olfactory bulb.
Puzzlingly, this high degree of organization appears to be undone at the next stage of processing. Mitral cells within glomeruli project to a small fraction of the vast number of neurons in the piriform cortex, but these projections lack any discernible spatial order. Furthermore, the resulting cortical responses are sparse and are spatially distributed across the cortex, such that similar odors are represented in largely non-overlapping and spatially distributed groups of cells.
We believe that this architecture may be ``unstructured'' in a manner that takes advantage of certain features of natural odor inputs, which are inherently different than, e.g., natural visual inputs.
The space of molecular compounds is huge, yet any natural odor is composed of a relatively small fraction of molecules. Phrased another way, natural odors are sparse (composed of a small number of all possible components) in the space of natural odors. Assuming that such input vectors can approximated as a linear combination of elements in the input space, recent results from compressed sensing have shown that an optimal representation of such sparse inputs can be achieved through random projections to a low-dimensional space. This suggests that random sampling may facilitate efficient representations of natural ador stimuli.
In terms of number of neurons, the olfactory bulb (second stage of processing) is quite small in comparison to the piriform cortex (third stage of processing). The expanded representation in the third stage is later recompressed, yielding a condensed representation in a fourth stage that is believed to be directly relevant for behavior. Given that any information about odor inputs is present at the second stage, and subsequent stages can only degrade this information, what is the role of the intermediate expansion? Why invest such a great number of neural resources in this expansion, only to recover a dense representation of information? We believe that this expansion may serve to shape the neural representation in a way that facilitates flexibility and adaptation to a dynamic odor space, and we are currently working toward understanding the functional benefits of such expansive architectures.
We observe that the olfactory system exhibits spatially-disordered projections, but we can imagine that the olfactory pathway could be structured in any number of alternate ways. It is possible that such alternative architectures would be optimal for a different input space, or alternatively that they would predict a different structure of interactions in subsequent processing stages. To explore these alternative design schemes, we have built a computational framework that incorporates known mechanistic interactions and reproduces qualitative features of neural responses. With this framework, we can manipulate specific features of the neural architecture and probe the consequences of different design principles.