Understanding olfactory coding is challenging due to the complexity of chemical stimuli, which are, by nature, complex, high-dimensional, and not easily organized along any obvious coordinate systems. We investigated this problem in the Drosophila olfactory system, whose core circuit architecture is similar to that of its vertebrate analogs. Olfactory inputs are randomly expanded onto a large population of third-order, mixed layer neurons, which, in the fly, are the principal neurons of the mushroom body (MB), a major associative olfactory area in the fly brain. Using large-scale calcium imaging in defined olfactory populations, we find that MB representations of odor are sparse and structured; odor relationships are reliable and predictable across individual MBs. However, the relationships between odors are unexpectedly remapped between the input odorant receptor layer and the mushroom body layer, in a manner that deviates from the simple predictions of a sparse random expansion of olfactory inputs. We will discuss new analytical approaches towards understanding alternative organizational frameworks by which odor representations are reformatted across successive stages of olfactory processing in the fly brain.