Abstract: The brain builds its internal sensory representations based on the structure of neural activity. A number of modalities, such as the early visual system and the spatial map in hippocampus, are relatively well-characterized. However some sensory systems, such as olfaction, remain enigmatic. The primary difficulty is that the underlying perceptual space is not well-understood. Can we "build" the sensory space from neural activity alone, without a prior understanding of how the stimuli are organized?
I will describe a set of mathematical tools, inspired from algebraic topology, that allow to infer the dimension of a stimulus space. I will then illustrate their utility for two neural systems: hippocampus and early olfaction.