Sensory systems in individual living cells, as well as in multi-cellular organisms, employ a variety of adaptation mechanisms in order to produce behaviors that are invariant to certain characteristics of environmental inputs, such as symmetries or background signal levels, while at the same time allowing the extraction of relevant features of these inputs. These mechanisms and behaviors are responsible for phenomena ranging from chemotaxis in bacteria to the logarithmic sensitivities to forces, sounds, and vision in humans revealed through psychophysical measurements.

Much of our recent research has been devoted to the understanding of feedforward and feedback circuits that produce adaptation behavior. While closely related to standard concepts in control theory such as disturbance rejection, completely new questions arise. For example, while the internal model principle (IMP) would predict that feedback systems must be present in order to guarantee robust adaptation, the lack of separation between plant and controller components makes the significance of the IMP questionable. More so, the need to perform coordinate changes to exhibit the internal model (transformations which, if at all possible, require strong nonsingularity and global properties on vector fields) typically leads to uninterpretable variables. Moreover, questions such as the invariance of transient behaviors to symmetries appear not to have been systematically studied in this context. We will discuss one such behavior (fold-invariance) and mention new experimental results that confirm theoretical predictions.