Exact PI in neural systems: The expert view
The recent paper by Issa and Zhang attempted to derive a set of necessary and sufficient conditions for a general class of systems that are capable of performing exact path integration (PI). Their project was to some extent inspired by rodent place cell firing which continues in the dark (therefore accurate PI is needed) and depends primarily on the spatial location of the animal regardless of the trajectory it followed to reach that position (therefore PI is path invariant). Not being an expert in PI modelling, I asked Allen Cheung and Rob Vickerstaff, as in http://wp.me/pFSBM-2c, for comments on the paper.
Their general view was that the, albeit, neat maths doesn’t really help us understand real-world PI, where, for instance, systems have to be robust against noise, nor, how a PI module might be integrated with vision, behavioural context, path planning or other key navigational components. For instance:
The involvement of vision in localisation. Vision complicates matters, especially inside experimental boxes, where it may not be the path integrator doing the bulk of the localization work, but possibly the visual cues. Therefore with vision, it is not necessary for a mathematically exact PI system to operate. Also, without vision, the rodent head direction system drifts significantly within the first 2 minutes, so PI alone is not sufficient to explain the stability of place fields.
The influence of noise. If the computations of PI are noisy, there are implications for the type of representation of space used. Issa and Zhang assume coordinate transforms to be trivial problems whereas it has been shown that models that are exact under noise-free conditions may behave very differently with noise (e.g. Cheung & Vickerstaff 2010). The constraints in the paper are not sufficient to guarantee a model is useful in practice, if noise is present.
John B. Issa and Kechen Zhang (2012) Universal conditions for exact path integration in neural systems. Online, April 9, 2012, doi: 10.1073/pnas.1119880109