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This type of code is used to encode continuous variables such as joint position, eye position, color, or sound frequency. Any individual neuron is too noisy to faithfully encode the variable using rate coding, but an entire population ensures greater fidelity and precision. For a population of unimodal tuning curves, i.e. with a single peak, the precision typically scales linearly with the number of neurons. Hence, for half the precision, half as many neurons are required. In contrast, when the tuning curves have multiple peaks, as in [[grid cell]]s that represent space, the precision of the population can scale exponentially with the number of neurons. This greatly reduces the number of neurons required for the same precision.<ref name="Mat">{{cite journal |vauthors=Mathis A, Herz AV, Stemmler MB |title=Resolution of nested neuronal representations can be exponential in the number of neurons |journal=Phys. Rev. Lett. |volume=109 |issue=1 |pages=018103 |date=July 2012 |pmid=23031134 |bibcode=2012PhRvL.109a8103M |doi=10.1103/PhysRevLett.109.018103|doi-access=free }}</ref>
==== Topology of population dynamics ====
[[Dimensionality reduction]] and [[topological data analysis]], have revealed that the population code is constrained to low-dimensional manifolds<ref>{{cite journal| title=Neural population dynamics during reaching|first1=MM|last1=Churchland|first2=JP|last2=Cunningham |first3=MT|last3=Kaufmann|first4=JD|last4=Foster|first5=P|last5=Nuyujukian|first6=SI|last6=Ryu|first7=KV|last7=Shenoy|journal=Nature|issue=487|pages=51-56|date=2012|doi=10.1038/nature11129}}</ref>. The position along the neural manifold correlates to certain behavioral conditions like head direction neurons in the anterodorsal thalamic nucleus forming a ring structure, [[grid cells]] encoding spatial position in [[entorhinal cortex]], or [[motor cortex]] neurons encoding hand movements<ref>{{cite journal |last1=Gallego |first1=JA |last2=Perich |first2=MG |last3=Miller |first3=LE |last4=Solla |first4=SA |title=Neural Manifolds for the Control of Movement |journal=Neuron |date=2017 |volume=94 |issue=5 |pages=978-984 |doi=10.1016/j.neuron.2017.05.025}}</ref> and preparatory activity.
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