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A sequence, or 'train', of spikes may contain information based on different coding schemes. In some neurons the strength with which a postsynaptic partner responds may depend solely on the 'firing rate', the average number of spikes per unit time (a 'rate code'). At the other end, a complex '[[temporal code]]' is based on the precise timing of single spikes. They may be locked to an external stimulus such as in the visual<ref>Burcas G.T & Albright T.D. Gauging sensory representations in the brain. http://www.vcl.salk.edu/Publications/PDF/Buracas_Albright_1999_TINS.pdf</ref> and [[auditory system]] or be generated intrinsically by the neural circuitry.<ref name="Gerstner97">{{cite journal |vauthors=Gerstner W, Kreiter AK, Markram H, Herz AV |title=Neural codes: firing rates and beyond |journal=Proc. Natl. Acad. Sci. U.S.A. |volume=94 |issue=24 |pages=12740–1 |date=November 1997 |pmid=9398065 |pmc=34168 |bibcode=1997PNAS...9412740G |doi=10.1073/pnas.94.24.12740|doi-access=free }}</ref>
Whether neurons use rate coding or temporal coding is a topic of intense debate within the neuroscience community, even though there is no clear definition of what these terms mean.<ref name=":0">{{Cite book|last=Gerstner, Wulfram.
=== Rate code ===
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Until recently, scientists had put the most emphasis on rate encoding as an explanation for [[post-synaptic potential]] patterns. However, functions of the brain are more temporally precise than the use of only rate encoding seems to allow.<ref name=":1" /> In other words, essential information could be lost due to the inability of the rate code to capture all the available information of the spike train. In addition, responses are different enough between similar (but not identical) stimuli to suggest that the distinct patterns of spikes contain a higher volume of information than is possible to include in a rate code.<ref name="Zador, Stevens">{{cite web|last=Zador, Stevens|first=Charles, Anthony|title=The enigma of the brain|url=https://docs.google.com/a/stolaf.edu/viewer?a=v&pid=gmail&attid=0.1&thid=1369b5e1cdf273f9&mt=application/pdf&url=https://mail.google.com/mail/u/0/?ui%3D2%26ik%3D0a436eb2a7%26view%3Datt%26th%3D1369b5e1cdf273f9%26attid%3D0.1%26disp%3Dsafe%26realattid%3Df_h0ty13ea0%26zw&sig=AHIEtbQB4vngr9nDZaMTLUOcrk5DzePKqA|work=© Current Biology 1995, Vol 5 No 12|access-date=August 4, 2012}}</ref>
Temporal codes (also called [https://lcnwww.epfl.ch/gerstner/SPNM/node8.html spike codes] <ref name=":0" />), employ those features of the spiking activity that cannot be described by the firing rate. For example, '''time-to-first-spike''' after the stimulus onset, '''phase-of-firing''' with respect to background oscillations, characteristics based on the second and higher statistical [[Moment (mathematics)|moments]] of the ISI [[probability distribution]], spike randomness, or precisely timed groups of spikes ('''temporal patterns''') are candidates for temporal codes.<ref name="Kostal">{{cite journal |vauthors=Kostal L, Lansky P, Rospars JP |title=Neuronal coding and spiking randomness |journal=Eur. J. Neurosci. |volume=26 |issue=10 |pages=2693–701 |date=November 2007 |pmid=18001270 |doi=10.1111/j.1460-9568.2007.05880.x |s2cid=15367988 }}</ref> As there is no absolute time reference in the nervous system, the information is carried either in terms of the relative timing of spikes in a population of neurons (temporal patterns) or with respect to an [[neural oscillations|ongoing brain oscillation]] (phase of firing).<ref name="thorpe" /><ref name="Stein" /> One way in which temporal codes are decoded, in presence of [[neural oscillations]], is that spikes occurring at specific phases of an oscillatory cycle are more effective in depolarizing the [[Chemical synapse|post-synaptic neuron]].<ref name = "Gupta2016">{{Cite journal|last1=Gupta|first1=Nitin|last2=Singh|first2=Swikriti Saran|last3=Stopfer|first3=Mark|date=2016-12-15|title=Oscillatory integration windows in neurons|journal=Nature Communications|volume=7|doi=10.1038/ncomms13808|issn=2041-1723|pmc=5171764|pmid=27976720|
The temporal structure of a spike train or firing rate evoked by a stimulus is determined both by the dynamics of the stimulus and by the nature of the neural encoding process. Stimuli that change rapidly tend to generate precisely timed spikes<ref>{{Cite journal|last1=Jolivet|first1=Renaud|last2=Rauch|first2=Alexander|last3=Lüscher|first3=Hans-Rudolf|last4=Gerstner|first4=Wulfram|date=2006-08-01|title=Predicting spike timing of neocortical pyramidal neurons by simple threshold models|url=https://doi.org/10.1007/s10827-006-7074-5|journal=Journal of Computational Neuroscience|language=en|volume=21|issue=1|pages=35–49|doi=10.1007/s10827-006-7074-5|pmid=16633938|s2cid=8911457|issn=1573-6873}}</ref> (and rapidly changing firing rates in PSTHs) no matter what neural coding strategy is being used. Temporal coding in the narrow sense refers to temporal precision in the response that does not arise solely from the dynamics of the stimulus, but that nevertheless relates to properties of the stimulus. The interplay between stimulus and encoding dynamics makes the identification of a temporal code difficult.
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[[File:NoisyNeuralResponse.png|thumb|Neural responses are noisy and unreliable.]]
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 |
==== 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=
=== Sparse coding ===
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