Neural coding (or Neural representation) is a
neuroscience
Neuroscience is the scientific study of the nervous system (the brain, spinal cord, and peripheral nervous system), its functions and disorders. It is a multidisciplinary science that combines physiology, anatomy, molecular biology, developme ...
field concerned with characterising the hypothetical relationship between the
stimulus
A stimulus is something that causes a physiological response. It may refer to:
*Stimulation
**Stimulus (physiology), something external that influences an activity
**Stimulus (psychology), a concept in behaviorism and perception
*Stimulus (economi ...
and the individual or
ensemble
Ensemble may refer to:
Art
* Architectural ensemble
* Ensemble (album), ''Ensemble'' (album), Kendji Girac 2015 album
* Ensemble (band), a project of Olivier Alary
* Ensemble cast (drama, comedy)
* Ensemble (musical theatre), also known as the ...
neuronal responses and the relationship among the
electrical activity
This is a list of electrical phenomena. Electrical phenomena are a somewhat arbitrary division of electromagnetic phenomena.
Some examples are:
* Biefeld–Brown effect — Thought by the person who coined the name, Thomas Townsend Brown, to ...
of the neurons in the ensemble.
Based on the theory that
sensory and other information is represented in the
brain
A brain is an organ that serves as the center of the nervous system in all vertebrate and most invertebrate animals. It is located in the head, usually close to the sensory organs for senses such as vision. It is the most complex organ in a v ...
by
networks of neurons, it is thought that
neuron
A neuron, neurone, or nerve cell is an electrically excitable cell that communicates with other cells via specialized connections called synapses. The neuron is the main component of nervous tissue in all animals except sponges and placozoa. N ...
s can encode both
digital and
analog
Analog or analogue may refer to:
Computing and electronics
* Analog signal, in which information is encoded in a continuous variable
** Analog device, an apparatus that operates on analog signals
*** Analog electronics, circuits which use analog ...
information.
Overview
Neurons are remarkable among the
cells of the body in their ability to propagate signals rapidly over large distances. They do this by generating characteristic electrical pulses called
action potentials
An action potential occurs when the membrane potential of a specific cell location rapidly rises and falls. This depolarization then causes adjacent locations to similarly depolarize. Action potentials occur in several types of animal cells ...
: voltage spikes that can travel down axons. Sensory neurons change their activities by firing sequences of action potentials in various temporal patterns, with the presence of external sensory stimuli, such as
light
Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 tera ...
,
sound
In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid.
In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by the ...
,
taste
The gustatory system or sense of taste is the sensory system that is partially responsible for the perception of taste (flavor). Taste is the perception produced or stimulated when a substance in the mouth reacts chemically with taste receptor ...
,
smell and
touch
In physiology, the somatosensory system is the network of neural structures in the brain and body that produce the perception of touch ( haptic perception), as well as temperature ( thermoception), body position (proprioception), and pain. It ...
. It is known that information about the stimulus is encoded in this pattern of action potentials and transmitted into and around the brain, but this is not the only method. Specialized neurons, such as those of the retina, can communicate more information through
graded potentials
Graded potentials are changes in membrane potential that vary in size, as opposed to being all-or-none law, all-or-none. They include diverse potentials such as receptor potentials, electrotonic potentials, subthreshold membrane potential oscillat ...
. This differs from action potentials because information about the strength of a stimulus directly correlates with the strength of the neurons output. The signal decays much faster for graded potentials, necessitating short inter-neuron distances and high neuronal density. The advantage of graded potentials are higher information rates capable of encoding more states (i.e. higher fidelity) than spiking neurons.
Although action potentials can vary somewhat in duration,
amplitude
The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of amplit ...
and shape, they are typically treated as identical stereotyped events in neural coding studies. If the
brief duration of an action potential (about 1ms) is ignored, an action potential sequence, or spike train, can be characterized simply by a series of
all-or-none
All or none (AON) is a finance term used in investment banking or securities transactions that refers to "an order to buy or sell a stock that must be executed in its entirety, or not executed at all". Partial execution is not acceptable; the order ...
point events in time.
The lengths of interspike intervals (
ISIs) between two successive spikes in a spike train often vary, apparently randomly.
The study of neural coding involves measuring and characterizing how stimulus attributes, such as light or sound intensity, or motor actions, such as the direction of an arm movement, are represented by neuron action potentials or spikes. In order to describe and analyze neuronal firing,
statistical methods
Statistics (from German: ''Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industria ...
and methods of
probability theory
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set o ...
and stochastic
point process
In statistics and probability theory, a point process or point field is a collection of mathematical points randomly located on a mathematical space such as the real line or Euclidean space. Kallenberg, O. (1986). ''Random Measures'', 4th editio ...
es have been widely applied.
With the development of large-scale neural recording and decoding technologies, researchers have begun to crack the neural code and have already provided the first glimpse into the real-time neural code as memory is formed and recalled in the hippocampus, a brain region known to be central for memory formation. Neuroscientists have initiated several large-scale brain decoding projects.
Encoding and decoding
The link between stimulus and response can be studied from two opposite points of view. Neural encoding refers to the map from stimulus to response. The main focus is to understand how neurons respond to a wide variety of stimuli, and to construct models that attempt to predict responses to other stimuli.
Neural decoding
Neural decoding is a neuroscience field concerned with the hypothetical reconstruction of sensory and other stimuli from information that has already been encoded and represented in the brain by networks of neurons. Reconstruction refers to the ab ...
refers to the reverse map, from response to stimulus, and the challenge is to reconstruct a stimulus, or certain aspects of that stimulus, from the spike sequences it evokes.
Hypothesized coding schemes
A sequence, or 'train', of spikes may contain information based on different coding schemes. In some neurons the strength with which an 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
Neural coding (or Neural representation) is a neuroscience field concerned with characterising the hypothetical relationship between the stimulus and the individual or ensemble neuronal responses and the relationship among the electrical activity o ...
' is based on the precise timing of single spikes. They may be locked to an external stimulus such as in the visual and
auditory system or be generated intrinsically by the neural circuitry.
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.
Rate coding
The rate coding model of
neuron
A neuron, neurone, or nerve cell is an electrically excitable cell that communicates with other cells via specialized connections called synapses. The neuron is the main component of nervous tissue in all animals except sponges and placozoa. N ...
al firing communication states that as the intensity of a stimulus increases, the
frequency
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
or rate of
action potential
An action potential occurs when the membrane potential of a specific cell location rapidly rises and falls. This depolarization then causes adjacent locations to similarly depolarize. Action potentials occur in several types of animal cells, ...
s, or "spike firing", increases. Rate coding is sometimes called frequency coding.
Rate coding is a traditional coding scheme, assuming that most, if not all, information about the stimulus is contained in the firing rate of the neuron. Because the sequence of action potentials generated by a given stimulus varies from trial to trial, neuronal responses are typically treated statistically or probabilistically. They may be characterized by firing rates, rather than as specific spike sequences. In most sensory systems, the firing rate increases, generally non-linearly, with increasing stimulus intensity.
Under a rate coding assumption, any information possibly encoded in the temporal structure of the spike train is ignored. Consequently, rate coding is inefficient but highly robust with respect to the ISI '
noise
Noise is unwanted sound considered unpleasant, loud or disruptive to hearing. From a physics standpoint, there is no distinction between noise and desired sound, as both are vibrations through a medium, such as air or water. The difference aris ...
'.
During rate coding, precisely calculating firing rate is very important. In fact, the term "firing rate" has a few different definitions, which refer to different averaging procedures, such as an average over time (rate as a single-neuron spike count) or an average over several repetitions (rate of PSTH) of experiment.
In rate coding, learning is based on activity-dependent synaptic weight modifications.
Rate coding was originally shown by
ED Adrian and
Y Zotterman in 1926. In this simple experiment different weights were hung from a
muscle
Skeletal muscles (commonly referred to as muscles) are organs of the vertebrate muscular system and typically are attached by tendons to bones of a skeleton. The muscle cells of skeletal muscles are much longer than in the other types of muscl ...
. As the weight of the stimulus increased, the number of spikes recorded from sensory nerves innervating the muscle also increased. From these original experiments, Adrian and Zotterman concluded that action potentials were unitary events, and that the frequency of events, and not individual event magnitude, was the basis for most inter-neuronal communication.
In the following decades, measurement of firing rates became a standard tool for describing the properties of all types of sensory or
cortical neurons, partly due to the relative ease of measuring rates experimentally. However, this approach neglects all the information possibly contained in the exact timing of the spikes. During recent years, more and more experimental evidence has suggested that a straightforward firing rate concept based on temporal averaging may be too simplistic to describe brain activity.
Spike-count rate (average over time)
The spike-count rate, also referred to as temporal average, is obtained by counting the number of spikes that appear during a trial and dividing by the duration of trial.
The length T of the time window is set by the experimenter and depends on the type of neuron recorded from and to the stimulus. In practice, to get sensible averages, several spikes should occur within the time window. Typical values are T = 100 ms or T = 500 ms, but the duration may also be longer or shorter
Chapter 1.5in the textbook 'Spiking Neuron Models'
)
The spike-count rate can be determined from a single trial, but at the expense of losing all temporal resolution about variations in neural response during the course of the trial. Temporal averaging can work well in cases where the stimulus is constant or slowly varying and does not require a fast reaction of the
organism
In biology, an organism () is any living system that functions as an individual entity. All organisms are composed of cells (cell theory). Organisms are classified by taxonomy into groups such as multicellular animals, plants, and ...
— and this is the situation usually encountered in experimental protocols. Real-world input, however, is hardly stationary, but often changing on a fast time scale. For example, even when viewing a static image, humans perform
saccades
A saccade ( , French for ''jerk'') is a quick, simultaneous movement of both eyes
Eyes are organs of the visual system. They provide living organisms with vision, the ability to receive and process visual detail, as well as enabling s ...
, rapid changes of the direction of gaze. The image projected onto the retinal
photoreceptors changes therefore every few hundred milliseconds
Chapter 1.5in
)
Despite its shortcomings, the concept of a spike-count rate code is widely used not only in experiments, but also in models of
neural networks. It has led to the idea that a neuron transforms information about a single input variable (the stimulus strength) into a single continuous output variable (the firing rate).
There is a growing body of evidence that in
Purkinje neurons, at least, information is not simply encoded in firing but also in the timing and duration of non-firing, quiescent periods. There is also evidence from retinal cells, that information is encoded not only in the firing rate but also in spike timing.
More generally, whenever a rapid response of an organism is required a firing rate defined as a spike-count over a few hundred milliseconds is simply too slow.
Time-dependent firing rate (averaging over several trials)
The time-dependent firing rate is defined as the average number of spikes (averaged over trials) appearing during a short interval between times t and t+Δt, divided by the duration of the interval.
It works for stationary as well as for time-dependent stimuli. To experimentally measure the time-dependent firing rate, the experimenter records from a neuron while stimulating with some input sequence. The same stimulation sequence is repeated several times and the neuronal response is reported in a
Peri-Stimulus-Time Histogram (PSTH). The time t is measured with respect to the start of the stimulation sequence. The Δt must be large enough (typically in the range of one or a few milliseconds) so that there is a sufficient number of spikes within the interval to obtain a reliable estimate of the average. The number of occurrences of spikes n
K(t;t+Δt) summed over all repetitions of the experiment divided by the number K of repetitions is a measure of the typical activity of the neuron between time t and t+Δt. A further division by the interval length Δt yields time-dependent firing rate r(t) of the neuron, which is equivalent to the spike density of PSTH
Chapter 1.5in
).
For sufficiently small Δt, r(t)Δt is the average number of spikes occurring between times t and t+Δt over multiple trials. If Δt is small, there will never be more than one spike within the interval between t and t+Δt on any given trial. This means that r(t)Δt is also the
fraction
A fraction (from la, fractus, "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight ...
of trials on which a spike occurred between those times. Equivalently, r(t)Δt is the
probability
Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and ...
that a spike occurs during this time interval.
As an experimental procedure, the time-dependent firing rate measure is a useful method to evaluate neuronal activity, in particular in the case of time-dependent stimuli. The obvious problem with this approach is that it can not be the coding scheme used by neurons in the brain. Neurons can not wait for the stimuli to repeatedly present in an exactly same manner before generating a response.
Nevertheless, the experimental time-dependent firing rate measure can make sense, if there are large populations of independent neurons that receive the same stimulus. Instead of recording from a population of N neurons in a single run, it is experimentally easier to record from a single neuron and average over N repeated runs. Thus, the time-dependent firing rate coding relies on the implicit assumption that there are always populations of neurons.
Temporal coding
When precise spike timing or high-frequency firing-rate
fluctuations are found to carry information, the neural code is often identified as a temporal code.
A number of studies have found that the temporal resolution of the neural code is on a millisecond time scale, indicating that precise spike timing is a significant element in neural coding.
Such codes, that communicate via the time between spikes are also referred to as interpulse interval codes, and have been supported by recent studies.
Neurons exhibit high-frequency fluctuations of firing-rates which could be noise or could carry information. Rate coding models suggest that these irregularities are noise, while temporal coding models suggest that they encode information. If the nervous system only used rate codes to convey information, a more consistent, regular firing rate would have been evolutionarily advantageous, and neurons would have utilized this code over other less robust options.
[J. Leo van Hemmen, TJ Sejnowski. 23 Problems in Systems Neuroscience. Oxford Univ. Press, 2006. p.143-158.] Temporal coding supplies an alternate explanation for the “noise," suggesting that it actually encodes information and affects neural processing. To model this idea, binary symbols can be used to mark the spikes: 1 for a spike, 0 for no spike. Temporal coding allows the sequence 000111000111 to mean something different from 001100110011, even though the mean firing rate is the same for both sequences, at 6 spikes/10 ms.
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.
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.
Temporal codes (also calle
spike codes), 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
moments of the ISI
probability distribution, spike randomness, or precisely timed groups of spikes (temporal patterns) are candidates for temporal codes.
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
ongoing brain oscillation. (phase of firing)
One way in which temporal codes are decoded, in presence of
neural oscillations
Neural oscillations, or brainwaves, are rhythmic or repetitive patterns of neural activity in the central nervous system. Neural tissue can generate oscillatory activity in many ways, driven either by mechanisms within individual neurons or by ...
, is that spikes occurring at specific phases of an oscillatory cycle are more effective in depolarizing the
post-synaptic neuron.
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 (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.
In temporal coding, learning can be explained by activity-dependent synaptic delay modifications. The modifications can themselves depend not only on spike rates (rate coding) but also on spike timing patterns (temporal coding), i.e., can be a special case of
spike-timing-dependent plasticity
Spike-timing-dependent plasticity (STDP) is a biological process that adjusts the strength of connections between neurons in the brain. The process adjusts the connection strengths based on the relative timing of a particular neuron's output and in ...
.
The issue of temporal coding is distinct and independent from the issue of independent-spike coding. If each spike is independent of all the other spikes in the train, the temporal character of the neural code is determined by the behavior of time-dependent firing rate r(t). If r(t) varies slowly with time, the code is typically called a rate code, and if it varies rapidly, the code is called temporal.
Temporal coding in sensory systems
For very brief stimuli, a neuron's maximum firing rate may not be fast enough to produce more than a single spike. Due to the density of information about the abbreviated stimulus contained in this single spike, it would seem that the timing of the spike itself would have to convey more information than simply the average frequency of action potentials over a given period of time. This model is especially important for
sound localization
Sound localization is a listener's ability to identify the location or origin of a detected sound in direction and distance.
The sound localization mechanisms of the mammalian auditory system have been extensively studied. The auditory system us ...
, which occurs within the brain on the order of milliseconds. The brain must obtain a large quantity of information based on a relatively short neural response. Additionally, if low firing rates on the order of ten spikes per second must be distinguished from arbitrarily close rate coding for different stimuli, then a neuron trying to discriminate these two stimuli may need to wait for a second or more to accumulate enough information. This is not consistent with numerous organisms which are able to discriminate between stimuli in the time frame of milliseconds, suggesting that a rate code is not the only model at work.
To account for the fast encoding of visual stimuli, it has been suggested that neurons of the retina encode visual information in the latency time between stimulus onset and first action potential, also called latency to first spike or time-to-first-spike. This type of temporal coding has been shown also in the auditory and somato-sensory system. The main drawback of such a coding scheme is its sensitivity to intrinsic neuronal fluctuations. In the
primary visual cortex
The visual cortex of the brain is the area of the cerebral cortex that processes visual information. It is located in the occipital lobe. Sensory input originating from the eyes travels through the lateral geniculate nucleus in the thalamus and ...
of macaques, the timing of the first spike relative to the start of the stimulus was found to provide more information than the interval between spikes. However, the interspike interval could be used to encode additional information, which is especially important when the spike rate reaches its limit, as in high-contrast situations. For this reason, temporal coding may play a part in coding defined edges rather than gradual transitions.
The mammalian
gustatory system
The gustatory system or sense of taste is the sensory system that is partially responsible for the perception of taste (flavor). Taste is the perception produced or stimulated when a substance in the mouth reacts chemically with taste receptor ...
is useful for studying temporal coding because of its fairly distinct stimuli and the easily discernible responses of the organism. Temporally encoded information may help an organism discriminate between different tastants of the same category (sweet, bitter, sour, salty, umami) that elicit very similar responses in terms of spike count. The temporal component of the pattern elicited by each tastant may be used to determine its identity (e.g., the difference between two bitter tastants, such as quinine and denatonium). In this way, both rate coding and temporal coding may be used in the gustatory system – rate for basic tastant type, temporal for more specific differentiation.
Research on mammalian gustatory system has shown that there is an abundance of information present in temporal patterns across populations of neurons, and this information is different from that which is determined by rate coding schemes. Groups of neurons may synchronize in response to a stimulus. In studies dealing with the front cortical portion of the brain in primates, precise patterns with short time scales only a few milliseconds in length were found across small populations of neurons which correlated with certain information processing behaviors. However, little information could be determined from the patterns; one possible theory is they represented the higher-order processing taking place in the brain.
As with the visual system, in
mitral/tufted cells in the
olfactory bulb
The olfactory bulb (Latin: ''bulbus olfactorius'') is a neural structure of the vertebrate forebrain involved in olfaction, the sense of smell. It sends olfactory information to be further processed in the amygdala, the orbitofrontal cortex ( ...
of mice, first-spike latency relative to the start of a sniffing action seemed to encode much of the information about an odor. This strategy of using spike latency allows for rapid identification of and reaction to an odorant. In addition, some mitral/tufted cells have specific firing patterns for given odorants. This type of extra information could help in recognizing a certain odor, but is not completely necessary, as average spike count over the course of the animal's sniffing was also a good identifier. Along the same lines, experiments done with the olfactory system of rabbits showed distinct patterns which correlated with different subsets of odorants, and a similar result was obtained in experiments with the locust olfactory system.
Temporal coding applications
The specificity of temporal coding requires highly refined technology to measure informative, reliable, experimental data. Advances made in
optogenetics
Optogenetics is a biological technique to control the activity of neurons or other cell types with light. This is achieved by expression of light-sensitive ion channels, pumps or enzymes specifically in the target cells. On the level of individ ...
allow neurologists to control spikes in individual neurons, offering electrical and spatial single-cell resolution. For example, blue light causes the light-gated ion channel
channelrhodopsin
Channelrhodopsins are a subfamily of retinylidene proteins ( rhodopsins) that function as light-gated ion channels. They serve as sensory photoreceptors in unicellular green algae, controlling phototaxis: movement in response to light. Express ...
to open, depolarizing the cell and producing a spike. When blue light is not sensed by the cell, the channel closes, and the neuron ceases to spike. The pattern of the spikes matches the pattern of the blue light stimuli. By inserting channelrhodopsin gene sequences into mouse DNA, researchers can control spikes and therefore certain behaviors of the mouse (e.g., making the mouse turn left).
[Karl Diesseroth, Lecture. "Personal Growth Series: Karl Diesseroth on Cracking the Neural Code." Google Tech Talks. November 21, 2008. https://www.youtube.com/watch?v=5SLdSbp6VjM] Researchers, through optogenetics, have the tools to effect different temporal codes in a neuron while maintaining the same mean firing rate, and thereby can test whether or not temporal coding occurs in specific neural circuits.
[Han X, Qian X, Stern P, Chuong AS, Boyden ES. "Informational lesions: optical perturbations of spike timing and neural synchrony via microbial opsin gene fusions." Cambridge, Massachusetts: MIT Media Lad, 2009.]
Optogenetic technology also has the potential to enable the correction of spike abnormalities at the root of several neurological and psychological disorders.
If neurons do encode information in individual spike timing patterns, key signals could be missed by attempting to crack the code while looking only at mean firing rates.
Understanding any temporally encoded aspects of the neural code and replicating these sequences in neurons could allow for greater control and treatment of neurological disorders such as
depression,
schizophrenia
Schizophrenia is a mental disorder characterized by continuous or relapsing episodes of psychosis. Major symptoms include hallucinations (typically hearing voices), delusions, and disorganized thinking. Other symptoms include social withdra ...
, and
Parkinson's disease
Parkinson's disease (PD), or simply Parkinson's, is a long-term degenerative disorder of the central nervous system that mainly affects the motor system. The symptoms usually emerge slowly, and as the disease worsens, non-motor symptoms becom ...
. Regulation of spike intervals in single cells more precisely controls brain activity than the addition of pharmacological agents intravenously.
Phase-of-firing code
Phase-of-firing code is a neural coding scheme that combines the
spike
Spike, spikes, or spiking may refer to:
Arts, entertainment, and media
Books
* ''The Spike'' (novel), a novel by Arnaud de Borchgrave
* ''The Spike'' (book), a nonfiction book by Damien Broderick
* ''The Spike'', a starship in Peter F. Hamilto ...
count code with a time reference based on
oscillations
Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum ...
. This type of code takes into account a time label for each spike according to a time reference based on phase of local ongoing oscillations at low
or high frequencies.
It has been shown that neurons in some cortical sensory areas encode rich naturalistic stimuli in terms of their spike times relative to the phase of ongoing network oscillatory fluctuations, rather than only in terms of their spike count.
The
local field potential
Local field potentials (LFP) are transient electrical signals generated in nervous and other tissues by the summed and synchronous electrical activity of the individual cells (e.g. neurons) in that tissue. LFP are "extracellular" signals, meaning ...
signals reflect population (network) oscillations. The phase-of-firing code is often categorized as a temporal code although the time label used for spikes (i.e. the network oscillation phase) is a low-resolution (coarse-grained) reference for time. As a result, often only four discrete values for the phase are enough to represent all the information content in this kind of code with respect to the phase of oscillations in low frequencies. Phase-of-firing code is loosely based on the
phase precession
Phase precession is a neurophysiological process in which the time of firing of action potentials by individual neurons occurs progressively earlier in relation to the phase of the local field potential oscillation with each successive cycle. In ...
phenomena observed in place cells of the
hippocampus
The hippocampus (via Latin from Greek , 'seahorse') is a major component of the brain of humans and other vertebrates. Humans and other mammals have two hippocampi, one in each side of the brain. The hippocampus is part of the limbic system, a ...
. Another feature of this code is that neurons adhere to a preferred order of spiking between a group of sensory neurons, resulting in firing sequence.
Phase code has been shown in visual cortex to involve also
high-frequency oscillations
High-frequency oscillations (HFO) are brain waves of the frequency faster than ~80 Hz, generated by neuronal cell population. High-frequency oscillations can be recorded during an electroencephalagram (EEG), local field potential (LFP) or electr ...
.
Within a cycle of gamma oscillation, each neuron has its own preferred relative firing time. As a result, an entire population of neurons generates a firing sequence that has a duration of up to about 15 ms.
Population coding
Population coding is a method to represent stimuli by using the joint activities of a number of neurons. In population coding, each neuron has a distribution of responses over some set of inputs, and the responses of many neurons may be combined to determine some value about the inputs. From the theoretical point of view, population coding is one of a few mathematically well-formulated problems in neuroscience. It grasps the essential features of neural coding and yet is simple enough for theoretic analysis.
Experimental studies have revealed that this coding paradigm is widely used in the sensor and motor areas of the brain.
For example, in the visual area
medial temporal (MT), neurons are tuned to the moving direction.
In response to an object moving in a particular direction, many neurons in MT fire with a noise-corrupted and
bell-shaped activity pattern across the population. The moving direction of the object is retrieved from the population activity, to be immune from the fluctuation existing in a single neuron's signal. When monkeys are trained to move a joystick towards a lit target, a single neuron will fire for multiple target directions. However it fires the fastest for one direction and more slowly depending on how close the target was to the neuron's "preferred" direction. If each neuron represents movement in its preferred direction, and the vector sum of all neurons is calculated (each neuron has a firing rate and a preferred direction), the sum points in the direction of motion. In this manner, the population of neurons codes the signal for the motion. This particular population code is referred to as
population vector coding.
Place-time population codes, termed the averaged-localized-synchronized-response (ALSR) code, have been derived for neural representation of auditory acoustic stimuli. This exploits both the place or tuning within the auditory nerve, as well as the phase-locking within each nerve fiber auditory nerve. The first ALSR representation was for steady-state vowels; ALSR representations of pitch and formant frequencies in complex, non-steady state stimuli were later demonstrated for voiced-pitch, and formant representations in consonant-vowel syllables.
The advantage of such representations is that global features such as pitch or formant transition profiles can be represented as global features across the entire nerve simultaneously via both rate and place coding.
Population coding has a number of other advantages as well, including reduction of uncertainty due to neuronal
variability and the ability to represent a number of different stimulus attributes simultaneously. Population coding is also much faster than rate coding and can reflect changes in the stimulus conditions nearly instantaneously.
Individual neurons in such a population typically have different but overlapping selectivities, so that many neurons, but not necessarily all, respond to a given stimulus.
Typically an encoding function has a peak value such that activity of the neuron is greatest if the perceptual value is close to the peak value, and becomes reduced accordingly for values less close to the peak value. It follows that the actual perceived value can be reconstructed from the overall pattern of activity in the set of neurons. Vector coding is an example of simple averaging. A more sophisticated mathematical technique for performing such a reconstruction is the method of
maximum likelihood
In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed stat ...
based on a multivariate distribution of the neuronal responses. These models can assume independence, second order correlations,
or even more detailed dependencies such as higher order
maximum entropy models, or
copulas.
Correlation coding
The correlation coding model of
neuron
A neuron, neurone, or nerve cell is an electrically excitable cell that communicates with other cells via specialized connections called synapses. The neuron is the main component of nervous tissue in all animals except sponges and placozoa. N ...
al firing claims that correlations between
action potential
An action potential occurs when the membrane potential of a specific cell location rapidly rises and falls. This depolarization then causes adjacent locations to similarly depolarize. Action potentials occur in several types of animal cells, ...
s, or "spikes", within a spike train may carry additional information above and beyond the simple timing of the spikes. Early work suggested that correlation between spike trains can only reduce, and never increase, the total
mutual information
In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual dependence between the two variables. More specifically, it quantifies the " amount of information" (in units such ...
present in the two spike trains about a stimulus feature. However, this was later demonstrated to be incorrect. Correlation structure can increase information content if noise and signal correlations are of opposite sign. Correlations can also carry information not present in the average firing rate of two pairs of neurons. A good example of this exists in the pentobarbital-anesthetized marmoset auditory cortex, in which a pure tone causes an increase in the number of correlated spikes, but not an increase in the mean firing rate, of pairs of neurons.
Independent-spike coding
The independent-spike coding model of
neuron
A neuron, neurone, or nerve cell is an electrically excitable cell that communicates with other cells via specialized connections called synapses. The neuron is the main component of nervous tissue in all animals except sponges and placozoa. N ...
al firing claims that each individual
action potential
An action potential occurs when the membrane potential of a specific cell location rapidly rises and falls. This depolarization then causes adjacent locations to similarly depolarize. Action potentials occur in several types of animal cells, ...
, or "spike", is independent of each other spike within the
spike train
An action potential occurs when the membrane potential of a specific cell location rapidly rises and falls. This depolarization then causes adjacent locations to similarly depolarize. Action potentials occur in several types of animal cells, c ...
.
Position coding
![PopulationCode](https://upload.wikimedia.org/wikipedia/commons/a/a1/PopulationCode.svg)
A typical population code involves neurons with a Gaussian tuning curve whose means vary linearly with the stimulus intensity, meaning that the neuron responds most strongly (in terms of spikes per second) to a stimulus near the mean. The actual intensity could be recovered as the stimulus level corresponding to the mean of the neuron with the greatest response. However, the noise inherent in neural responses means that a maximum likelihood estimation function is more accurate.
![NoisyNeuralResponse](https://upload.wikimedia.org/wikipedia/commons/6/66/NoisyNeuralResponse.png)
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
A grid cell is a type of neuron within the entorhinal cortex that fires at regular intervals as an animal navigates an open area, allowing it to understand its position in space by storing and integrating information about location, distance, and ...
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.
Sparse coding
The sparse code is when each item is encoded by the strong activation of a relatively small set of neurons. For each item to be encoded, this is a different subset of all available neurons. In contrast to sensor-sparse coding, sensor-dense coding implies that all information from possible sensor locations is known.
As a consequence, sparseness may be focused on temporal sparseness ("a relatively small number of time periods are active") or on the sparseness in an activated population of neurons. In this latter case, this may be defined in one time period as the number of activated neurons relative to the total number of neurons in the population. This seems to be a hallmark of neural computations since compared to traditional computers, information is massively distributed across neurons. Sparse coding of natural images produces
wavelet
A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the num ...
-like oriented filters that resemble the receptive fields of simple cells in the visual cortex. The capacity of sparse codes may be increased by simultaneous use of temporal coding, as found in the locust olfactory system.
Given a potentially large set of input patterns, sparse coding algorithms (e.g.
sparse autoencoder) attempt to automatically find a small number of representative patterns which, when combined in the right proportions, reproduce the original input patterns. The sparse coding for the input then consists of those representative patterns. For example, the very large set of English sentences can be encoded by a small number of symbols (i.e. letters, numbers, punctuation, and spaces) combined in a particular order for a particular sentence, and so a sparse coding for English would be those symbols.
Linear generative model
Most models of sparse coding are based on the linear generative model.
In this model, the symbols are combined in a
linear fashion to approximate the input.
More formally, given a k-dimensional set of real-numbered input vectors
, the goal of sparse coding is to determine n k-dimensional
basis vectors
In mathematics, a set of vectors in a vector space is called a basis if every element of may be written in a unique way as a finite linear combination of elements of . The coefficients of this linear combination are referred to as componen ...
along with a
sparse n-dimensional vector of weights or coefficients
for each input vector, so that a linear combination of the basis vectors with proportions given by the coefficients results in a close approximation to the input vector:
.
The codings generated by algorithms implementing a linear generative model can be classified into codings with ''soft sparseness'' and those with ''hard sparseness''.
[ These refer to the distribution of basis vector coefficients for typical inputs. A coding with soft sparseness has a smooth ]Gaussian
Carl Friedrich Gauss (1777–1855) is the eponym of all of the topics listed below.
There are over 100 topics all named after this German mathematician and scientist, all in the fields of mathematics, physics, and astronomy. The English eponymo ...
-like distribution, but peakier than Gaussian, with many zero values, some small absolute values, fewer larger absolute values, and very few very large absolute values. Thus, many of the basis vectors are active. Hard sparseness, on the other hand, indicates that there are many zero values, ''no'' or ''hardly any'' small absolute values, fewer larger absolute values, and very few very large absolute values, and thus few of the basis vectors are active. This is appealing from a metabolic perspective: less energy is used when fewer neurons are firing.[
Another measure of coding is whether it is ''critically complete'' or ''overcomplete''. If the number of basis vectors n is equal to the dimensionality k of the input set, the coding is said to be critically complete. In this case, smooth changes in the input vector result in abrupt changes in the coefficients, and the coding is not able to gracefully handle small scalings, small translations, or noise in the inputs. If, however, the number of basis vectors is larger than the dimensionality of the input set, the coding is ''overcomplete''. Overcomplete codings smoothly interpolate between input vectors and are robust under input noise.] The human primary visual cortex
The visual cortex of the brain is the area of the cerebral cortex that processes visual information. It is located in the occipital lobe. Sensory input originating from the eyes travels through the lateral geniculate nucleus in the thalamus and ...
is estimated to be overcomplete by a factor of 500, so that, for example, a 14 x 14 patch of input (a 196-dimensional space) is coded by roughly 100,000 neurons.[
Other models are based on ]matching pursuit
Matching pursuit (MP) is a sparse approximation algorithm which finds the "best matching" projections of multidimensional data onto the span of an over-complete (i.e., redundant) dictionary D. The basic idea is to approximately represent a signal ...
, a sparse approximation Sparse approximation (also known as sparse representation) theory deals with sparse solutions for systems of linear equations. Techniques for finding these solutions and exploiting them in applications have found wide use in image processing, sign ...
algorithm which finds the "best matching" projections of multidimensional data, and dictionary learning
Sparse coding is a representation learning method which aims at finding a sparse representation of the input data (also known as sparse coding) in the form of a linear combination of basic elements as well as those basic elements themselves. These ...
, a representation learning method which aims to find a sparse matrix
In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. There is no strict definition regarding the proportion of zero-value elements for a matrix to qualify as sparse b ...
representation of the input data in the form of a linear combination of basic elements as well as those basic elements themselves.
Biological evidence
Sparse coding may be a general strategy of neural systems to augment memory capacity. To adapt to their environments, animals must learn which stimuli are associated with rewards or punishments and distinguish these reinforced stimuli from similar but irrelevant ones. Such tasks require implementing stimulus-specific associative memories in which only a few neurons out of a population
Population typically refers to the number of people in a single area, whether it be a city or town, region, country, continent, or the world. Governments typically quantify the size of the resident population within their jurisdiction using a ...
respond to any given stimulus and each neuron responds to only a few stimuli out of all possible stimuli.
Theoretical work on sparse distributed memory Sparse distributed memory (SDM) is a mathematical model of human long-term memory introduced by Pentti Kanerva in 1988 while he was at NASA Ames Research Center. It is a generalized random-access memory (RAM) for long (e.g., 1,000 bit) binary words. ...
has suggested that sparse coding increases the capacity of associative memory by reducing overlap between representations. Experimentally, sparse representations of sensory information have been observed in many systems, including vision, audition, touch, and olfaction. However, despite the accumulating evidence for widespread sparse coding and theoretical arguments for its importance, a demonstration that sparse coding improves the stimulus-specificity of associative memory has been difficult to obtain.
In the ''Drosophila
''Drosophila'' () is a genus of flies, belonging to the family Drosophilidae, whose members are often called "small fruit flies" or (less frequently) pomace flies, vinegar flies, or wine flies, a reference to the characteristic of many species ...
'' olfactory system
The olfactory system, or sense of smell, is the sensory system used for smelling ( olfaction). Olfaction is one of the special senses, that have directly associated specific organs. Most mammals and reptiles have a main olfactory system and an ...
, sparse odor coding by the Kenyon cell Kenyon cells are the intrinsic neurons of the mushroom body, a neuropil found in the brains of most arthropods and some annelids. They were first described by F. C. Kenyon in 1896. The number of Kenyon cells in an organism varies greatly between s ...
s of the mushroom body
The mushroom bodies or ''corpora pedunculata'' are a pair of structures in the brain of insects, other arthropods, and some annelids (notably the ragworm ''Platynereis dumerilii''). They are known to play a role in olfactory learning and memory. ...
is thought to generate a large number of precisely addressable locations for the storage of odor-specific memories. Sparseness is controlled by a negative feedback circuit between Kenyon cells and GABAergic anterior paired lateral (APL) neurons. Systematic activation and blockade of each leg of this feedback circuit shows that Kenyon cells activate APL neurons and APL neurons inhibit Kenyon cells. Disrupting the Kenyon cell–APL feedback loop decreases the sparseness of Kenyon cell odor responses, increases inter-odor correlations, and prevents flies from learning to discriminate similar, but not dissimilar, odors. These results suggest that feedback inhibition suppresses Kenyon cell activity to maintain sparse, decorrelated odor coding and thus the odor-specificity of memories.[Lin, Andrew C., et al.]
Sparse, decorrelated odor coding in the mushroom body enhances learned odor discrimination
" Nature Neuroscience 17.4 (2014): 559-568.
See also
* Artificial neural network
Artificial neural networks (ANNs), usually simply called neural networks (NNs) or neural nets, are computing systems inspired by the biological neural networks that constitute animal brains.
An ANN is based on a collection of connected unit ...
* Autoencoder
An autoencoder is a type of artificial neural network used to learn efficient codings of unlabeled data ( unsupervised learning). The encoding is validated and refined by attempting to regenerate the input from the encoding. The autoencoder lea ...
* Biological neuron model
Biological neuron models, also known as a spiking neuron models, are mathematical descriptions of the properties of certain cells in the nervous system that generate sharp electrical potentials across their cell membrane, roughly one millisecon ...
* Binding problem The consciousness and binding problem is the problem of how objects, background and abstract or emotional features are combined into a single experience.
The binding problem refers to the overall encoding of our brain circuits for the combination o ...
* Cognitive map
A cognitive map is a type of mental representation which serves an individual to acquire, code, store, recall, and decode information about the relative locations and attributes of phenomena in their everyday or metaphorical spatial environment. T ...
* Deep learning
* Feature integration theory Feature integration theory is a theory of attention developed in 1980 by Anne Treisman and Garry Gelade that suggests that when perceiving a stimulus, features are "registered early, automatically, and in parallel, while objects are identified separ ...
* Grandmother cell
* Models of neural computation
Models of neural computation are attempts to elucidate, in an abstract and mathematical fashion, the core principles that underlie information processing in biological nervous systems, or functional components thereof. This article aims to provide ...
* Neural correlate
The neural correlates of consciousness (NCC) refer to the relationships between mental states and neural states and constitute the minimal set of neuronal events and mechanisms sufficient for a specific conscious percept. Neuroscientists use emp ...
* Neural decoding
Neural decoding is a neuroscience field concerned with the hypothetical reconstruction of sensory and other stimuli from information that has already been encoded and represented in the brain by networks of neurons. Reconstruction refers to the ab ...
* Neural oscillation
Neural oscillations, or brainwaves, are rhythmic or repetitive patterns of neural activity in the central nervous system. Neural tissue can generate oscillatory activity in many ways, driven either by mechanisms within individual neurons or by ...
* Sparse distributed memory Sparse distributed memory (SDM) is a mathematical model of human long-term memory introduced by Pentti Kanerva in 1988 while he was at NASA Ames Research Center. It is a generalized random-access memory (RAM) for long (e.g., 1,000 bit) binary words. ...
* Vector quantization
Vector quantization (VQ) is a classical quantization technique from signal processing that allows the modeling of probability density functions by the distribution of prototype vectors. It was originally used for data compression. It works by di ...
References
Further reading
* Földiák P, Endres D
Sparse coding
Scholarpedia
''Scholarpedia'' is an English-language wiki-based online encyclopedia with features commonly associated with open-access online academic journals, which aims to have quality content in science and medicine.
''Scholarpedia'' articles are written ...
, 3(1):2984, 2008.
* Dayan P & Abbott LF. ''Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems''. Cambridge, Massachusetts: The MIT Press; 2001.
* Rieke F, Warland D, de Ruyter van Steveninck R, Bialek W. ''Spikes: Exploring the Neural Code''. Cambridge, Massachusetts: The MIT Press; 1999.
*
*{{cite journal , last1 = Tsien , first1 = JZ. , display-authors = etal , year = 2014 , title = On initial Brain Activity Mapping of episodic and semantic memory code in the hippocampus , journal = Neurobiology of Learning and Memory , volume = 105 , pages = 200–210 , doi=10.1016/j.nlm.2013.06.019, pmid = 23838072 , pmc = 3769419
Computational neuroscience
Neural circuits