User:Peter Cariani/Proposed/Neuronal code

• Peter Cariani, Dept. of Otology & Laryngology, Harvard Medical School

• Eugene M. Izhikevich, Editor-in-Chief of Scholarpedia, the peer-reviewed open-access encyclopedia

This article will briefly cover:

1. Outline of the neural coding problem
   1. Functionalist conceptions -- relation to specific informational functions (e.g. perceptual discrimination, action selection/implementation)
   2. Information-theoretic conceptions -- Shannonian informational content vis-a-vis signals or actions (stimulus reconstruction from spike data)
2. Basic requirements for a neural code
   1. Encoding of signal type (e.g. neuronal information subserving pitch)
   2. Encoding of signal value (e.g. specific pitch frequency)
   3. Capable of being decoded in a coherent way
   4. Evaluation of candidate codes (e.g. effective retrodiction of percept or action based on spike data and coding assumptions; role of informational adequency in eliminating candidate codes, issue of whether optimality per se constitutes positive evidence for a code)
3. A taxonomy of possible pulse codes
   1. Channel-based codes
   2. Temporal pattern codes
   3. Spike Latency codes
   4. Other kinds of codes (e.g. rate or latency variance, higher-order statistics, ordinal and sequence codes)
4. A table listing evidence for candidate codes
5. General observations (neural codes, signal multiplexing, and multimodal integration)
6. Relation of codes to neural processing architectures (codes & computational architectures mutually determined)
7. Conclusions

I will be working intensively on this article over Labor Day Weekend, 2010 and the week following. PAC. I will write the text first, incorporate figures, then references and footnotes, then go back and edit, adjust figure sizes, and proof the whole thing. I am in the process of redrawing the figures.

The neural coding problem

The problem of neural coding involves identification of those aspects of neuronal activity that convey informational distinctions that govern internal representations and, ultimately, the coordinated behavior of the whole organism. Informational distinctions are configurations of activity that, by virtue of differences of form, switch the behavior of a system. Internal representations are sets of functional states that are associated with sensory, cognitive, conative, affective, mnemonic, and motor distinctions.

The problem of neural coding is a critical part of the more general program of discovering the essential functional principles that underly the operation of the brain as an effective, survival-enhancing informational system ("reverse-engineering the brain"). Success of this larger project entails identification of several complementary aspects of the system:

• The informational functions that the system carries out in order to enhance survival and reproduction (psychological functions, e.g. the detection, analysis, and recognition of patterns of sensory inputs, the organization of internal models of the external world, selection of appropriate action-alternatives contingent on internal states, internal goals, and the current perceived state of the world; the coordination of action, the storage and retrieval of relevant information; internal adjustment of informational mechanisms so as to improve performance)
• The signals of the system (neuronal codes and representations)
• The information-processing operations that are carried out by the system (neural computations, neural signal processing functions)
• The information-processing substrates, mechanisms, and organizations that operate on the signals (molecular and cellular components, biophysics, neurophysiology, neuroanatomy, neuronal network architectures)

Brief history of the field

Interest in the neural coding problem has waxed and waned at different points in the history of neuroscience. Nineteenth century theories of neural coding advanced from "specific nerve energies" (Mueller) to more modern neural excitation maps (e.g. Helmholtz' cochlear place theory of hearing) and temporal coding (Rutherford's "telephone theory" of hearing, Boring, 1942). In the twentieth century Lord Adrian's investigations in sensory physiology supported neural codes based on firing rates amongst sensory neurons that are tuned to different stimulus properties and parameters. Discoveries of temporal patterning of neural response in the auditory system by Troland and Weaver provided neurophysiological grounding for temporal theories. However, the first major wave of interest in neural coding occurred in the 1960's and early 1970's (following discovery of the genetic code and the advent of single-unit neurophysiology), when concerted attempts were made to understand the neural basis of specific percepts and actions, and to compare neural codes across modalities and phyla. A seminal meeting on Neural Coding considered alternative coding schemes and cataloged the evidence for them (Perkell and Bullock, 1968). Activity in the field waned until neural coding issues were revisited two decades later amidst the resurgence of work on neural networks and the subsequent creation of the field of computational neuroscience.

Basic approaches to neural coding

Two major approaches to neural coding are commonly found in the current literature.

• Functionalist or semantic approaches seek to understand which aspects of neuronal activity play specific functional roles in the nervous system, i.e. the "meaning" of a particular pattern of neuronal activity in terms of the informational functions of the system. This approach focuses on "differences [of neuronal activity] that make a difference" – not all neuronal activity is necessarily meaningful vis-a-vis some specific function.
• Information-theoretic approaches seek to quantify the Shannonian information content of prospective coding schemes (the number of distinguishable messages that can be encoded or conveyed irrespective of their functional role or import). Studies typically analyze the degree to which the structure of a stimulus can be reconstructed from a neuronal representation based on a particular coding scheme.

Related to, but also distinct from the functionalist approach, is the neurophenomenological problem of neural coding: what patterns of neuronal activity are necessary for conscious awareness ("the neural correlates of consciousness" or NCCs) and for producing specific conscious experiences (("the neural correlates of the contents of consciousness, NCCCs). Here the "meanings" that are sought in connection with neuronal activity are in terms of the existence and structure of subjective experience rather than informational function per se.

Figure 1 situates different approaches to neural coding in sensory realms within the context of psychophysical and neurophysiological investigations. Psychophysics studies the relation of stimulus to percept (psychological informational functions), whereas sensory neurophysiology and modelling for the most part attempts to characterize and account for neuronal responses to different stimuli. Functional, computational neuroscience and neuropsychology attempt to understand essential relations between neural activity and informational function.

Although one approach focuses on the functional role of a code vis-a-vis the receiver/analyzer and the other on the carrying capacity of the encoding system, the two approaches are not completely disjoint. If it can be determined that there is insufficient information available in a given candidate neuronal coding scheme to account for some psychological function (e.g. frequency discrimination of pure tones or vernier acuity), then that coding scheme can be rejected outright as a viable explanation. [Comment on the fallability of optimal coding assumptions in inferring functional relevance.] This article will concentrate on functionalist approaches to coding.

Basic requirements for a functional neuronal code

Nervous systems are essentially cybernetic percept-action systems whose main organismic role is the effective coordination of behavior. This entails choosing actions that are appropriate to current internal needs and external conditions, such that the organism is able to maintain itself and persist. Nervous systems have evolved complex sensory, motor, and coordinative repertoires that simultaneously analyze many different types of incoming sensory information to sort out which of many action-alternatives are likely to best realize current internal goal-imperatives.

Given the diversity of informational types, a neuronal code must therefore

• encode signal type (what kind of information does the signal carry?)
• encode signal value (what specific distinctions does the signal indicate?)
• be capable of being decoded in a coherent way by individual neurons or neural ensembles

An informational system that handles different types of information requires coding schemes that convey both the types of information encoded (e.g. luminance vs. spectrum) as well as the specific distinctions (dark vs. light; short vs. long wavelength). Further, the coding scheme must be interpretable by architectures consisting of neuronal elements (having limited discriminatory capacities and some degree of internal noise).

A neural coding hypothesis posits that a given neural coding scheme subserves a particular functional role by encoding a set of informational distinctions that are used by the nervous system to realize some function. For example, humans and other animals can distinguish between different vibration rates on their skin, up to frequencies of several hundred Hz. The perception of "flutter-vibration" can be attributed to different kinds of neural codes, for example, channel codes that depend on the differential responses of cutaneous receptors with different tunings or alternatively, to temporal codes that depend on temporal patterns of spikes generated.

Neural coding hypotheses can be empirically tested by presenting stimuli that can be discriminated by the nervous system and recording the neuronal responses that are produced within the system. Although this discussion is couched in terms of coding of sensory information that supports perceptual functions, similar strategies can be used for investigating neural codes related to other faculties. Although the neural responses that are typically observed in neural coding studies involve spike trains of single neurons ("single units") and/or small local ensembles ("multi-units"), measures of population responses via gross electrodes, magnetic sensors, and various imaging techniques can also be used to test hypotheses related to some classes of neuronal codes that rely on population-wide responses. Analysis of the neuronal data using a set of neural coding assumptions then produces estimates of the information available within the real nervous system. Given further assumptions about the utilization of this information (e.g. optimal coding, pooling of responses across populations, selection of responses that yield greatest discrimination), predictions are then made of which stimuli are discriminable via that code or representation. A candidate code can be eliminated from consideration if the information in the encoded neuronal responses is insufficient to account for the discriminative power of the nervous system of a real human or animal. If a particular neuronal code is in fact utilized by the system to support a given set of informational functions, then the structure of the encoded and analyzed information should systematically correspond to the structure of perception (as revealed by overt perceptual judgements). The more systematic and precise the correspondence between the behavior of the representation produced by the coding scheme and the actual perceptual functions, the stronger is the evidence that in fact the system is utilizing that code to carry out its functions (or another one that is isomorphic to it). Perceptual invariances and equivalence classes can be used to further stress-test neural coding hypotheses. If a perceptual quality is invariant with respect to stimulus intensity, then so its representation should be. If a given quality can be produced by a family of different stimuli (metamery), then the representations associated with those various stimuli should similarly predict the perceptual equivalence.

Basic dimensions of neural pulse codes

The neural coding problem is invariably conceived in terms of patterns of action potentials ("spikes") that are produced by neuronal elements. This is the assumption that the predominant signals in the nervous system are trains of functionally-equivalent pulses. However, taking the widest perspective, any difference in neuronal response can be potentially used to convey information, and some neuronal systems exist that utilize differences in pulse amplitude, width or shape; graded, nonpulsatile signals, including electrical, ionic volume conduction; signals that are differentiated by the neurotransmitters or neurohormones that are consequently released, as well as a host of chemical messengers that are released by neurons, glial cells, and other cell types. Much more speculative (and unproven) are hypotheses that postulate long-range quantum-mechanical mechanisms for information transmission.

For the most part, investigation of neuronal codes has concentrated on pulse-coding schemes based on action potentials because

• action potentials transmitted through axons are the cellular nexus through which most information appears to pass, independent of whatever the molecular and biophysical factors are that play roles in spike generation; therefore, most information must be encoded in patterns of spikes
• communication by means of action potentials appears to convey most incoming sensory information and motor commands
• axonal transmission of action potentials permit rapid transmission times over relatively large distances that are consistent with the fastest behavioral responses
• use of action potentials permit highly precise informational distinctions to be made, through differences in spike timing or spike counts
• informational functions are remarkably resilient to insertions of conductive objects in tissues that would be expected to disrupt volume conduction mechanisms (Sperry's classic experiments) but not the axonal transmission of action potentials (analogous arguments could be made for various targeted pharmacological interventions that disrupt various forms of non-axonal transmission).

Given the assumption that all pulses are equivalent and indistinguishable, a neural ensemble's response is fully characterized by a list of spike occurrences that contains the absolute-time-of-arrival of each spike and the neural channel that produced it. Equivalent descriptions are an array of channels with two-valued spike arrival time-series signals (Fig. 2). Xij= 0 if no spike was produced in the i-th channel at time bin j, and Xij= 1 if a spike was produced in that channel at that time. Because spike occurrences are sparse in time, the list description is much more compact.

In such pulse code schemes informational distinctions can be encoded in terms of patterns of channel response (which channels respond), patterns of response latency (time-of-arrival of responses relative to some reference time t0, vertical dotted line), or temporal patterns amongst spikes amongst consecutive or nonconsecutive spikes within or across channels, horizontal dotted lines).

Channel, time-of-arrival, and temporal pattern (including periodicity, spectrum, interval sequences, spectrotemporal structure) are general, complementary aspects of all time-series signals that can be used to convey either signal type or signal value. Channel codes utilize the identity of a channel to encode signal type paired with some other aspect of response (typically firing rate or spike latency) to encode signal value. Time-of-arrival codes utilize the relative time-of-arrival (latency) of spikes to encode signal type, and some other aspect of response to encode signal value. In temporal pattern codes, relations between spikes, irrespective of absolute time of arrival, encode the type of signal conveyed.

Examples of neural codes

Figure 3 illustrates some basic types of neural codes. Doorbell codes involve activation of particular neuronal channels that are exclusively devoted to the detection of a particular stimulus. Perhaps the most common codes that are encountered in the current neurophysiological literature are rate-place channel codes that convey information by profiles of firing rates amongst neuronal populations that are tuned to different stimulus parameters or attributes. All channel codes are essentially labelled-line codes in that they depend on the specific identities of the channels involved. [More discussion of concrete coding examples......]

A useful means to conceptually test what type of code is involved in a given system is to disrupt one or more aspects of a neural ensemble response pattern. Channel codes are disrupted by relabeling of channels, time-of-arrival codes are disrupted by scrambling spike latencies, and temporal pattern codes are disrupted by scrambling temporal relations between spikes.

RAW DRAFT: Rate-codes and temporal codes

A space of possible pulse codes

It is useful to attempt a systematic outline of a space of possible neuronal codes. Essentially any orderly set of relations between channels and spike times can serve as a potential code, and the space of possible codes can complexify very rapidly. Different distinctions can be encoded in different signal values in a manifold of ways. Relations can include:

• Metrical relations (e.g. interspike interval codes in which the time interval is directly related to a stimulus periodicity, spike latency codes in which a continuous range of first spike latencies is monotonically related to stimulus intensity)
• Ordinal relations (e.g. spike precedence codes in which the order of firing amongst channels determines the message)
• Properties of distributions (these are properties of ensembles of spike events). Moments of distributions. Most common is average firing rate, but codes can also be based on the variance of firing rates across channels or the variance of temporal patterns across channels (e.g. for loudness). Fraction of channels responding above some threshold firing rate of within some threshold first spike latency.
• Extrema of distributions (e.g. the channel with the maximal or minimal firing rate, the channel with the shortest first spike latency)
• Joint property codes: conjunctions of two or more sets of relations.
• Temporal sequence codes (e.g. sequences of interspike intervals, sequences of channels with maximal firing rates)
• Counting and duration codes -- e.g. burst length code, burst duration code, ratio of intraburst to interburst interspike interval duration

Low dimensional coding spaces vs. high dimensional ones Single unit vs. local ensemble vs. population codes Deterministic vs. mass statistical codes Sparse vs. compact codes, in terms of responding channels and in terms of time Temporal vs. channel codes (common dichotomy) Autocorrelation, crosscorrelation, triple-correlation and higher order correlation codes Continuous vs. discrete codes, analog vs. digital, iconic vs. symbolic Scalar (opaque, one-dimensional) vs. multiplexing (transparent, multidimensional) codes

Dimensional considerations in the coding problem Systematicity (ability to flexibly and arbitrarily combine primitive attributes) Generativity (ability to generate new signal types)

Conclusions