scholarly journals Optimal Short-Term Population Coding: When Fisher Information Fails

2002 ◽  
Vol 14 (10) ◽  
pp. 2317-2351 ◽  
Author(s):  
M. Bethge ◽  
D. Rotermund ◽  
K. Pawelzik
Keyword(s):  
Fisher Information ◽  
Dynamic Range ◽  
Mean Squared Error ◽  
Average Rate ◽  
Neuronal Response ◽  
Minimum Mean Square Error ◽  
Population Coding ◽  
Neuronal Firing ◽  
Tuning Curves ◽  
Efficient Coding

Efficient coding has been proposed as a first principle explaining neuronal response properties in the central nervous system. The shape of optimal codes, however, strongly depends on the natural limitations of the particular physical system. Here we investigate how optimal neuronal encoding strategies are influenced by the finite number of neurons N (place constraint), the limited decoding time window length T (time constraint), the maximum neuronal firing rate fmax (power constraint), and the maximal average rate fmax (energy constraint). While Fisher information provides a general lower bound for the mean squared error of unbiased signal reconstruction, its use to characterize the coding precision is limited. Analyzing simple examples, we illustrate some typical pitfalls and thereby show that Fisher information provides a valid measure for the precision of a code only if the dynamic range (fmin T, fmax T) is sufficiently large. In particular, we demonstrate that the optimal width of gaussian tuning curves depends on the available decoding time T. Within the broader class of unimodal tuning functions, it turns out that the shape of a Fisher-optimal coding scheme is not unique. We solve this ambiguity by taking the minimum mean square error into account, which leads to flat tuning curves. The tuning width, however, remains to be determined by energy constraints rather than by the principle of efficient coding.

scholarly journals Mutual Information, Fisher Information, and Population Coding

1998 ◽  
Vol 10 (7) ◽  
pp. 1731-1757 ◽  
Author(s):  
Nicolas Brunel ◽  
Jean-Pierre Nadal
Keyword(s):  
Information Theory ◽  
Mutual Information ◽  
Fisher Information ◽  
Population Coding ◽  
Angular Variable ◽  
Large Array ◽  
Direct Link ◽  
Information Theoretic ◽  
Tuning Curves ◽  
Standard Framework

In the context of parameter estimation and model selection, it is only quite recently that a direct link between the Fisher information and information-theoretic quantities has been exhibited. We give an interpretation of this link within the standard framework of information theory. We show that in the context of population coding, the mutual information between the activity of a large array of neurons and a stimulus to which the neurons are tuned is naturally related to the Fisher information. In the light of this result, we consider the optimization of the tuning curves parameters in the case of neurons responding to a stimulus represented by an angular variable.

Mutual Information, Fisher Information, and Efficient Coding

2016 ◽  
Vol 28 (2) ◽  
pp. 305-326 ◽  
Author(s):  
Xue-Xin Wei ◽  
Alan A. Stocker
Keyword(s):  
Mutual Information ◽  
Fisher Information ◽  
Neural Coding ◽  
Population Coding ◽  
Neural Population ◽  
Small Noise ◽  
Efficient Coding ◽  
Coding Efficiency ◽  
Stimulus Variable ◽  
Neural Populations

Fisher information is generally believed to represent a lower bound on mutual information (Brunel & Nadal, 1998 ), a result that is frequently used in the assessment of neural coding efficiency. However, we demonstrate that the relation between these two quantities is more nuanced than previously thought. For example, we find that in the small noise regime, Fisher information actually provides an upper bound on mutual information. Generally our results show that it is more appropriate to consider Fisher information as an approximation rather than a bound on mutual information. We analytically derive the correspondence between the two quantities and the conditions under which the approximation is good. Our results have implications for neural coding theories and the link between neural population coding and psychophysically measurable behavior. Specifically, they allow us to formulate the efficient coding problem of maximizing mutual information between a stimulus variable and the response of a neural population in terms of Fisher information. We derive a signature of efficient coding expressed as the correspondence between the population Fisher information and the distribution of the stimulus variable. The signature is more general than previously proposed solutions that rely on specific assumptions about the neural tuning characteristics. We demonstrate that it can explain measured tuning characteristics of cortical neural populations that do not agree with previous models of efficient coding.

Response Properties of Single Auditory Nerve Fibers in the Mouse

2005 ◽  
Vol 93 (1) ◽  
pp. 557-569 ◽  
Author(s):  
Annette M. Taberner ◽  
M. Charles Liberman
Keyword(s):  
Auditory Nerve ◽  
Dynamic Range ◽  
Phase Locking ◽  
Nerve Fibers ◽  
Cochlear Function ◽  
Response Properties ◽  
Tuning Curves ◽  
Rate Versus ◽  
Interstrain Difference ◽  
Mutant Lines

The availability of transgenic and mutant lines makes the mouse a valuable model for study of the inner ear, and a powerful window into cochlear function can be obtained by recordings from single auditory nerve (AN) fibers. This study provides the first systematic description of spontaneous and sound-evoked discharge properties of AN fibers in mouse, specifically in CBA/CaJ and C57BL/6 strains, both commonly used in auditory research. Response properties of 196 AN fibers from CBA/CaJ and 58 from C57BL/6 were analyzed, including spontaneous rates (SR), tuning curves, rate versus level functions, dynamic range, response adaptation, phase-locking, and the relation between SR and these response properties. The only significant interstrain difference was the elevation of high-frequency thresholds in C57BL/6. In general, mouse AN fibers showed similar responses to other mammals: sharpness of tuning increased with characteristic frequency, which ranged from 2.5 to 70 kHz; SRs ranged from 0 to 120 sp/s, and fibers with low SR (<1 sp/s) had higher thresholds, and wider dynamic ranges than fibers with high SR. Dynamic ranges for mouse high-SR fibers were smaller (<20 dB) than those seen in other mammals. Phase-locking was seen for tone frequencies <4 kHz. Maximum synchronization indices were lower than those in cat but similar to those found in guinea pig.

scholarly journals Neural Rate and Timing Cues for Detection and Discrimination of Amplitude-Modulated Tones in the Awake Rabbit Inferior Colliculus

2007 ◽  
Vol 97 (1) ◽  
pp. 522-539 ◽  
Author(s):  
Paul C. Nelson ◽  
Laurel H. Carney
Keyword(s):  
Inferior Colliculus ◽  
Dynamic Range ◽  
Modulation Depth ◽  
Average Rate ◽  
Modulation Frequency ◽  
Detection Threshold ◽  
Depth Functions ◽  
Depth Discrimination ◽  
High Modulation ◽  
Envelope Processing

Neural responses to amplitude-modulated (AM) tones in the unanesthetized rabbit inferior colliculus (IC) were studied in an effort to establish explicit relationships between physiological and psychophysical measures of temporal envelope processing. Specifically, responses to variations in modulation depth ( m) at the cell’s best modulation frequency, with and without modulation maskers, were quantified in terms of average rate and synchronization to the envelope over the entire perceptual dynamic range of depths. Statistically significant variations in the metrics were used to define neural AM detection and discrimination thresholds. Synchrony emerged at modulation depths comparable with psychophysical AM detection sensitivities in some neurons, whereas the lowest rate-based neural thresholds could not account for psychoacoustical thresholds. The majority of rate thresholds (85%) were −10 dB or higher (in 20 log m), and 16% of the population exhibited no systematic dependence of average rate on m. Neural thresholds for AM detection did not decrease systematically at higher SPLs (as observed psychophysically): thresholds remained constant or increased with level for most cells tested at multiple sound-pressure levels (SPLs). At depths higher than the rate-based detection threshold, some rate modulation-depth functions were sufficiently steep with respect to the across-trial variability of the rate to predict depth discrimination thresholds as low as 1 dB (comparable with the psychophysics). Synchrony, on the other hand, did not vary systematically with m in many cells at high modulation depths. A simple computational model was extended to reproduce several features of the modulation frequency and depth dependence of both transient and sustained pure-tone responders.

scholarly journals The Effect of Correlated Neuronal Firing and Neuronal Heterogeneity on Population Coding Accuracy in Guinea Pig Inferior Colliculus

PLoS ONE ◽  
2013 ◽  
Vol 8 (12) ◽  
pp. e81660 ◽  
Author(s):  
Oran Zohar ◽  
Trevor M. Shackleton ◽  
Alan R. Palmer ◽  
Maoz Shamir
Keyword(s):  
Guinea Pig ◽  
Inferior Colliculus ◽  
Population Coding ◽  
Neuronal Firing

scholarly journals Angiotensin II increases GABAB receptor expression in nucleus tractus solitarii of rats

2008 ◽  
Vol 294 (6) ◽  
pp. H2712-H2720 ◽  
Author(s):  
Fanrong Yao ◽  
Colin Sumners ◽  
Stephen T. O'Rourke ◽  
Chengwen Sun
Keyword(s):  
Angiotensin Ii ◽  
Gabab Receptor ◽  
Neuronal Response ◽  
Neuronal Firing ◽  
Receptor Expression ◽  
Nucleus Tractus Solitarii ◽  
Neuronal Cultures ◽  
Ang Ii ◽  
Western Blots ◽  
Intracerebroventricular Infusion

Increasing evidence indicates that both the angiotensin II (ANG II) and γ-aminobutyric acid (GABA) systems play a very important role in the regulation of blood pressure (BP). However, there is little information concerning the interactions between these two systems in the nucleus tractus solitarii (NTS). In the present study, we examined the effects of ANG II on GABAA and GABAB receptor (GAR and GBR) expression in the NTS of Sprague-Dawley rats. The direct effect of ANG II on GBR expression was determined in neurons cultured from NTS. Treatment of neuronal cultures with ANG II (100 nM, 5 h) induced a twofold increase in GBR1 expression, as detected with real-time RT-PCR and Western blots, but had no effect on GBR2 or GAR expression. In electrophysiological experiments, perfusion of neuronal cultures with the GBR agonist baclofen decreased neuronal firing rate by 39% and 63% in neurons treated with either PBS (control) or ANG II, respectively, indicating that chronic ANG II treatment significantly enhanced the neuronal response to GBR activation. In contrast, ANG II had no significant effect on the inhibitory action of the GAR agonist muscimol. In whole animal studies, intracerebroventricular infusion of ANG II induced a sustained increase in mean BP and an elevation of GBR1 mRNA and protein levels in the NTS. These results indicate that ANG II stimulates GBR expression in NTS neurons, and this could contribute to the central nervous system actions of ANG II that result in dampening of baroreflexes and elevated BP in the central actions of ANG II.

Activity of trigeminothalamic neurons in medullary dorsal horn of awake monkeys trained in a thermal discrimination task

1984 ◽  
Vol 52 (1) ◽  
pp. 170-187 ◽  
Author(s):  
M. C. Bushnell ◽  
G. H. Duncan ◽  
R. Dubner ◽  
L. F. He
Keyword(s):  
Dorsal Horn ◽  
Discrimination Task ◽  
Dynamic Range ◽  
Neuronal Response ◽  
Static Properties ◽  
Medullary Dorsal Horn ◽  
Behavioral Tasks ◽  
Behavioral Trials ◽  
Behaving Monkeys ◽  
Thermal Stimuli

We analyzed the activity of 51 trigeminothalamic neurons in the medullary dorsal horn (trigeminal nucleus caudalis) of monkeys during the performance of behavioral tasks requiring the monkeys to discriminate innocuous and noxious thermal stimuli applied to the face and to detect the onset of visual stimuli. Static properties of trigeminothalamic neurons in behaving monkeys were similar to those in anesthetized monkeys. Responses to passively presented mechanical and thermal stimuli, receptive-field properties, and conduction velocities did not differ in the awake and anesthetized states. For most wide dynamic range and nociceptive-specific trigeminothalamic neurons, there was a negative correlation between the magnitude of thermally evoked activity and behavioral latencies to discriminate 47 and 49 degrees C stimuli. Thus, both groups of neurons provide information that could be used by the monkey to discriminate noxious thermal stimuli. The magnitude of thermal responses of trigeminothalamic neurons was modulated by the behavioral significance of the stimulus. Behaviorally relevant thermal stimuli presented during the thermal discrimination task produced a greater neuronal response than equivalent irrelevant thermal stimuli presented between behavioral trials or presented while the monkey performed the visual detection task. Neurons whose activity is modulated by behavioral state are likely to be involved in discrimination of thermal stimuli, since the activity of these neurons correlates with the behavioral response to the stimuli and information from the modulated neurons is sent to the thalamus. Some trigeminothalamic neurons that exhibited somatosensory responses also responded to behaviorally relevant stimuli and events associated with trial initiation and receipt of reward in the behavioral tasks. Similar events outside a behavioral task evoked no neuronal responses. These task-related responses were similar to those described previously for medullary dorsal horn neurons not identified as to projection sites (14).(ABSTRACT TRUNCATED AT 400 WORDS)

Difficulty of Singularity in Population Coding

2005 ◽  
Vol 17 (4) ◽  
pp. 839-858 ◽  
Author(s):  
Shun-ichi Amari ◽  
Hiroyuki Nakahara
Keyword(s):  
Fisher Information ◽  
Regularity Condition ◽  
Information Matrix ◽  
Population Coding ◽  
Neural Population ◽  
Binding Problem ◽  
Synchronous Firing ◽  
Novel Method ◽  
Pathological Behavior ◽  
Pathological Case

Fisher information has been used to analyze the accuracy of neural population coding. This works well when the Fisher information does not degenerate, but when two stimuli are presented to a population of neurons, a singular structure emerges by their mutual interactions. In this case, the Fisher information matrix degenerates, and the regularity condition ensuring the Cramér-Rao paradigm of statistics is violated. An animal shows pathological behavior in such a situation. We present a novel method of statistical analysis to understand information in population coding in which algebraic singularity plays a major role. The method elucidates the nature of the pathological case by calculating the Fisher information. We then suggest that synchronous firing can resolve singularity and show a method of analyzing the binding problem in terms of the Fisher information. Our method integrates a variety of disciplines in population coding, such as nonregular statistics, Bayesian statistics, singularity in algebraic geometry, and synchronous firing, under the theme of Fisher information.

scholarly journals Optimal Tuning Widths in Population Coding of Periodic Variables

2006 ◽  
Vol 18 (7) ◽  
pp. 1555-1576 ◽  
Author(s):  
Marcelo A. Montemurro ◽  
Stefano Panzeri
Keyword(s):  
Cortical Neurons ◽  
Neuronal Population ◽  
Population Coding ◽  
Model Parameters ◽  
Population Activity ◽  
Sensory Stimuli ◽  
Tuning Curves ◽  
Periodic Stimulus ◽  
Tuning Width ◽  
Stimulus Features

We study the relationship between the accuracy of a large neuronal population in encoding periodic sensory stimuli and the width of the tuning curves of individual neurons in the population. By using general simple models of population activity, we show that when considering one or two periodic stimulus features, a narrow tuning width provides better population encoding accuracy. When encoding more than two periodic stimulus features, the information conveyed by the population is instead maximal for finite values of the tuning width. These optimal values are only weakly dependent on model parameters and are similar to the width of tuning to orientation ormotion direction of real visual cortical neurons. A very large tuning width leads to poor encoding accuracy, whatever the number of stimulus features encoded. Thus, optimal coding of periodic stimuli is different from that of nonperiodic stimuli, which, as shown in previous studies, would require infinitely large tuning widths when coding more than two stimulus features.

scholarly journals Coexistence of critical sensitivity and subcritical specificity can yield optimal population coding

2017 ◽  
Vol 14 (134) ◽  
pp. 20170207 ◽  
Author(s):  
Leonardo L. Gollo
Keyword(s):  
Dynamic Range ◽  
Heterogeneous Systems ◽  
External Input ◽  
Population Coding ◽  
Small Subset ◽  
Entire System ◽  
Critical Elements ◽  
Enhanced Sensitivity ◽  
Collective Response ◽  
Optimal Population

The vicinity of phase transitions selectively amplifies weak stimuli, yielding optimal sensitivity to distinguish external input. Along with this enhanced sensitivity, enhanced levels of fluctuations at criticality reduce the specificity of the response. Given that the specificity of the response is largely compromised when the sensitivity is maximal, the overall benefit of criticality for signal processing remains questionable. Here, it is shown that this impasse can be solved by heterogeneous systems incorporating functional diversity , in which critical and subcritical components coexist. The subnetwork of critical elements has optimal sensitivity, and the subnetwork of subcritical elements has enhanced specificity. Combining segregated features extracted from the different subgroups, the resulting collective response can maximize the trade-off between sensitivity and specificity measured by the dynamic-range-to-noise ratio. Although numerous benefits can be observed when the entire system is critical, our results highlight that optimal performance is obtained when only a small subset of the system is at criticality.

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