Multidimensional Encoding Strategy of Spiking Neurons

Eurich, Christian W.; Wilke, Stefan

doi:10.1162/089976600300015240

Cited by 65 publications

(39 citation statements)

References 12 publications

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“…Following the tradition of comparing neuronal codes on the basis of the Fisher information (Zhang & Sejnowski, 1999;Eurich & Wilke, 2000;Wilke & Eurich, 2002;Brown & Bäcker, 2006), we ask: Based on the error measures χ 2 MLE and χ 2 AE , can a grid code outperform a place code? In particular, which spatial periods should be present in the grid code?…”

Section: Population Coding Modelmentioning

confidence: 99%

“…The Cramér-Rao bound states that the inverse of the Fisher information yields the minimum achievable square error, provided the estimator is unbiased; furthermore, maximum likelihood decoding attains this bound (Lehmann & Casella, 1998). In the context of neural population coding, many authors have calculated the Fisher information (Paradiso, 1988;Seung & Sompolinsky, 1993;Brunel & Nadal, 1998;Zhang & Sejnowski, 1999;Pouget et al, 1999;Eurich & Wilke, 2000;Wilke & Eurich, 2002;Bethge et al, 2002;Brown & Bäcker, 2006). However, it is also known that no such estimator will attain the lower bound if the neurons have Poisson spike statistics and the expected number of spikes is low, even when a neuron is firing at its maximal rate (Bethge et al, 2002).…”

Section: Introductionmentioning

confidence: 99%

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Optimal Population Codes for Space: Grid Cells Outperform Place Cells

2012

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Rodents use two distinct neuronal coordinate systems to estimate their position: place fields in the hippocampus and grid fields in the entorhinal cortex. Whereas place cells spike at only one particular spatial location, grid cells fire at multiple sites that correspond to the points of an imaginary hexagonal lattice. We study how to best construct place and grid codes, taking the probabilistic nature of neural spiking into account. Which spatial encoding properties of individual neurons confer the highest resolution when decoding the animal's position from the neuronal population response? A priori, estimating a spatial position from a grid code could be ambiguous, as regular periodic lattices possess translational symmetry. The solution to this problem requires lattices for grid cells with different spacings; the spatial resolution crucially depends on choosing the right ratios of these spacings across the population. We compute the expected error in estimating the position in both the asymptotic limit, using Fisher information, and for low spike counts, using maximum likelihood estimation. Achieving high spatial resolution and covering a large range of space in a grid code leads to a trade-off: the best grid code for spatial resolution is built of nested modules with different spatial periods, one inside the other, whereas maximizing the spatial range requires distinct spatial periods that are pairwisely incommensurate. Optimizing the spatial resolution predicts two grid cell properties that have been experimentally observed. First, short lattice spacings should outnumber long lattice spacings. Second, the grid code should be self-similar across different lattice spacings, so that the grid field always covers a fixed fraction of the lattice period. If these conditions are satisfied and the spatial "tuning curves" for each neuron span the same range of firing rates, then the resolution of the grid code easily exceeds that of the best possible place code with the same number of neurons.

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Section: Population Coding Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal Population Codes for Space: Grid Cells Outperform Place Cells

2012

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“…From the perspective of information theory, whether a broadly tuned neuron is more effective or less effective than a narrowly tuned neuron depends on several factors, e.g., how many dimensions are to be discriminated, whether noise levels remain proportional to the bandwidth of the filters (Eurich and Wilke 2000;Pouget et al 1999;Wilke and Eurich 2002;Zhang and Sejnowski 1999). It is generally agreed that narrow tuning is more effective in coding a single dimension; however, severely narrow tuning that prevents adequate overlap of receptive fields results in degraded coding (Eurich and Wilke 2000). A recent analysis of Fisher information concluded that optimal coding strategies may not be separable on the basis of a simple dichotomy between narrow and broad tuning (Wilke and Eurich 2002).…”

Section: Broad and Narrow Tuning To Binaural Level By Ai Neuronsmentioning

confidence: 99%

Modulation of Level Response Areas and Stimulus Selectivity of Neurons in Cat Primary Auditory Cortex

Zhang

Nakamoto²,

Kitzes³

2005

Journal of Neurophysiology

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Zhang, Jiping, Kyle T. Nakamoto, and Leonard M. Kitzes. Modulation of level response areas and stimulus selectivity of neurons in cat primary auditory cortex. J Neurophysiol 94: 2263-2274, 2005. First published May 25, 2005 10.1152/jn.01207.2004. Sounds commonly occur in sequences, such as in speech. It is therefore important to understand how the occurrence of one sound affects the response to a subsequent sound. We approached this question by determining how a conditioning stimulus alters the response areas of single neurons in the primary auditory cortex (AI) of barbiturate-anesthetized cats. The response areas consisted of responses to stimuli that varied in level at the two ears and delivered at the characteristic frequency of each cell. A binaural conditioning stimulus was then presented Ն50 ms before each of the stimuli comprising the level response area. An effective preceding stimulus alters the shape and severely reduces the size and response magnitude of the level response area. This ability of the preceding stimulus depends on its proximity in the level domain to the level response area, not on its absolute level or on the size of the response it evokes. Preceding stimuli evoke a nonlinear inhibition across the level response area that results in an increased selectivity of a cortical neuron for its preferred binaural stimuli. The selectivity of AI neurons during the processing of a stream of acoustic stimuli is likely to be restricted to a portion of their level response areas apparent in the tone-alone condition. Thus rather than being static, level response areas are fluid; they can vary greatly in extent, shape and response magnitude. The dynamic modulation of the level response area and level selectivity of AI neurons might be related to several tasks confronting the central auditory system. I N T R O D U C T I O NAs acoustic stimuli commonly occur in a temporal relation to other acoustic stimuli, it is important to understand how responses of cortical neurons vary during the processing of a stream of acoustic signals. Throughout the auditory neuroaxis, discharge rate as a function of monaural stimulus level (so called rate-level functions) have been shown to be displaced to higher stimulus levels when stimuli are presented either during or after a conditioning stimulus (Boettcher et

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“…Thus information about a stimulus is available in the activity of many neurons. This coding strategy is evidently robust to noise and cell death; its other computational characteristics and advantages have been the subject of much investigation (Hinton 1984;Snippe and Koenderink 1992;Zhang and Sejnowski 1999;Eurich and Wilke 2000).…”

Section: Introductionmentioning

confidence: 99%

“…1999;Eurich and Wilke 2000;Dayan and Abbott 2001;Wilke and Eurich 2002) The experiments that inspired the encoding model of equation 1 involved relatively simple scenarios in which a single-valued stimulus was presented (or, for the motor system, a single movement elicited). However, in a more realistic setting, two complications arise that increase the demands on the representational capacity of population codes.…”

Section: Introductionmentioning

confidence: 99%

Doubly Distributional Population Codes: Simultaneous Representation of Uncertainty and Multiplicity

Sahani

Dayan

2003

Neural Computation

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Perceptual inference fundamentally involves uncertainty, arising from noise in sensation and the ill-posed nature of many perceptual problems. Accurate perception requires that this uncertainty be correctly represented, manipulated, and learned about. The choices made by subjects in various psychophysical experiments suggest that they do indeed take such uncertainty into account when making perceptual inferences, posing the question as to how uncertainty is represented in the activities of neuronal populations. Most theoretical investigations of population coding have ignored this issue altogether; the few existing proposals that address it, do so in such a way that it is fatally conflated with another facet of perceptual problems that also needs correct handling, namely multiplicity (that is, the simultaneous presence of multiple distinct stimuli). We present and validate a more powerful proposal for the way that population activity may encode uncertainty, both distinctly from, and simultaneously with, multiplicity.

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Multidimensional Encoding Strategy of Spiking Neurons

Cited by 65 publications

References 12 publications

Optimal Population Codes for Space: Grid Cells Outperform Place Cells

Optimal Population Codes for Space: Grid Cells Outperform Place Cells

Modulation of Level Response Areas and Stimulus Selectivity of Neurons in Cat Primary Auditory Cortex

Doubly Distributional Population Codes: Simultaneous Representation of Uncertainty and Multiplicity

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