nips nips2002 nips2002-141 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Tatyana Sharpee, Nicole C. Rust, William Bialek
Abstract: unkown-abstract
Reference: text
sentIndex sentText sentNum sentScore
1 edu ¡ ¤ We propose a method that allows for a rigorous statistical analysis of neural responses to natural stimuli, which are non-Gaussian and exhibit strong correlations. [sent-7, score-0.281]
2 We have in mind a model in which neurons are selective for a small number of stimulus dimensions out of the high dimensional stimulus space, but within this subspace the responses can be arbitrarily nonlinear. [sent-8, score-0.769]
3 Therefore we maximize the mutual information between the sequence of elicited neural responses and an ensemble of stimuli that has been projected on trial directions in the stimulus space. [sent-9, score-1.135]
4 The procedure can be done iteratively by increasing the number of directions with respect to which information is maximized. [sent-10, score-0.22]
5 Those directions that allow the recovery of all of the information between spikes and the full unprojected stimuli describe the relevant subspace. [sent-11, score-0.818]
6 If the dimensionality of the relevant subspace indeed is much smaller than that of the overall stimulus space, it may become experimentally feasible to map out the neuron’s input-output function even under fully natural stimulus conditions. [sent-12, score-0.891]
7 ) which all require simplified stimulus statistics if we are to use them rigorously. [sent-16, score-0.238]
8 1 Introduction From olfaction to vision and audition, there is an increasing need, and a growing number of experiments [1]-[8] that study responses of sensory neurons to natural stimuli. [sent-17, score-0.275]
9 Natural stimuli have specific statistical properties [9, 10], and therefore sample only a subspace of all possible spatial and temporal frequencies explored during stimulation with white noise. [sent-18, score-0.598]
10 Observing the full dynamic range of neural responses may require using stimulus ensembles which approximate those occurring in nature, and it is an attractive hypothesis that the neural representation of these natural signals may be optimized in some way. [sent-19, score-0.523]
11 Finally, some neuron responses are strongly nonlinear and adaptive, and may not be predicted from a combination of responses to simple stimuli. [sent-20, score-0.405]
12 It has also been shown that the variability in neural response decreases substantially when dynamical, rather than static, stimuli are used [11, 12]. [sent-21, score-0.519]
13 For all these reasons, it would be attractive to have a rigorous method of analyzing neural responses to complex, naturalistic inputs. [sent-22, score-0.317]
14 The stimuli analyzed by sensory neurons are intrinsically high-dimensional, with dimen- ¤ ¥ § ¥£ ¡ ©£ ¨¡ ¦¤¢ sions . [sent-23, score-0.46]
15 In the simplest model, the probability of response can be described by one receptive field (RF) [13]. [sent-28, score-0.201]
16 The receptive field can be thought of as a special direction in the stimulus space such that the neuron’s response depends only on a projection of a given stimulus onto . [sent-29, score-0.821]
17 This special direction is the one found by the reverse correlation method [13, 14]. [sent-30, score-0.261]
18 In a more general case, the probability of the response depends on projections , , of the stimulus on a set of vectors , : ¥£ ¥ ¦¦£ ! [sent-31, score-0.489]
19 98 ¡ & 6 42 72 '44 53£ # 1 V U S P IGE 0 bT'RQYaFD where is the probability of a spike given a stimulus and is the average firing rate. [sent-39, score-0.484]
20 In what follows we will call the subspace spanned by the set of vectors the relevant subspace (RS). [sent-40, score-0.428]
21 Even though the ideas developed below can be used to analyze input-output functions with respect to different neural responses, we settle on a single spike as the response of interest. [sent-41, score-0.364]
22 (1) in itself is not yet a simplification if the dimensionality of the RS is equal to the dimensionality of the stimulus space. [sent-44, score-0.366]
23 & C" 98 V U S P IGE © b3R cYaFD Once the relevant subspace is known, the probability becomes a function of only few parameters, and it becomes feasible to map this function experimentally, inverting the probability distributions according to Bayes’ rule: (2) V ! [sent-53, score-0.308]
24 0E If stimuli are correlated Gaussian noise, then the neural response can be characterized by the spike-triggered covariance method [15, 16]. [sent-56, score-0.628]
25 It can be shown that the dimensionality of the RS is equal to the number of non-zero eigenvalues of a matrix given by a difference between covariance matrices of all presented stimuli and stimuli conditional on a spike. [sent-57, score-0.919]
26 Compared to the reverse correlation method, we are no longer limited to finding only one of the relevant directions . [sent-59, score-0.38]
27 However because of the necessity to probe a two-point correlation function, the spiketriggered covariance method requires better sampling of distributions of inputs conditional on a spike. [sent-60, score-0.132]
28 " & In this paper we investigate whether it is possible to lift the requirement for stimuli to be Gaussian. [sent-62, score-0.392]
29 When using natural stimuli, which are certainly non-Gaussian, the RS cannot be found by the spike-triggered covariance method. [sent-63, score-0.203]
30 Similarly, the reverse correlation method does not give the correct RF, even in the simplest case where the input-output function (1) depends only on one projection. [sent-64, score-0.149]
31 However, vectors that span the RS are clearly special directions in the stimulus space. [sent-65, score-0.433]
32 Therefore the current implementation of the dimensionality reduction idea is complimentary to the clustering of stimuli done in the information bottleneck method [17]; see also Ref. [sent-67, score-0.506]
33 We illustrate how the optimization scheme of maximizing information as function of direction in the stimulus space works with natural stimuli for model orientation sensitive cells with one and two relevant directions, much like simple and complex cells found in primary visual cortex. [sent-70, score-1.238]
34 The advantage of this optimization scheme is that it does not rely on any specific statistical properties of the stimulus ensemble, and can be used with natural stimuli. [sent-72, score-0.335]
35 V T'RQY UG FD S PI E V E 0 FD 2 Information as an objective function When analyzing neural responses, we compare the a priori probability distribution of all presented stimuli with the probability distribution of stimuli which lead to a spike. [sent-73, score-0.958]
36 For Gaussian signals, the probability distribution can be characterized by its second moment, the covariance matrix. [sent-74, score-0.156]
37 However, an ensemble of natural stimuli is not Gaussian, so that neither second nor any other finite number of moments is sufficient to describe the probability distribution. [sent-75, score-0.624]
38 The average information carried by the arrival time of one spike is given by [20] ! [sent-77, score-0.249]
39 However it is possible to calculate in a model-independent way, if stimuli are presented . [sent-81, score-0.392]
40 Note that for a finite dataset of repetitions, the obtained value will be on average larger than , with difference , where is the number of different stimuli, is the number of elicited spikes [21] across all of the repetitions. [sent-83, score-0.186]
41 The knowledge of the total information per spike will characterize the quality of the reconstruction of the neuron’s input-output relation. [sent-85, score-0.427]
42 S I S I D X 2 "V ¤RE P D ©V 3R PcY UG ¤RE P D 5¡ V 3R PQC UG $RE P 9R Y# V E V $ § ¤RE ¤UT# V ¤RE P D ( S V S PI ( T'RQC UG V $ V W provides an invariant measure of how much the occurrence of a spike is determined by projection on the direction . [sent-88, score-0.39]
43 It is a function only of direction in the stimulus space and does not change when vector is multiplied by a constant. [sent-89, score-0.315]
44 The total information can be recovered along one particular direction only if , and the RS is one-dimensional. [sent-92, score-0.204]
45 "' & If we are successful in finding all of the directions in the input-output relation (1), then the information evaluated along the found set will be equal to the total information . [sent-95, score-0.344]
46 When we calculate information along a set of vectors that are slightly off from the RS, the answer is, of course, smaller than and is quadratic in deviations . [sent-96, score-0.156]
47 One can therefore find the RS by maximizing information with respect to vectors simultaneously. [sent-97, score-0.239]
48 On the other hand, the result of optimization with respect to the number of vectors may deviate from the RS if stimuli are correlated. [sent-99, score-0.532]
49 If the difference exceeds that expected from finite sampling corrections, we increment the number of directions with respect to which information is simultaneously maximized. [sent-103, score-0.22]
50 As an optimization algorithm, we have used a combination of gradient ascent and simulated annealing algorithms: successive line maximizations were done along the direction of the gradient. [sent-110, score-0.246]
51 During line maximizations, a point with a smaller value of information was accepted according to Boltzmann statistics, with probability . [sent-111, score-0.134]
52 %© $ 3 Discussion We tested the scheme of looking for the most informative directions on model neurons that respond to stimuli derived from natural scenes. [sent-115, score-0.689]
53 As stimuli we used patches of digitized to 8-bit scale photos, in which no corrections were made for camera’s light intensity transformation function. [sent-116, score-0.435]
54 Our goal is to demonstrate that even though spatial correlations present in natural scenes are non-Gaussian, they can be successfully removed from the estimate of vectors defining the RS. [sent-117, score-0.25]
55 1 Simple Cell Our first example is taken to mimic properties of simple cells found in the primary visual cortex. [sent-119, score-0.198]
56 A model phase and orientation sensitive cell has a single relevant direction shown in Fig. [sent-120, score-0.28]
57 A given frame leads to a spike if projection reaches a threshold value in the presence of noise: ! [sent-122, score-0.313]
58 Panel (c) shows an attempt to remove correlations accordaverage ing to reverse correlation method, ; (d) vector found by maximizing information; (e) The probability of a spike (crosses) is compared to used in generating spikes (solid line). [sent-129, score-0.718]
59 ] (f) Convergence of the algorithm according to information and projection as a function of inverse effective temperature . [sent-131, score-0.215]
60 1(b), is broadened because of spatial correlations present in natural stimuli. [sent-139, score-0.187]
61 If stimuli were drawn from a Gaussian probability distribution, they could be decorrelated by multiplying by the inverse of the a priori covariance matrix, according to the reverse correlation method. [sent-140, score-0.659]
62 The procedure is not valid for non-Gaussian stimuli and nonlinear input-output functions (1). [sent-141, score-0.439]
63 However, it is possible to obtain a good estimate of it by maximizing information directly, see panel (d). [sent-145, score-0.197]
64 A typical progress of the simulated annealing algorithm with decreasing temperature is shown in panel (e). [sent-146, score-0.145]
65 There we plot both the information along the vector, and its projection on . [sent-147, score-0.207]
66 The final value of projection depends on the size of the data set, see below. [sent-148, score-0.114]
67 1 there were spikes with average probability of spike per frame. [sent-150, score-0.432]
68 This is done by constructing histograms for and of projections onto vector found by maximizing information, and taking their ratio. [sent-152, score-0.176]
69 2 Estimated deviation from the optimal direction When information is calculated with respect to a finite data set, the vector which maximizes will deviate from the true RF . [sent-160, score-0.292]
70 8 0 A Figure 2: Projection of vector that maximizes information on RF is plotted as a function of the number of spikes to show the linear scaling in (solid line is a fit). [sent-168, score-0.28]
71 For a simple cell, the quality of reconstruction can be characterized by the projection , where both and are normalized, and is by definition orthogonal to . [sent-170, score-0.255]
72 By discretizing both the space of stimuli and possible projections , and assuming that the probability of generating a spike is independent for different bins, one could obtain that . [sent-177, score-0.691]
73 Therefore an expected error in the reconstruction of the optimal filter is inversely proportional to the number of spikes and is given by: ! [sent-178, score-0.248]
74 Q( § £ ¦ ¨ means that the trace is taken in the subspace orthogonal to the model filter, since where by definition . [sent-182, score-0.115]
75 3 Complex Cell A sequence of spikes from a model cell with two relevant directions was simulated by projecting each of the stimuli on vectors that differ by in their spatial phase, taken to mimic properties of complex cells, see Fig. [sent-188, score-1.044]
76 A particular frame leads to a spike according to a logical OR, that is if either , , , or exceeds a threshold value in the presence of noise. [sent-190, score-0.199]
77 The sampling of this input-output function by our particular set of natural stimuli is shown in Fig. [sent-203, score-0.489]
78 b 3 We start by maximizing information with respect to one direction. [sent-208, score-0.176]
79 Contrary to analysis for a simple cell, one optimal direction recovers only about 60% of the total information per spike. [sent-209, score-0.202]
80 This is significantly different from the total for stimuli drawn from natural scenes, where due to correlations even a random vector has a high probability of explaining 60% of total information per spike. [sent-210, score-0.75]
81 We therefore go on to maximize information with respect to two directions. [sent-211, score-0.133]
82 An example of the reconstruction of input-output function of a complex cell is given in Fig. [sent-212, score-0.207]
83 However, the quality of reconstruction nal, and are also rotated with respect to is independent of a particular choice of basis with the RS. [sent-215, score-0.141]
84 Maximizing information with respect to two directions requires a significantly slower cooling rate, and consequently longer computational times. [sent-224, score-0.22]
85 model (2) (b) 20 reconstruction c 6 ¨ ¥ £ ©§ %$¡ (1) e (a) Figure 3: Analysis of a model complex cell with relevant directions and shown in (a) and (b). [sent-233, score-0.438]
86 Below, and found by maximizing information together with the we show vectors corresponding input-output function with respect to projections and . [sent-237, score-0.327]
87 3 ¡ E c¥ # 4 & In conclusion, features of the stimulus that are most relevant for generating the response of a neuron can be found by maximizing information between the sequence of responses and the projection of stimuli on trial vectors within the stimulus space. [sent-243, score-1.609]
88 Calculated in this manner, information becomes a function of direction in a stimulus space. [sent-244, score-0.365]
89 Those directions that maximize the information and account for the total information per response of interest span the relevant subspace. [sent-245, score-0.539]
90 This analysis allows the reconstruction of the relevant subspace without assuming a particular form of the input-output function. [sent-246, score-0.317]
91 It can be strongly nonlinear within the relevant subspace, and is to be estimated from experimental histograms. [sent-247, score-0.19]
92 Most importantly, this method can be used with any stimulus ensemble, even those that are strongly non-Gaussian as in the case of natural images. [sent-248, score-0.379]
93 Naturalistic stimuli increase the rate and efficiency of information transmission by primary auditory afferents. [sent-259, score-0.527]
94 Sparse coding and decorrelation in primary visual cortex during natural vision. [sent-270, score-0.276]
95 Spectral-temporal receptive fields of nonlinear auditory neurons obtained using natural sounds. [sent-278, score-0.325]
96 Feature analysis of natural sounds in the songbird auditory forebrain. [sent-308, score-0.144]
97 Receptive field structure of neurons in monkey visual cortex revealed by stimulation with natural image sequences. [sent-318, score-0.269]
98 Natural stimulation of the nonclassical receptive field increases information transmission efficiency in V1. [sent-325, score-0.172]
99 Relations between the statistics of natural images and the response properties of cortical cells. [sent-341, score-0.185]
100 Real-time performance of a movement-sensitive neuron in the blowfly visual system: coding and information transfer in short spike sequences. [sent-392, score-0.435]
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Abstract: We introduce the notion of Morton-style factorial coding and illustrate how it may help understand information integration and perceptual coding in the brain. We show that by focusing on average responses one may miss the existence of factorial coding mechanisms that become only apparent when analyzing spike count histograms. We show evidence suggesting that the classical/non-classical receptive field organization in the cortex effectively enforces the development of Morton-style factorial codes. This may provide some cues to help understand perceptual coding in the brain and to develop new unsupervised learning algorithms. While methods like ICA (Bell & Sejnowski, 1997) develop independent codes, in Morton-style coding the goal is to make two or more external aspects of the world become independent when conditioning on internal representations. In this paper we introduce the notion of Morton-style factorial coding and illustrate how it may help analyze information integration and perceptual organization in the brain. In the neurosciences factorial codes are often studied in the context of mean tuning curves. A tuning curve is called separable if it can be expressed as the product of terms selectively influenced by different stimulus dimensions. Separable tuning curves are taken as evidence of factorial coding mechanisms. In this paper we show that by focusing on average responses one may miss the existence of factorial coding mechanisms that become only apparent when analyzing spike count histograms. Morton (1969) analyzed a wide variety of psychophysical experiments on word perception and showed that they could be explained using a model in which stimulus and context have separable effects on perception. More precisely, in Mortons’ model the joint effect of stimulus and context on a perceptual representation can be obtained by multiplying terms selectively controlled by stimulus and by context, i.e., £ © # #
5 0.23524055 43 nips-2002-Binary Coding in Auditory Cortex
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Abstract: Cortical neurons have been reported to use both rate and temporal codes. Here we describe a novel mode in which each neuron generates exactly 0 or 1 action potentials, but not more, in response to a stimulus. We used cell-attached recording, which ensured single-unit isolation, to record responses in rat auditory cortex to brief tone pips. Surprisingly, the majority of neurons exhibited binary behavior with few multi-spike responses; several dramatic examples consisted of exactly one spike on 100% of trials, with no trial-to-trial variability in spike count. Many neurons were tuned to stimulus frequency. Since individual trials yielded at most one spike for most neurons, the information about stimulus frequency was encoded in the population, and would not have been accessible to later stages of processing that only had access to the activity of a single unit. These binary units allow a more efficient population code than is possible with conventional rate coding units, and are consistent with a model of cortical processing in which synchronous packets of spikes propagate stably from one neuronal population to the next. 1 Binary coding in auditory cortex We recorded responses of neurons in the auditory cortex of anesthetized rats to pure-tone pips of different frequencies [1, 2]. Each pip was presented repeatedly, allowing us to assess the variability of the neural response to multiple presentations of each stimulus. We first recorded multi-unit activity with conventional tungsten electrodes (Fig. 1a). The number of spikes in response to each pip fluctuated markedly from one trial to the next (Fig. 1e), as though governed by a random mechanism such as that generating the ticks of a Geiger counter. Highly variable responses such as these, which are at least as variable as a Poisson process, are the norm in the cortex [3-7], and have contributed to the widely held view that cortical spike trains are so noisy that only the average firing rate can be used to encode stimuli. Because we were recording the activity of an unknown number of neurons, we could not be sure whether the strong trial-to-trial fluctuations reflected the underlying variability of the single units. We therefore used an alternative technique, cell- a b Single-unit recording method 5mV Multi-unit 1sec Raw cellattached voltage 10 kHz c Single-unit . . . . .. .. ... . . .... . ... . Identified spikes Threshold e 28 kHz d Single-unit 80 120 160 200 Time (msec) N = 29 tones 3 2 1 Poisson N = 11 tones ry 40 4 na bi 38 kHz 0 Response variance/mean (spikes/trial) High-pass filtered 0 0 1 2 3 Mean response (spikes/trial) Figure 1: Multi-unit spiking activity was highly variable, but single units obeyed binomial statistics. a Multi-unit spike rasters from a conventional tungsten electrode recording showed high trial-to-trial variability in response to ten repetitions of the same 50 msec pure tone stimulus (bottom). Darker hash marks indicate spike times within the response period, which were used in the variability analysis. b Spikes recorded in cell-attached mode were easily identified from the raw voltage trace (top) by applying a high-pass filter (bottom) and thresholding (dark gray line). Spike times (black squares) were assigned to the peaks of suprathreshold segments. c Spike rasters from a cell-attached recording of single-unit responses to 25 repetitions of the same tone consisted of exactly one well-timed spike per trial (latency standard deviation = 1.0 msec), unlike the multi-unit responses (Fig. 1a). Under the Poisson assumption, this would have been highly unlikely (P ~ 10 -11). d The same neuron as in Fig. 1c responds with lower probability to repeated presentations of a different tone, but there are still no multi-spike responses. e We quantified response variability for each tone by dividing the variance in spike count by the mean spike count across all trials for that tone. Response variability for multi-unit tungsten recording (open triangles) was high for each of the 29 tones (out of 32) that elicited at least one spike on one trial. All but one point lie above one (horizontal gray line), which is the value produced by a Poisson process with any constant or time varying event rate. Single unit responses recorded in cell-attached mode were far less variable (filled circles). Ninety one percent (10/11) of the tones that elicited at least one spike from this neuron produced no multi-spike responses in 25 trials; the corresponding points fall on the diagonal line between (0,1) and (1,0), which provides a strict lower bound on the variability for any response set with a mean between 0 and 1. No point lies above one. attached recording with a patch pipette [8, 9], in order to ensure single unit isolation (Fig. 1b). This recording mode minimizes both of the main sources of error in spike detection: failure to detect a spike in the unit under observation (false negatives), and contamination by spikes from nearby neurons (false positives). It also differs from conventional extracellular recording methods in its selection bias: With cell- attached recording neurons are selected solely on the basis of the experimenter’s ability to form a seal, rather than on the basis of neuronal activity and responsiveness to stimuli as in conventional methods. Surprisingly, single unit responses were far more orderly than suggested by the multi-unit recordings; responses typically consisted of either 0 or 1 spikes per trial, and not more (Fig. 1c-e). In the most dramatic examples, each presentation of the same tone pip elicited exactly one spike (Fig. 1c). In most cases, however, some presentations failed to elicit a spike (Fig. 1d). Although low-variability responses have recently been observed in the cortex [10, 11] and elsewhere [12, 13], the binary behavior described here has not previously been reported for cortical neurons. a 1.4 N = 3055 response sets b 1.2 1 Poisson 28 kHz - 100 msec 0.8 0.6 0.4 0.2 0 0 ry na bi Response variance/mean (spikes/trial) The majority of the neurons (59%) in our study for which statistical significance could be assessed (at the p<0.001 significance level; see Fig. 2, caption) showed noisy binary behavior—“binary” because neurons produced either 0 or 1 spikes, and “noisy” because some stimuli elicited both single spikes and failures. In a substantial fraction of neurons, however, the responses showed more variability. We found no correlation between neuronal variability and cortical layer (inferred from the depth of the recording electrode), cortical area (inside vs. outside of area A1) or depth of anesthesia. Moreover, the binary mode of spiking was not due to the brevity (25 msec) of the stimuli; responses that were binary for short tones were comparably binary when longer (100 msec) tones were used (Fig. 2b). Not assessable Not significant Significant (p<0.001) 0.2 0.4 0.6 0.8 1 1.2 Mean response (spikes/trial) 28 kHz - 25 msec 1.4 0 40 80 120 160 Time (msec) 200 Figure 2: Half of the neuronal population exhibited binary firing behavior. a Of the 3055 sets of responses to 25 msec tones, 2588 (gray points) could not be assessed for significance at the p<0.001 level, 225 (open circles) were not significantly binary, and 242 were significantly binary (black points; see Identification methods for group statistics below). All points were jittered slightly so that overlying points could be seen in the figure. 2165 response sets contained no multi-spike responses; the corresponding points fell on the line from [0,1] to [1,0]. b The binary nature of single unit responses was insensitive to tone duration, even for frequencies that elicited the largest responses. Twenty additional spike rasters from the same neuron (and tone frequency) as in Fig. 1c contain no multi-spike responses whether in response to 100 msec tones (above) or 25 msec tones (below). Across the population, binary responses were as prevalent for 100 msec tones as for 25 msec tones (see Identification methods for group statistics). In many neurons, binary responses showed high temporal precision, with latencies sometimes exhibiting standard deviations as low as 1 msec (Fig. 3; see also Fig. 1c), comparable to previous observations in the auditory cortex [14], and only slightly more precise than in monkey visual area MT [5]. High temporal precision was positively correlated with high response probability (Fig. 3). a b N = (44 cells)x(32 tones) 14 N = 32 tones 12 30 Jitter (msec) Jitter (msec) 40 10 8 6 20 10 4 2 0 0 0 0.2 0.4 0.6 0.8 Mean response (spikes/trial) 1 0 0.4 0.8 1.2 1.6 Mean response (spikes/trial) 2 Figure 3: Trial-to-trial variability in latency of response to repeated presentations of the same tone decreased with increasing response probability. a Scatter plot of standard deviation of latency vs. mean response for 25 presentations each of 32 tones for a different neuron as in Figs. 1 and 2 (gray line is best linear fit). Rasters from 25 repeated presentations of a low response tone (upper left inset, which corresponds to left-most data point) display much more variable latencies than rasters from a high response tone (lower right inset; corresponds to right-most data point). b The negative correlation between latency variability and response size was present on average across the population of 44 neurons described in Identification methods for group statistics (linear fit, gray). The low trial-to-trial variability ruled out the possibility that the firing statistics could be accounted for by a simple rate-modulated Poisson process (Fig. 4a1,a2). In other systems, low variability has sometimes been modeled as a Poisson process followed by a post-spike refractory period [10, 12]. In our system, however, the range in latencies of evoked binary responses was often much greater than the refractory period, which could not have been longer than the 2 msec inter-spike intervals observed during epochs of spontaneous spiking, indicating that binary spiking did not result from any intrinsic property of the spike generating mechanism (Fig. 4a3). Moreover, a single stimulus-evoked spike could suppress subsequent spikes for as long as hundreds of milliseconds (e.g. Figs. 1d,4d), supporting the idea that binary spiking arises through a circuit-level, rather than a single-neuron, mechanism. Indeed, the fact that this suppression is observed even in the cortex of awake animals [15] suggests that binary spiking is not a special property of the anesthetized state. It seems surprising that binary spiking in the cortex has not previously been remarked upon. In the auditory cortex the explanation may be in part technical: Because firing rates in the auditory cortex tend to be low, multi-unit recording is often used to maximize the total amount of data collected. Moreover, our use of cell-attached recording minimizes the usual bias toward responsive or active neurons. Such explanations are not, however, likely to account for the failure to observe binary spiking in the visual cortex, where spike count statistics have been scrutinized more closely [3-7]. One possibility is that this reflects a fundamental difference between the auditory and visual systems. An alternative interpretation— a1 b Response probability 100 spikes/s 2 kHz Poisson simulation c 100 200 300 400 Time (msec) 500 20 Ratio of pool sizes a2 0 16 12 8 4 0 a3 Poisson with refractory period 0 40 80 120 160 200 Time (msec) d Response probability PSTH 0.2 0.4 0.6 0.8 1 Mean spike count per neuron 1 0.8 N = 32 tones 0.6 0.4 0.2 0 2.0 3.8 7.1 13.2 24.9 46.7 Tone frequency (kHz) Figure 4: a The lack of multi-spike responses elicited by the neuron shown in Fig. 3a were not due to an absolute refractory period since the range of latencies for many tones, like that shown here, was much greater than any reasonable estimate for the neuron’s refractory period. (a1) Experimentally recorded responses. (a2) Using the smoothed post stimulus time histogram (PSTH; bottom) from the set of responses in Fig. 4a, we generated rasters under the assumption of Poisson firing. In this representative example, four double-spike responses (arrows at left) were produced in 25 trials. (a3) We then generated rasters assuming that the neuron fired according to a Poisson process subject to a hard refractory period of 2 msec. Even with a refractory period, this representative example includes one triple- and three double-spike responses. The minimum interspike-interval during spontaneous firing events was less than two msec for five of our neurons, so 2 msec is a conservative upper bound for the refractory period. b. Spontaneous activity is reduced following high-probability responses. The PSTH (top; 0.25 msec bins) of the combined responses from the 25% (8/32) of tones that elicited the largest responses from the same neuron as in Figs. 3a and 4a illustrates a preclusion of spontaneous and evoked activity for over 200 msec following stimulation. The PSTHs from progressively less responsive groups of tones show progressively less preclusion following stimulation. c Fewer noisy binary neurons need to be pooled to achieve the same “signal-to-noise ratio” (SNR; see ref. [24]) as a collection of Poisson neurons. The ratio of the number of Poisson to binary neurons required to achieve the same SNR is plotted against the mean number of spikes elicited per neuron following stimulation; here we have defined the SNR to be the ratio of the mean spike count to the standard deviation of the spike count. d Spike probability tuning curve for the same neuron as in Figs. 1c-e and 2b fit to a Gaussian in tone frequency. and one that we favor—is that the difference rests not in the sensory modality, but instead in the difference between the stimuli used. In this view, the binary responses may not be limited to the auditory cortex; neurons in visual and other sensory cortices might exhibit similar responses to the appropriate stimuli. For example, the tone pips we used might be the auditory analog of a brief flash of light, rather than the oriented moving edges or gratings usually used to probe the primary visual cortex. Conversely, auditory stimuli analogous to edges or gratings [16, 17] may be more likely to elicit conventional, rate-modulated Poisson responses in the auditory cortex. Indeed, there may be a continuum between binary and Poisson modes. Thus, even in conventional rate-modulated responses, the first spike is often privileged in that it carries most of the information in the spike train [5, 14, 18]. The first spike may be particularly important as a means of rapidly signaling stimulus transients. Binary responses suggest a mode that complements conventional rate coding. In the simplest rate-coding model, a stimulus parameter (such as the frequency of a tone) governs only the rate at which a neuron generates spikes, but not the detailed positions of the spikes; the actual spike train itself is an instantiation of a random process (such as a Poisson process). By contrast, in the binomial model, the stimulus parameter (frequency) is encoded as the probability of firing (Fig. 4d). Binary coding has implications for cortical computation. In the rate coding model, stimulus encoding is “ergodic”: a stimulus parameter can be read out either by observing the activity of one neuron for a long time, or a population for a short time. By contrast, in the binary model the stimulus value can be decoded only by observing a neuronal population, so that there is no benefit to integrating over long time periods (cf. ref. [19]). One advantage of binary encoding is that it allows the population to signal quickly; the most compact message a neuron can send is one spike [20]. Binary coding is also more efficient in the context of population coding, as quantified by the signal-to-noise ratio (Fig. 4c). The precise organization of both spike number and time we have observed suggests that cortical activity consists, at least under some conditions, of packets of spikes synchronized across populations of neurons. Theoretical work [21-23] has shown how such packets can propagate stably from one population to the next, but only if neurons within each population fire at most one spike per packet; otherwise, the number of spikes per packet—and hence the width of each packet—grows at each propagation step. Interestingly, one prediction of stable propagation models is that spike probability should be related to timing precision, a prediction born out by our observations (Fig. 3). The role of these packets in computation remains an open question. 2 Identification methods for group statistics We recorded responses to 32 different 25 msec tones from each of 175 neurons from the auditory cortices of 16 Sprague-Dawley rats; each tone was repeated between 5 and 75 times (mean = 19). Thus our ensemble consisted of 32x175=5600 response sets, with between 5 and 75 samples in each set. Of these, 3055 response sets contained at least one spike on at least on trial. For each response set, we tested the hypothesis that the observed variability was significantly lower than expected from the null hypothesis of a Poisson process. The ability to assess significance depended on two parameters: the sample size (5-75) and the firing probability. Intuitively, the dependence on firing probability arises because at low firing rates most responses produce only trials with 0 or 1 spikes under both the Poisson and binary models; only at high firing rates do the two models make different predictions, since in that case the Poisson model includes many trials with 2 or even 3 spikes while the binary model generates only solitary spikes (see Fig. 4a1,a2). Using a stringent significance criterion of p<0.001, 467 response sets had a sufficient number of repeats to assess significance, given the observed firing probability. Of these, half (242/467=52%) were significantly less variable than expected by chance, five hundred-fold higher than the 467/1000=0.467 response sets expected, based on the 0.001 significance criterion, to yield a binary response set. Seventy-two neurons had at least one response set for which significance could be assessed, and of these, 49 neurons (49/72=68%) had at least one significantly sub-Poisson response set. Of this population of 49 neurons, five achieved low variability through repeatable bursty behavior (e.g., every spike count was either 0 or 3, but not 1 or 2) and were excluded from further analysis. The remaining 44 neurons formed the basis for the group statistics analyses shown in Figs. 2a and 3b. Nine of these neurons were subjected to an additional protocol consisting of at least 10 presentations each of 100 msec tones and 25 msec tones of all 32 frequencies. Of the 100 msec stimulation response sets, 44 were found to be significantly sub-Poisson at the p<0.05 level, in good agreement with the 43 found to be significant among the responses to 25 msec tones. 3 Bibliography 1. Kilgard, M.P. and M.M. Merzenich, Cortical map reorganization enabled by nucleus basalis activity. Science, 1998. 279(5357): p. 1714-8. 2. Sally, S.L. and J.B. Kelly, Organization of auditory cortex in the albino rat: sound frequency. J Neurophysiol, 1988. 59(5): p. 1627-38. 3. Softky, W.R. and C. Koch, The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs. J Neurosci, 1993. 13(1): p. 334-50. 4. Stevens, C.F. and A.M. Zador, Input synchrony and the irregular firing of cortical neurons. Nat Neurosci, 1998. 1(3): p. 210-7. 5. Buracas, G.T., A.M. Zador, M.R. DeWeese, and T.D. Albright, Efficient discrimination of temporal patterns by motion-sensitive neurons in primate visual cortex. Neuron, 1998. 20(5): p. 959-69. 6. Shadlen, M.N. and W.T. Newsome, The variable discharge of cortical neurons: implications for connectivity, computation, and information coding. J Neurosci, 1998. 18(10): p. 3870-96. 7. Tolhurst, D.J., J.A. Movshon, and A.F. Dean, The statistical reliability of signals in single neurons in cat and monkey visual cortex. Vision Res, 1983. 23(8): p. 775-85. 8. Otmakhov, N., A.M. Shirke, and R. Malinow, Measuring the impact of probabilistic transmission on neuronal output. Neuron, 1993. 10(6): p. 1101-11. 9. Friedrich, R.W. and G. Laurent, Dynamic optimization of odor representations by slow temporal patterning of mitral cell activity. Science, 2001. 291(5505): p. 889-94. 10. Kara, P., P. Reinagel, and R.C. Reid, Low response variability in simultaneously recorded retinal, thalamic, and cortical neurons. Neuron, 2000. 27(3): p. 635-46. 11. Gur, M., A. Beylin, and D.M. Snodderly, Response variability of neurons in primary visual cortex (V1) of alert monkeys. J Neurosci, 1997. 17(8): p. 2914-20. 12. Berry, M.J., D.K. Warland, and M. Meister, The structure and precision of retinal spike trains. Proc Natl Acad Sci U S A, 1997. 94(10): p. 5411-6. 13. de Ruyter van Steveninck, R.R., G.D. Lewen, S.P. Strong, R. Koberle, and W. Bialek, Reproducibility and variability in neural spike trains. Science, 1997. 275(5307): p. 1805-8. 14. Heil, P., Auditory cortical onset responses revisited. I. First-spike timing. J Neurophysiol, 1997. 77(5): p. 2616-41. 15. Lu, T., L. Liang, and X. Wang, Temporal and rate representations of timevarying signals in the auditory cortex of awake primates. Nat Neurosci, 2001. 4(11): p. 1131-8. 16. Kowalski, N., D.A. Depireux, and S.A. Shamma, Analysis of dynamic spectra in ferret primary auditory cortex. I. Characteristics of single-unit responses to moving ripple spectra. J Neurophysiol, 1996. 76(5): p. 350323. 17. deCharms, R.C., D.T. Blake, and M.M. Merzenich, Optimizing sound features for cortical neurons. Science, 1998. 280(5368): p. 1439-43. 18. Panzeri, S., R.S. Petersen, S.R. Schultz, M. Lebedev, and M.E. Diamond, The role of spike timing in the coding of stimulus location in rat somatosensory cortex. Neuron, 2001. 29(3): p. 769-77. 19. Britten, K.H., M.N. Shadlen, W.T. Newsome, and J.A. Movshon, The analysis of visual motion: a comparison of neuronal and psychophysical performance. J Neurosci, 1992. 12(12): p. 4745-65. 20. Delorme, A. and S.J. Thorpe, Face identification using one spike per neuron: resistance to image degradations. Neural Netw, 2001. 14(6-7): p. 795-803. 21. Diesmann, M., M.O. Gewaltig, and A. Aertsen, Stable propagation of synchronous spiking in cortical neural networks. Nature, 1999. 402(6761): p. 529-33. 22. Marsalek, P., C. Koch, and J. Maunsell, On the relationship between synaptic input and spike output jitter in individual neurons. Proc Natl Acad Sci U S A, 1997. 94(2): p. 735-40. 23. Kistler, W.M. and W. Gerstner, Stable propagation of activity pulses in populations of spiking neurons. Neural Comp., 2002. 14: p. 987-997. 24. Zohary, E., M.N. Shadlen, and W.T. Newsome, Correlated neuronal discharge rate and its implications for psychophysical performance. Nature, 1994. 370(6485): p. 140-3. 25. Abbott, L.F. and P. Dayan, The effect of correlated variability on the accuracy of a population code. Neural Comput, 1999. 11(1): p. 91-101.
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Abstract: Cortical neurons have been reported to use both rate and temporal codes. Here we describe a novel mode in which each neuron generates exactly 0 or 1 action potentials, but not more, in response to a stimulus. We used cell-attached recording, which ensured single-unit isolation, to record responses in rat auditory cortex to brief tone pips. Surprisingly, the majority of neurons exhibited binary behavior with few multi-spike responses; several dramatic examples consisted of exactly one spike on 100% of trials, with no trial-to-trial variability in spike count. Many neurons were tuned to stimulus frequency. Since individual trials yielded at most one spike for most neurons, the information about stimulus frequency was encoded in the population, and would not have been accessible to later stages of processing that only had access to the activity of a single unit. These binary units allow a more efficient population code than is possible with conventional rate coding units, and are consistent with a model of cortical processing in which synchronous packets of spikes propagate stably from one neuronal population to the next. 1 Binary coding in auditory cortex We recorded responses of neurons in the auditory cortex of anesthetized rats to pure-tone pips of different frequencies [1, 2]. Each pip was presented repeatedly, allowing us to assess the variability of the neural response to multiple presentations of each stimulus. We first recorded multi-unit activity with conventional tungsten electrodes (Fig. 1a). The number of spikes in response to each pip fluctuated markedly from one trial to the next (Fig. 1e), as though governed by a random mechanism such as that generating the ticks of a Geiger counter. Highly variable responses such as these, which are at least as variable as a Poisson process, are the norm in the cortex [3-7], and have contributed to the widely held view that cortical spike trains are so noisy that only the average firing rate can be used to encode stimuli. Because we were recording the activity of an unknown number of neurons, we could not be sure whether the strong trial-to-trial fluctuations reflected the underlying variability of the single units. We therefore used an alternative technique, cell- a b Single-unit recording method 5mV Multi-unit 1sec Raw cellattached voltage 10 kHz c Single-unit . . . . .. .. ... . . .... . ... . Identified spikes Threshold e 28 kHz d Single-unit 80 120 160 200 Time (msec) N = 29 tones 3 2 1 Poisson N = 11 tones ry 40 4 na bi 38 kHz 0 Response variance/mean (spikes/trial) High-pass filtered 0 0 1 2 3 Mean response (spikes/trial) Figure 1: Multi-unit spiking activity was highly variable, but single units obeyed binomial statistics. a Multi-unit spike rasters from a conventional tungsten electrode recording showed high trial-to-trial variability in response to ten repetitions of the same 50 msec pure tone stimulus (bottom). Darker hash marks indicate spike times within the response period, which were used in the variability analysis. b Spikes recorded in cell-attached mode were easily identified from the raw voltage trace (top) by applying a high-pass filter (bottom) and thresholding (dark gray line). Spike times (black squares) were assigned to the peaks of suprathreshold segments. c Spike rasters from a cell-attached recording of single-unit responses to 25 repetitions of the same tone consisted of exactly one well-timed spike per trial (latency standard deviation = 1.0 msec), unlike the multi-unit responses (Fig. 1a). Under the Poisson assumption, this would have been highly unlikely (P ~ 10 -11). d The same neuron as in Fig. 1c responds with lower probability to repeated presentations of a different tone, but there are still no multi-spike responses. e We quantified response variability for each tone by dividing the variance in spike count by the mean spike count across all trials for that tone. Response variability for multi-unit tungsten recording (open triangles) was high for each of the 29 tones (out of 32) that elicited at least one spike on one trial. All but one point lie above one (horizontal gray line), which is the value produced by a Poisson process with any constant or time varying event rate. Single unit responses recorded in cell-attached mode were far less variable (filled circles). Ninety one percent (10/11) of the tones that elicited at least one spike from this neuron produced no multi-spike responses in 25 trials; the corresponding points fall on the diagonal line between (0,1) and (1,0), which provides a strict lower bound on the variability for any response set with a mean between 0 and 1. No point lies above one. attached recording with a patch pipette [8, 9], in order to ensure single unit isolation (Fig. 1b). This recording mode minimizes both of the main sources of error in spike detection: failure to detect a spike in the unit under observation (false negatives), and contamination by spikes from nearby neurons (false positives). It also differs from conventional extracellular recording methods in its selection bias: With cell- attached recording neurons are selected solely on the basis of the experimenter’s ability to form a seal, rather than on the basis of neuronal activity and responsiveness to stimuli as in conventional methods. Surprisingly, single unit responses were far more orderly than suggested by the multi-unit recordings; responses typically consisted of either 0 or 1 spikes per trial, and not more (Fig. 1c-e). In the most dramatic examples, each presentation of the same tone pip elicited exactly one spike (Fig. 1c). In most cases, however, some presentations failed to elicit a spike (Fig. 1d). Although low-variability responses have recently been observed in the cortex [10, 11] and elsewhere [12, 13], the binary behavior described here has not previously been reported for cortical neurons. a 1.4 N = 3055 response sets b 1.2 1 Poisson 28 kHz - 100 msec 0.8 0.6 0.4 0.2 0 0 ry na bi Response variance/mean (spikes/trial) The majority of the neurons (59%) in our study for which statistical significance could be assessed (at the p<0.001 significance level; see Fig. 2, caption) showed noisy binary behavior—“binary” because neurons produced either 0 or 1 spikes, and “noisy” because some stimuli elicited both single spikes and failures. In a substantial fraction of neurons, however, the responses showed more variability. We found no correlation between neuronal variability and cortical layer (inferred from the depth of the recording electrode), cortical area (inside vs. outside of area A1) or depth of anesthesia. Moreover, the binary mode of spiking was not due to the brevity (25 msec) of the stimuli; responses that were binary for short tones were comparably binary when longer (100 msec) tones were used (Fig. 2b). Not assessable Not significant Significant (p<0.001) 0.2 0.4 0.6 0.8 1 1.2 Mean response (spikes/trial) 28 kHz - 25 msec 1.4 0 40 80 120 160 Time (msec) 200 Figure 2: Half of the neuronal population exhibited binary firing behavior. a Of the 3055 sets of responses to 25 msec tones, 2588 (gray points) could not be assessed for significance at the p<0.001 level, 225 (open circles) were not significantly binary, and 242 were significantly binary (black points; see Identification methods for group statistics below). All points were jittered slightly so that overlying points could be seen in the figure. 2165 response sets contained no multi-spike responses; the corresponding points fell on the line from [0,1] to [1,0]. b The binary nature of single unit responses was insensitive to tone duration, even for frequencies that elicited the largest responses. Twenty additional spike rasters from the same neuron (and tone frequency) as in Fig. 1c contain no multi-spike responses whether in response to 100 msec tones (above) or 25 msec tones (below). Across the population, binary responses were as prevalent for 100 msec tones as for 25 msec tones (see Identification methods for group statistics). In many neurons, binary responses showed high temporal precision, with latencies sometimes exhibiting standard deviations as low as 1 msec (Fig. 3; see also Fig. 1c), comparable to previous observations in the auditory cortex [14], and only slightly more precise than in monkey visual area MT [5]. High temporal precision was positively correlated with high response probability (Fig. 3). a b N = (44 cells)x(32 tones) 14 N = 32 tones 12 30 Jitter (msec) Jitter (msec) 40 10 8 6 20 10 4 2 0 0 0 0.2 0.4 0.6 0.8 Mean response (spikes/trial) 1 0 0.4 0.8 1.2 1.6 Mean response (spikes/trial) 2 Figure 3: Trial-to-trial variability in latency of response to repeated presentations of the same tone decreased with increasing response probability. a Scatter plot of standard deviation of latency vs. mean response for 25 presentations each of 32 tones for a different neuron as in Figs. 1 and 2 (gray line is best linear fit). Rasters from 25 repeated presentations of a low response tone (upper left inset, which corresponds to left-most data point) display much more variable latencies than rasters from a high response tone (lower right inset; corresponds to right-most data point). b The negative correlation between latency variability and response size was present on average across the population of 44 neurons described in Identification methods for group statistics (linear fit, gray). The low trial-to-trial variability ruled out the possibility that the firing statistics could be accounted for by a simple rate-modulated Poisson process (Fig. 4a1,a2). In other systems, low variability has sometimes been modeled as a Poisson process followed by a post-spike refractory period [10, 12]. In our system, however, the range in latencies of evoked binary responses was often much greater than the refractory period, which could not have been longer than the 2 msec inter-spike intervals observed during epochs of spontaneous spiking, indicating that binary spiking did not result from any intrinsic property of the spike generating mechanism (Fig. 4a3). Moreover, a single stimulus-evoked spike could suppress subsequent spikes for as long as hundreds of milliseconds (e.g. Figs. 1d,4d), supporting the idea that binary spiking arises through a circuit-level, rather than a single-neuron, mechanism. Indeed, the fact that this suppression is observed even in the cortex of awake animals [15] suggests that binary spiking is not a special property of the anesthetized state. It seems surprising that binary spiking in the cortex has not previously been remarked upon. In the auditory cortex the explanation may be in part technical: Because firing rates in the auditory cortex tend to be low, multi-unit recording is often used to maximize the total amount of data collected. Moreover, our use of cell-attached recording minimizes the usual bias toward responsive or active neurons. Such explanations are not, however, likely to account for the failure to observe binary spiking in the visual cortex, where spike count statistics have been scrutinized more closely [3-7]. One possibility is that this reflects a fundamental difference between the auditory and visual systems. An alternative interpretation— a1 b Response probability 100 spikes/s 2 kHz Poisson simulation c 100 200 300 400 Time (msec) 500 20 Ratio of pool sizes a2 0 16 12 8 4 0 a3 Poisson with refractory period 0 40 80 120 160 200 Time (msec) d Response probability PSTH 0.2 0.4 0.6 0.8 1 Mean spike count per neuron 1 0.8 N = 32 tones 0.6 0.4 0.2 0 2.0 3.8 7.1 13.2 24.9 46.7 Tone frequency (kHz) Figure 4: a The lack of multi-spike responses elicited by the neuron shown in Fig. 3a were not due to an absolute refractory period since the range of latencies for many tones, like that shown here, was much greater than any reasonable estimate for the neuron’s refractory period. (a1) Experimentally recorded responses. (a2) Using the smoothed post stimulus time histogram (PSTH; bottom) from the set of responses in Fig. 4a, we generated rasters under the assumption of Poisson firing. In this representative example, four double-spike responses (arrows at left) were produced in 25 trials. (a3) We then generated rasters assuming that the neuron fired according to a Poisson process subject to a hard refractory period of 2 msec. Even with a refractory period, this representative example includes one triple- and three double-spike responses. The minimum interspike-interval during spontaneous firing events was less than two msec for five of our neurons, so 2 msec is a conservative upper bound for the refractory period. b. Spontaneous activity is reduced following high-probability responses. The PSTH (top; 0.25 msec bins) of the combined responses from the 25% (8/32) of tones that elicited the largest responses from the same neuron as in Figs. 3a and 4a illustrates a preclusion of spontaneous and evoked activity for over 200 msec following stimulation. The PSTHs from progressively less responsive groups of tones show progressively less preclusion following stimulation. c Fewer noisy binary neurons need to be pooled to achieve the same “signal-to-noise ratio” (SNR; see ref. [24]) as a collection of Poisson neurons. The ratio of the number of Poisson to binary neurons required to achieve the same SNR is plotted against the mean number of spikes elicited per neuron following stimulation; here we have defined the SNR to be the ratio of the mean spike count to the standard deviation of the spike count. d Spike probability tuning curve for the same neuron as in Figs. 1c-e and 2b fit to a Gaussian in tone frequency. and one that we favor—is that the difference rests not in the sensory modality, but instead in the difference between the stimuli used. In this view, the binary responses may not be limited to the auditory cortex; neurons in visual and other sensory cortices might exhibit similar responses to the appropriate stimuli. For example, the tone pips we used might be the auditory analog of a brief flash of light, rather than the oriented moving edges or gratings usually used to probe the primary visual cortex. Conversely, auditory stimuli analogous to edges or gratings [16, 17] may be more likely to elicit conventional, rate-modulated Poisson responses in the auditory cortex. Indeed, there may be a continuum between binary and Poisson modes. Thus, even in conventional rate-modulated responses, the first spike is often privileged in that it carries most of the information in the spike train [5, 14, 18]. The first spike may be particularly important as a means of rapidly signaling stimulus transients. Binary responses suggest a mode that complements conventional rate coding. In the simplest rate-coding model, a stimulus parameter (such as the frequency of a tone) governs only the rate at which a neuron generates spikes, but not the detailed positions of the spikes; the actual spike train itself is an instantiation of a random process (such as a Poisson process). By contrast, in the binomial model, the stimulus parameter (frequency) is encoded as the probability of firing (Fig. 4d). Binary coding has implications for cortical computation. In the rate coding model, stimulus encoding is “ergodic”: a stimulus parameter can be read out either by observing the activity of one neuron for a long time, or a population for a short time. By contrast, in the binary model the stimulus value can be decoded only by observing a neuronal population, so that there is no benefit to integrating over long time periods (cf. ref. [19]). One advantage of binary encoding is that it allows the population to signal quickly; the most compact message a neuron can send is one spike [20]. Binary coding is also more efficient in the context of population coding, as quantified by the signal-to-noise ratio (Fig. 4c). The precise organization of both spike number and time we have observed suggests that cortical activity consists, at least under some conditions, of packets of spikes synchronized across populations of neurons. Theoretical work [21-23] has shown how such packets can propagate stably from one population to the next, but only if neurons within each population fire at most one spike per packet; otherwise, the number of spikes per packet—and hence the width of each packet—grows at each propagation step. Interestingly, one prediction of stable propagation models is that spike probability should be related to timing precision, a prediction born out by our observations (Fig. 3). The role of these packets in computation remains an open question. 2 Identification methods for group statistics We recorded responses to 32 different 25 msec tones from each of 175 neurons from the auditory cortices of 16 Sprague-Dawley rats; each tone was repeated between 5 and 75 times (mean = 19). Thus our ensemble consisted of 32x175=5600 response sets, with between 5 and 75 samples in each set. Of these, 3055 response sets contained at least one spike on at least on trial. For each response set, we tested the hypothesis that the observed variability was significantly lower than expected from the null hypothesis of a Poisson process. The ability to assess significance depended on two parameters: the sample size (5-75) and the firing probability. Intuitively, the dependence on firing probability arises because at low firing rates most responses produce only trials with 0 or 1 spikes under both the Poisson and binary models; only at high firing rates do the two models make different predictions, since in that case the Poisson model includes many trials with 2 or even 3 spikes while the binary model generates only solitary spikes (see Fig. 4a1,a2). Using a stringent significance criterion of p<0.001, 467 response sets had a sufficient number of repeats to assess significance, given the observed firing probability. Of these, half (242/467=52%) were significantly less variable than expected by chance, five hundred-fold higher than the 467/1000=0.467 response sets expected, based on the 0.001 significance criterion, to yield a binary response set. Seventy-two neurons had at least one response set for which significance could be assessed, and of these, 49 neurons (49/72=68%) had at least one significantly sub-Poisson response set. Of this population of 49 neurons, five achieved low variability through repeatable bursty behavior (e.g., every spike count was either 0 or 3, but not 1 or 2) and were excluded from further analysis. The remaining 44 neurons formed the basis for the group statistics analyses shown in Figs. 2a and 3b. Nine of these neurons were subjected to an additional protocol consisting of at least 10 presentations each of 100 msec tones and 25 msec tones of all 32 frequencies. Of the 100 msec stimulation response sets, 44 were found to be significantly sub-Poisson at the p<0.05 level, in good agreement with the 43 found to be significant among the responses to 25 msec tones. 3 Bibliography 1. Kilgard, M.P. and M.M. Merzenich, Cortical map reorganization enabled by nucleus basalis activity. Science, 1998. 279(5357): p. 1714-8. 2. Sally, S.L. and J.B. Kelly, Organization of auditory cortex in the albino rat: sound frequency. J Neurophysiol, 1988. 59(5): p. 1627-38. 3. Softky, W.R. and C. Koch, The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs. J Neurosci, 1993. 13(1): p. 334-50. 4. Stevens, C.F. and A.M. Zador, Input synchrony and the irregular firing of cortical neurons. Nat Neurosci, 1998. 1(3): p. 210-7. 5. Buracas, G.T., A.M. Zador, M.R. DeWeese, and T.D. Albright, Efficient discrimination of temporal patterns by motion-sensitive neurons in primate visual cortex. Neuron, 1998. 20(5): p. 959-69. 6. Shadlen, M.N. and W.T. Newsome, The variable discharge of cortical neurons: implications for connectivity, computation, and information coding. J Neurosci, 1998. 18(10): p. 3870-96. 7. Tolhurst, D.J., J.A. Movshon, and A.F. Dean, The statistical reliability of signals in single neurons in cat and monkey visual cortex. Vision Res, 1983. 23(8): p. 775-85. 8. Otmakhov, N., A.M. Shirke, and R. Malinow, Measuring the impact of probabilistic transmission on neuronal output. Neuron, 1993. 10(6): p. 1101-11. 9. Friedrich, R.W. and G. Laurent, Dynamic optimization of odor representations by slow temporal patterning of mitral cell activity. Science, 2001. 291(5505): p. 889-94. 10. Kara, P., P. Reinagel, and R.C. Reid, Low response variability in simultaneously recorded retinal, thalamic, and cortical neurons. Neuron, 2000. 27(3): p. 635-46. 11. Gur, M., A. Beylin, and D.M. Snodderly, Response variability of neurons in primary visual cortex (V1) of alert monkeys. J Neurosci, 1997. 17(8): p. 2914-20. 12. Berry, M.J., D.K. Warland, and M. Meister, The structure and precision of retinal spike trains. Proc Natl Acad Sci U S A, 1997. 94(10): p. 5411-6. 13. de Ruyter van Steveninck, R.R., G.D. Lewen, S.P. Strong, R. Koberle, and W. Bialek, Reproducibility and variability in neural spike trains. Science, 1997. 275(5307): p. 1805-8. 14. Heil, P., Auditory cortical onset responses revisited. I. First-spike timing. J Neurophysiol, 1997. 77(5): p. 2616-41. 15. Lu, T., L. Liang, and X. Wang, Temporal and rate representations of timevarying signals in the auditory cortex of awake primates. Nat Neurosci, 2001. 4(11): p. 1131-8. 16. Kowalski, N., D.A. Depireux, and S.A. Shamma, Analysis of dynamic spectra in ferret primary auditory cortex. I. Characteristics of single-unit responses to moving ripple spectra. J Neurophysiol, 1996. 76(5): p. 350323. 17. deCharms, R.C., D.T. Blake, and M.M. Merzenich, Optimizing sound features for cortical neurons. Science, 1998. 280(5368): p. 1439-43. 18. Panzeri, S., R.S. Petersen, S.R. Schultz, M. Lebedev, and M.E. Diamond, The role of spike timing in the coding of stimulus location in rat somatosensory cortex. Neuron, 2001. 29(3): p. 769-77. 19. Britten, K.H., M.N. Shadlen, W.T. Newsome, and J.A. Movshon, The analysis of visual motion: a comparison of neuronal and psychophysical performance. J Neurosci, 1992. 12(12): p. 4745-65. 20. Delorme, A. and S.J. Thorpe, Face identification using one spike per neuron: resistance to image degradations. Neural Netw, 2001. 14(6-7): p. 795-803. 21. Diesmann, M., M.O. Gewaltig, and A. Aertsen, Stable propagation of synchronous spiking in cortical neural networks. Nature, 1999. 402(6761): p. 529-33. 22. Marsalek, P., C. Koch, and J. Maunsell, On the relationship between synaptic input and spike output jitter in individual neurons. Proc Natl Acad Sci U S A, 1997. 94(2): p. 735-40. 23. Kistler, W.M. and W. Gerstner, Stable propagation of activity pulses in populations of spiking neurons. Neural Comp., 2002. 14: p. 987-997. 24. Zohary, E., M.N. Shadlen, and W.T. Newsome, Correlated neuronal discharge rate and its implications for psychophysical performance. Nature, 1994. 370(6485): p. 140-3. 25. Abbott, L.F. and P. Dayan, The effect of correlated variability on the accuracy of a population code. Neural Comput, 1999. 11(1): p. 91-101.
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These binary units allow a more efficient population code than is possible with conventional rate coding units, and are consistent with a model of cortical processing in which synchronous packets of spikes propagate stably from one neuronal population to the next. 1 Binary coding in auditory cortex We recorded responses of neurons in the auditory cortex of anesthetized rats to pure-tone pips of different frequencies [1, 2]. Each pip was presented repeatedly, allowing us to assess the variability of the neural response to multiple presentations of each stimulus. We first recorded multi-unit activity with conventional tungsten electrodes (Fig. 1a). The number of spikes in response to each pip fluctuated markedly from one trial to the next (Fig. 1e), as though governed by a random mechanism such as that generating the ticks of a Geiger counter. Highly variable responses such as these, which are at least as variable as a Poisson process, are the norm in the cortex [3-7], and have contributed to the widely held view that cortical spike trains are so noisy that only the average firing rate can be used to encode stimuli. Because we were recording the activity of an unknown number of neurons, we could not be sure whether the strong trial-to-trial fluctuations reflected the underlying variability of the single units. We therefore used an alternative technique, cell- a b Single-unit recording method 5mV Multi-unit 1sec Raw cellattached voltage 10 kHz c Single-unit . . . . .. .. ... . . .... . ... . Identified spikes Threshold e 28 kHz d Single-unit 80 120 160 200 Time (msec) N = 29 tones 3 2 1 Poisson N = 11 tones ry 40 4 na bi 38 kHz 0 Response variance/mean (spikes/trial) High-pass filtered 0 0 1 2 3 Mean response (spikes/trial) Figure 1: Multi-unit spiking activity was highly variable, but single units obeyed binomial statistics. a Multi-unit spike rasters from a conventional tungsten electrode recording showed high trial-to-trial variability in response to ten repetitions of the same 50 msec pure tone stimulus (bottom). Darker hash marks indicate spike times within the response period, which were used in the variability analysis. b Spikes recorded in cell-attached mode were easily identified from the raw voltage trace (top) by applying a high-pass filter (bottom) and thresholding (dark gray line). Spike times (black squares) were assigned to the peaks of suprathreshold segments. c Spike rasters from a cell-attached recording of single-unit responses to 25 repetitions of the same tone consisted of exactly one well-timed spike per trial (latency standard deviation = 1.0 msec), unlike the multi-unit responses (Fig. 1a). Under the Poisson assumption, this would have been highly unlikely (P ~ 10 -11). d The same neuron as in Fig. 1c responds with lower probability to repeated presentations of a different tone, but there are still no multi-spike responses. e We quantified response variability for each tone by dividing the variance in spike count by the mean spike count across all trials for that tone. Response variability for multi-unit tungsten recording (open triangles) was high for each of the 29 tones (out of 32) that elicited at least one spike on one trial. All but one point lie above one (horizontal gray line), which is the value produced by a Poisson process with any constant or time varying event rate. Single unit responses recorded in cell-attached mode were far less variable (filled circles). Ninety one percent (10/11) of the tones that elicited at least one spike from this neuron produced no multi-spike responses in 25 trials; the corresponding points fall on the diagonal line between (0,1) and (1,0), which provides a strict lower bound on the variability for any response set with a mean between 0 and 1. No point lies above one. attached recording with a patch pipette [8, 9], in order to ensure single unit isolation (Fig. 1b). This recording mode minimizes both of the main sources of error in spike detection: failure to detect a spike in the unit under observation (false negatives), and contamination by spikes from nearby neurons (false positives). It also differs from conventional extracellular recording methods in its selection bias: With cell- attached recording neurons are selected solely on the basis of the experimenter’s ability to form a seal, rather than on the basis of neuronal activity and responsiveness to stimuli as in conventional methods. Surprisingly, single unit responses were far more orderly than suggested by the multi-unit recordings; responses typically consisted of either 0 or 1 spikes per trial, and not more (Fig. 1c-e). In the most dramatic examples, each presentation of the same tone pip elicited exactly one spike (Fig. 1c). In most cases, however, some presentations failed to elicit a spike (Fig. 1d). Although low-variability responses have recently been observed in the cortex [10, 11] and elsewhere [12, 13], the binary behavior described here has not previously been reported for cortical neurons. a 1.4 N = 3055 response sets b 1.2 1 Poisson 28 kHz - 100 msec 0.8 0.6 0.4 0.2 0 0 ry na bi Response variance/mean (spikes/trial) The majority of the neurons (59%) in our study for which statistical significance could be assessed (at the p<0.001 significance level; see Fig. 2, caption) showed noisy binary behavior—“binary” because neurons produced either 0 or 1 spikes, and “noisy” because some stimuli elicited both single spikes and failures. In a substantial fraction of neurons, however, the responses showed more variability. We found no correlation between neuronal variability and cortical layer (inferred from the depth of the recording electrode), cortical area (inside vs. outside of area A1) or depth of anesthesia. Moreover, the binary mode of spiking was not due to the brevity (25 msec) of the stimuli; responses that were binary for short tones were comparably binary when longer (100 msec) tones were used (Fig. 2b). Not assessable Not significant Significant (p<0.001) 0.2 0.4 0.6 0.8 1 1.2 Mean response (spikes/trial) 28 kHz - 25 msec 1.4 0 40 80 120 160 Time (msec) 200 Figure 2: Half of the neuronal population exhibited binary firing behavior. a Of the 3055 sets of responses to 25 msec tones, 2588 (gray points) could not be assessed for significance at the p<0.001 level, 225 (open circles) were not significantly binary, and 242 were significantly binary (black points; see Identification methods for group statistics below). All points were jittered slightly so that overlying points could be seen in the figure. 2165 response sets contained no multi-spike responses; the corresponding points fell on the line from [0,1] to [1,0]. b The binary nature of single unit responses was insensitive to tone duration, even for frequencies that elicited the largest responses. Twenty additional spike rasters from the same neuron (and tone frequency) as in Fig. 1c contain no multi-spike responses whether in response to 100 msec tones (above) or 25 msec tones (below). Across the population, binary responses were as prevalent for 100 msec tones as for 25 msec tones (see Identification methods for group statistics). In many neurons, binary responses showed high temporal precision, with latencies sometimes exhibiting standard deviations as low as 1 msec (Fig. 3; see also Fig. 1c), comparable to previous observations in the auditory cortex [14], and only slightly more precise than in monkey visual area MT [5]. High temporal precision was positively correlated with high response probability (Fig. 3). a b N = (44 cells)x(32 tones) 14 N = 32 tones 12 30 Jitter (msec) Jitter (msec) 40 10 8 6 20 10 4 2 0 0 0 0.2 0.4 0.6 0.8 Mean response (spikes/trial) 1 0 0.4 0.8 1.2 1.6 Mean response (spikes/trial) 2 Figure 3: Trial-to-trial variability in latency of response to repeated presentations of the same tone decreased with increasing response probability. a Scatter plot of standard deviation of latency vs. mean response for 25 presentations each of 32 tones for a different neuron as in Figs. 1 and 2 (gray line is best linear fit). Rasters from 25 repeated presentations of a low response tone (upper left inset, which corresponds to left-most data point) display much more variable latencies than rasters from a high response tone (lower right inset; corresponds to right-most data point). b The negative correlation between latency variability and response size was present on average across the population of 44 neurons described in Identification methods for group statistics (linear fit, gray). The low trial-to-trial variability ruled out the possibility that the firing statistics could be accounted for by a simple rate-modulated Poisson process (Fig. 4a1,a2). In other systems, low variability has sometimes been modeled as a Poisson process followed by a post-spike refractory period [10, 12]. In our system, however, the range in latencies of evoked binary responses was often much greater than the refractory period, which could not have been longer than the 2 msec inter-spike intervals observed during epochs of spontaneous spiking, indicating that binary spiking did not result from any intrinsic property of the spike generating mechanism (Fig. 4a3). Moreover, a single stimulus-evoked spike could suppress subsequent spikes for as long as hundreds of milliseconds (e.g. Figs. 1d,4d), supporting the idea that binary spiking arises through a circuit-level, rather than a single-neuron, mechanism. Indeed, the fact that this suppression is observed even in the cortex of awake animals [15] suggests that binary spiking is not a special property of the anesthetized state. It seems surprising that binary spiking in the cortex has not previously been remarked upon. In the auditory cortex the explanation may be in part technical: Because firing rates in the auditory cortex tend to be low, multi-unit recording is often used to maximize the total amount of data collected. Moreover, our use of cell-attached recording minimizes the usual bias toward responsive or active neurons. Such explanations are not, however, likely to account for the failure to observe binary spiking in the visual cortex, where spike count statistics have been scrutinized more closely [3-7]. One possibility is that this reflects a fundamental difference between the auditory and visual systems. An alternative interpretation— a1 b Response probability 100 spikes/s 2 kHz Poisson simulation c 100 200 300 400 Time (msec) 500 20 Ratio of pool sizes a2 0 16 12 8 4 0 a3 Poisson with refractory period 0 40 80 120 160 200 Time (msec) d Response probability PSTH 0.2 0.4 0.6 0.8 1 Mean spike count per neuron 1 0.8 N = 32 tones 0.6 0.4 0.2 0 2.0 3.8 7.1 13.2 24.9 46.7 Tone frequency (kHz) Figure 4: a The lack of multi-spike responses elicited by the neuron shown in Fig. 3a were not due to an absolute refractory period since the range of latencies for many tones, like that shown here, was much greater than any reasonable estimate for the neuron’s refractory period. (a1) Experimentally recorded responses. (a2) Using the smoothed post stimulus time histogram (PSTH; bottom) from the set of responses in Fig. 4a, we generated rasters under the assumption of Poisson firing. In this representative example, four double-spike responses (arrows at left) were produced in 25 trials. (a3) We then generated rasters assuming that the neuron fired according to a Poisson process subject to a hard refractory period of 2 msec. Even with a refractory period, this representative example includes one triple- and three double-spike responses. The minimum interspike-interval during spontaneous firing events was less than two msec for five of our neurons, so 2 msec is a conservative upper bound for the refractory period. b. Spontaneous activity is reduced following high-probability responses. The PSTH (top; 0.25 msec bins) of the combined responses from the 25% (8/32) of tones that elicited the largest responses from the same neuron as in Figs. 3a and 4a illustrates a preclusion of spontaneous and evoked activity for over 200 msec following stimulation. The PSTHs from progressively less responsive groups of tones show progressively less preclusion following stimulation. c Fewer noisy binary neurons need to be pooled to achieve the same “signal-to-noise ratio” (SNR; see ref. [24]) as a collection of Poisson neurons. The ratio of the number of Poisson to binary neurons required to achieve the same SNR is plotted against the mean number of spikes elicited per neuron following stimulation; here we have defined the SNR to be the ratio of the mean spike count to the standard deviation of the spike count. d Spike probability tuning curve for the same neuron as in Figs. 1c-e and 2b fit to a Gaussian in tone frequency. and one that we favor—is that the difference rests not in the sensory modality, but instead in the difference between the stimuli used. In this view, the binary responses may not be limited to the auditory cortex; neurons in visual and other sensory cortices might exhibit similar responses to the appropriate stimuli. For example, the tone pips we used might be the auditory analog of a brief flash of light, rather than the oriented moving edges or gratings usually used to probe the primary visual cortex. Conversely, auditory stimuli analogous to edges or gratings [16, 17] may be more likely to elicit conventional, rate-modulated Poisson responses in the auditory cortex. Indeed, there may be a continuum between binary and Poisson modes. Thus, even in conventional rate-modulated responses, the first spike is often privileged in that it carries most of the information in the spike train [5, 14, 18]. The first spike may be particularly important as a means of rapidly signaling stimulus transients. Binary responses suggest a mode that complements conventional rate coding. In the simplest rate-coding model, a stimulus parameter (such as the frequency of a tone) governs only the rate at which a neuron generates spikes, but not the detailed positions of the spikes; the actual spike train itself is an instantiation of a random process (such as a Poisson process). By contrast, in the binomial model, the stimulus parameter (frequency) is encoded as the probability of firing (Fig. 4d). Binary coding has implications for cortical computation. In the rate coding model, stimulus encoding is “ergodic”: a stimulus parameter can be read out either by observing the activity of one neuron for a long time, or a population for a short time. By contrast, in the binary model the stimulus value can be decoded only by observing a neuronal population, so that there is no benefit to integrating over long time periods (cf. ref. [19]). One advantage of binary encoding is that it allows the population to signal quickly; the most compact message a neuron can send is one spike [20]. Binary coding is also more efficient in the context of population coding, as quantified by the signal-to-noise ratio (Fig. 4c). The precise organization of both spike number and time we have observed suggests that cortical activity consists, at least under some conditions, of packets of spikes synchronized across populations of neurons. Theoretical work [21-23] has shown how such packets can propagate stably from one population to the next, but only if neurons within each population fire at most one spike per packet; otherwise, the number of spikes per packet—and hence the width of each packet—grows at each propagation step. Interestingly, one prediction of stable propagation models is that spike probability should be related to timing precision, a prediction born out by our observations (Fig. 3). The role of these packets in computation remains an open question. 2 Identification methods for group statistics We recorded responses to 32 different 25 msec tones from each of 175 neurons from the auditory cortices of 16 Sprague-Dawley rats; each tone was repeated between 5 and 75 times (mean = 19). Thus our ensemble consisted of 32x175=5600 response sets, with between 5 and 75 samples in each set. Of these, 3055 response sets contained at least one spike on at least on trial. For each response set, we tested the hypothesis that the observed variability was significantly lower than expected from the null hypothesis of a Poisson process. The ability to assess significance depended on two parameters: the sample size (5-75) and the firing probability. Intuitively, the dependence on firing probability arises because at low firing rates most responses produce only trials with 0 or 1 spikes under both the Poisson and binary models; only at high firing rates do the two models make different predictions, since in that case the Poisson model includes many trials with 2 or even 3 spikes while the binary model generates only solitary spikes (see Fig. 4a1,a2). Using a stringent significance criterion of p<0.001, 467 response sets had a sufficient number of repeats to assess significance, given the observed firing probability. Of these, half (242/467=52%) were significantly less variable than expected by chance, five hundred-fold higher than the 467/1000=0.467 response sets expected, based on the 0.001 significance criterion, to yield a binary response set. Seventy-two neurons had at least one response set for which significance could be assessed, and of these, 49 neurons (49/72=68%) had at least one significantly sub-Poisson response set. Of this population of 49 neurons, five achieved low variability through repeatable bursty behavior (e.g., every spike count was either 0 or 3, but not 1 or 2) and were excluded from further analysis. The remaining 44 neurons formed the basis for the group statistics analyses shown in Figs. 2a and 3b. Nine of these neurons were subjected to an additional protocol consisting of at least 10 presentations each of 100 msec tones and 25 msec tones of all 32 frequencies. Of the 100 msec stimulation response sets, 44 were found to be significantly sub-Poisson at the p<0.05 level, in good agreement with the 43 found to be significant among the responses to 25 msec tones. 3 Bibliography 1. Kilgard, M.P. and M.M. Merzenich, Cortical map reorganization enabled by nucleus basalis activity. Science, 1998. 279(5357): p. 1714-8. 2. Sally, S.L. and J.B. Kelly, Organization of auditory cortex in the albino rat: sound frequency. J Neurophysiol, 1988. 59(5): p. 1627-38. 3. Softky, W.R. and C. Koch, The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs. J Neurosci, 1993. 13(1): p. 334-50. 4. Stevens, C.F. and A.M. Zador, Input synchrony and the irregular firing of cortical neurons. Nat Neurosci, 1998. 1(3): p. 210-7. 5. Buracas, G.T., A.M. Zador, M.R. DeWeese, and T.D. Albright, Efficient discrimination of temporal patterns by motion-sensitive neurons in primate visual cortex. Neuron, 1998. 20(5): p. 959-69. 6. Shadlen, M.N. and W.T. Newsome, The variable discharge of cortical neurons: implications for connectivity, computation, and information coding. J Neurosci, 1998. 18(10): p. 3870-96. 7. Tolhurst, D.J., J.A. Movshon, and A.F. Dean, The statistical reliability of signals in single neurons in cat and monkey visual cortex. Vision Res, 1983. 23(8): p. 775-85. 8. Otmakhov, N., A.M. Shirke, and R. Malinow, Measuring the impact of probabilistic transmission on neuronal output. Neuron, 1993. 10(6): p. 1101-11. 9. Friedrich, R.W. and G. Laurent, Dynamic optimization of odor representations by slow temporal patterning of mitral cell activity. Science, 2001. 291(5505): p. 889-94. 10. Kara, P., P. Reinagel, and R.C. Reid, Low response variability in simultaneously recorded retinal, thalamic, and cortical neurons. Neuron, 2000. 27(3): p. 635-46. 11. Gur, M., A. Beylin, and D.M. Snodderly, Response variability of neurons in primary visual cortex (V1) of alert monkeys. J Neurosci, 1997. 17(8): p. 2914-20. 12. Berry, M.J., D.K. Warland, and M. Meister, The structure and precision of retinal spike trains. Proc Natl Acad Sci U S A, 1997. 94(10): p. 5411-6. 13. de Ruyter van Steveninck, R.R., G.D. Lewen, S.P. Strong, R. Koberle, and W. Bialek, Reproducibility and variability in neural spike trains. Science, 1997. 275(5307): p. 1805-8. 14. Heil, P., Auditory cortical onset responses revisited. I. First-spike timing. J Neurophysiol, 1997. 77(5): p. 2616-41. 15. Lu, T., L. Liang, and X. Wang, Temporal and rate representations of timevarying signals in the auditory cortex of awake primates. Nat Neurosci, 2001. 4(11): p. 1131-8. 16. Kowalski, N., D.A. Depireux, and S.A. Shamma, Analysis of dynamic spectra in ferret primary auditory cortex. I. Characteristics of single-unit responses to moving ripple spectra. J Neurophysiol, 1996. 76(5): p. 350323. 17. deCharms, R.C., D.T. Blake, and M.M. Merzenich, Optimizing sound features for cortical neurons. Science, 1998. 280(5368): p. 1439-43. 18. Panzeri, S., R.S. Petersen, S.R. Schultz, M. Lebedev, and M.E. Diamond, The role of spike timing in the coding of stimulus location in rat somatosensory cortex. Neuron, 2001. 29(3): p. 769-77. 19. Britten, K.H., M.N. Shadlen, W.T. Newsome, and J.A. Movshon, The analysis of visual motion: a comparison of neuronal and psychophysical performance. J Neurosci, 1992. 12(12): p. 4745-65. 20. Delorme, A. and S.J. Thorpe, Face identification using one spike per neuron: resistance to image degradations. Neural Netw, 2001. 14(6-7): p. 795-803. 21. Diesmann, M., M.O. Gewaltig, and A. Aertsen, Stable propagation of synchronous spiking in cortical neural networks. Nature, 1999. 402(6761): p. 529-33. 22. Marsalek, P., C. Koch, and J. Maunsell, On the relationship between synaptic input and spike output jitter in individual neurons. Proc Natl Acad Sci U S A, 1997. 94(2): p. 735-40. 23. Kistler, W.M. and W. Gerstner, Stable propagation of activity pulses in populations of spiking neurons. Neural Comp., 2002. 14: p. 987-997. 24. Zohary, E., M.N. Shadlen, and W.T. Newsome, Correlated neuronal discharge rate and its implications for psychophysical performance. Nature, 1994. 370(6485): p. 140-3. 25. Abbott, L.F. and P. Dayan, The effect of correlated variability on the accuracy of a population code. Neural Comput, 1999. 11(1): p. 91-101.
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