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The Journal of Neuroscience, April 1, 2002, 22(7):2904-2915
Natural Stimulation of the Nonclassical Receptive Field Increases Information Transmission Efficiency in V1
William E. Vinje1, 2 and Jack L. Gallant1, 3 1 Neuroscience Program and Departments of 2 Molecular and Cellular Biology and 3 Psychology, University of California at Berkeley, Berkeley, California 94720-1650
ABSTRACT
TOP
ABSTRACT
INTRODUCTION
We have investigated how the nonclassical receptive field (nCRF) affects information transmission by V1 neurons during simulated natural vision in awake, behaving macaques. Stimuli were centered over the classical receptive field (CRF) and stimulus size was varied from one to four times the diameter of the CRF. Stimulus movies reproduced the spatial and temporal stimulus dynamics of natural vision while maintaining constant CRF stimulation across all sizes. In individual neurons, stimulation of the nCRF significantly increases the information rate, the information per spike, and the efficiency of information transmission. Furthermore, the population averages of these quantities also increase significantly with nCRF stimulation. These data demonstrate that the nCRF increases the sparseness of the stimulus representation in V1, suggesting that the nCRF tunes V1 neurons to match the highly informative components of the natural world.
Key words: information theory; nonclassical receptive field; V1; sparse coding; efficiency; natural vision
INTRODUCTION
The classical receptive field (CRF) of a visual neuron is traditionally defined as the region of space where stimuli evoke action potentials. Surrounding the CRF is the nonclassical receptive field (nCRF), where stimuli can modulate the responses evoked by CRF stimulation (Allman et al., 1985
). The nCRF may serve to mediate contrast gain control through divisive modulation of the responses evoked by CRF stimulation (Heeger, 1992
In a previous study, we showed that natural stimulation of the nCRF increases the selectivity of V1 neurons and decorrelates their responses (Vinje and Gallant, 2000
In a sparse representation, neurons are narrowly tuned and relatively few are active at any moment. A central tenet of sparse coding is that information should be translated without loss into an efficient representation where the responses of a few active neurons are rich in information content. Reducing the number of active neurons is metabolically economical, thus easing a major constraint on information processing in the brain (Laughlin et al., 1998
The optimal level of sparseness is a function of the goals of the system and the resources available. Recent theoretical work suggests that natural images can be efficiently represented by a sparse code (Srinivasan et al., 1982
The hypothesis that nCRF stimulation increases the sparseness of individual V1 neurons leads to numerous predictions. Several of these predictions were confirmed in a previous report (Vinje and Gallant, 2000
The hypothesis that nCRF stimulation increases sparseness also leads to four additional predictions. First, the average response rate should decrease as sparseness increases in order to reduce the metabolic demands of visual processing. Second, the reduction in spiking activity should not reduce the information carried by the population of V1 neurons. Third, the average information content per spike should increase. Finally, as sparseness increases, individual neurons should become more efficient at information transmission.
MATERIALS AND METHODS
Subjects and physiological procedures. All animal procedures were approved by oversight committees at the University of Washington (St. Louis, MO) and the University of California at Berkeley and conformed to or exceeded all relevant National Institutes of Health and United States Department of Agriculture standards. Surgical procedures were conducted under appropriate anesthesia using standard sterile techniques (Connor et al., 1997
Extracellular, single-neuron recordings were made with epoxy-coated tungsten electrodes (AM Systems, Everett, WA and FHC, Bowdoinham, ME) from two awake, behaving monkeys (Macaca mulata). Signals were amplified, band-pass filtered, and isolated with a hardware window discriminator. Spike triggers were monitored at 8 kHz. Only clearly isolated single units were included in the data set.
Chambers were located over putative V1 by means of external cranial landmarks. To confirm that recordings were obtained from V1 neurons, we compared measured receptive field sizes and electrophysiological response properties with those expected from the literature.
Receptive-field estimation. The boundaries of the CRF were estimated using bars and gratings for which characteristics and placement were manually controlled. We estimated the size of the CRF as the diameter of the circle that circumscribed the minimum response field of the neuron. For most neurons, these manual estimates were confirmed by reverse correlation analysis using a dynamic (72 Hz) sequence of small white squares flashed randomly in and around the CRF. Reliable CRF estimates were typically obtained from 100-300 sec of data, representing 20-60 behavioral fixation trials. In most cases there was excellent agreement between CRF profiles estimated using the two methods. In those cases in which the methods disagreed, the reverse correlation size estimates were used. CRF diameters ranged from ~20 to 50 min of arc, consistent with other studies (Snodderly and Gur, 1995
Simulated eye-movement model. During natural vision, primates make stereotyped eye movements consisting of relatively long, stable fixations interspersed with rapid saccades from one point to another (Keating and Keating, 1982
Natural-vision movies. Natural-vision movies were constructed by extracting image patches from natural scenes along the simulated eye-scan path. Scenes were chosen from a commercial, high-resolution photo-CD image library of landscapes, structures, people, and animals (Corel Corp., Ottawa, Ontario, Canada) and were converted to grayscale before display. Image patches were extracted along a simulated scan path that was sampled at ~1 kHz. Each 13.8 msec (72 Hz) movie frame was constructed by averaging 14 separate image patches. Individual frames were then concatenated to form movies. This over-sampling followed by averaging minimized the potential of introducing temporal aliasing artifacts into the movie.
Patches of one, two, three, or four times the diameter of the CRF were used to create a set of natural-vision movies. Movies of different sizes were not scaled versions of one another. Instead, the patch boundary was changed to reveal more or less of the underlying natural scene. Thus, the region of the natural vision movie covering the CRF was identical across all movie sizes, and any response modulation attributable to stimulus size should reflect the effects of nCRF stimulation. Figure 1 illustrates the stimulus generation method.
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Figure 1. Natural-vision movies reproduce the stimulation that occurs during free viewing of natural scenes. To construct a natural vision movie, a saccadic scan path (white line) is generated using a model derived from previously recorded eye movements. Image patches centered on the scan path coordinates (white circles) are then extracted from the underlying image. Image patches were from one to four times the size of the CRF. (The small circle indicates 1 × CRF diameter, whereas the large circle indicates 4 × CRF diameter.) Note that although nCRF stimulation varied substantially with stimulus size, the stimulus falling on the CRF was the same for all sizes.
Flashed natural-image patches. An additional stimulus set was constructed by extracting image patches from along an eye-scan path that was recorded during free viewing of natural scenes (Gallant et al., 1998
The image patches were presented in grayscale under behavioral conditions similar to those used for natural vision movies (see below). Patches were shown at either the same size as the estimated CRF or three times larger than the CRF. Each behavioral trial included four random patches flashed for 500 msec each and separated by 700 msec interstimulus intervals.
Stimulus presentation. Stimulus presentation and behavioral control were handled by an Indigo2 workstation (SGI, Mountain View, CA) using custom software. Stimuli were presented on a high-quality video monitor (Sony Trinitron; Sony, Tokyo, Japan) at 1280 × 1024 pixel resolution. Movies were broken into 5 sec segments (trials) and were shown centered on the CRF center of the recorded neuron. During movie display, the animal fixated on a small target spot near the center of the monitor. Eye position was monitored using a scleral search coil, and trials were aborted if the eye deviated from fixation by >0.35°. At the end of each successful trial, the animal earned a liquid reward. Only one stimulus size was shown on each trial; stimuli of different sizes were randomly interleaved across trials.
Response modulation ratio. The nCRF modulation produced by stimuli of a given diameter is quantified in terms of the response modulation ratio:
(1) In our analysis, the fundamental quantity of interest is the average number of action potentials occurring in each time bin of the natural-vision movie. In Equation 1,
r
is the average response recorded during the ith time bin for stimuli confined to the CRF, and
Selectivity index for natural-vision movies. We define a selectivity index based on the responses of a neuron across a stimulus set:
(2) Here µ is the mean response of the cell,
is its SD, and the number of time bins is given by n.
The terms in braces define the activity fraction of the neuron across the stimulus set (Tovee et al., 1993
would be constant across stimuli and the numerator and denominator of the activity fraction would be equal. In contrast, if a neuron responded to only the kth stimulus then the numerator would be given by (r )2, whereas the denominator would be larger by a factor of n, n(r )2. Thus, the activity fraction ranges from 1, when the cell is nonselective, to 1/n, when the cell responds to a single stimulus frame. Equation 2 rescales the activity fraction so that it conveniently ranges from 0 to 1. S will be 0 if a neuron is completely nonselective and 1 if it responds only to a single stimulus. For convenience, we express S as a percentage. In a previous publication, the selectivity index was referred to as the sparseness index (Vinje and Gallant, 2000
Information transmission in sensory neurons. From the perspective of information theory, an axon is a biological communication channel. Consider an observer who is monitoring the axon of a sensory neuron with known filtering properties. Before the neuron responds, the observer is uncertain about the nature of the stimulus. After observing the responses of the neuron, the observer can determine the overlap between the stimulus and the neural filtering properties. Thus, the response of the neuron reduces the observer's uncertainty about the stimulus. The amount by which a response reduces uncertainty is referred to as the mutual information carried between stimulus and response.
The total stimulus entropy, H(s), quantifies the observer's uncertainty regarding the stimulus before the response of the neuron is observed. The conditional stimulus entropy H(s|r), gives the stimulus uncertainty that remains after response observation. If the response is reliably influenced by the stimulus, then the conditional stimulus entropy will necessarily be less than the total stimulus entropy. The transmitted mutual information is given by (Cover and Thomas, 1991
(3) The stochastic nature of spike generation means that neural responses are variable even when a stimulus is repeated exactly. The response variability caused by noise (noise entropy) limits the amount of information that can be transmitted about a stimulus. Figure 2A illustrates the relationship between stimulus entropy, noise entropy, and mutual information. The reduction in stimulus uncertainty is equal to the reduction in uncertainty regarding the response:
(4)
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Figure 2. Sensory neurons transmit information when their responses allow an observer to reduce uncertainty regarding the nature of the stimulus. A, Diagram illustrating relationship between uncertainty and information. The first rectangle symbolizes the total uncertainty present in the set of all stimulus-response pairings for a given neuron; the second rectangle represents the observer's a priori uncertainty about the stimuli in a natural-vision movie; the third rectangle represents the uncertainty in the observed responses of the neuron. These uncertainties can be translated into entropies by means of Equation 5. The single number that summarizes overall stimulus uncertainty is the total stimulus entropy, H(s), while the total response entropy is H(r). The remaining rectangles are the conditional stimulus uncertainty (C.S.U.) and the conditional response uncertainty (C.R.U.) (quantified by the entropies H(s|r) and H(r|s), respectively). The gray-shaded region denotes correlations between the stimulus and the responses of the neuron; this correlation is what allows information, I(s, r), to be transmitted. If every stimulus evokes a unique and repeatable response, then response uncertainty will be entirely determined by stimulus uncertainty. In this case the gray-shaded region would completely overlap both stimulus and response uncertainties. In real neurons, repeated presentation of a stimulus produced a range of responses, so H(r) > I(s, r). The remaining uncertainty, H(r|s), is attributable to noise in the encoding and transmission process. B, Grayscale rastergram of single neuron responses to repeated movie presentations. Rows represent repeated presentations of the movie, whereas columns represent individual time bins. Each time bin contains a single response word whose identity is determined by the number of action potentials (identity is indicated by the shading of each bin). The total response entropy, H(r), is a function of the frequency with which each word is observed, p . C, Magnified view of responses to one stimulus repeated 20 times. Variation in the identity of the response words is clearly visible across trials and is quantified as noise entropy, H(r|s = k). Noise entropy is a function of the probability that each word occurs in response to the kth stimulus, p .
Here, H(r) is the total response entropy, which quantifies the overall variability of the responses of a neuron across the stimulus ensemble. H(r|s) is the conditional response entropy, describing the average variability in responses evoked by a single stimulus. The conditional response entropy is equivalent to the noise entropy. In practice it is often easier to evaluate response entropies than stimulus entropies.
Calculation of total response entropy and conditional response entropy. It is straightforward to compute the total response entropy via the direct method (de Ruyter van Steveninck et al., 1997
If the firing rate possesses temporal correlations extending across multiple time bins, then the assumption of a memory-less rate code may lead to overestimation of the information transmission rate of the neuron. Conversely, if information is carried by the temporal structure of the spiking activity within a time bin, then the memory-less rate code assumption may lead to underestimation of the information transmission rate. Clearly, the assumption of a memory-less rate code has strengths and weaknesses. Many more complex neural codes have been proposed (for example, see Optican and Richmond, 1987
After the spike train is translated into discrete words, the probability of word occurrence is determined empirically from the data. After determining the occurrence probability of each word, the entropy can be found using (Shannon and Weaver, 1949
(5) The summation runs over discrete words, and pj is the probability of the occurrence of the jth word.
Under the assumption of a memory-less rate code, the spike train is divided into nonoverlapping time bins that are treated as independent words. Each word is uniquely identified via the number of spikes that it contains (Reich et al., 2000
(6) Where p
is the number of time bins containing exactly j action potentials divided by the total number of time bins. The total response entropy is a function of both the number of distinct response words and their frequency of occurrence. Total response entropy is therefore related to the dynamic range of a neuron; neurons with larger dynamic ranges will be able to generate a larger variety of spike patterns in response to a given stimulus set. The noise entropy describes the average variability of responses to single stimuli. Let p
be the probability that the jth word occurred in response to the kth stimulus. The noise entropy for stimulus k is given by:
(7) The probability of word occurrence for each stimulus, p
, is equal to the number of stimulus-repetition trials on which the kth stimulus produces j action potentials, divided by the overall number of repetitions. (In the experiments reported in this paper, each stimulus was repeated between 10 and 40 times.) The overall noise entropy of the neuron is found by averaging across the noise entropies of the individual stimuli:
Given H(r) and H(r|s), Equation 4 provides information transmission per time bin. Figure 2B, C provides a graphical overview of how the response probabilities are determined from the data. From Equation 4 it can be seen that the fundamental quantity in the analysis is the information per time bin. However, to allow comparison with other studies, it is desirable to report information transmission rates per second or per spike. Information per second is found by dividing the information per time bin by the duration of each time bin. Information per spike is found by dividing the information per second by the mean number of spikes per second.
(8) In the current study, two experimental factors may result in underestimation of information transmission rates. First, visual stimuli were presented while animals performed a simple visual fixation task. During fixation the eye is not entirely steady; a small degree of ocular drift and corrective microsaccadic eye movements are inevitable. These small eye movements introduce variability in retinal stimulation that in turn increases response variability. This artificially inflates our estimates of H(r|s) and thereby decreases our estimates of I(s, r). A second source of bias might arise from the absence of top-down influences that could influence V1 responses during natural vision. For example, during natural vision the ocular-motor system might provide V1 with an efference signal denoting eye movements that could allow V1 to process information more efficiently. This possibility is clearly speculative, but the possible role of extraretinal influences is poorly understood in V1. Both factors suggest that our experimental estimates of information transmission should be interpreted as de facto lower bounds on the true capabilities of V1 neurons. Fortunately, our analysis centers on the changes in information transmission that result from differential stimulation of the nCRF. These factors should be common across nCRF stimulation conditions and have little or no effect on our results.
Choice of time-bin duration. Because our analysis assumes a rate code, the duration of the time bins should match the true integration time of the target neurons. Unfortunately, this critical time constant is unknown. To compensate, we analyze the data using several different binning times (4.6, 13.8, 25, and 50 msec) that span the range of plausible integration times (Bair, 1999
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Table 1. Population averages as a function of stimulus size and time bin duration Correction for finite data bias in the response entropies. The values for p
and p are estimated from the experimental data, leading to uncertainty in H(r) and H(r|s). The uncertainties in the entropy estimates contain both random error (because of sampling) and systematic biases. Error attributable to sampling is handled conventionally, by considering whether results are statistically significant. The bias, however, can be removed explicitly. In particular, the noise entropy is strongly affected by limitations in the number of trial repetitions. In general, this results in potential underestimation of the noise entropy (which would produce an overestimation of information transmission). For both H(r) and H(r|s), the relationship between the true entropy and the experimental estimate of the entropy is given by (Treves and Panzeri, 1995
where c
(9) is an empirically determined weighting coefficient for the
th correction term and N denotes the number of times each stimulus was repeated. In our data, the linear bias term dominates the sum in Equation 9. In light of this, we consider only the first- and second-order correction terms:
(10) All of the analyses presented in this report used the bias-corrected entropies, Htrue.
To find Htrue, we divide the original data set into several subsets, each containing N trials, and evaluate H
for each subset. Subsets contain, respectively, one-quarter, one-third, one-half, or all of the original trials. Second, we fit Equation 10 to these data via least-squares minimization. The value of Htrue is the ordinate intercept of the best-fit function. Figure 3 illustrates this process for an example neuron.
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Figure 3. Finite repetitions of each stimulus lead to systematic biases in the experimentally measured entropies. Response entropy (circles) and noise entropy (squares) are plotted versus 1/N, where N is the number of trials used in the calculation of p and p . Error bars were determined by the Jackknife method (Efron and Tibshirani, 1993
Testing for excessive finite data bias. The number of trials required for accurate bias correction depends on time-bin duration and the response properties of the neuron under study. If there are too few repeated stimulus presentations, higher-order correction terms become important and Equation 10 fails to sufficiently describe the finite data bias. Fortunately excessive levels of bias contamination can be detected by testing whether the experimentally estimated entropies violate the Ma bound (Strong et al., 1998
The Ma bound is a lower bound on response entropy and can be estimated for both the total response entropy, H(r), and the noise entropy H(r|s). For words composed of single time bins, the general expression for the Ma bound is given by (Ma, 1981
(11) HMa is useful because it is less susceptible to finite data bias than Hexp. The response entropy can sink below the Ma bound only if Hexp is strongly contaminated by finite data bias (Strong et al., 1998
We computed the Ma bounds on both total response entropy and noise entropy to allow exclusion of any neurons with gross levels of bias contamination. During responses to natural-vision movies, both response entropies were greater than HMa for all neurons. This satisfies the Ma bound criterion and indicates that our entropy estimates are free from excessive finite data bias.
Significance testing. We determined whether the descriptive statistics of two sample sets are significantly different via randomized, two-tailed t tests (Manly, 1991
0.05 is sufficient when comparing two collections of neurons. However, when judging significant differences in single neurons or time bins, we use a more restrictive significance criterion, p
RESULTS
Response modulation by the nCRF in area V1 during natural vision
Many studies have demonstrated that the nCRF has pronounced, generally suppressive effects on responses (Hubel and Wiesel, 1965
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Figure 4. The nCRF modulates responses during natural vision. A, PSTH obtained from one V1 neuron in response to a natural-vision movie confined to the CRF. Responses are weakly modulated by the simulated fixations (information per second, 13.1 bits/sec; information per spike, 0.18 bits/spike; efficiency, 10%; selectivity index, 13%). B, Responses of the same cell to a natural-vision movie composed of the CRF stimulation used in A plus a circular surrounding region. The overall stimulus size was 4 × CRF diameter. Stimulation of the nCRF dramatically increases variation of responses across fixations (information per second, 28.4 bits/sec; information per spike, 0.67 bits/spike; efficiency, 26%; selectivity index, 51%). Responses to some stimuli are significantly enhanced (black bins; p
To quantify the observed modulation, we calculated Ri values for all time bins in our data set (Fig. 5A-C). Again, Ri values are colored according to their significance: white for significant suppression, black for significant enhancement. (Modulation ratios and histogram values are plotted on logarithmic scales because of the large dynamic range of modulation produced by natural stimulation of the nCRF.) As stimulus size increases, there is a modest increase in the number of significantly modulated time bins. In general, enhancement is always less pronounced than suppression. However, for all stimulus sizes a substantial fraction of modulation is positive. As stimulus size increases, the net modulation becomes steadily more suppressive.
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Figure 5. Stimulus size affects the modulation ratio and the mean spike rate. A-C, Modulation ratios, Ri, for stimuli of sizes 2 × CRF, 3 × CRF, and 4 × CRF. Both axes are presented on a logarithmic scale (base 10) to facilitate display. Positive values of log[Ri] indicate relative enhancement, whereas negative values of log[Ri] indicate relative suppression. Those time bins with significantly enhanced ratios are shown in black, whereas those with significantly decreased ratios are shown in white (p ; and the number of time bins demonstrating significant suppression, n , are indicated to the right of each histogram. Not all time bins are included in the histogram. Time bins for which Ri = 0 are indicated by no. These bins are included in the total number of valid bins, but have undefined logarithms. Time bins where CRF-sized stimuli evoke no spikes are indicated by ne. These bins have undefined modulation ratios and are not included in the total number of valid time bins. Enhancement is less frequent than suppression, especially at larger stimulus sizes. Significant enhancement occurs in 1.7, 2.3, and 3.0% of the time bins for stimulus sizes of 2 × CRF, 3 × CRF and 4 × CRF, respectively, whereas significant suppression occurs in 4.6, 6.4, and 8.0%. D, Average spikes per second versus stimulus size. The mean spike rate falls monotonically as stimulus size increases. The mean spike rate in response to 4 × CRF stimuli is ~75% of mean the rate observed with CRF stimulation alone.
Suppression also significantly decreases the mean spiking rate of individual neurons. The fractions of neurons whose spike rates are significantly suppressed by nCRF stimulation are 50% at 2 × CRF, 59% at 3 × CRF, and 73% at 4 × CRF (p
In a previous study, we showed that increasing stimulus size decorrelated the responses of neuron pairs (Vinje and Gallant, 2000
Increasing nCRF stimulation produces a net increase in suppressive modulation, a reduction in the overall population activity rate, and a reduction in tuning overlap. These results support the first untested prediction: increasing nCRF stimulation reduces metabolic load by lowering mean spike rates. Furthermore, these three findings suggest that nCRF stimulation reduces the effective bandwidth of single neurons, thereby restricting the range of stimuli that they represent.
nCRF stimulation increases information transmission rate
Does this shrinkage in effective bandwidth reduce the amount of information represented by V1 neurons? If information is lost, then the stimulus representation will be coarsened rather than made sparser (Foldiak and Young, 1995
Information transmission rates (bits per second) for our sample of V1 neurons are shown in Figure 6A-D. For each neuron at each stimulus size, we compared information rates observed with and without nCRF stimulation. Neurons with significantly increased information rates are shown in black, while those with significantly decreased rates are shown in white (p
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Figure 6. Information transmission in V1 neurons increases with stimulus size. A-D, Information transmission rates for stimuli of sizes 1 × CRF, 2 × CRF, 3 × CRF, and 4 × CRF. Neurons in which stimulus size significantly increases information transmission per second are shown in black, whereas those neurons with significant decreases in transmission are shown in white (p ; and the number of time bins demonstrating significant decreases, n
For our sample of neurons, the average information transmission rate also increases with stimulus size (Fig. 6E). The increase in mean rate is modest but statistically significant for stimulus sizes of 2 × CRF and 3 × CRF (p
Table 1 shows the average information rate as a function of stimulus size and time-bin duration. In general, the average rate increases as time-bin duration decreases. From 50 msec to 4.6 msec, the information transmission rate increases by ~250%. The increase in information rates for short binning times is commonly observed in neurophysiological data sets (Strong et al., 1998
Our second prediction is that the average information transmission rate should not decrease as stimulus size increases. Our results demonstrate that information transmission actually increases with stimulus size. This is consistent with the predicted preservation of information. It also suggests that nCRF stimulation may be necessary to fully realize the information-processing potential of V1 neurons.
nCRF stimulation increases information per spike
As discussed in the introductory remarks, sparse coding offers several potential advantages to the nervous system. It may simplify development of neural connections, increase learning rates, and increase memory capacity (Barlow, 1961
The average information that a spike transmits about the stimulus is found by simply dividing the information per second by the mean number of spikes per second: Ispike = Isec/µ, where µ is the mean spike rate of the neuron for all stimuli of a given size.
Information transmission per spike is shown in Figure 7A-D. Figure conventions are identical to those used in Figure 6. Stimulation of the nCRF can increase or decrease the information per spike, but the trend is strongly toward increasing the information content of spikes. The ratio of neurons with significant increases to those with significant decreases is 6.5:1 at 2 × CRF and 26:1 at 3 × CRF. For data obtained with stimuli of 4 × CRF diameter, all significantly modulated neurons show increases in their information transmission per spike.
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Figure 7. Information per spike increases with stimulus size. A-D, Information transmission per spike versus stimulus size. Figure conventions match those used in Figure 6. Significant increases in information per spike occur in 59, 70, and 79% and significant decreases occur in 9, 3, and 0% of the neurons for stimulus sizes of 2 × CRF, 3 × CRF, and 4 × CRF, respectively. E, Mean (black circles) and median (gray triangles) information per spike estimates as a function of stimulus size. The mean information per spike obtained with 2 × CRF and larger stimuli is significantly higher than that observed with stimuli confined to the CRF (p
The mean information per spike also increases substantially as a function of stimulus size (Fig. 7E, black circles). For stimuli of 4 × CRF diameter, the mean information per spike is 1.85 times larger than that of the value obtained with CRF-sized stimuli. All stimuli of a size
2 × CRF produce significant increases in information per spike (p
Natural nCRF stimulation increases the information content of each spike for most neurons in our sample. This confirms the third prediction of the hypothesis that nCRF stimulation increases sparseness in V1.
nCRF stimulation during natural vision increases efficiency
As nCRF stimulation increases sparseness, it should also increase the efficiency of information processing. In information theoretic terms, efficiency measures the fraction of available bandwidth that a neuron actually uses to transmit information. Formally this is expressed as the ratio of the amount of information actually transmitted over the theoretical maximum amount of information that could be transmitted (Cover and Thomas, 1991
Figure 8A-D shows efficiency versus stimulus size for our sample of neurons. Figure conventions again match those used in Figure 6. As stimulus size increases, so does the efficiency of single neurons. The ratio of neurons with significant increases to those with significant decreases is 6.3:1 at 2 × CRF and 26:1 at 3 × CRF. With 4 × CRF stimuli, all significantly modulated neurons show increases in the efficiency of information transmission.
(12)
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Figure 8. Efficiency of information transmission increases with stimulus size. A-D, Efficiency versus stimulus size. Figure conventions match those used in Figure 6. Significant increases in efficiency occur in 57, 70, and 82% and significant decreases occur in 9, 3, and 0% of the neurons for stimulus sizes of 2 × CRF, 3 × CRF, and 4 × CRF, respectively. E, Mean efficiency as a function of stimulus size. Efficiency observed with 2 × CRF and larger stimuli is significantly higher than that observed with stimuli confined to the CRF (p
Mean efficiency increases with nCRF stimulation (Fig. 8E); for 4 × CRF-sized stimuli, the mean efficiency is 1.6 times larger than the value obtained with CRF-sized stimuli. The increases in mean efficiency are statistically significant for all stimuli of a size
Neurons use their available transmission bandwidth more efficiently when the nCRF is stimulated than when stimuli are confined to the CRF. Because efficiency does not explicitly depend on spike rate, this result complements the finding that nCRF stimulation increases the amount of information available in each spike and confirms the last of our predictions.
Information transmission and efficiency correlate with selectivity
Thus far we have shown that nCRF stimulation increases information transmission rates, the information content of single spikes, and processing efficiency in both individual neurons and our sample population. In a previous study (Vinje and Gallant, 2000
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Figure 9. Stimulus selectivity increases with stimulus size. A-D, Selectivity versus stimulus size. Figure conventions match those used in Figure 6. Significant increases in selectivity occur in 61, 70, and 88% and significant decreases occur in 11, 5, and 2% of the neurons for stimulus sizes of 2 × CRF, 3 × CRF, and 4 × CRF, respectively. E, Mean selectivity versus stimulus size. Selectivity obtained with 2 × CRF and larger stimuli is significantly higher than that found with stimuli confined to the CRF (p
Stimulus selectivity is not significantly correlated with information per second in our sample of cells (Fig. 10A-D). However, selectivity is significantly correlated with information per spike for all stimulus sizes (Fig. 10E-H; p
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Figure 10. Information per spike and efficiency are correlated with selectivity. A-D, Information transmission rate versus selectivity for stimuli 2 × CRF, 3 × CRF, and 4 × CRF. The lack of meaningful correlation is immediately apparent. E-H, Information per spike versus selectivity. These measures are strongly correlated for all stimulus sizes. I-L, Efficiency versus selectivity. The measures are also correlated for all stimulus sizes.
The lack of correlation between information transmission per second and selectivity suggests that the observed increases in information rate may not be central to the process of increasing sparseness. This is perhaps unsurprising, given that the prediction was merely that average information transmission should be preserved. In contrast, the correlation of selectivity with information per spike and efficiency suggests that these three measures are related by an underlying causal factor. It seems likely that this causal factor is the sparseness of information representation in V1. As sparseness increases, there are corresponding increases in selectivity, information per spike, and efficiency of information transmission.
Results obtained with flashed natural-image patches
Natural-vision movies are designed to mimic the stimulation that occurs during saccadic vision of a static scene. The majority of the movie consists of fixations where image content is held constant. These fixations are linked by simulated saccades with realistic acceleration profiles. The stimulation contained in saccades blends together image patches and avoids any discontinuous change in stimulus content. Most previous physiology experiments use flashed stimuli that contain instantaneous onset and offset transitions and substantial interstimulus intervals. Clearly the nature of the transitions between image patches is very different in these two procedures.
To facilitate comparisons between our results and those obtained using flashed stimuli, we performed the following control experiment. Image patches were selected from natural scenes and presented as flashed stimuli (n = 10 neurons; see Materials and Methods). Responses to the flashed stimuli were concatenated to form a pseudo-movie and analyzed in the same manner as natural-vision movies (responses during interstimulus intervals were discarded).
Unfortunately, flashed stimulus patches were presented only five times; therefore, this data set suffers from larger entropy biases than our main data set. This problem is partially caused by difficulty in accurately estimating the second correction term in Equation 10 and was partially ameliorated by using only the linear correction term. To enable comparison with data from natural-vision movies, we also limited the natural-vision data to the first five trials and applied only the linear bias correction. This approach subjected both data sets to the same bias-producing conditions and thus allowed a fair comparison between the results from the natural vision and the flashed stimuli.
The effects of nCRF stimulation with flashed stimuli are generally similar to those obtained with natural-vision movies. Both the information per spike and the efficiency increase with stimulus size. For the largest flashed stimulus size (3 × CRF), the average information per spike increases by 25% and the average efficiency increases by 10%. Information transmission per second does not increase.
These results suggest that increasing stimulus size increases response sparseness with flashed stimuli, as it does with natural-vision movies. However, these effects are somewhat smaller with flashed stimuli. This may be an artifact of small sample size, because not all neurons demonstrate strong nCRF modulation effects. Alternatively, this may reflect differences in the transient responses evoked by the two stimulus classes. When the first 200 msec are removed from the response to each flashed-image patch, information transmission more closely matches that obtained with natural-vision movies.
Total entropy and noise entropy both decrease with increasing stimulus size
Information is the difference between two measures of variance, the total response entropy and the noise entropy. An increase in information can reflect a decrease in noise entropy, an increase in total entropy, or some combination of the two. Each of these changes would alter neuronal spiking patterns in ways that allow insight into the specific biophysical mechanisms underlying nCRF modulation. If nCRF stimulation increases the total response entropy, then the nCRF must increase the dynamic range of the neuron and/or the reliability of spikes elicited by the stimulus. In contrast, if the noise entropy decreases consequent to nCRF stimulation, then the nCRF must suppress spikes that are not relevant to encoding the stimulus.
Entropy measures are summarized in Figure 11. Figure 11A-D shows total stimulus entropy, and Figure 11E-H shows noise entropy. Those neurons with significantly increased entropies are shown in black, while those with significantly decreased entropies are shown in white (p
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Figure 11. Stimulation of the nCRF decreases both total response entropy and noise entropy. A-D, Total response entropy versus stimulus size. Significant increases in total response entropy occur in 30, 16, and 14%, and significant decreases occur in 50, 57, and 71% of the neurons for stimulus sizes of 2 × CRF, 3 × CRF, and 4 × CRF, respectively. E-H, Noise entropy versus stimulus size. Significant increases in noise entropy occur in 18, 14, and 8% and significant decreases occur in 55, 65, and 80% of the neurons for stimulus sizes of 2 × CRF, 3 × CRF and 4 × CRF, respectively. Larger stimuli tend to reduce both the total response entropy and the noise entropy of individual neurons.
The differential effect of nCRF stimulation on these two entropies underlies the observed increases in information rate, information per spike, and efficiency. The simultaneous decrease of both total and noise entropies explains why nCRF stimulation has a relatively weak effect on information per second: such stimulation decreases both total entropy and noise entropy and dilutes the effective increase in overall information transmission rates.
Information per spike and efficiency are both ratio measures with the weakly increasing information rate in their numerators. However, the denominator terms of both measures (µ and H(r), respectively) shrink with increasing stimulus size. This convergence of a weakly increasing numerator and a decreasing denominator underlies the strong increases in information per spike and efficiency as a function of stimulus size. The nCRF appears to suppress most responses and enhance a select few. As sparseness increases, those action potentials that are not reliably linked to stimulus properties are winnowed from the responses of the neuron.
DISCUSSION
Our results show that nCRF stimulation changes the response entropies of V1 neurons. Stimulation of the nCRF decreases total response entropy but has an even greater effect on the noise entropy. This differential modulation underlies the pattern of results we observed: relative to CRF stimulation alone, naturalistic nCRF stimulation increases selectivity, information per second, information per spike, and efficiency.
Previous theoretical research has shown that the informative components of natural scenes are sparsely distributed (Field, 1987
The level of sparseness in the neural code does not necessarily match that of natural images; the sparse components of natural images are determined by the physical structure of the world, while the sparseness of a neural code also reflects biophysical, computational, and behavioral constraints (van Hateren and Ruderman, 1998
