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7 nips-2003-A Functional Architecture for Motion Pattern Processing in MSTd

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Author: Scott A. Beardsley, Lucia M. Vaina

Abstract: Psychophysical studies suggest the existence of specialized detectors for component motion patterns (radial, circular, and spiral), that are consistent with the visual motion properties of cells in the dorsal medial superior temporal area (MSTd) of non-human primates. Here we use a biologically constrained model of visual motion processing in MSTd, in conjunction with psychophysical performance on two motion pattern tasks, to elucidate the computational mechanisms associated with the processing of widefield motion patterns encountered during self-motion. In both tasks discrimination thresholds varied significantly with the type of motion pattern presented, suggesting perceptual correlates to the preferred motion bias reported in MSTd. Through the model we demonstrate that while independently responding motion pattern units are capable of encoding information relevant to the visual motion tasks, equivalent psychophysical performance can only be achieved using interconnected neural populations that systematically inhibit non-responsive units. These results suggest the cyclic trends in psychophysical performance may be mediated, in part, by recurrent connections within motion pattern responsive areas whose structure is a function of the similarity in preferred motion patterns and receptive field locations between units. 1 In trod u ction A major challenge in computational neuroscience is to elucidate the architecture of the cortical circuits for sensory processing and their effective role in mediating behavior. In the visual motion system, biologically constrained models are playing an increasingly important role in this endeavor by providing an explanatory substrate linking perceptual performance and the visual properties of single cells. Single cell studies indicate the presence of complex interconnected structures in middle temporal and primary visual cortex whose most basic horizontal connections can impart considerable computational power to the underlying neural population [1, 2]. Combined psychophysical and computational studies support these findings Figure 1: a) Schematic of the graded motion pattern (GMP) task. Discrimination pairs of stimuli were created by perturbing the flow angle (φ) of each 'test' motion (with average dot speed, vav), by ±φp in the stimulus space spanned by radial and circular motions. b) Schematic of the shifted center-of-motion (COM) task. Discrimination pairs of stimuli were created by shifting the COM of the ‘test’ motion to the left and right of a central fixation point. For each motion pattern the COM was shifted within the illusory inner aperture and was never explicitly visible. and suggest that recurrent connections may play a significant role in encoding the visual motion properties associated with various psychophysical tasks [3, 4]. Using this methodology our goal is to elucidate the computational mechanisms associated with the processing of wide-field motion patterns encountered during self-motion. In the human visual motion system, psychophysical studies suggest the existence of specialized detectors for the motion pattern components (i.e., radial, circular and spiral motions) associated with self-motion [5, 6]. Neurophysiological studies reporting neurons sensitive to motion patterns in the dorsal medial superior temporal area (MSTd) support the existence of such mechanisms [7-10], and in conjunction with psychophysical studies suggest a strong link between the patterns of neural activity and motion-based perceptual performance [11, 12]. Through the combination of human psychophysical performance and biologically constrained modeling we investigate the computational role of simple recurrent connections within a population of MSTd-like units. Based on the known visual motion properties within MSTd we ask what neural structures are computationally sufficient to encode psychophysical performance on a series of motion pattern tasks. 2 M o t i o n pa t t e r n d i sc r i m i n a t i o n Using motion pattern stimuli consistent with previous studies [5, 6], we have developed a set of novel psychophysical tasks designed to facilitate a more direct comparison between human perceptual performance and the visual motion properties of cells in MSTd that have been found to underlie the discrimination of motion patterns [11, 12]. The psychophysical tasks, referred to as the graded motion pattern (GMP) and shifted center-of-motion (COM) tasks, are outlined in Fig. 1. Using a temporal two-alternative-forced-choice task we measured discrimination thresholds to global changes in the patterns of complex motion (GMP task), [13], and shifts in the center-of-motion (COM task). Stimuli were presented with central fixation using a constant stimulus paradigm and consisted of dynamic random dot displays presented in a 24o annular region (central 4o removed). In each task, the stimulus duration was randomly perturbed across presentations (440±40 msec) to control for timing-based cues, and dots moved coherently through a radial speed Figure 2: a) GMP thresholds across 8 'test' motions at two mean dot speeds for two observers. Performance varied continuously with thresholds for radial motions (φ=0, 180o) significantly lower than those for circular motions (φ=90,270o), (p<0.001; t(37)=3.39). b) COM thresholds at three mean dot speeds for two observers. As with the GMP task, performance varied continuously with thresholds for radial motions significantly lower than those for circular motions, (p<0.001; t(37)=4.47). gradient in directions consistent with the global motion pattern presented. Discrimination thresholds were obtained across eight ‘test’ motions corresponding to expansion, contraction, CW and CCW rotation, and the four intermediate spiral motions. To minimize adaptation to specific motion patterns, opposing motions (e.g., expansion/ contraction) were interleaved across paired presentations. 2.1 Results Discrimination thresholds are reported here from a subset of the observer population consisting of three experienced psychophysical observers, one of which was naïve to the purpose of the psychophysical tasks. For each condition, performance is reported as the mean and standard error averaged across 8-12 thresholds. Across observers and dot speeds GMP thresholds followed a distinct trend in the stimulus space [13], with radial motions (expansion/contraction) significantly lower than circular motions (CW/CCW rotation), (p<0.001; t(37)=3.39), (Fig. 2a). While thresholds for the intermediate spiral motions were not significantly different from circular motions (p=0.223, t(60)=0.74), the trends across 'test' motions were well fit within the stimulus space (SB: r>0.82, SC: r>0.77) by sinusoids whose period and phase were 196 ± 10o and -72 ± 20o respectively (Fig. 1a). When the radial speed gradient was removed by randomizing the spatial distribution of dot speeds, threshold performance increased significantly across observers (p<0.05; t(17)=1.91), particularly for circular motions (p<0.005; t(25)=3.31), (data not shown). Such performance suggests a perceptual contribution associated with the presence of the speed gradient and is particularly interesting given the fact that the speed gradient did not contribute computationally relevant information to the task. However, the speed gradient did convey information regarding the integrative structure of the global motion field and as such suggests a preference of the underlying motion mechanisms for spatially structured speed information. Similar trends in performance were observed in the COM task across observers and dot speeds. Discrimination thresholds varied continuously as a function of the 'test' motion with thresholds for radial motions significantly lower than those for circular motions, (p<0.001; t(37)=4.47) and could be well fit by a sinusoidal trend line (e.g. SB at 3 deg/s: r>0.91, period = 178 ± 10 o and phase = -70 ± 25o), (Fig. 2b). 2.2 A local or global task? The consistency of the cyclic threshold profile in stimuli that restricted the temporal integration of individual dot motions [13], and simultaneously contained all directions of motion, generally argues against a primary role for local motion mechanisms in the psychophysical tasks. While the psychophysical literature has reported a wide variety of “local” motion direction anisotropies whose properties are reminiscent of the results observed here, e.g. [14], all would predict equivalent thresholds for radial and circular motions for a set of uniformly distributed and/or spatially restricted motion direction mechanisms. Together with the computational impact of the speed gradient and psychophysical studies supporting the existence of wide-field motion pattern mechanisms [5, 6], these results suggest that the threshold differences across the GMP and COM tasks may be associated with variations in the computational properties across a series of specialized motion pattern mechanisms. 3 A computational model The similarities between the motion pattern stimuli used to quantify human perception and the visual motion properties of cells in MSTd suggests that MSTd may play a computational role in the psychophysical tasks. To examine this hypothesis, we constructed a population of MSTd-like units whose visual motion properties were consistent with the reported neurophysiology (see [13] for details). Across the population, the distribution of receptive field centers was uniform across polar angle and followed a gamma distribution Γ(5,6) across eccenticity [7]. For each unit, visual motion responses followed a gaussian tuning profile as a function of the stimulus flow angle G( φ), (σi=60±30o; [10]), and the distance of the stimulus COM from the unit’s receptive field center Gsat(xi, yi, σs=19o), Eq. 1, such that its preferred motion response was position invariant to small shifts in the COM [10] and degraded continuously for large shifts [9]. Within the model, simulations were categorized according to the distribution of preferred motions represented across the population (one reported in MSTd and a uniform control). The first distribution simulated an expansion bias in which the density of preferred motions decreased symmetrically from expansions to contraction [10]. The second distribution simulated a uniform preference for all motions and was used as a control to quantify the effects of an expansion bias on psychophysical performance. Throughout the paper we refer to simulations containing these distributions as ‘Expansion-biased’ and ‘Uniform’ respectively. 3.1 Extracting perceptual estimates from the neural code For each stimulus presentation, the ith unit’s response was calculated as the average firing rate, Ri, from the product of its motion pattern and spatial tuning profiles, ( ) Ri = Rmax G min[φ − φi ] ,σ ti G sati (x− xi , y − y i ,σ s ) + P (λ = 12 ) (1) where Rmax is the maximum preferred stimulus response (spikes/s), min[ ] refers to the minimum angular distance between the stimulus flow angle φ and the unit’s preferred motion φi, Gsat is the unit’s spatial tuning profile saturated within the central 5±3o, σti and σs are the standard deviations of the unit’s motion pattern and Figure 3: Model vs. psychophysical performance for independently responding units. Model thresholds are reported as the average (±1 S.E.) across five simulated populations. a) GMP thresholds were highest for contracting motions and lowest for expanding motions across all Expansion-biased populations. b) Comparable trends in performance were observed for COM thresholds. Comparison with the Uniform control simulations in both tasks (2000 units shown here) indicates that thresholds closely followed the distribution of preferred motions simulated within the model. spatial tuning profiles respectively, (xi,yi) is the spatial location of the unit’s receptive field center, (x,y) is the spatial location of the stimulus COM, and P(λ=12) is the background activity simulated as an uncorrelated Poisson process. The psychophysical tasks were simulated using a modified center-of-gravity ^ approach to decode estimates of the stimulus properties, i.e. flow angle (φ ) and ˆ ˆ COM location in the visual field (x, y ) , from the neural population   ∑ xi Ri ∑ y i Ri v  , i , ∑ φ i Ri  ∑ Ri i   i i   i (xˆ, yˆ , φˆ) =  i∑ R  (2) v where φi is the unit vector in the stimulus space (Fig. 1a) corresponding to the unit’s preferred motion. For each set of paired stimuli, psychophysical judgments were made by comparing the estimated stimulus properties according to the discrimination criteria, specified in the psychophysical tasks. As with the psychophysical experiments, discrimination thresholds were computed using a leastsquares fit to percent correct performance across constant stimulus levels. 3.2 Simulation 1: Independent neural responses In the first series of simulations, GMP and COM thresholds were quantified across three populations (500, 1000, and 2000 units) of independently responding units for each simulated distribution (Expansion-biased and Uniform). Across simulations, both the range in thresholds and their trends across ‘test’ motions were compared with human psychophysical performance to quantify the effects of population size and an expansion biased preferred motion distribution on model performance. Over the psychophysical range of interest (φp ± 7o), GMP thresholds for contracting motions were at chance across all Expansion-biased populations, (Fig. 3a). While thresholds for expanding motions were generally consistent with those for human observers, those for circular motions remained significantly higher for all but the largest populations. Similar trends in performance were observed for the COM task, (Fig. 3b). Here the range of COM thresholds was well matched with human performance for simulations containing 1000 units, however, the trends across motion patterns remained inconsistent even for the largest populations. Figure 4: Proposed recurrent connection profile between motion pattern units. a) Across the motion pattern space connection strength followed an inverse gaussian profile such that the ith unit (with preferred motion φi) systematically inhibited units with anti-preferred motions centered at 180+φi. b) Across the visual field connection strength followed a difference-of-gaussians profile as a function of the relative distance between receptive field centers such that spatially local units are mutually excitatory (σRe=10o) and more distant units were mutually inhibitory (σRi=80o). For simulations containing a uniform distribution of preferred motions, the threshold range was consistent with human performance on both tasks, however, the trend across motion patterns was generally flat. What variability did occur was due primarily to the discrete sampling of preferred motions across the population. Comparison of the discrimination thresholds for the Expansion-biased and Uniform populations indicates that the trend across thresholds was closely matched to the underlying distributions of preferred motions. This result in due in part to the nearequal weighting of independently responding units and can be explained to a first approximation by the proportional increase in the signal-to-noise ratio across the population as a function of the density of units responsive to a given 'test' motion. 3.3 Simulation 2: An interconnected neural structure In a second series of simulations, we examined the computational effect of adding recurrent connections between units. If the distribution of preferred motions in MSTd is in fact biased towards expansions, as the neurophysiology suggests, it seems unlikely that independent estimates of the visual motion information would be sufficient to yield the threshold profiles observed in the psychophysical tasks. We hypothesize that a simple fixed architecture of excitatory and/or inhibitory connections is sufficient to account for the cyclic trends in discrimination thresholds. Specifically, we propose that a recurrent connection profile whose strength varies as a function of (a) the similarity between preferred motion patterns and (b) the distance between receptive field centers, is computationally sufficient to recover the trends in GMP/COM performance (Fig. 4), wij = S R e − ( xi − x j )2 + ( yi − y j )2 2 2σ R e − SR e 2 − −(min[ φi − φ j ])2 ( xi − x j )2 + ( yi − y j )2 2 2 σ Ri − Sφ e 2σ I2 (3) Figure 5: Model vs. psychophysical performance for populations containing recurrent connections (σI=80o). As the number of units increased for Expansionbiased populations, discrimination thresholds decreased to psychophysical levels and the sinusoidal trend in thresholds emerged for both the (a) GMP and (b) COM tasks. Sinusoidal trends were established for as few as 1000 units and were well fit (r>0.9) by sinusoids whose periods and phases were (193.8 ± 11.7o, -70.0 ± 22.6o) and (168.2 ± 13.7o, -118.8 ± 31.8o) for the GMP and COM tasks respectively. where wij is the strength of the recurrent connection between ith and jth units, (xi,yi) and (xj,yj) denote the spatial locations of their receptive field centers, σRe (=10o) and σRi (=80o) together define the spatial extent of a difference-of-gaussians interaction between receptive field centers, and SR and Sφ scale the connection strength. To examine the effects of the spread of motion pattern-specific inhibition and connection strength in the model, σI, Sφ, and SR were considered free parameters. Within the parameter space used to define recurrent connections (i.e., σI, Sφ and SR), Monte Carlo simulations of Expansion-biased model performance (1000 units) yielded regions of high correlation on both tasks (with respect to the psychophysical thresholds, r>0.7) that were consistent across independently simulated populations. Typically these regions were well defined over a broad range such that there was significant overlap between tasks (e.g., for the GMP task (SR=0.03), σI=[45,120o], Sφ=[0.03,0.3] and for the COM task (σI=80o), Sφ = [0.03,0.08], SR = [0.005, 0.04]). Fig. 5 shows averaged threshold performance for simulations of interconnected units drawn from the highly correlated regions of the (σI, Sφ, SR) parameter space. For populations not explicitly examined in the Monte Carlo simulations connection strengths (Sφ, SR) were scaled inversely with population size to maintain an equivalent level of recurrent activity. With the incorporation of recurrent connections, the sinusoidal trend in GMP and COM thresholds emerged for Expansion-biased populations as the number of units increased. In both tasks the cyclic threshold profiles were established for 1000 units and were well fit (r>0.9) by sinusoids whose periods and phases were consistent with human performance. Unlike the Expansion-biased populations, Uniform populations were not significantly affected by the presence of recurrent connections (Fig. 5). Both the range in thresholds and the flat trend across motion patterns were well matched to those in Section 3.2. Together these results suggest that the sinusoidal trends in GMP and COM performance may be mediated by the combined contribution of the recurrent interconnections and the bias in preferred motions across the population. 4 D i s c u s s i on Using a biologically constrained computational model in conjunction with human psychophysical performance on two motion pattern tasks we have shown that the visual motion information encoded across an interconnected population of cells responsive to motion patterns, such as those in MSTd, is computationally sufficient to extract perceptual estimates consistent with human performance. Specifically, we have shown that the cyclic trend in psychophysical performance observed across tasks, (a) cannot be reproduced using populations of independently responding units and (b) is dependent, in part, on the presence of an expanding motion bias in the distribution of preferred motions across the neural population. The model’s performance suggests the presence of specific recurrent structures within motion pattern responsive areas, such as MSTd, whose strength varies as a function of the similarity between preferred motion patterns and the distance between receptive field centers. While such structures have not been explicitly examined in MSTd and other higher visual motion areas there is anecdotal support for the presence of inhibitory connections [8]. Together, these results suggest that robust processing of the motion patterns associated with self-motion and optic flow may be mediated, in part, by recurrent structures in extrastriate visual motion areas whose distributions of preferred motions are biased strongly in favor of expanding motions. Acknowledgments This work was supported by National Institutes of Health grant EY-2R01-07861-13 to L.M.V. References [1] Malach, R., Schirman, T., Harel, M., Tootell, R., & Malonek, D., (1997), Cerebral Cortex, 7(4): 386-393. [2] Gilbert, C. D., (1992), Neuron, 9: 1-13. [3] Koechlin, E., Anton, J., & Burnod, Y., (1999), Biological Cybernetics, 80: 2544. [4] Stemmler, M., Usher, M., & Niebur, E., (1995), Science, 269: 1877-1880. [5] Burr, D. C., Morrone, M. C., & Vaina, L. M., (1998), Vision Research, 38(12): 1731-1743. [6] Meese, T. S. & Harris, S. J., (2002), Vision Research, 42: 1073-1080. [7] Tanaka, K. & Saito, H. A., (1989), Journal of Neurophysiology, 62(3): 626-641. [8] Duffy, C. J. & Wurtz, R. H., (1991), Journal of Neurophysiology, 65(6): 13461359. [9] Duffy, C. J. & Wurtz, R. H., (1995), Journal of Neuroscience, 15(7): 5192-5208. [10] Graziano, M. S., Anderson, R. A., & Snowden, R., (1994), Journal of Neuroscience, 14(1): 54-67. [11] Celebrini, S. & Newsome, W., (1994), Journal of Neuroscience, 14(7): 41094124. [12] Celebrini, S. & Newsome, W. T., (1995), Journal of Neurophysiology, 73(2): 437-448. [13] Beardsley, S. A. & Vaina, L. M., (2001), Journal of Computational Neuroscience, 10: 255-280. [14] Matthews, N. & Qian, N., (1999), Vision Research, 39: 2205-2211.

Reference: text

Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 edu Abstract Psychophysical studies suggest the existence of specialized detectors for component motion patterns (radial, circular, and spiral), that are consistent with the visual motion properties of cells in the dorsal medial superior temporal area (MSTd) of non-human primates. [sent-7, score-1.256]

2 Here we use a biologically constrained model of visual motion processing in MSTd, in conjunction with psychophysical performance on two motion pattern tasks, to elucidate the computational mechanisms associated with the processing of widefield motion patterns encountered during self-motion. [sent-8, score-2.018]

3 In both tasks discrimination thresholds varied significantly with the type of motion pattern presented, suggesting perceptual correlates to the preferred motion bias reported in MSTd. [sent-9, score-1.782]

4 These results suggest the cyclic trends in psychophysical performance may be mediated, in part, by recurrent connections within motion pattern responsive areas whose structure is a function of the similarity in preferred motion patterns and receptive field locations between units. [sent-11, score-2.109]

5 1 In trod u ction A major challenge in computational neuroscience is to elucidate the architecture of the cortical circuits for sensory processing and their effective role in mediating behavior. [sent-12, score-0.087]

6 In the visual motion system, biologically constrained models are playing an increasingly important role in this endeavor by providing an explanatory substrate linking perceptual performance and the visual properties of single cells. [sent-13, score-0.794]

7 Single cell studies indicate the presence of complex interconnected structures in middle temporal and primary visual cortex whose most basic horizontal connections can impart considerable computational power to the underlying neural population [1, 2]. [sent-14, score-0.343]

8 Combined psychophysical and computational studies support these findings Figure 1: a) Schematic of the graded motion pattern (GMP) task. [sent-15, score-0.878]

9 Discrimination pairs of stimuli were created by perturbing the flow angle (φ) of each 'test' motion (with average dot speed, vav), by ±φp in the stimulus space spanned by radial and circular motions. [sent-16, score-0.931]

10 Discrimination pairs of stimuli were created by shifting the COM of the ‘test’ motion to the left and right of a central fixation point. [sent-18, score-0.525]

11 For each motion pattern the COM was shifted within the illusory inner aperture and was never explicitly visible. [sent-19, score-0.508]

12 and suggest that recurrent connections may play a significant role in encoding the visual motion properties associated with various psychophysical tasks [3, 4]. [sent-20, score-1.2]

13 Using this methodology our goal is to elucidate the computational mechanisms associated with the processing of wide-field motion patterns encountered during self-motion. [sent-21, score-0.589]

14 In the human visual motion system, psychophysical studies suggest the existence of specialized detectors for the motion pattern components (i. [sent-22, score-1.515]

15 , radial, circular and spiral motions) associated with self-motion [5, 6]. [sent-24, score-0.167]

16 Through the combination of human psychophysical performance and biologically constrained modeling we investigate the computational role of simple recurrent connections within a population of MSTd-like units. [sent-26, score-0.707]

17 Based on the known visual motion properties within MSTd we ask what neural structures are computationally sufficient to encode psychophysical performance on a series of motion pattern tasks. [sent-27, score-1.476]

18 The psychophysical tasks, referred to as the graded motion pattern (GMP) and shifted center-of-motion (COM) tasks, are outlined in Fig. [sent-29, score-0.843]

19 Using a temporal two-alternative-forced-choice task we measured discrimination thresholds to global changes in the patterns of complex motion (GMP task), [13], and shifts in the center-of-motion (COM task). [sent-31, score-0.872]

20 Stimuli were presented with central fixation using a constant stimulus paradigm and consisted of dynamic random dot displays presented in a 24o annular region (central 4o removed). [sent-32, score-0.177]

21 In each task, the stimulus duration was randomly perturbed across presentations (440±40 msec) to control for timing-based cues, and dots moved coherently through a radial speed Figure 2: a) GMP thresholds across 8 'test' motions at two mean dot speeds for two observers. [sent-33, score-1.142]

22 Performance varied continuously with thresholds for radial motions (φ=0, 180o) significantly lower than those for circular motions (φ=90,270o), (p<0. [sent-34, score-1.274]

23 b) COM thresholds at three mean dot speeds for two observers. [sent-37, score-0.347]

24 As with the GMP task, performance varied continuously with thresholds for radial motions significantly lower than those for circular motions, (p<0. [sent-38, score-0.972]

25 gradient in directions consistent with the global motion pattern presented. [sent-41, score-0.538]

26 Discrimination thresholds were obtained across eight ‘test’ motions corresponding to expansion, contraction, CW and CCW rotation, and the four intermediate spiral motions. [sent-42, score-0.757]

27 To minimize adaptation to specific motion patterns, opposing motions (e. [sent-43, score-0.796]

28 1 Results Discrimination thresholds are reported here from a subset of the observer population consisting of three experienced psychophysical observers, one of which was naïve to the purpose of the psychophysical tasks. [sent-47, score-0.961]

29 For each condition, performance is reported as the mean and standard error averaged across 8-12 thresholds. [sent-48, score-0.195]

30 Across observers and dot speeds GMP thresholds followed a distinct trend in the stimulus space [13], with radial motions (expansion/contraction) significantly lower than circular motions (CW/CCW rotation), (p<0. [sent-49, score-1.566]

31 While thresholds for the intermediate spiral motions were not significantly different from circular motions (p=0. [sent-53, score-1.183]

32 74), the trends across 'test' motions were well fit within the stimulus space (SB: r>0. [sent-55, score-0.698]

33 77) by sinusoids whose period and phase were 196 ± 10o and -72 ± 20o respectively (Fig. [sent-57, score-0.037]

34 When the radial speed gradient was removed by randomizing the spatial distribution of dot speeds, threshold performance increased significantly across observers (p<0. [sent-59, score-0.554]

35 Such performance suggests a perceptual contribution associated with the presence of the speed gradient and is particularly interesting given the fact that the speed gradient did not contribute computationally relevant information to the task. [sent-64, score-0.198]

36 However, the speed gradient did convey information regarding the integrative structure of the global motion field and as such suggests a preference of the underlying motion mechanisms for spatially structured speed information. [sent-65, score-1.157]

37 Similar trends in performance were observed in the COM task across observers and dot speeds. [sent-66, score-0.373]

38 Discrimination thresholds varied continuously as a function of the 'test' motion with thresholds for radial motions significantly lower than those for circular motions, (p<0. [sent-67, score-1.634]

39 47) and could be well fit by a sinusoidal trend line (e. [sent-69, score-0.189]

40 The consistency of the cyclic threshold profile in stimuli that restricted the temporal integration of individual dot motions [13], and simultaneously contained all directions of motion, generally argues against a primary role for local motion mechanisms in the psychophysical tasks. [sent-76, score-1.415]

41 While the psychophysical literature has reported a wide variety of “local” motion direction anisotropies whose properties are reminiscent of the results observed here, e. [sent-77, score-0.827]

42 [14], all would predict equivalent thresholds for radial and circular motions for a set of uniformly distributed and/or spatially restricted motion direction mechanisms. [sent-79, score-1.26]

43 3 A computational model The similarities between the motion pattern stimuli used to quantify human perception and the visual motion properties of cells in MSTd suggests that MSTd may play a computational role in the psychophysical tasks. [sent-81, score-1.493]

44 To examine this hypothesis, we constructed a population of MSTd-like units whose visual motion properties were consistent with the reported neurophysiology (see [13] for details). [sent-82, score-0.849]

45 Across the population, the distribution of receptive field centers was uniform across polar angle and followed a gamma distribution Γ(5,6) across eccenticity [7]. [sent-83, score-0.547]

46 For each unit, visual motion responses followed a gaussian tuning profile as a function of the stimulus flow angle G( φ), (σi=60±30o; [10]), and the distance of the stimulus COM from the unit’s receptive field center Gsat(xi, yi, σs=19o), Eq. [sent-84, score-1.093]

47 1, such that its preferred motion response was position invariant to small shifts in the COM [10] and degraded continuously for large shifts [9]. [sent-85, score-0.653]

48 Within the model, simulations were categorized according to the distribution of preferred motions represented across the population (one reported in MSTd and a uniform control). [sent-86, score-0.818]

49 The first distribution simulated an expansion bias in which the density of preferred motions decreased symmetrically from expansions to contraction [10]. [sent-87, score-0.636]

50 The second distribution simulated a uniform preference for all motions and was used as a control to quantify the effects of an expansion bias on psychophysical performance. [sent-88, score-0.78]

51 Throughout the paper we refer to simulations containing these distributions as ‘Expansion-biased’ and ‘Uniform’ respectively. [sent-89, score-0.06]

52 Model thresholds are reported as the average (±1 S. [sent-93, score-0.277]

53 a) GMP thresholds were highest for contracting motions and lowest for expanding motions across all Expansion-biased populations. [sent-96, score-1.11]

54 b) Comparable trends in performance were observed for COM thresholds. [sent-97, score-0.13]

55 Comparison with the Uniform control simulations in both tasks (2000 units shown here) indicates that thresholds closely followed the distribution of preferred motions simulated within the model. [sent-98, score-1.066]

56 spatial tuning profiles respectively, (xi,yi) is the spatial location of the unit’s receptive field center, (x,y) is the spatial location of the stimulus COM, and P(λ=12) is the background activity simulated as an uncorrelated Poisson process. [sent-99, score-0.477]

57 The psychophysical tasks were simulated using a modified center-of-gravity ^ approach to decode estimates of the stimulus properties, i. [sent-100, score-0.517]

58 flow angle (φ ) and ˆ ˆ COM location in the visual field (x, y ) , from the neural population   ∑ xi Ri ∑ y i Ri v  , i , ∑ φ i Ri  ∑ Ri i   i i   i (xˆ, yˆ , φˆ) =  i∑ R  (2) v where φi is the unit vector in the stimulus space (Fig. [sent-102, score-0.454]

59 For each set of paired stimuli, psychophysical judgments were made by comparing the estimated stimulus properties according to the discrimination criteria, specified in the psychophysical tasks. [sent-104, score-0.846]

60 As with the psychophysical experiments, discrimination thresholds were computed using a leastsquares fit to percent correct performance across constant stimulus levels. [sent-105, score-0.968]

61 2 Simulation 1: Independent neural responses In the first series of simulations, GMP and COM thresholds were quantified across three populations (500, 1000, and 2000 units) of independently responding units for each simulated distribution (Expansion-biased and Uniform). [sent-107, score-0.71]

62 Across simulations, both the range in thresholds and their trends across ‘test’ motions were compared with human psychophysical performance to quantify the effects of population size and an expansion biased preferred motion distribution on model performance. [sent-108, score-1.895]

63 Over the psychophysical range of interest (φp ± 7o), GMP thresholds for contracting motions were at chance across all Expansion-biased populations, (Fig. [sent-109, score-1.05]

64 While thresholds for expanding motions were generally consistent with those for human observers, those for circular motions remained significantly higher for all but the largest populations. [sent-111, score-1.235]

65 Similar trends in performance were observed for the COM task, (Fig. [sent-112, score-0.13]

66 Here the range of COM thresholds was well matched with human performance for simulations containing 1000 units, however, the trends across motion patterns remained inconsistent even for the largest populations. [sent-114, score-1.142]

67 Figure 4: Proposed recurrent connection profile between motion pattern units. [sent-115, score-0.752]

68 a) Across the motion pattern space connection strength followed an inverse gaussian profile such that the ith unit (with preferred motion φi) systematically inhibited units with anti-preferred motions centered at 180+φi. [sent-116, score-1.794]

69 b) Across the visual field connection strength followed a difference-of-gaussians profile as a function of the relative distance between receptive field centers such that spatially local units are mutually excitatory (σRe=10o) and more distant units were mutually inhibitory (σRi=80o). [sent-117, score-0.811]

70 For simulations containing a uniform distribution of preferred motions, the threshold range was consistent with human performance on both tasks, however, the trend across motion patterns was generally flat. [sent-118, score-1.112]

71 What variability did occur was due primarily to the discrete sampling of preferred motions across the population. [sent-119, score-0.627]

72 Comparison of the discrimination thresholds for the Expansion-biased and Uniform populations indicates that the trend across thresholds was closely matched to the underlying distributions of preferred motions. [sent-120, score-1.099]

73 This result in due in part to the nearequal weighting of independently responding units and can be explained to a first approximation by the proportional increase in the signal-to-noise ratio across the population as a function of the density of units responsive to a given 'test' motion. [sent-121, score-0.539]

74 3 Simulation 2: An interconnected neural structure In a second series of simulations, we examined the computational effect of adding recurrent connections between units. [sent-123, score-0.262]

75 If the distribution of preferred motions in MSTd is in fact biased towards expansions, as the neurophysiology suggests, it seems unlikely that independent estimates of the visual motion information would be sufficient to yield the threshold profiles observed in the psychophysical tasks. [sent-124, score-1.522]

76 We hypothesize that a simple fixed architecture of excitatory and/or inhibitory connections is sufficient to account for the cyclic trends in discrimination thresholds. [sent-125, score-0.364]

77 Specifically, we propose that a recurrent connection profile whose strength varies as a function of (a) the similarity between preferred motion patterns and (b) the distance between receptive field centers, is computationally sufficient to recover the trends in GMP/COM performance (Fig. [sent-126, score-1.304]

78 As the number of units increased for Expansionbiased populations, discrimination thresholds decreased to psychophysical levels and the sinusoidal trend in thresholds emerged for both the (a) GMP and (b) COM tasks. [sent-129, score-1.179]

79 Sinusoidal trends were established for as few as 1000 units and were well fit (r>0. [sent-130, score-0.258]

80 To examine the effects of the spread of motion pattern-specific inhibition and connection strength in the model, σI, Sφ, and SR were considered free parameters. [sent-141, score-0.531]

81 Within the parameter space used to define recurrent connections (i. [sent-142, score-0.219]

82 , σI, Sφ and SR), Monte Carlo simulations of Expansion-biased model performance (1000 units) yielded regions of high correlation on both tasks (with respect to the psychophysical thresholds, r>0. [sent-144, score-0.484]

83 Typically these regions were well defined over a broad range such that there was significant overlap between tasks (e. [sent-146, score-0.075]

84 5 shows averaged threshold performance for simulations of interconnected units drawn from the highly correlated regions of the (σI, Sφ, SR) parameter space. [sent-157, score-0.301]

85 For populations not explicitly examined in the Monte Carlo simulations connection strengths (Sφ, SR) were scaled inversely with population size to maintain an equivalent level of recurrent activity. [sent-158, score-0.403]

86 With the incorporation of recurrent connections, the sinusoidal trend in GMP and COM thresholds emerged for Expansion-biased populations as the number of units increased. [sent-159, score-0.753]

87 In both tasks the cyclic threshold profiles were established for 1000 units and were well fit (r>0. [sent-160, score-0.35]

88 9) by sinusoids whose periods and phases were consistent with human performance. [sent-161, score-0.107]

89 Unlike the Expansion-biased populations, Uniform populations were not significantly affected by the presence of recurrent connections (Fig. [sent-162, score-0.427]

90 Both the range in thresholds and the flat trend across motion patterns were well matched to those in Section 3. [sent-164, score-0.99]

91 Together these results suggest that the sinusoidal trends in GMP and COM performance may be mediated by the combined contribution of the recurrent interconnections and the bias in preferred motions across the population. [sent-166, score-1.021]

92 The model’s performance suggests the presence of specific recurrent structures within motion pattern responsive areas, such as MSTd, whose strength varies as a function of the similarity between preferred motion patterns and the distance between receptive field centers. [sent-169, score-1.63]

93 While such structures have not been explicitly examined in MSTd and other higher visual motion areas there is anecdotal support for the presence of inhibitory connections [8]. [sent-170, score-0.635]

94 Together, these results suggest that robust processing of the motion patterns associated with self-motion and optic flow may be mediated, in part, by recurrent structures in extrastriate visual motion areas whose distributions of preferred motions are biased strongly in favor of expanding motions. [sent-171, score-1.801]

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Stimuli were sequences from Walt Disney’s “Tarzan”. From Mante et al. (2002). The linear model, however, suffers from limitations. For example, consider the response of an LGN neuron to a complex dynamic video sequences (Figure 1). The response is characterized by long periods of relative silence interspersed with brief events of high firing rate (Figure 1, thick traces). The linear model (Figure 1, thin traces) successfully predicts the timing of these firing events but fails to account for their magnitude (Mante et al., 2002). The limitations of the linear model are not surprising since there is ample evidence that LGN responses are nonlinear. For instance, responses to drifting gratings saturate as contrast is increased (Sclar et al., 1990) and are reduced, or masked, by superposition of a second grating (Bonin et al., 2002). 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Here we show that a single model with fixed parameters predicts responses to a broad range of stimuli. 2 Mod el In the model (Figure 2), the linear response of the receptive field L(t) is divided by the output of the suppressive field. The latter is a measure of local root-mean-square contrast c local. The result of the division is a generator potential V (t ) = Vmax L (t ) c50 + clocal , where c 50 is a constant. F(x,t) Stimulus S(x,t) V0 L(t) Receptive Field R(t) Firing rate Rectification H(x,t) S*(x,t) c50 clocal Suppressive Field Filter Figure 2. Nonlinear model of LGN responses. The suppressive field operates on a filtered version of the stimulus, S*=S*H, where H is a linear filter and * denotes convolution. The squared output of the suppressive field is the local mean square (the local variance) of the filtered stimulus: clocal = S ( x, t ) G ( x ) dx dt , 2 * 2 ∫∫ where G(x) is a 2-dimensional Gaussian. Firing rate is a rectified version of generator potential, with threshold V thresh:   R(t ) = V (t ) − Vthresh + .   To test the nonlinear model, we recorded responses from neurons in the LGN of anesthetized paralyzed cats. Methods for these recordings were described elsewhere (Freeman et al., 2002). 3 Resu l t s We proceed in two steps: first we estimate model parameters by fitting the model to a large set of canonical data; second we fix model parameters and evaluate the model by predicting responses to a novel set of stimuli. B 60 40 20 0 0.01 0.2 4 Spatial Frequency (cpd) Response (spikes/s) Response (spikes/s) A 80 60 40 20 0 0.5 5 50 Temporal Frequency (Hz) Figure 3. Estimating the receptive field in an example LGN cell. Stimuli are gratings varying in spatial (A) and temporal (B) frequency. Responses are the harmonic component of spike trains at the grating temporal frequency. Error bars represent standard deviation of responses. Curves indicate model fit. Response (spikes/s) 0.25 0.50 0.75 Test contrast 100 80 60 40 20 0 1.00 100 D 80 60 40 20 0 0.5 Response (spikes/s) 50 0 C B 100 Response (spikes/s) Response (spikes/s) A 0.25 0.50 0.75 1.00 Mask contrast 100 80 60 40 20 4.0 32.0 Mask diameter (deg) 0 0.01 0.20 4.00 Mask spatial frequency (cpd) Figure 4. Estimating the suppressive field in the example LGN cell. Stimuli are sums of a test grating and a mask grating. Responses are the harmonic component of spike trains at the temporal frequency of test. A: Responses to test alone. B-D: Responses to test+mask as function of three mask attributes: contrast (B), diameter (C) and spatial frequency (D). Gray areas indicate baseline response (test alone, 50% contrast). Dashed curves are predictions of linear model. Solid curves indicate fit of nonlinear model. 3.1 C h a r a c te r i z i n g t he r e c e p ti v e fi e l d We obtain the parameters of the receptive field F(x,t) from responses to large drifting gratings (Figure 3). These stimuli elicit approximately constant output in the suppressive field, so they allow us to characterize the receptive field. Responses to different spatial frequencies constrain F(x,t) in space (Figure 3A). Responses to different temporal frequencies constrain F(x,t) in time (Figure 3B). 3.2 C h a r a c te r i z i n g t he s u p p r e s s i v e f i e l d To characterize the divisive stage, we start by measuring how responses saturate at high contrast (Figure 4A). A linear model cannot account for this contrast saturation (Figure 4A, dashed curve). The nonlinear model (Figure 4A, solid curve) captures saturation because increases in receptive field output are attenuated by increases in suppressive field output. At low contrast, no saturation is observed because the output of the suppressive field is dominated by the constant c 50. From these data we estimate the value of c50. To obtain the parameters of the suppressive field, we recorded responses to sums of two drifting gratings (Figure 4B-D): an optimal test grating at 50% contrast, which elicits a large baseline response, and a mask grating that modulates this response. Test and mask temporal frequencies are incommensurate so that they temporally label a test response (at the frequency of the test) and a mask response (at the frequency of the mask) (Bonds, 1989). We vary mask attributes and study how they affect the test responses. Increasing mask contrast progressively suppresses responses (Figure 4B). The linear model fails to account for this suppression (Figure 4B, dashed curve). The nonlinear model (Figure 4B, solid curve) captures it because increasing mask contrast increases the suppressive field output while the receptive field output (at the temporal frequency of the test) remains constant. With masks of low contrast there is little suppression because the output of the suppressive field is dominated by the constant c 50 . Similar effects are seen if we increase mask diameter. Responses decrease until they reach a plateau (Figure 4C). A linear model predicts no decrease (Figure 4C, dashed curve). The nonlinear model (Figure 4C, solid curve) captures it because increasing mask diameter increases the suppressive field output while it does not affect the receptive field output. A plateau is reached once masks extend beyond the suppressive field. From these data we estimate the size of the Gaussian envelope G(x) of the suppressive field. Finally, the strength of suppression depends on mask spatial frequency (Figure 4D). At high frequencies, no suppression is elicited. Reducing spatial frequency increases suppression. This dependence of suppression on spatial frequency is captured in the nonlinear model by the filter H(x,t). From these data we estimate the spatial characteristics of the filter. From similar experiments involving different temporal frequencies (not shown), we estimate the filter’s selectivity for temporal frequency. 3.3 P r e d i c ti n g r e s p o n s e s t o n o v e l s ti m u l i We have seen that with a fixed set of parameters the model provides a good fit to a large set of measurements (Figure 3 and Figure 4). We now test whether the model predicts responses to a set of novel stimuli: drifting gratings varying in contrast and diameter. Responses to high contrast stimuli exhibit size tuning (Figure 5A, squares): they grow with size for small diameters, reach a maximum value at intermediate diameter and are reduced for large diameters (Jones and Sillito, 1991). Size tuning , however, strongly depends on stimulus contrast (Solomon et al., 2002): no size tuning is observed at low contrast (Figure 5A, circles). The model predicts these effects (Figure 5A, curves). For large, high contrast stimuli the output of the suppressive field is dominated by c local, resulting in suppression of responses. At low contrast, c local is much smaller than c50, and the suppressive field does not affect responses. Similar considerations can be made by plotting these data as a function of contrast (Figure 5B). As predicted by the nonlinear model (Figure 5B, curves), the effect of increasing contrast depends on stimulus size: responses to large stimuli show strong saturation (Figure 5B, squares), whereas responses to small stimuli grow linearly (Figure 5B, circles). The model predicts these effects because only large, high contrast stimuli elicit large enough responses from the suppressive field to cause suppression. For small, low contrast stimuli, instead, the linear model is a good approximation. B 100 Response (spikes/s) A 80 60 40 20 0 0.50 4.00 32.00 Diameter (deg) 0.00 0.25 0.50 0.75 1.00 Contrast Figure 5. Predicting responses to novel stimuli in the example LGN cell. Stimuli are gratings varying in diameter and contrast, and responses are harmonic component of spike trains at grating temporal frequency. Curves show model predictions based on parameters as estimated in previous figures, not fitted to these data. A: Responses as function of diameter for different contrasts. B: Responses as function of contrast for different diameters. 3.4 M o d e l pe r f or m a nc e To assess model performance across neurons we calculate the percentage of variance in the data that is explained by the model (see Freeman et al., 2002 for methods). The model provides good fits to the data used to characterize the suppressive field (Figure 4), explaining more than 90% of the variance in the data for 9/13 cells (Figure 6A). Model parameters are then held fixed, and the model is used to predict responses to gratings of different contrast and diameter (Figure 5). The model performs well, explaining in 10/13 neurons above 90% of the variance in these novel data (Figure 6B, shaded histogram). The agreement between the quality of the fits and the quality of the predictions suggests that model parameters are well constrained and rules out a role of overfitting in determining the quality of the fits. To further confirm the performance of the model, in an additional 54 cells we ran a subset of the whole protocol, involving only the experiment for characterizing the receptive field (Figure 3), and the experiment involving gratings of different contrast and diameter (Figure 5). For these cells we estimate the suppressive field by fitting the model directly to the latter measurements. The model explains above 90% of the variance in these data in 20/54 neurons and more than 70% in 39/54 neurons (Figure 6B, white histogram). Considering the large size of the data set (more than 100 stimuli, requiring several hours of recordings per neuron) and the small number of free parameters (only 6 for the purpose of this work), the overall, quality of the model predictions is remarkable. Estimating the suppressive field A # cells 6 n=13 4 2 0 Size tuning at different contrasts 15 n=54 10 # cells B 5 0 0 50 100 Explained variance (%) Figure 6. Percentage of variance in data explained by model. A: Experiments to estimate the suppressive field. B: Experiments to test the model. Gray histogram shows quality of predictions. White histogram shows quality of fits. 4 Co n cl u si o n s The nonlinear model provides a unified description of visual processing in LGN neurons. Based on a fixed set of parameters, it can predict both linear properties (Figure 3), as well as nonlinear properties such as contrast saturation (Figure 4A) and masking (Figure 4B-D). Moreover, once the parameters are fixed, it predicts responses to novel stimuli (Figure 5). The model explains why responses are tuned for stimulus size at high contrast but not at low contrast, and it correctly predicts that only responses to large stimuli saturate with contrast, while responses to small stimuli grow linearly. The model implements a form of contrast gain control. A possible purpose for this gain control is to increase the range of contrast that can be transmitted given the limited dynamic range of single neurons. Divisive gain control may also play a role in population coding: a similar model applied to responses of primary visual cortex was shown to maximize independence of the responses across neurons (Schwartz and Simoncelli, 2001). We are working towards improving the model in two ways. First, we are characterizing the dynamics of the suppressive field, e.g. to predict how it responds to transient stimuli. Second, we are testing the assumption that the suppressive field computes root-mean-square contrast, a measure that solely depends on the secondorder moments of the light distribution. Our ultimate goal is to predict responses to complex stimuli such as those shown in Figure 1 and quantify to what degree the nonlinear model improves on the predictions of the linear model. Determining the role of visual nonlinearities under more natural stimulation conditions is also critical to understanding their function. The nonlinear model synthesizes more than 30 years of research. It is robust, tractable and generalizes to arbitrary stimuli. As a result it might serve as the new standard model of LGN responses. Because the nonlinearities we discussed are already present in the retina (Shapley and Victor, 1978), and tend to get stronger as one ascends the visual hierarchy (Sclar et al., 1990), it may also be used to study how responses take shape from one stage to another in the visual system. A c k n o w l e d g me n t s This work was supported by the Swiss National Science Foundation and by the James S McDonnell Foundation 21st Century Research Award in Bridging Brain, Mind & Behavior. References Bonds, A. B. (1989). Role of inhibition in the specification of orientation selectivity of cells in the cat striate cortex. Vis Neurosci 2, 41-55. Bonin, V., Mante, V., and Carandini, M. (2002). The contrast integration field of cat LGN neurons. Program No. 352.16. In Abstract Viewer/Itinerary Planner (Washington, DC, Society for Neuroscience). Cai, D., DeAngelis, G. C., and Freeman, R. D. (1997). Spatiotemporal receptive field organization in the lateral geniculate nucleus of cats and kittens. J Neurophysiol 78, 10451061. Cavanaugh, J. R., Bair, W., and Movshon, J. A. (2002). Selectivity and spatial distribution of signals from the receptive field surround in macaque v1 neurons. J Neurophysiol 88, 25472556. Cleland, B. G., Lee, B. B., and Vidyasagar, T. R. (1983). Response of neurons in the cat's lateral geniculate nucleus to moving bars of different length. J Neurosci 3, 108-116. Dan, Y., Atick, J. J., and Reid, R. C. (1996). Efficient coding of natural scenes in the lateral geniculate nucleus: experimental test of a computational theory. J Neurosci 16, 3351-3362. Enroth-Cugell, C., and Robson, J. G. (1966). The contrast sensitivity of retinal ganglion cells of the cat. J Physiol (Lond) 187, 517-552. Freeman, T., Durand, S., Kiper, D., and Carandini, M. (2002). Suppression without Inhibition in Visual Cortex. Neuron 35, 759. Heeger, D. J. (1992). Normalization of cell responses in cat striate cortex. Vis Neurosci 9, 181-197. Hubel, D., and Wiesel, T. N. (1961). Integrative action in the cat's lateral geniculate body. J Physiol (Lond) 155, 385-398. Jones, H. E., and Sillito, A. M. (1991). The length-response properties of cells in the feline dorsal lateral geniculate nucleus. J Physiol (Lond) 444, 329-348. Levick, W. R., Cleland, B. G., and Dubin, M. W. (1972). Lateral geniculate neurons of cat: retinal inputs and physiology. Invest Ophthalmol 11, 302-311. Mante, V., Bonin, V., and Carandini, M. (2002). Responses of cat LGN neurons to plaids and movies. Program No. 352.15. In Abstract Viewer/Itinerary Planner (Washington, DC, Society for Neuroscience). Rodieck, R. W. (1965). Quantitative analysis of cat retina ganglion cell response to visual stimuli. Vision Res 5, 583-601. Schwartz, O., and Simoncelli, E. P. (2001). Natural signal statistics and sensory gain control. Nat Neurosci 4, 819-825. Sclar, G., Maunsell, J. H. R., and Lennie, P. (1990). Coding of image contrast in central visual pathways of the macaque monkey. Vision Res 30, 1-10. Shapley, R. M., and Victor, J. D. (1978). The effect of contrast on the transfer properties of cat retinal ganglion cells. J Physiol 285, 275-298. Solomon, S. G., White, A. J., and Martin, P. R. (2002). 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Elevated charge levels activate a KCa-like current that throttles the spike-rate of the neuron. 3.2 Experimental Setup Our setup uses either a silicon retina [8] or a National Instruments DIO (digital input–output) card as input to the bump chip. This allows us to test our V1 model with real-time visual stimuli, similar to the experimental paradigm of electrophysiologists. More specifically, the setup uses an address-event link [5] to establish virtual point-to-point connectivity between ON or OFF ganglion cells from the retina chip (or DIO card) with ON or OFF synapses on the bump chip. Both the input activity and the output activity of the bump chip is displayed in real-time using receiver chips, which integrate incoming spikes and displays their rates as pixel intensities on a monitor. A logic analyzer is used to capture spike output from the bump chip so it can be further analyzed. We investigated responses of the bump chip to gratings moving in sixteen different directions, both qualitatively and quantitatively. For the qualitative aspect, we created a PO map by taking each cell’s average activity for each stimulus direction and computing the vector sum. To obtain a quantitative measure, we looked at the normalized vector magnitude (NVM), which reveals the sharpness of a cell’s tuning. The NVM is calculated by dividing the vector sum by the magnitude sum for each cell. The NVM is 0 if a cell responds equally to all orientations, and 1 if a cell’s orientation selectivity is perfect such that it only responds at a single orientation. 4 Results We presented sixteen moving gratings to the network, with directions ranging from 0 to 360 degrees. The spatial frequency of the grating is tuned to match the size of the average bump, and the temporal frequency is 1 Hz. Figure 3a shows a resulting PO map for directions from 180 to 360 degrees, looking at the inhibitory cell population (the data looks similar for other cell types). Black contours represent stable bump regions, or equivalently, the regions that exceed a prescribed threshold (90 spikes) for all directions. The PO map from the bump chip reveals structure that resembles data from real cortex. Nearby cells tend to prefer similar orientations except at fractures. There are even regions that are similar to pinwheels (delimited by a white rectangle). A PO is a useful tool to describe a network’s selectivity, but it only paints part of the picture. So we have additionally computed a NVM map and a NVM histogram, shown in Figure 3b and 3c respectively. The NVM map shows that cells with sharp selectivity tend to cluster, particularly around the edge of the bumps. The histogram also reveals that the distribution of cell selectivity across the network varies considerably, skewed towards broadly tuned cells. We also looked at spike rasters from different cell-types to gain insight into their phase relationship with the stimulus. In particular, we present recordings for the site indicated by the arrow (see Figure 3a) for gratings moving in eight directions ranging from 0 to 360 degrees in 45-degree increments (this location was chosen because it is in the vicinity of a pinwheel, is reasonably selective, and shows considerable modulation in its firing rate). Figure 4 shows the luminance of the stimulus (bottom sinusoids), ON- (cyan) and OFF-input (magenta) spike trains, and the resulting spike trains from EXC (yellow), INH (blue), ON- (green), and OFFdriven (red) cell types for each of the eight directions. The center polar plot summarizes the orientation selectivity for each cell-type by showing the normalized number of spikes for each stimulus. Data is shown for one period. Even though all cells-types are selective for the same orientation (regardless of grating direction), complex cell responses tend to be phase-insensitive while the simple cell responses are modulated at the fundamental frequency. It is worth noting that the simple cells have sharper orientation selectivity compared to the complex cells. This trend is characteristic of our data. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 300 250 200 150 100 50 20 40 60 80 100 120 140 160 180 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Figure 3: (a) PO map for the inhibitory cell population stimulated with eight different directions from 180 to 360 degrees (black represents no activity, contours delineate regions that exceed 90 spikes for all stimuli). Normalized vector magnitude (NVM) data is presented as (b) a map and (c) a histogram. Figure 4: Spike rasters and polar plot for 8 directions ranging from 0 to 360 degrees. Each set of spike rasters represent from bottom to top, ON- (cyan) and OFF-input (magenta), INH (yellow), EXC (blue), and ON- (green) and OFF-driven (red). The stimulus period is 1 sec. 5 Discussion We have implemented a large-scale network of spiking neurons in a silicon chip that is based on layer 4 of the visual cortex. The initial testing of the network reveals a PO map, inherited from innate chip heterogeneities, resembling cortical maps. Our microcircuit proposes a novel function for complex-like cells; that is they create a sign-independent orientation selective signal, which through a push-pull circuit creates sharply tuned simple cells with the same orientation preference. Recently, Ringach et al. surveyed orientation selectivity in the macaque [9]. They observed that, in a population of V1 neurons (N=308) the distribution of orientation selectivity is quite broad, having a median NVM of 0.39. We have measured median NVM’s ranging from 0.25 to 0.32. Additionally, Ringach et al. found a negative correlation between spontaneous firing rate and NVM. This is consistent with our model because cells closer to the center of the bump have higher firing rates and broader tuning. While the results from the bump chip are promising, our maps are less consistent and noisier than the maps Ernst et al. have reported. We believe this is because our network is tuned to operate in a fluid state where bumps come on, travel a short distance and disappear (motivated by cortical imaging studies). But excessive fluidity can cause non-dominant bumps to briefly appear and adversely shift the PO maps. We are currently investigating the role of lateral connections between bumps as a means to suppress these spontaneous shifts. The neural mechanisms that underlie the orientation selectivity of V1 neurons are still highly debated. This may be because neuron responses are not only shaped by feedforward inputs, but are also influenced at the network level. If modeling is going to be a useful guide for electrophysiologists, we must model at the network level while retaining cell level detail. Our results demonstrate that a spike-based neuromorphic system is well suited to model layer 4 of the visual cortex. The same approach may be used to build large-scale models of other cortical regions. References 1. Hubel, D. and T. Wiesel, Receptive firelds, binocular interaction and functional architecture in the cat's visual cortex. J. Physiol, 1962. 160: p. 106-154. 2. Blasdel, G.G., Orientation selectivity, preference, and continuity in monkey striate cortex. J Neurosci, 1992. 12(8): p. 3139-61. 3. Crair, M.C., D.C. Gillespie, and M.P. Stryker, The role of visual experience in the development of columns in cat visual cortex. Science, 1998. 279(5350): p. 566-70. 4. Ernst, U.A., et al., Intracortical origin of visual maps. Nat Neurosci, 2001. 4(4): p. 431-6. 5. Boahen, K., Point-to-Point Connectivity. IEEE Transactions on Circuits & Systems II, 2000. vol 47 no 5: p. 416-434. 6. Boahen, K. and Andreou. A contrast sensitive silicon retina with reciprocal synapses. in NIPS91. 1992: IEEE. 7. Culurciello, E., R. Etienne-Cummings, and K. Boahen, A Biomorphic Digital Image Sensor. IEEE Journal of Solid State Circuits, 2003. vol 38 no 2: p. 281-294. 8. Zaghloul, K., A silicon implementation of a novel model for retinal processing, in Neuroscience. 2002, UPENN: Philadelphia. 9. Ringach, D.L., R.M. Shapley, and M.J. Hawken, Orientation selectivity in macaque V1: diversity and laminar dependence. J Neurosci, 2002. 22(13): p. 5639-51.

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