Context-dependent selection of visuomotor maps

Abstract

Background: Behavior results from the integration of ongoing sensory signals and contextual information in various forms, such as past experience, expectations, current goals, etc. Thus, the response to a specific stimulus, say the ringing of a doorbell, varies depending on whether you are at home or in someone else's house. What is the neural basis of this flexibility? What mechanism is capable of selecting, in a context-dependent way an adequate response to a given stimulus? One possibility is based on a nonlinear neural representation in which context information regulates the gain of stimulus-evoked responses. Here I explore the properties of this mechanism.

Results: By means of three hypothetical visuomotor tasks, I study a class of neural network models in which any one of several possible stimulus-response maps or rules can be selected according to context. The underlying mechanism based on gain modulation has three key features: (1) modulating the sensory responses is equivalent to switching on or off different subpopulations of neurons, (2) context does not need to be represented continuously, although this is advantageous for generalization, and (3) context-dependent selection is independent of the discriminability of the stimuli. In all cases, the contextual cues can quickly turn on or off a sensory-motor map, effectively changing the functional connectivity between inputs and outputs in the networks.

Conclusions: The modulation of sensory-triggered activity by proprioceptive signals such as eye or head position is regarded as a general mechanism for performing coordinate transformations in vision. The present results generalize this mechanism to situations where the modulatory quantity and the input-output relationships that it selects are arbitrary. The model predicts that sensory responses that are nonlinearly modulated by arbitrary context signals should be found in behavioral situations that involve choosing or switching between multiple sensory-motor maps. Because any relevant circumstancial information can be part of the context, this mechanism may partly explain the complex and rich behavioral repertoire of higher organisms.

Figure 1

Antisaccade task. In each trial, a stimulus (black dot) is presented at a distance x from the fixation point (colored dot); the stimulus disappears; two targets appear (gray dots) and the subject responds by making an eye movement (arrow) to one of them. The color of the fixation spot indicates whether the movement should be a saccade or an antisaccade. a: In context 1 the fixation spot is red and the movement is to the target at x. b: In context 2 the fixation spot is green and the movement is to the opposite target, at -x. In the model, x is between -15 and +15, with distance in arbitrary units.

Figure 2

Responses of GM neurons in the antisaccade task. Each graph plots the mean firing rate of a model neuron as a function of stimulus location. Red and green traces correspond to sensory responses evoked during contexts 1 and 2, respectively. The gain in the preferred condition is 1. a: A unit that prefers context 1 and is 100% suppressed in the non-preferred condition; its minimum gain is γ = 0. b: A unit that prefers context 2 and is 62% suppressed in the non-preferred condition; its minimum gain is γ = 0.38. c: Another unit that prefers context 1; its minimum gain is γ = 0.61. d: Another unit that prefers context 2; its minimum gain is γ = 0.87. Firing rates are in spikes/s. Model responses are based on Equations 1 and 3.

Figure 3

Network performance in the antisaccade task. a: Firing rates of all model cells when the GM units are fully modulated (γ = 0). The box marks a single trial. Colored traces are the firing rates of the 60 GM neurons in the network; 30 of them (red) prefer the direct saccade condition and 30 (green) prefer the antisaccade condition. Black dots are the 25 motor responses driven by the GM neurons. For GM responses, x-axis is preferred stimulus location; for output responses, x-axis is preferred movement location. Context in each of the four trials is indicated on the left. Trials with x = -15 and x = 10 alternate. The profile of output activity always peaks at the correct location. b: As in a, but when all GM neurons are partially modulated by the same amount (γ = 0.5). c: As in a, but when the maximum and minimum gains of the GM units are chosen randomly from uniform distributions. d-f: Connection matrices for the networks in the respective columns. Each point shows the synaptic weight, coded by color, from one GM neuron to one output neuron. GM units 1–30 (red points in upper panels) prefer context 1, whereas GM units 31–60 (green points in upper panels) prefer context 2. No noise was included in the simulations (α = 0).

Figure 4

Sensitivity to noise as a function of modulation strength in the antisaccade task. All results are for networks of 60 GM and 30 output neurons. The x-axes indicate γ, which is the minimum gain of the GM neurons; the maximum is always 1. In all panels, the three curves are for three levels of noise: α = 0.04 (thin lines), α = 0.36 (medium lines), or α = 2.25 (thick lines). a: Standard deviation of single output firing rates, averaged over stimulus locations and contexts, as a function of γ. Data points are from simulations; continuous lines are analytic results from Equation 39, with a = 1.42. For each data point, the average output responses, as functions of x and y, were the same. To achieve this, the synaptic weights for γ > 0 were obtained by a linear transformation of the weights for γ = 0 (Appendices B, C). b: Error between correct and encoded movement locations as a function of γ. Results are from the same simulations as in a. c, d: As in a, b, respectively, but for simulations in which the synaptic weights were computed using the standard, optimal algorithm (see Methods). Note that σ_CM always increases with γ.

Figure 5

Responses of four model GM neurons in the scaling task. Same format as in Fig. 2, except that there are five possible contexts, corresponding to y = -1, -0.5, 0, 0.5 and 1. a: Tuning curves for a model neuron that responds maximally to stimuli at x = -15 and prefers the green condition (y = 0). The order of effectiveness for the five scales was set randomly, so context is encoded discontinuously. b: As in a, but for another neuron that prefers x = 2 and y = 1. c: Tuning curves for a model neuron that encodes context in a smooth, continuous way. The unit responds maximally to stimuli at x = -1 and prefers the cyan condition (y = -0.5). The gain of the cell decreases progressively as y deviates from the preferred scale – note the order of the colors. d: As in c, but for a neuron that prefers x = 9 and y = 1. All units have a maximum gain of 1 and a minimum gain near 0.5. Model responses were based on Equations 1, 3, 5 and 6.

Figure 6

Network performance in the scaling task. Results are from two networks, one that encodes context discontinuously (first two columns) and another that encodes it continuously (third and fourth columns). a: The box encloses all model responses in a single trial with x = -5 and y = 1. The color plot shows all 900 GM responses, color coded. Neurons are arranged by preferred stimulus location along the x-axis and by preferred context along the y-axis. Black traces are the firing rates of the 25 driven output neurons. The black line indicates intended target location (xy = -5); the red line indicates encoded target location (center of mass). Their difference (error) is -0.73. b: A trial with x = -5, y = -1 and error = 0.02. c: A trial with x = 15, y = -1 and error = -1.54. d: A trial with x = 15, y = 0.5 and error = 0.63. e-h: Same combinations of stimulus and context as in a-d, but using a smooth representation for context. Errors are -0.07, 0.34, -1.84, and 0.8, respectively. The variance of each GM rate is equal to its mean (α = 1).

Figure 7

Robustness and generalization in the scaling task. Left and right columns are for networks in which scale is encoded discontinuously and continuously, respectively. Each panel shows results for three noise levels: α = 0.09 (squares), α = 1 (circles) and α = 9 (triangles). a: Error in encoded movement location as a function of the number of GM neurons. Each point represents an average over stimulus locations, scales and trials; 31 stimulus locations and 5 scales were used both to set the connections and test the networks. The filled symbol indicates the network in Figs. 6a-d. b: As in a but for networks in which scale is encoded continuously. The filled symbol indicates the network in Figs. 6e-h. c, d: σ_CM vs network size in networks with corrupted synaptic weights. These simulations proceed as in a, b, except that performance is tested after deleting 25% of the synaptic connections, chosen randomly. e: σ_CM vs network size when only 8 stimulus locations (combined with the 5 scales) are used to set the connections and the network is tested with all combinations of 31 stimulus locations and 5 scales. f: σ_CM vs network size when combinations of only 8 stimulus locations and 8 scales are used to set the connections and performance is evaluated with all combinations of 31 stimulus locations and 31 scales. Continuous lines are linear fits to the data points above 250 units. Note logarithmic axes.

Figure 8

Orientation discrimination task. In each trial, a bar oriented at an angle x is presented while the subject fixates; the stimulus disappears; two targets appear (gray dots), and the subject indicates whether the bar was tilted to the left or to the right by making an eye movement (horizontal arrow). Vertical bars correspond to x = 0°. a: The bar is tilted to the left (x < 0). With a red fixation spot (y = 1), responses to left- and right-tilted bars should be to the left and right targets, respectively. The correct response is thus to the left. b: With a green fixation spot (y = 2), left- and right-tilted bars correspond to right and left targets, respectively. The correct response is now to the right. A no-go condition (y = 3; not shown) is included in the simulations in addition to the two go conditions. Orientation is in degrees, with x between -8° and +8°.

Figure 9

Network performance during orientation discrimination. Panels a-h show all 25 output responses, as driven by the GM neurons (not shown), in single trials. Continuous lines indicate intended target location (-10 or +10); dashed lines indicate the center of mass of the output activity. Right and left columns have identical stimuli and conditions, but with (α = 1) and without (α = 0) noise, respectively. A trial is deemed correct if the higher peak of activity is situated at the intended target location. a: Single trial with x = 5°, y = 1 and error = 0.15. b: As in a, but error = 0.001. c: Single trial with x = 1°, y = 1 and error= 6.7. d: As in c, but error = 12.2. The response is scored as incorrect because the tallest hill of activity is not at the intended target. e: Single trial with x = 1°, y = 2 and error = 6.7. f: As in e, but error = -2.9. g, h: No-go trials. i: Probability of making a movement to the right target as a function of stimulus orientation, in condition 1 (y = 1) and with noise. Gray lines are fits to the simulation data. The center point or bias of the fit is indicated by the dashed line and is equal to -0.06°. Discrimination threshold is 1.5°. j: As in i, but with the association between orientation and targets reversed (y = 2). The center point is -0.04°; the discrimination threshold is 1.4°.

Figure 10

Robustness and generalization in the orientation discrimination task. Left and right columns show the bias and discrimination threshold, respectively of the neurometric fits (as in Figs. 9i,j) as functions of network size. a, b: Bias and discrimination threshold under standard conditions, which include 64 orientations used to set the connections and test the model. For each network size, results are absolute values averaged over the two go conditions and multiple networks. Filled symbols indicate the network used in Fig. 9. c, d: As in a, b, except that performance was tested after deleting 25% of the synaptic connections, chosen randomly. e, f: As in a, b, but when only 2 stimulus orientations (-8° and +8°) are used to set the connections, in combination with the 3 possible contexts, and performance is tested with all 64 orientations and 3 contexts. Straight lines are fits to the data points above 250 units.