Neural circuit dynamics underlying accumulation of time-varying evidence during perceptual decision making

Abstract

How do neurons in a decision circuit integrate time-varying signals, in favor of or against alternative choice options? To address this question, we used a recurrent neural circuit model to simulate an experiment in which monkeys performed a direction-discrimination task on a visual motion stimulus. In a recent study, it was found that brief pulses of motion perturbed neural activity in the lateral intraparietal area (LIP), and exerted corresponding effects on the monkey's choices and response times. Our model reproduces the behavioral observations and replicates LIP activity which, depending on whether the direction of the pulse is the same or opposite to that of a preferred motion stimulus, increases or decreases persistently over a few hundred milliseconds. Furthermore, our model accounts for the observation that the pulse exerts a weaker influence on LIP neuronal responses when the pulse is late relative to motion stimulus onset. We show that this violation of time-shift invariance (TSI) is consistent with a recurrent circuit mechanism of time integration. We further examine time integration using two consecutive pulses of the same or opposite motion directions. The induced changes in the performance are not additive, and the second of the paired pulses is less effective than its standalone impact, a prediction that is experimentally testable. Taken together, these findings lend further support for an attractor network model of time integration in perceptual decision making.

Keywords: attractor network; computational modeling; intraparietal cortex; reaction time; visual motion discrimination.

Figure 1

Schematic diagram of a reduced decision making network model. (A) The network consists of two units, representing two competing neural pools selective for leftward and rightward motion direction, respectively. Each is endowed with strong self-excitatory recurrent coupling (sharp arrowheads). Cross-coupling between the two units is effectively inhibitory (circular arrowheads) (through a shared inhibitory neural pool which is not explicitly represented in this reduced model). I_L (I_R) encompasses the external inputs from motion-selective (MT) neurons, target-sensitive neurons, and background neurons. (B) Inputs to the decision units within a trial consist of both target stimulus inputs (dashed line) and motion stimulus from the random-dots (bold line; shown here with zero motion coherence). According to the model, the target inputs are reduced when the random-dot motion appears because attention is directed to the motion. (C) The directional input comes from MT cells, whose firing rates depend linearly on motion coherence. Coherent motion toward (opposite) the response field, RF, increases (decreases) the cell's output firing rate.

Figure 2

Neural dynamics of the decision network model. (A) Top: A sample trial with zero motion coherence. During target presentation, both neural pools (black and orange lines) achieve a relatively high steady state firing rate, similar to the observation of LIP neurons. During motion stimulus presentation (gray box), the firing rates of the two neural pools first increase together, then diverge over time, one ramping up whereas the other ramping down, resulting in a categorical choice (the decision bound is fixed at 55 Hz). Bottom: inputs. The target input represents static visual stimulus inputs with adaptation, as observed in experiments. The motion stimulus resembles the output firing rates of MT neurons. Note that in order to reproduce the “dip” immediately in neural activity immediately after motion stimulus onset, the target input is assumed to decrease (due to divided attention) after the motion stimulus onset but before the motion signals reach the LIP neurons. (B) Trial-averaged neural activities of the two neural pools with five motion coherence levels. Solid curves: winning population; dashed curves: losing population. Time courses of neural activity are aligned at the time of motion onset. Note slower ramping activity at a lower motion coherence. Only correct trials are shown.

Figure 3

Decision attractor network is reconfigured during different epochs of a trial. In the phase-plane plot, orange and green lines are, respectively, nullclines of the population firing rates selective to leftward (r_L) and rightward (r_R) motion. Black (brown) filled circles are the stable (unstable) steady-states of the network. In (C) and (D), black lines with direction of arrows toward and away from the unstable steady-state (i.e., saddle point) are the stable and unstable manifolds of the saddle point. In the absence of noise, these manifolds determine the network dynamics. In (A) and (B), only the stable manifolds are plotted to show the multiple basins of attraction. Gray region is the basin of attraction of the spontaneous state in (A), or that of the symmetrical stable state in (B). (A) Without visual target nor motion stimulus input to decision network. (B) With target input only. Steady-states after adaptation. (C) With both (reduced) saccadic target input and motion stimulus of zero coherence. The stable time constant τ_stable (= 79 ms) toward the saddle unstable steady-state is about half that of the unstable time constant τ_unstable (= 175 ms). (D) With both (reduced) saccade target input and motion stimulus of 12.8% coherence. τ_stable = 77 ms and τ_unstable = 159 ms. See the text for more details.

Figure 4

Network dynamics with two levels of motion coherence. Time course of neural responses and corresponding phase-plane plots during presentation of motion stimulus at c′ = 0% (A,C) and c′ = 12.8% (B,D). (A,C) Purple: trial-averaged neural activity after stimulus onset. Same for both selective pool of neurons, due to symmetry. (B,D) Blue: correct trials, red: error trials. In (C,D), black lines with arrows are the stable and unstable manifolds of the saddle point, respectively, and they control the flow of trajectories in the phase-plane in the absence of noise. Note that with a nonzero motion coherence, the temporal dynamics are slower on error trials (red) than on correct trials (blue) (B). In the phase-plane (D), the network's trajectory on error trials passes by the saddle point where the dynamics are slow. Each trajectory or time course is the average over 1000 trials.

Figure 5

Single motion pulse results in persistent change of neural response in the model. (A) After motion stimulus onset, a 100 ms pulse is presented either in the same (green) or opposite (red) direction as the coherent random-dot motion. As in the experiment of Huk and Shadlen (2005), five different motion pulse onset times were used: 100 , 150, 211, 287, and 392 ms after motion stimulus onset. (B) Pulse onset is 100 ms after onset of a c′ = 12.8% motion stimulus. The neural traces are trial-averaged firing rates in trials when the choice is the preferred direction of the cell. Only correct trials are shown here. Black: no motion pulse; green: positive pulse; red: negative pulse. All firing rate traces shown are truncated at the time the decision threshold is crossed, hence the apparent saturation of firing rates due to averaging effect near threshold. A pulse takes 225 ms to reach the decision neurons, and the induced change in the neural activity persists even after pulse is switched off.

Figure 6

Mean persistent change of neural activity due to a brief motion pulse. Effects of a pulse perturbation, averaged over all trials, motion coherence levels and pulse onset times. A single pulse of 100 ms duration induces a long-lasting change in the trial-averaged neural activity in both the experiment (A) and in the model simulation (B). Green: positive pulse; red: negative pulse. Colored light green (red) bars denote the duration of the positive (negative) motion pulse (panel A is reproduced from Huk and Shadlen (2005) with permission.)

Figure 7

Effect of a motion pulse on decision accuracy and reaction time of the model. Choices (A,C) and mean reaction times (B,D) are shown as function of the motion coherence. Black: no motion pulse. Green (respectively red): a positive (respectively negative) pulse shift the psychometric and chronometric functions leftward (respectively rightward). (A,B) Data from experiments (reproduced from Huk and Shadlen (2005) with permission); (C,D) model simulations. Psychometric function is fitted by a logistic function (see section Materials and Methods). Curves were calculated by averaging over pulses of five different onset times.

Figure 8

Violation of TSI: weaker influence of a later pulse on neural activity and choice accuracy in the model. () Average instantaneous change in neural firing rate as a function of the pulse onset time. The instantaneous change is calculated from 250 to 350 ms after pulse onset, as in the experiment. The green (red) trace denotes the change in firing rates due to positive (negative) pulse. Only data from trials with weak motion coherence of 0 and 3.2% were used. (B) Shift in psychometric function decreases with increased pulse onset time. Psychometric function shift is calculated from the shift of the fitted logistic functions (see section Materials and Methods). Standard errors are small, and hence omitted.

Figure 9

Effect of motion pulse on a nonlinear attractor network. Diagram depicts a network whose dynamics are described by an energy function (or potential well) of the neural firing rate. The speed of the temporal dynamics is proportional to the slope of the potential well, and the steady-states correspond to the minima and maxima (where the slope is zero). Magenta, blue and pink regions denote the basins of attractions. Each black mark denote the unstable steady-state that separates the two neighboring basins of attraction. The brown ball represents the instantaneous state of the network. Configurations of the network before motion stimulus presentation (top), and during motion viewing with a low motion coherence (middle) favoring the blue choice attractor. The black arrow indicates that the network is more inclined to move toward the blue attractor. When a positive motion pulse is added, the blue decision state has a deeper basin of attraction than before. Therefore, the network dynamics exhibit a faster ramping speed toward the blue state (bottom, left). When a negative motion pulse is presented instead, the blue decision state becomes less attractive while the pink decision state becomes more attractive (bottom, right). This results in a network state less inclined to move to the blue attractor. Green (red) arrow on the ball represents the average effect of a positive (negative) pulse on the network dynamics. With later motion pulse onset, the network becomes harder to influence since it is more likely to have commenced acceleration toward one of the choice attractors, thereby violating TSI. Not shown in the figure is that the ball is always under the continuous influence of noisy perturbations.

Figure 10

Nonlinearities in time integration using a double-pulse protocol. (A) A positive pulse is immediately followed by a negative pulse of the same magnitude but opposite direction. In principle, there are four possible combinations of the two pulses: positive → positive, positive → negative, negative → positive, negative → negative. (B) Two pulses, each of 100 ms duration, are presented at 150 and 250 ms after motion stimulus onset. Shift of the psychometric function for each of the four possible paired-pulse combinations (black bar) is compared to the linear sum of the shifts due to two individual pulses (gray bar). The second pulse in the paired-pulse protocol has a weaker effect than its standalone counterpart. In the (+) → (+) and (−) → (−) pairs, the double pulse is weaker than the sum of the effects produced by the two pulses on their own. In the (+) → (−) and (−) → (+) pairs, the first pulse controls the sign of the effect. The sum of single pulse effects would be cancelation were it not for the violation of TSI. There is less cancelation by the second pulse in the double-pulse protocol.

Figure 11

Changes in the neural response by paired pulses in the model. (A) Black: a positive pulse is followed by a negative pulse. The time course of neural activity is compared with that produced by a single positive pulse (green). Light green and pink regions represent the duration of the first and second pulse, respectively. Effectively, the second pulse in the double pulses is unable to completely suppress the change caused by the first pulse. Because of the input latency of 225 ms, the neural response to the first pulse occurs in the time window from 225 to 325 ms, and to the second pulse from 325 to 425 ms. Motion coherence is 12.8% in the neuron's preferred direction. (B) Gray: a negative pulse is followed by a positive pulse. The time course of neural activity is compared with that produced by a single negative pulse (red). Same label convention as in (A). The second positive pulse does not suppress the change due to the first negative pulse. Motion coherence is 25.6%. The neural responses were obtained in correct trials when the choice is the preferred direction. In both panels, the difference in the neural response is measured with respect to the average of trials without pulses that lead to the same correct choice.