Changes of mind in an attractor network of decision-making

Abstract

Attractor networks successfully account for psychophysical and neurophysiological data in various decision-making tasks. Especially their ability to model persistent activity, a property of many neurons involved in decision-making, distinguishes them from other approaches. Stable decision attractors are, however, counterintuitive to changes of mind. Here we demonstrate that a biophysically-realistic attractor network with spiking neurons, in its itinerant transients towards the choice attractors, can replicate changes of mind observed recently during a two-alternative random-dot motion (RDM) task. Based on the assumption that the brain continues to evaluate available evidence after the initiation of a decision, the network predicts neural activity during changes of mind and accurately simulates reaction times, performance and percentage of changes dependent on difficulty. Moreover, the model suggests a low decision threshold and high incoming activity that drives the brain region involved in the decision-making process into a dynamical regime close to a bifurcation, which up to now lacked evidence for physiological relevance. Thereby, we further affirmed the general conformance of attractor networks with higher level neural processes and offer experimental predictions to distinguish nonlinear attractor from linear diffusion models.

Figure 1. Experimental design, network architecture and stimulation protocol.

(A) RDM paradigm with manual indication of choice as in Resulaj et al. . See text for task details. In the majority of trials the subjects moved the handle directly to one of the targets. Some trajectories, however, revealed a change of mind during the movement: they started towards one direction but terminated at the opposite target. (B) Diagram of the binary attractor model for decision-making . The network consists of a population of excitatory pyramidal neurons, structured into 2 selective pools (red, each contains 20% of the excitatory neurons) and a nonselective population, that inhibit each other through shared feedback from an inhibitory pool of interneurons (orange). Unlabeled arrows denote a connectivity of 1 (baseline). Recurrent connectivity within a selective pool is high, ω₊ = 1.51, whereas the connection weight between the selective pools is below average ω₋ = 0.8725. Inhibitory connections have a weight ω_I = 1.125. The network consists of 1,000 Neurons. (C) Time course of target and motion input to the selective populations in order to model the experimental design of the RDM task. The target input starts with a latency of 100 ms, the motion signal 200 ms after the respective stimulus onset (see methods).

Figure 2. Simulated psychometric functions, reaction times and rates of changes compared to experimental data.

(A) Simulation data. The firing rate threshold to determine the first decision (and also a subsequent change) was set to 44 Hz in the simulations. The reaction times include a non-decision time (t_ND) of 380 ms; t_ND also set the time limit for changes of mind. A trial was considered a change of mind, if the firing rate of the initially losing selective pool crossed the decision threshold within t_ND after the first crossing of the other pool, and their rates differed by more than 10 Hz. The probabilities of correct responses were fitted to a logistic function, the reaction time to a hyperbolic tangent function. The model parameters were adjusted by hand to fairly fit the average performance of the three subjects that participated in the experiments by Resulaj et al. . For comparison, the experimental performance of one of the subjects (Subject S) is shown in (B) with permission from Resulaj et al. . (Left panel) As in the experimental data, the performance improves through the changes. The first decision (black trace, corresponding to choice at movement initiation) is less accurate than the final choice (red trace, corresponding to the finally chosen target). (Middle panel) The model fits the experimental reaction times well. (Right panel) In the simulations and the experiments, changes to the incorrect choice (black, solid line) decayed monotonically with increasing motion coherence, while changes to the correct choice (red, solid line) peaked at intermediate motion strength and were generally more frequent. Double changes in the simulations are shown on a ten times smaller timescale (right) (open circles, dashed lines). Black (red): proportion of erroneous (correcting) changes that switched a second time. Error bars denote SEM.

Figure 3. Distribution of change times.

(A) Histogram of the time difference between the first and second threshold crossing (change of mind) for all change trials. The change times are broadly distributed from about 50 ms after the first decision to the timeout t_ND for changing. (B) Same as (A) separated into coherence levels. All changes are shown in dark grey. The correcting changes are overlaid in red, except for 0% coherence, where changes are neither correcting nor erroneous.

Figure 4. Model prediction of LIP firing rate.

(A, E) Simulated temporal evolution of population-averaged firing rates for single trials. The dotted lines mark times of threshold crossings. The black line at 44 Hz indicates the threshold. (A) Example for a regular trial without change. As observed in recent neurophysiological studies of LIP , , , the firing rates of the selective populations show a high increase during target presentation (from 500 to 1,300 ms), followed by a dip after the onset of the motion stimulus. The activities of both selective populations ramp up with the application of the motion input (beginning at 1,500 ms), while the transients compete for the higher attractor state. (C, D) Mean of correct trials from 1,000 network simulations, shown for all motion coherences (Color code according to B). For each motion strength the firing rates were averaged according to the “winners” and “losers” of the first decision. After an initial joint build-up, the slope of the ramping activity is flatter with smaller motion coherence. (D) Blow up of dotted rectangle from (C). (E) In some cases the initially winning population (first threshold crossing) is overtaken by the other transient, which is counted as a “change of mind” trial. (F) Mean of all trials with changes (correct and error trials, all motion coherences) aligned to the first threshold crossing (dotted vertical line). Black: initially winning selective pool, red: finally winning selective pool.

Figure 5. Influence of input noise on changes of mind.

The variation from the mean input difference of the selective populations, signed according to which pool first crossed the decision threshold, was averaged, aligned to first threshold crossing, for all trials and all change trials. The insets show the input variation for change trials aligned to the second threshold crossing. (A) Mean across all coherence levels. (B) Separated by motion coherence. Overall and for low coherences, the input fluctuations change sign before a change. For high motion coherence neither correct initial choices, nor changes depend on noise fluctuations (see text).

Figure 6. Proximity to bifurcation is important to obtain changes of mind.

(A) Mean-field analysis of attractor network. For the parameters used in the spiking model simulation, the stable (solid black line) and unstable (dotted black line) fixed points were calculated with the mean-field approximation over a range of external inputs, applied symmetrically to both selective pools (0% coherence) from 0 to 200 Hz in steps of 1 Hz, in addition to the background input of 2.4 kHz to all neurons. There are three qualitatively different regions to distinguish, separated by bifurcations. In the blue shaded region up to about 20 Hz the spontaneous state (both pools firing at low rates, ↓↓) and the decision state (one pool firing at high, the other at low rates ↓↑) are simultaneously stable. The spontaneous state becomes unstable for higher inputs (white region) until at about 125 Hz a symmetrical state with both pools firing at elevated rates appears (grey shaded area, ↑↑). The blue crosses show the fixed points of the spiking-neuron model for several discrete selective input amplitudes (see methods). The second bifurcation there is shifted by about 25 Hz to higher selective inputs (to the right) for the spiking simulations with respect to the mean-field approximation. The input used in the spiking simulation (blue vertical line, 155 Hz) lies close to the real second bifurcation point. Also, the double-up symmetric state lies below the decision-threshold (44 Hz, horizontal dashed line) while the upper branch of the decision attractor (“winner”) lies above. (B, C) Changes of mind and single trial examples for lower (B) and higher (C) network inputs (yellow and orange lines in (A)). All parameters and the motion input were the same as in the other simulations, only the target input after motion onset was set to 25 Hz for (B) and to 125 Hz for (C). Dashed lines in the left panels give changes of mind from Fig. 2A for comparison. Red: changes to correct, black: changes to wrong choice. With less selective inputs (B), fewer changes of mind are obtained, although the threshold was adapted to fit the reaction times and performance (Fig. S2). With higher selective inputs (C) too many changes are predicted for low motion coherences and the selective transients no longer separate, but stay in the symmetric state. Color of single trial firing rates are the same as in Fig. 3. Error bars denote SEM.

Figure 7. Model predictions for different levels of common selective inputs.

The baseline external input, common to both selective populations, as well as the input bias to one of the selective populations were varied in steps of 8.75 Hz. Different colors indicate the amount of common inputs, starting from 120 Hz to 155 Hz (standard input to model the experimental changes of mind). Mean reaction times (A), performance (B) and changes to correct (C, solid lines) and wrong (C, dashed line) alternative are plotted against the input bias between the selective populations. The decision threshold was fixed at the standard decision criteria (44 Hz, 10 Hz difference). 1,000 trials were simulated for each data point. The pink and red dots correspond (approximately) to the standard input parameters used above at 0% and 25.6% (here actually 25%) motion coherence. Increasing the baseline inputs leads to faster reaction times, lower performance and overall more changes. (D) Evolution of the mean firing rate variance across trials for one selective population, starting from shortly before motion input onset (1,500 ms). The firing rate variances increase quite linearly with time. With increasing baseline inputs to both selective populations, the variance across trials becomes lower from ∼150 ms after motion onset.

Figure 8. Modifying the variance in the diffusion model.

Behavioral predictions of an extended linear accumulator-to-bound model, as used in Resulaj et al. (see methods) for three different levels of input variance (0.7, 1.0, 1.3). Increasing the input variance leads to faster mean reaction times (A), worse performance (B) and more changes of mind (C). (C) Solid lines indicate changes to the correct alternative, dashed lines erroneous changes. 10,000 trials were simulated for each data point. (D) Evolution of the output variance with time. As expected for the diffusion model, the variance rises linearly with time. More input variance leads to more variance across the trials in the output.