Abstract
The unfolding of neural population activity can be described as a dynamical system. Stability in the latent dynamics that characterize neural population activity has been linked with consistency in animal behavior, such as motor control or value-based decision-making. However, whether such characteristics of neural dynamics can explain visual perceptual behavior is not well understood. To study this, we recorded V4 populations in two male monkeys engaged in a non-match-to-sample visual change-detection task that required sustained engagement. We measured how the stability in the latent dynamics in V4 might affect monkeys’ perceptual behavior. Specifically, we reasoned that unstable sensory neural activity around dynamic attractor boundaries may make animals susceptible to taking incorrect actions when withholding action would have been correct (“false alarms”). We made three key discoveries: (1) greater stability was associated with longer trial sequences; (2) false alarm rate decreased (and response times slowed) when neural dynamics were more stable; and (3) low stability predicted false alarms on a single-trial level, and this relationship depended on the position of the neural activity within the state space, consistent with the latent neural state approaching an attractor boundary. Our results suggest the same outward false alarm behavior can be attributed to two different potential strategies that can be disambiguated by examining neural stability: (1) premeditated false alarms that might lead to greater stability in population dynamics and faster response time and (2) false alarms due to unstable sensory activity consistent with misperception.
Significance Statement
Many of the primate visual behaviors are recurrent, repetitive, and require sustained engagement. Computational rules guiding the neural dynamics for such behaviors are not well understood. Using a model-free approach to study these neural computations, we discovered that dynamical stability in population activity could explain many facets of visual perceptual behavior. Greater dynamical stability led to fewer lapses in desired behavioral outcomes and made the animal slower to act when such lapses occurred. The degree of stability could nuance whether the lapses in perceptual decisions were premeditated or likely generated due to misperception. These results improve our understanding of the link between the dynamic nature of neural processes and behavior.
Introduction
In a dynamical system framework, the system’s future states can be predicted from its current state. For a population of neurons in a cortical area, this would mean that if we know its joint activity level, or state, at one time-point (the initial condition), we can approximately predict how its state trajectory would evolve. In some cases, many different initial conditions may lead to a common fixed state or a repeating sequence of states in the future, which is termed an attractor or attractor cycle, respectively. The set of initial conditions leading to that attractor or attractor cycle form its “basin of attraction;” the separatrix between two different basins of attraction (i.e., corresponding to different system behaviors) is an “attractor boundary.”
Attractor cycles represent periodic trajectories that the system recurrently traverses. One defining characteristic of an attractor cycle is its stability, as it is less susceptible to perturbations, both external and internal. Here, the term “stability” implies not an unchanging state, but rather that small deviations of the system state from the attractor cycle due to noise or outside influence will remain within the basin of attraction and be pulled back to the attractor cycle at some point in the future (in the near-future for a more dynamically stable system, in the further-future for a less-stable one). As a result, dynamic stability enables more reliable predictions further into the future about the system’s trajectory. For these reasons, attractor cycles provide an advantageous mechanism for guiding behavior; especially in the context of repetitive and recurrent behavior. For example, Li et al. (2016) tasked mice to locate objects by whisking, and then during movement preparation, the experimenters optogenetically perturbed large portions of the premotor cortical network. They found that the premotor network as a whole rapidly compensated for this perturbation consistent with a dynamic attractor, leading to motor behavior being largely unaffected. The dynamical systems framework for behavior has benefited the study of motor control (Shenoy et al., 2013), but the extent to which such dynamic principles guide perceptual processing is much less understood.
In this study, we demonstrate that a dynamical system framework can prove useful in linking the neural state space to primate visual behavior, which is interactive and intermittent. For example, when on a long road trip on a highway, much of the task is to remain vigilant, and, having determined that no hazards have arisen, take no action. This perceptual decision-making loop leading to inaction is then repeated for a long time (hopefully). Many tasks share this pattern of vigilant perception and inaction. However, it is common to spontaneously break out of this deliberative loop, leading to a suboptimal break in concentration or impulsive action (“false alarm”). We hypothesized that such perceptual decision-making loops are guided by dynamical systems, much as for motor control, and that false alarms may be caused, at least in part, by a weakening of dynamic stability that dictates the evolution of system states. Specifically, we theorized that the neural state in macaque cortical area V4, a mid-level visual area linked to perceptual decision-making processes (Roe et al., 2012), traverses a dynamic attractor on each iteration of the perception-decision loop, and that periods preceding false alarms would be characterized by slower attraction towards that attractor, consistent with weakened dynamic stability.
Methods
Ethical oversight
Experimental procedures were approved by the Institutional Animal Care and Use Committee of the University of Pittsburgh and were performed in accordance with the United States National Research Council’s Guide for the Care and Use of Laboratory Animals.
Subjects
Two adult male rhesus macaques (Macaca mulatta) were used for this study. Surgeries were performed in aseptic conditions under isoflurane anesthesia. Opiate analgesics were used to minimize pain and discomfort perioperatively. A titanium head post was attached to the skull with titanium screws to immobilize the head during experiments.
Array recordings
After each subject was trained to perform the spatial attention task, we implanted a 96-electrode Utah array (Blackrock Microsystems, Salt Lake City, UT, USA) in V4. The array was implanted in the right hemisphere V4 for monkey M1, and the left V4 for monkey M2. A detailed description of these methods and separate analyses of a portion of these data were published previously (Snyder et al., 2018; Cowley et al., 2020; Snyder et al., 2021; Umakantha et al., 2021; Johnston et al., 2022; Sachse and Snyder, 2023). Signals from the arrays were band-pass filtered (0.3–7500 Hz), digitized at 1 kHz and amplified by a Grapevine system (Ripple Neuro, Salt Lake City, UT, USA). Signals crossing a threshold (periodically adjusted using a multiple of the root-mean-squared noise) were stored for offline analysis as candidate neural spikes. For this report, we analyze only local field potentials (LFPs); identification of candidate spikes was relevant only for receptive field mapping for stimulus selection. LFPs were advantageous for this study because of three properties: (1) they are intracranial signals so we have microscale sampling of a specific brain area (in contrast to e.g., EEG, fMRI, etc.), (2) they integrate signals across a wider area than e.g., single-unit spiking, therefore they more completely sample the population around the implanted electrodes, and (3) their continuously valued and regularly sampled nature, in contrast to point-process metrics such as spiking, is conducive to dynamical systems analysis because they are continuously differentiable, unlike spike trains. LFPs were low-pass filtered on-line at 250 Hz by the Grapevine amplifier, then resampled off-line to 500 Hz.
Receptive field (RF) mapping
Before beginning the behavioral task, we mapped the RFs of the spiking neurons recorded on the V4 arrays by presenting small (≈1°) sinusoidal gratings (four orientations) at a grid of positions. We subsequently used Gabor stimuli scaled and positioned to roughly cover the aggregate receptive field (RF) area determined by the responses to the small gratings at the grid of positions. For monkey M1 this was 7.02° full-width at half-maximum (FWHM) centered 7.02° below and 7.02° to the left of fixation, and for monkey M2 this was 4.70° FWHM centered 2.35° below and 4.70° to the right of fixation. We next measured tuning curves by presenting gratings at the RF area with four orientations and a variety of spatial and temporal frequencies. For each subject we used full-contrast Gabor stimuli with a temporal and spatial frequency that evoked a robust response from the population overall (i.e., our stimulus was not optimized for any single neuron). For monkey M1 this was 0.85 cycles/° and 8 cycles/s. For monkey M2 this was 0.85 cycles/° and 7 cycles/s. For the task, we presented a Gabor stimulus at the estimated RF location, at the mirror-symmetric location in the opposite hemifield, or at both locations simultaneously.
Gaze tracking
We tracked the subjects’ gaze using an infrared eye-tracking system (EyeLink 1000; SR Research, Ottawa, Ontario, Canada) sampled at 1000 Hz.
Behavioral task
Subjects initiated each trial by fixating a 0.6° yellow dot at the center of a mid-gray, flat-screen cathode ray tube monitor positioned 36 cm from the subjects’ eyes, and then maintaining that central fixation. Each trial consisted of a sequence of oriented Gabor stimuli (400 ms duration), separated by interstimulus intervals with only a fixation point on a gray screen (300–500 ms, uniformly distributed; Fig. 1a). For the main task trials, one Gabor was presented in each visual hemifield, for a total of two Gabor stimuli at a time. We refer to each such flash of a pair of Gabors as a “stimulus repetition” for a trial. The first such stimulus presentation on a trial established the reference orientation for each Gabor (either 45° in the left hemifield and 135° in the right, or vice versa). The task for the animal was to detect if the orientation of either Gabor on subsequent stimulus repetitions differed from this initial reference orientation (a “target”). The monkeys reported detecting such an orientation change by making a saccade to the target, at which point they were rewarded with water or juice. Orientation changes could be 1, 3, 6, or 15 degrees in either the clockwise or counter-clockwise direction (monkey M1: 11.49 ± 3.14 (mean ± SD, across sessions) valid targets of each orientation at each location; monkey M2: 14.56 ± 4.75 valid targets of each orientation at each location).
Each stimulus repetition in the sequence had a fixed probability of containing a target (30% for monkey M1, 40% for monkey M2), i.e., a change in orientation of one of the Gabor stimuli compared to the preceding stimulus presentations in the trial (except the first stimulus presentation in the sequence, which established the reference orientations and was never a target). Stimulus sequences continued until the subject made an eye movement for any reason (hit, false alarm, or non-task-related broken fixation; physiology data during saccades were excluded from analysis), or a target was presented but the subject did not respond to it within 700 ms (i.e., a Miss). Because each stimulus (after the first) had a fixed probability of being a target, sequence lengths were roughly exponentially distributed; sequences predominantly had two stimulus presentations (standard then target), and very few sequences had more than four stimulus presentations. For monkey M1, the average trial duration was 2.44 ± 1.42 s (mean ± SD; N = 33,344 trials). For monkey M2, the average trial duration was 2.44 ± 1.41 s (mean ± SD; N = 31,556 trials).
The probable target location was block-randomized such that 90% of the targets would occur in one hemifield (“valid” targets; the remaining 10% were termed “invalid” targets) until the subject made 80 correct detections in that block (including cue trials, described below), at which point the probable target location was changed to the opposite hemifield. For invalid targets, the orientation change was always the value of 3°, clockwise or anti-clockwise (because invalid targets occur infrequently, we restricted the number of orientation change magnitudes for this condition in order to derive a reasonable estimate of the target detection rate). For the initial trials within a block, a Gabor stimulus was presented only in the hemifield that was chosen to have a high probability of target occurrence for the block, in order to “cue” the animal as to which location had high target probability. These cue trials were excluded from the analysis. There were two cue conditions: a cue at the RF location (cue-RF) or a cue in the opposite hemifield (cue-away). The initial cue location was counterbalanced across recording sessions. Once a subject correctly detected five orientation changes during the cue trials, bilateral Gabor stimuli were presented for the remainder of the block.
During the task-training phase of the project, we observed that animals’ strategy varied strongly as a function of sequence position, as evidenced by changes in discrimination sensitivity and criterion. Because we were interested in the potentially subtle contributions of visual neural dynamics on decision-making, and concerned that large variation in cognitive strategy might swamp those effects, we titrated the reward schedule to approximately stabilize sensitivity (d′) and criterion as a function of time elapsed during the trial: the number of rewards (fluid drops) given for a correct trial increased with the whole number of seconds (s) of trial duration following the formula:
We analyzed trials including either valid or invalid targets, but excluded from analysis all neural data from the time of target onset through the end of the trial. That is, we only analyzed responses to non-targets, of which there were two types: one with a 45° stimulus in the RF, and the other with a 135° stimulus in the RF. Trials where monkeys’ response time (square-root transformed) exceeded ±3 standard deviations from the mean, have been excluded from all behavioral analyses (on average 3.27% of all epochs in a session for M1 and 3.19% for M2). For monkey M1, 1376.58 ± 337.56 (mean ± SD) stimuli with the 45-degree grating in the RF, and 1403.21 ± 325.71 (mean ± SD) stimuli with the 135-degree grating in the RF per session have been included in this study. For monkey M2, 1812.13 ± 552.87 (mean ± SD) stimuli with the 45-degree grating in the RF, and 1779.13 ± 556.93 (mean ± SD) stimuli with the 135-degree grating in the RF have been included in this study. Monkey M1 completed 25 sessions of the experiment; monkey M2 completed 24 sessions. One session for each subject was subsequently excluded from the analysis because of recording equipment failure.
Behavioral analysis
To quantify monkeys’ perceptual sensitivity (d′) in the task, we used a signal detection model developed for multi-alternative change-detection (m-ADC) tasks (Sridharan et al., 2014), where m corresponds to the number of distinct choice locations. In a typical Go/No-Go task, m is the number of locations for a Go choice. The model estimates d′ for each of the m choice locations. In our task, for each stimulus presentation, the monkeys either made a saccade to either of the two stimuli locations or maintained fixation on the central dot on the screen. In other words, the monkeys made three possible choices (two Go and one No-Go), which correspond to a 2-ADC framework. For each session, we estimated two d′ values for the two choice locations and averaged them to get a representative estimate of d′ for the said session. Sridharan et al. (2014) provided us the MATLAB code for estimating d′ using the m-ADC model.
To quantify the association between stimulus repetition number (repetition in Eq. 2) and false alarm likelihood, we fitted a generalized linear mixed-effect model with the slope of repetition (β in Eq. 3) as the main effect predictor. We used random-effect terms for intercept and slope of repetition grouped by session to account for session-specific variations. The Wilkinson notation of the model used is:
Data pre-processing
For each session, field potential data were band-pass filtered using a finite-impulse-response (FIR) filter with cut-off frequencies at 1 and 40 Hz. In trials where monkeys correctly withheld saccade, data were epoched for each trial between −300 and +700 ms w.r.t. stimulus onset. In trials where monkeys made false alarms, data were epoched both w.r.t. stimulus onset and w.r.t. saccade onset. To detect and exclude artifacts, we computed the peak-to-peak amplitude in the LFPs for each channel on each trial and averaged them across channels to get a single representative value for each trial. Trials for which these values exceeded ±4 standard deviations from the mean value were indexed as bad trials and removed from subsequent analysis. For trials with saccades (e.g., false alarm or correct hits), we log-transformed the response time values, and trials exceeding ±4 standard deviations from the mean were indexed as outliers and removed from subsequent analyses. After excluding bad trials, we averaged the peak-to-peak amplitudes across trials to get a representative value for each channel. Channels for which these values exceeded ±4 standard deviations from the mean, were indexed as bad channels and were interpolated using all other channels weighted by the inverse of the distance between the bad channel and good channel, where all the weights summed to a unit.
Dimensionality reduction
Demixed principal components analysis (dPCA)
To confirm that LFPs reliably encoded relevant task variables such as repetition number, we used dPCA. dPCA decomposes population activity into multiple components that explain as much variance in the data as possible, while maximally capturing the dependence between individual task parameters and neural signals. We used cue, orientation of stimulus in the RF, and stimulus repetition number as the marginalization factors for performing dPCA. Details of this method can be found elsewhere (Kobak et al., 2016). We used publicly available MATLAB code to perform this analysis (https://github.com/machenslab/dPCA).
Generalized eigenvalue problem (GEV)
GEV, or joint diagonalization, is a general framework underlying various commonly used source separation techniques such as Common Spatial Patterns, Independent Component Analysis, Denoising Source Separation etc. (for reviews see: de Cheveigné and Parra, 2014; Särelä et al., 2005). It seeks to extract components from multidimensional data that maximize signal-to-noise ratio. The flexibility and versatility of the tool lie in defining what constitutes the signal in the data. For example, one common problem faced in electrophysiological recordings is the contamination of neural signals by ambient electrical line noise (i.e., 60 Hz for our data). In such cases, one can use GEV to identify components that maximally explain the 60 Hz signal in the data while minimally capturing signals in other frequency bands which are potentially neural signals. The data then can be denoised by regressing out the contribution of such components.
In our case, we wanted to extract components that maximally capture neural activity common across trials with minimal residual activity. So, we defined signal as the trial-averaged LFPs (Xsignal in Eq. 5). Xsignal has a dimensionality of T × D (2 ms time bins times the number of channels).
diagonalization of Cnoise, i.e.
After removing the components contributing negligible variance to Cnoise, Csignal is diagonalized in the following manner:
W is computed as follows:
For each trial k, the signal component of Xk that is most consistent (stable) across trials, i.e., Sk, is estimated by Equation 14a. The stable trajectory of X is computed as the trial-average of Sk, which is our estimate of the limit cycle attractor (Eq. 14b).
Stability estimation
One approach in studies of dynamical systems in neuroscience has been to fit parameters of a linear time-invariant dynamical systems model to neural data, and then interpret the fitted parameters. One limitation of this approach is that the strength of conclusions that may be drawn depends on the quality of the fit of the model to the data (i.e., the estimated model parameters are hard to interpret if the model is a poor fit). Moreover, such approaches include assumptions that are likely violated for neural signals (i.e., linearity and time-invariance). Such limitations could have an out-sized influence when aiming to study noisy neurophysiological data at the single-trial level, as we did for this study. To eschew these limitations, we used a data-driven estimate of dynamic stability that does not depend on modeling. We reasoned that a system’s degree of stability is reflected in its response to external perturbations (by definition). When the system’s states deviate from its attractor trajectory because of perturbation, it should exert force in the direction opposite to the perturbation to bring it back to the attractor cycle. In other words, the pulling force opposite to the perturbations signifies the degree of stability.
We conceptualized the residual activity as the perturbations away from the attractor cycle, i.e., the trial-averaged neural data, and estimated the moment-by-moment perturbations using Equation 15. For simplicity, only the time dimension has been denoted in the subsequent equations in this section and has been indexed using the subscript t.
To normalize the SI values, before estimating SI, we applied a “z-score” transformation to Δe along the time dimension in each trial. As the trial-by-trial Δe estimates were very noisy, where appropriate (Fig. 3a,c), we applied a 150 ms moving-window average to smooth the resultant SI estimates. Smaller window sizes produced qualitatively similar results. In analyses concerning epochs where time was aligned to stimuli onset (Fig. 3a–c), in each trial we subtracted the average of SI within the time window [−200 ms, 0 ms] from the entire epoch as a baseline correction.
Statistical analysis
To test the regression coefficients between false alarm rate and repetition number (Fig. 1c), we used a two-sided hypothesis test of the t-statistics estimated from the coefficient estimates and corresponding standard errors, with sessions as the degrees of freedom and significance threshold α = 0.05. A similar procedure was used to test the regression coefficients between false alarm RT and repetition number (Fig. 1d).
Furthermore, we fitted generalized linear mixed-models between false alarm occurrence (
To test the decoding performance of LFPs (section Variance in LFPs explained by stimuli repetition), we used the dpca_classificationAccuracy function of the dPCA toolbox (Kobak et al., 2016). For each session, we organized the LFP data as a 6-D matrix (Y) of dimension C × M1 × M2 × M3 × T × NM, where C refers to channel index (96 channels). M1, M2 and M3 refer to number of conditions in the marginalization factors used, i.e., cue (M1 = 2), orientation of the stimulus in RF (M2 = 2) and stimulus repetition (M3 = 4, repetition number ≥4 were grouped). NM is the maximum number of trials corresponding to any condition in any of the marginalization factors. The entries in the matrix where NM exceeded the number of possible trials for a condition were filled with NaN (not-a-number). To estimate the discriminability of different conditions for each marginalization, a sub-matrix Ytest was carved out of Y, consisting of a random combination of trials for each condition and each marginalization. Ytest was of dimension C × M1 × M2 × M3 × T. The remainder of Y was considered as the training data i.e., Ytrain. dPCA was performed on the marginalization average of Ytrain, i.e.,
To test the association between SI and stimulus repetition number (Fig. 3a), we estimated the Spearman’s rank correlation between stimulus repetition number and SI at each time point t within each session (ρ of dimension T × K, K refers to the number of sessions). Unless otherwise noted, we applied a “Fisher z-transformation” (Eq. 18) to correlation values throughout the study, before performing any statistical test on them. We used a cluster-based permutation test to evaluate the statistical significance of zρ (Maris and Oostenveld, 2007). We performed a two-sided t-test at each time point, using α = 0.05 as a preliminary significance threshold to test if zρ is significantly different from 0. We summed the t-scores of adjacent significant time points (a “cluster”). The resultant sum is the “cluster statistic”. We then randomly permuted the group labels between zρ and [0] along the session dimension while keeping the time dimension consistent between the two. We performed a two-sided t-test between the two pseudo-groups, identified clusters in the permuted groups, and stored only the cluster score with the largest absolute value. We repeated this procedure for 10000 times. The originally identified clusters for which the absolute values of corresponding cluster statistics were above the 95 percentile of the absolute values of the permuted cluster scores were deemed statistically significant. We used publicly available MATLAB code to perform this analysis (Gerber, 2019).
In Figure 3c, to further signify the association between repetition number and SI, we estimated the rank correlation between repetition number and SI across sessions, after averaging the SI values for each repetition number within a session (resulting matrix ρ is of dimension T × 4 × K; trials with stimuli repetition number ≥4 were grouped). To perform a cluster-based permutation test and estimate cluster statistics, we transformed the correlation values to t-scores using Equation 19. We permuted the repetition number values across sessions, computed the correlation between the permuted repetition number and SI, converted the estimates to t-scores, and estimated the pseudo cluster score. This procedure was repeated 1000 times to get a distribution of pseudo-cluster statistics, against which the statistical significance of the original clusters was tested.
To test the association between SI and RTFA (Fig. 5a,b), we computed the partial rank correlation between SI and RTFA in each session, accounting for variations due to stimuli repetition number and inter-stimulus interval (ISI) in RTFA. Similarly, the partial rank correlation was computed between SI and RTHit, accounting for variations due to stimulus repetition and target orientation change magnitude. In Figure 5a,c, cluster-based permutation tests were used to identify clusters along the time dimension, for which the estimated correlations were significantly different from 0 across sessions (1000 permutations). In Figure 5b,d, we computed the partial correlation between RT (RTFA and RTHit) and SI estimates averaged within the time window [−600 ms, −100 ms] w.r.t. saccade onset in each trial. We performed a two-tailed t-test to test statistical significance.
To test the association between global field power (GFP), i.e., the spatial standard deviation of voltage across the electrode array, and SI (Fig. 6a,b), for each session, we averaged the GFP within a SI quintile and normalized the session average to unit-value (resultant GFP matrix is of dimension T × 5 × K). At each time point t, we computed the rank correlation between GFP and SI bin numbers across sessions. We used a cluster-based permutation test, as described above in this section, to identify statistically significant clusters along the time dimension, where the estimated correlations were significantly different from 0 (1000 permutations).
To test the trend in the slope (βRT) between RTFA and ISI with SI decile index ([1,2,…,10]), we fitted a linear regression model between the two (Fig. 7b). The p-value was estimated from the F-statistics corresponding to the regression coefficients. The R2 value signified the goodness-of-fit of the regression.
To test how the dependence between stability and false alarm likelihood (i.e., “criticality”) varies across the state space (Fig. 8), we first divided the state space in each session into 12 regions or partitions. Since there are infinite ways to divide a subspace, we chose the following criteria to constrain the partitions: (1) the regions are disjoint, i.e., no signal observation is a member of two different partitions; (2) observations within a partition are temporally contiguous, which helps individual partitions have a consistent identity across sessions; and (3) each partition has an equal number of signal observations (or samples). We calculated the centroid of each partition. In each trial, for both false alarms and correct rejects, we indexed each signal sample in terms of its proximity to the partition centroids, i.e., we identified the sample as a member of the partition for which it has the shortest Euclidian distance to the partition centroid. Following this procedure, we estimated the SI for each individual partition and trial. Subsequently, we estimated the relationship between false alarm likelihood and SI across trials using linear regression (after regressing the contribution of ISI and repetition number). Since the directionality of the regression coefficients (i.e., positive or negative) and the strength of the regression (R2) were consistent across sessions in each monkey, in terms of the individual partition labels, we combined the sessions in each monkey for more statistical power. To assess the significance of the partition membership to the strength of the relationship between SI and FA likelihood, we permuted the partition labels while keeping the samples belonging to each partition constant so that across trials, the association between the partition label and the regression R2 is likely destroyed. We iterated this process over 2000 times to create a null distribution of the R2, absent its partition membership. The partitions where the original R2 exceeded the 95 percentile of this null distribution were deemed statistically significant, i.e., the strength of association between false alarm likelihood and SI was particularly stronger due to the observations belonging to the said partition than would be expected by chance.
To observe the trend in the explanatory power of SI for false alarm occurrence (
Results
We recorded LFPs from area V4 of two adult male macaques (Macaca mulatta) engaged in a non-match-to-sample grating orientation change-detection task (Fig. 1a). Separate analyses of other data from these experiments have been previously reported (Snyder et al., 2018; Cowley et al., 2020; Snyder et al., 2021; Umakantha et al., 2021; Johnston et al., 2022; Sachse and Snyder, 2023). The task included a spatial attention manipulation across blocks of trials, and our previous reports concerned spatial attention effects and did not specifically analyze false alarm behaviors. Because monkeys overwhelmingly directed false alarms towards the spatially attended stimulus (89.8% for monkey M1, 90.1% for M2), we did not analyze false alarm behavior in the context of spatial attention for this report. In general, monkeys performed the task well, correctly discriminating targets with an orientation change from the repeated standard stimuli (i.e., “no change” stimuli; d′ = 1.26 (0.12) [mean (SD)] for M1, d′ = 1.06 (0.16) for M2 (see Methods for the d′ estimation); for reference, in a typical two-alternative change detection task, chance performance equates to a d′ = 0 while a hit rate of 80% and false alarm rate of 28% equates to d′ = 1). However, performance was not perfect, and monkeys incorrectly made saccades to standard stimuli (false alarms) at a moderate rate; 0.25 (0.06) [mean (SD)] false alarms per standard stimulus presentation for M1, 0.37 (0.11) false alarms per standard stimulus presentation for M2. One feature of our task was that trials could contain several repeated standard stimuli before the presentation of a target, requiring the monkeys to perform a cognitive “loop” of deliberative inaction (number of repetitions N ≤ 19, mostly 1–3 repetitions per trial). We reasoned that this repetitive task structure might be particularly well-suited for revealing the nature of the relationship between stable behavior and neural population dynamics. To build a cohesive and mechanistic explanation of the false alarm behavior, we studied three types of relationships: (1) the correlation between monkeys’ false alarm rate and time-lapsed since the trial onset, i.e., non-target (standard) stimuli repetition number; (2) the correlation between estimates of stability of neural trajectories (“stability index”) and stimuli repetition number; and (3) the correlation between SI and response time (RT).
Experimental paradigm and behavioral results. a, Non-match-to-sample change detection task; each trial sequence contained several repetitions of the sample stimuli (the first set of stimuli or non-targets) before an orientation-changed stimulus, i.e., target, appeared in either location. The monkey was required to saccade to the target stimulus. b, Schematic of our dynamic attractor framework: state-space illustration of the neural trajectories for a trial sequence with two repetitions of the non-target stimuli where the monkey correctly withheld saccade. The thick blue line denotes the hypothetical attractor around which individual-trial neural trajectories (thin dashed lines) traverse. All the observations where the monkey correctly withheld saccades constitute the correct-reject basin of attraction. In this example, one neural trajectory has been schematized to be more stable (cyan dashed line) and, therefore, less likely to escape the correct-reject basin of attraction and subsequently lead to a false alarm than the other less-stable trajectory (purple dashed line). The false alarm attractor boundary has been demarcated by the magenta dotted line. The upward and downward green triangles denote the onset and offset of the stimulus, respectively. c, False alarm rate (%FA) decreased as stimuli repetitions increased (inset shows regression coefficients and corresponding statistical significance of curve fits between %FA and repetition number for individual monkeys; **p ≤ 0.01, ***p ≤ 0.001). d, RTFA slowed as stimuli repetitions increased. That is, when monkeys experienced longer sequences of non-target stimuli, they were less likely to commit false alarms and were also slower to act if/when they did so.
False alarm behavior improved with repetition number
We examined how the monkeys’ false alarm behavior was related to the number of such deliberative loops that had been performed in a trial sequence (i.e., the stimulus repetition number). We considered two potential cognitive mechanisms whereby false alarm behavior and repetition number could be associated. One mechanism could be that repeating a behavior causes it to be more likely to be executed again in the future through, e.g., Hebbian plasticity mechanisms (Hebb, 1949). Another mechanism could be that if the monkey is in a state indisposed to false alarms, this would lead it to “last” longer into the trial and, therefore, to experience more stimulus repetitions (i.e., a survivorship effect). Both of these hypothetical mechanisms predict an inverse association between false alarm rate and repetition number. Moreover, reasoning that the same factors that might make the monkey disinclined to act likely also lead to longer latencies for actions when they do occur, both hypothetical mechanisms correspondingly predict a direct association between RTFA and repetition number. To test for such associations, we calculated the monkeys’ false alarm rate and RTFA as a function of repetition number in each session. We considered a decrease in false alarm rate (%FA) and a slowing in RTFA as a signature of behavioral improvement. Our results concurred with these predictions (Fig. 1c,d; Spearman’s rank correlation between false alarm rate and repetition number for monkey M1: ρ = −0.34, p = 0.0001, N = 24 sessions; M2: ρ = −0.23, p = 0.0143, N = 23; rank correlation between false alarm RT and repetition number, M1: ρ = 0.35, p = 0.0001; M2: ρ = 0.51, p = 7.520 × 10−9). Estimates from a generalized linear mixed model with session number as the random-effect term (Eqs. 2–4b in Methods) produced similar results (false alarm rate, M1: βrepetition = −0.0090, P < 0.001, 95% CI =[ − 0.0117, − 0.0060], N = 24; M2: βrepetition = −0.0078, P < 0.001, 95% CI =[ − 0.0116, − 0.0034], N = 23; false alarm RT, M1: βrepetition = 0.0017, P < 0.001, 95% CI =[0.0012, 0.0021], N = 24, M2: βrepetition = 0.0044, P < 0.001, 95%CI =[0.0040, 0.0051], N = 23). This pattern of improved (slower and less common) false alarm behavior as repetition number increased suggests the potential for our hypothesized mechanisms linking dynamic neural stability to false alarm behavior, such as reinforcement through plasticity or survivorship effects.
We further explored the behavioral implications of the hypothetical mechanisms described earlier in this section. If, because of a general state of disengagement after a higher number of repetitions of non-target stimuli, the monkey makes fewer false alarm saccades and is slower, this should also result in a lower number of hits in detecting actual stimulus changes. However, we did not find much evidence in favor of this hypothesis (rank correlation between hit rate and repetition number; for monkey M1: ρ = −0.12, p = 0.2010, N = 24 sessions; for M2: ρ = −0.17, p = 0.0680, N = 23). The rank correlation between response time for correct change detection trials and repetition number was estimated to be ρ = 0.35, p = 0.0001, N = 24 for M1, and ρ = 0.25, p = 0.0079, N = 23 for M2. Even though saccadic actions, whether deemed correct or incorrect, slowed with stimuli repetition, the negative relationship with the rate of these actions was specific to incorrect ones, i.e., false alarms. Therefore, it is unlikely that a general tendency for disengagement over successive stimulus repetitions fully explains monkeys’ false alarm behavior. We next sought to test how the dynamics of V4 neural activity explains additional moment-to-moment variation in false alarm behavior.
Variance in LFPs explained by stimuli repetition
Before diving into the dynamic attractor framework to explain the link between false alarm behavior and neural activity, it is pertinent to ask if the task variable that modulated behavior is reflected in any manner in the recorded neural data, i.e., local field potentials from the extrastriate area V4. Local field potentials are advantageous for studying neural population dynamics because they are continuous-valued over their amplitude range and regularly sampled (unlike binary spike trains), which facilitates analysis methods based on differentiation. Because false alarm behavior varied with stimulus repetitions, we sought to understand how the neural activity varied with the same. It is axiomatic that behavior and neural activity are intrinsically linked, either endogenously or exogenously, or both. Whether the modulation in neural activity is shaped by stimuli repetition or that the neural activity shapes the animal behavior so that the monkey can fixate longer in a trial sequence and thereby be exposed to more stimuli repetitions is not a question that can be answered with our experiment. So, we only report their association here without any unwarranted interpretation.
Measures of explained variance by a set of factors in a dataset can signify each factor’s relative importance in the data’s production. To gauge the relative importance of repetition numbers in the LFPs, as a first step, we tested whether the variance in the LFPs can be explained by repetition number. We performed dPCA on the LFP data and considered attention condition, stimulus orientation presented in the RF, and repetition number as three marginalization factors in the analysis (Kobak et al., 2016). We found that all our task variables of interest were reflected in V4 LFP activity: the average variance contribution of the principal component for cue was 0.10% (SEM 0.02%), for stimulus orientation
Stimuli repetition predicted stability in population dynamics
We estimated the dimensions in the LFP activity subspace that maximized the stimulus SNR. We used a GEV method to identify the dimensions that maximally explained activity elicited as a response to stimulus while minimizing the residual noise (de Cheveigné and Parra, 2014). We considered the trial-averaged response in this subspace as the estimate of the hypothesized limit cycle attractor (Fig. 2c). One aspect of a dynamically stable system is that when its trajectory is perturbed, it subsequently acts against the perturbation and converges onto its prior attractor cycle. Our estimation of stability hinges on this logic. For each time point on each individual trial, we estimated the projection of the change in residual activity (i.e., difference from the trial-average) at the immediate future time point along the direction of the trial-averaged trajectory, which is the “pulling force” towards the attractor when a deviation occurs away from it (Fig. 2c). We computed a metric for estimating stability in neural dynamics, i.e., stability index as the net pulling force towards the attractor cycle over a time period. For each repetition number, we estimated the average pulling force at each time point and the net stability during the stimulus presentation period. We found that stability index estimates and repetition number were positively correlated (Fig. 3; for monkey M1: across-sessions median Spearman’s ρ = 0.0226, p = 0.0446, N = 24 sessions; M2: ρ = 0.0496, p = 0.0001, N = 23; right-tailed sign-rank test), suggesting the attractor cycle became more attractive with each successive stimulus presentation.
Estimation of stability of neural trajectories. a, Schematic of computing stability at a given time point t, as the amount of change in perturbation in the direction of the limit cycle attractor (blue). Subscript t denotes time.
Neural activity during the stimulus-response grew more dynamically stable as stimuli repetition increased. a, Session-averaged time series of Fisher-transformed correlation (
Response time slowed, and false alarm likelihood decreased with stability in the neural dynamics
We reasoned that trials with higher estimates of stability index would experience a greater pulling force towards the trial-averaged trajectory, and thereby would be less likely to drift away to other parts of the neural state space corresponding to different behaviors. In other words, trials with a higher stability index would be less likely to lead to false alarms. We first tested this by comparing SI estimates between correct-reject and false alarm trials (Fig. 4a). In the pre-stimulus period, we found that SI estimates for correct-reject trials were higher than false alarm trials (two-tailed cluster-based permutation test with threshold p = 0.025; cluster 1 time window [−300, −156] ms, p < 0.001, N = 47 sessions). Furthermore, we fitted generalized linear models between SI estimates and behavioral outcomes for no-change stimuli presentations (i.e., correctly continued fixation:
Stability estimates were generally higher for trials where the monkey correctly or incorrectly withheld saccades. a, The plot shows the session-averaged time series of SI estimates, normalized to unit-average for each session, for correct rejects and false alarms. Sessions from the two monkeys were combined. Thick lines indicate periods where SI estimates significantly differed between the two conditions (two-tailed cluster-based permutation test with threshold p = 0.025; cluster 1 time window [−300, −156] ms, p < 0.001, N = 47 sessions). The color of the thick lines indicates the trial type with a higher SI than the other. In cluster 1, SI estimates for correct-reject trials were higher compared to false alarm trials. (b) Conventions are the same as (a). In cluster 1 ([−290, −220] ms, p = 0.002), SI estimates were higher for misses than for correct hits. In cluster 2 ([−18, 68] ms, p < 0.001), SI estimates were higher for correct hits than for misses.
In addition to the previous binary result, one more nuanced prediction of the dynamic attractor framework is that, given that a saccade does occur, that action should take more time to escape from the deliberative loop of action inhibition when neural activity is more stable; because it has to overcome a stronger attractive force. In this scenario, response time will be positively correlated with the stability of the neural system, i.e., the more stable the system is, the slower the response time will be. Importantly, this reasoning applies not only to the response time for false alarms but also to correct saccades. To test this prediction, we analyzed the monkeys’ LFP aligned to saccade onset in each trial. We estimated the stability index for each trial in a session, and computed the partial correlation between stability index and response time within a session after accounting for the variation due to stimuli repetition number (Fig. 5a,b). Response time was positively correlated with stability index for both false alarms (M1: mean Spearman’s ρ = 0.1153, t23 = 6.23, p = 2.360 × 10−6, N = 24 sessions; M2: ρ = 0.2411, t22 = 14.72, p = 7.189 × 10−13, N = 23), and for correct saccades (Fig. 5c,d, M1: ρ = 0.0840, z = 0.0850, t23 = 4.40, p = 0.0002; M2: ρ = 0.1835, z = 0.1876, t22 = 9.12, p = 6.225 × 10−9). In M1 only, the relationship between pre-stimulus SI and subsequent reaction time (RT) reversed when SI was measured even earlier (>150 ms) before saccade onset. As we discuss below (section Discussion), this may be related to a periodic process that alternates sensory and motoric phases. Overall, the consistent direct relationship between pre-stimulus SI and RT across different stimulus contexts, i.e., being a target or non-target, suggests it to be a generic contributor to saccade behavior. Indeed, as with the difference in SI during spontaneous activity preceding false alarms versus correct rejections, we found that V4 activity was less dynamically stable preceding correctly detected targets (hits), which requires a shift in behavior consistent with escaping an attractor, compared to “missing” the target, which does not require such a shift (Fig. 4b). Interestingly, around the time of the initial transient V4 response to the target this relationship between stability and trial result reversed, with greater stability in visual responses before hits compared to misses. Taken together these results suggest that low stability during spontaneous activity is beneficial for detecting stimulus input, while stability during the visual response is beneficial for the subsequent processing of that input. Our next analysis more directly characterized these complementary effects of dynamic stability during the transition from spontaneous activity to stimulus processing in visual cortex.
Response time for both false alarm and correct saccades was slower when neural activity preceding them was more dynamically stable. a, Time series of partial correlation between stability and RTFA, i.e.,
Spontaneous dynamic stability was inversely related to strength of visual evoked responses
Under the dynamic attractor framework, dynamic (in)stability is related to the sensitivity of the neural population to perturbation. For a traditionally-regarded sensory population such as V4, this suggests that stimulus input arriving during periods of relative dynamic instability should be associated with more robust evoked responses compared to stimulus input arriving during periods of relative dynamic stability. To test this, we divided trials into quintile bins based on the average SI during the prestimulus spontaneous activity. Then, we quantified the overall magnitude of the evoked response as the global field power (standard deviation of voltage across the electrode array) during the stimulus-response period in each bin. Confirming our prediction, we found that prestimulus dynamic stability was significantly negatively correlated with the magnitude of the evoked response to the stimulus (Fig. 6a,b; for monkey M1: cluster 1 [−40, 512] ms, p = 0.001; M2: cluster 1 [−22, 98] ms, p = 0.002, and cluster 2 [110, 302] ms, p = 0.006; two-tailed cluster-based permutation test; see Methods). This suggests dynamic stability may index periods of relatively stronger or weaker visual sensitivity within V4 populations.
Relationship between baseline stability and GFP. a, Time series of normalized GFP averaged across sessions for individual monkeys (average of GFPs within a session scaled to unit value). Each thick line and the thin lines around it, correspond to the session-averaged GFPs and associated ±SEM, respectively. In each session, the GFP estimates were averaged across trials belonging to one quintile of baseline SI estimates. Blue and magenta lines correspond to the highest and the lowest quintiles of SI estimates, respectively. b, Rank correlation between SI bin numbers and average GFP for each bin, estimated across sessions for individual monkeys. Thick lines denote statistically significant correlation values (two-tailed cluster-based permutation test, threshold p = 0.05; for monkey M1: cluster 1 [−40, 512] ms, p = 0.001; M2: cluster 1 [−22, 98] ms, p = 0.002, and cluster 2 [110, 302] ms, p = 0.006).
Low and high stability were associated with distinct types of false alarm behavior
Because we found that the V4 population had different stimulus-evoked response magnitudes depending on whether the pre-stimulus spontaneous activity was especially stable or unstable, we asked whether dynamic stability might reflect differences in the monkeys’ engagement with visual processing. For example, a period of high stability might indicate the monkey is withdrawn from (or insensitive to) the visual task, while a period of low stability might indicate the monkey is engaged in (or sensitive to) it. These different regimes of task-engagement or task-sensitivity would likely be associated with different “types” of false alarm behavior. In the task-engaged/sensitive state, the monkey may false alarm because it believed that it perceived a target when in fact no target had been presented (a “misperception”). In the disengaged state, the visual stimulus is unlikely to trigger a false alarm, but rather the monkey may decide to make a false alarm for non-sensory reasons, such as impatience with the task (a “premeditated” false alarm). In this case the timing of responses might depend less on actually detecting a visual stimulus, and be more related to other aspects of the task structure, such as the elapsed time since the previous stimulus. We previously found that such impulsive actions are indexed by a shared activity pattern across prefrontal cortex and visual cortex (Cowley et al., 2020), suggesting that in such cases a large-scale signal might dominate the intrinsic dynamics within V4. Thus, the difference between these “misperception” and “premeditated” types of false alarms could be expected to relate to the detailed structure of the task and the timing of visual stimuli, as well as the dynamic stability of V4, which we tested with our next analysis.
Enhanced stability was associated with “premeditated” false alarms
Since the ISI is the time between the current stimulus onset (which is unknown to the monkey in advance) and the previous stimulus offset (which is known) if the monkeys preemptively decided to make a saccade (a “premeditated” saccade) using the previous stimulus offset to anticipate the correct timing, this could result in an inverse relationship between ISI and response time. As an analogy, imagine a baseball player trying to hit a pitch: because the timing is so quick, they have to plan their swing based on the wind-up of the pitcher; if the pitcher then throws a faster-than-expected pitch (short ISI) the batter will swing too late (slow RT), but if the pitcher throws a change-up, slower-than-expected pitch (long ISI) the batter will swing too early (fast RT), thus an inverse relationship between ISI and RT (Fig. 7a). Since we hypothesized that especially high stability in V4 might indicate a “premeditated” false alarm, we predicted that ISI and response time should be particularly inversely related for the most stable trials, whereas ISI and response time would be less strongly related (or even unrelated) for trials with low stability. To test this, we divided trials into decile bins based on the average stability index measured 600–100 ms before the saccade, and measured the strength of the relationship between ISI and response time within each bin.
Variation in RTFA with ISI during premeditated false alarm saccades. a, Schematic describing a negative relationship between RT and ISI for premeditated false alarms. b, Plot of the slope between RTFA and ISI for trials within each SI decile, after controlling for the trend between ISI vs. SI, and, RTFA vs. SI. Error bars correspond to 95% CI calculated as 1.96 × SE. As SI increases, the inverse relationship between ISI and response time strengthens.
In general, RTFA was inversely related to ISI across all SI bins (Fig. 7b). That is, monkeys were faster to false alarm to a stimulus if they had waited a relatively longer time since the previous stimulus. However, the slope of this relationship became steeper with the increase in SI (Fig. 7b; lowest SI decile: for monkey M1, βRT = 0.0255, t895 = 1.7197, p = 0.0858, for M2, βRT = −0.0452, t1556 = −3.6523, p = 0.0003; highest SI decile: for M1, βRT = −0.0989, t895 = −7.5729, p = 9.084 × 10−13, for M2, βRT = −0.1684, t1556 = −11.7127, p = 9.084 × 10−13). In other words, when V4 activity had high dynamic stability, there was an especially strong inverse relationship between ISI and false alarm response time.
To summarize the findings thus far: in general, dynamic neural stability was inversely related to the prevalence and speed of false alarms; however, although false alarms during periods of especially high dynamic stability were rare, when such false alarms did occur, the pattern of response time was consistent with a class of “premeditated” false alarms, where the monkey tries to time its next saccade. We next considered how false alarm behavior would be related to neural activity at the other end of the spectrum during periods of relatively low dynamic stability.
Unstable sensory activity near attractor boundaries and “misperception” false alarms
Under the dynamic attractor framework, state instability would be most critical when the state is near the attractor boundary. That is, unstable perturbations far from the attractor boundary would be less likely to push the visual system out of the basin of attraction corresponding to correctly withholding the saccade, and presumably into a new basin of attraction that leads to false alarm behavior. In contrast, similar-magnitude perturbations near the boundary are more likely to do so. Such an excursion could be called a “misperception false alarm,” since we are considering activity in a cortical area with a predominantly sensory function. To test this, we sought to compare the strength of the relationship between stability and false alarm rate when the state was (1) near the attractor boundary versus (2) far from the attractor boundary. Because we do not have explicit knowledge of the dynamic landscape of the system but can only infer dynamics in the vicinity of states visited by the system through observation, we do not know where the attractor boundaries are. However, the signature of an attractor boundary is that small perturbations of state in the vicinity of the attractor boundary lead to large divergences in the long-term behavior of the system (such as, we reasoned, a false alarm versus a correct rejection). Thus, we systematically divided the state space into neighborhoods and tested the strength of the relationship between the stability index and false alarm rate for neural activity in each neighborhood (Fig. 8a; see Methods). Because we had already determined that especially high (above-median) stability could be explained as “premeditated” false alarms that were likely due to executive function rather than misinterpretation of sensory signals, we separately performed this analysis for trials with below-median stability index (where proximity to attractor boundaries is most likely to be critical) and for trials with above-median stability. As we predicted, dynamic instability had a strong effect on the behavioral outcome of the trial in particular regions of the state space (Fig. 8). For trials with below-median stability, we found neighborhoods where instability was much more likely to lead to false alarms compared to other neighborhoods in the state space (Fig. 8b,c). While overall false alarm likelihood decreased as stability increased (see section Response time slowed, and false alarm likelihood decreased with stability in the neural dynamics), one noteworthy observation within the subset of high stability trials was that the false alarm likelihood increased with stability (Fig. 8d). We speculate this may index the monkey’s resolve about committing to the action. To summarize, the overall relationships we observed between stability and false alarm behavior were especially critical in a particular neighborhood of the state space, consistent with proximity to an attractor boundary.
Variation in false alarm likelihood as individual trajectories traverse the state-space. a, The plot shows how the fraction of variance explained (R2) in false alarm likelihood by SI varied at different locations along the attractor trajectory (partitioning was performed in the high-dimensional state space; only the top two dimensions are plotted for illustration). The small-size scatter points represent all the observations from a representative session in monkey M1. The state space has been partitioned into 12 bins (see Methods). The color of the dots represents the bin identity. Overlaid, the large filled dots represent the centroid of each bin. The overlay dot color indicates the R2 between false alarm occurrence and SI estimate in the corresponding bin. The upward and downward triangles indicate the average neural state at stimulus onset and offset, respectively. It can be observed that, at some locations in the state space, the R2 was particularly higher than in other parts of the state space. b, Plots of regression coefficients between false alarm occurrence (
Our previous analysis considered the position of the neural state in the state space but did not take into account the timing of the activity. We next asked how the passage of time interacted with the traversal of the state space in driving false alarm behavior. We found that for trials with below-median stability, the relationship between SI and false alarm rate for both monkeys was not constant over the course of a trial but rather varied in strength in a consistent way as a function of ISI, with two “critical” periods (i.e., when stability makes a substantial difference between committing or avoiding a false alarm) roughly 100 ms apart (Fig. 9a). This is consistent with the idea that the system approaches and recedes from attractor boundaries periodically over the course of a trial in a consistent way, and dynamic instability is more critical when near such a boundary. For both monkeys, the relationship between SI and false alarm rate was weaker at shorter ISIs (the 2nd and 3rd ISI deciles in Fig. 9a; 300 ms was the shortest ISI in the experiment), but then grew to a significantly stronger relationship peaking at intermediate ISIs (5th decile for both monkeys; ∼470 ms for monkey M1 and ∼520 ms for monkey M2). This relationship then weakened again for ISIs in the 6th to 8th decile, before growing to another peak at relatively higher ISIs (9th decile for both monkeys; ∼560 ms for M1, and ∼600 ms for M2). Because the period between peak relationships was approximately 80–90 ms, this could be consistent with the neural state traversing a limit cycle attractor at a frequency of around 11–12.5 Hz. For trials with above-median stability (for which proximity to an attractor boundary should be less consequential), we found no such relationship (Fig. 9b).
Fraction of variance in false alarm likelihood explained by SI for different ISI bins. a, The plot shows estimated R2 for low stability trials for individual monkeys (in thick lines). Dotted lines denote 95 percentile estimates of R2 after permuting trial labels corresponding ISI bins. *: ISI bins for which original R2 values were significantly larger (p < 0.05, one-tailed) compared to the permuted ones. b, Plots of R2 for high stability trials. Conventions are the same as that in (a).
To summarize, we found that dynamic stability in V4 predicted false alarm behavior. The relationship between stability and false alarms could take two forms. In the highly-stable regime, the pattern of response times was consistent with “premeditated” false alarms that do not depend on visual activity. As we discuss below, this form of stability is likely inherited from executive control regions imposing this premeditated decision signal on visual populations. In the highly-unstable regime, the position of the neural state within the state space reveals a “critical” neighborhood where perturbations in neural activity are more likely to lead to false alarms (“misperception”), suggesting proximity to a boundary between basins of attraction for withholding versus generating a saccade. The timing of observed criticality over the interstimulus interval suggests the state makes consistent, periodic traversals of the critical state neighborhood.
Discussion
We asked whether dynamic (in)stability in visual cortical activity could explain animals’ false alarm behavior on a task requiring long periods of vigilant inaction. We found that animals were less likely to commit false alarms following periods of high dynamic stability in V4 and that such dynamic stability also led to a slowing of saccadic actions (both correct and incorrect actions). On a more fine-grained level, our results were consistent with a break-down of false alarms into two broad categories: “premeditated” false alarms, characterized by high dynamic stability in V4 overall, but little dependence on the moment-to-moment details of the activity, and “misperception” false alarms, consistent with perturbations in V4 activity cascading across attractor boundaries during periods of low dynamic stability. Thus we found that measuring the dynamical properties in visual cortex during this task improves our understanding of false alarm behavior.
Exploiting the properties of dynamical stability may be an important and universal principle underlying cortical computation. Much of the research into how the dynamical systems framework explains brain circuit function has come through the study of skeletomuscular motor control, but it has been unclear the extent to which the same framework applies across different functional domains. The current findings in the visual cortex would be consistent with a universal principle.
The dynamical systems framework is natural for motor control, where the coordinated kinematics of muscles unfold in time. In this context, motor preparation is viewed as setting the initial condition, which allows the appropriate motor action to unfold (Vyas et al., 2020). The motor preparatory activity uses mixtures of neurons that are orthogonal to those that drive motor outputs, which enables the preparatory state to be set covertly without leading to premature motor action. We recently showed evidence that a similar principle guides the preparation of visuospatial selective attention in V4 (Snyder et al., 2018): a consistent attention-dependent system state is established prior to stimulus onset, but that state does not change the overall level of V4 activity; once the stimulus perturbs the state, however, the response unfolds differentially depending on that covert initial condition. We showed that a minimal dynamical systems model recreated the experimentally observed patterns of neurophysiological results. The dynamics of visual perception may even be directly linked to those of motor control through the process of biological motion perception (Krakowski et al., 2011), through a sort of dynamical analog of the so-called mirror neurons (Rizzolatti and Craighero, 2004) that recognize supramodal features of the dynamics underlying visual perception of actions and motor execution thereof.
Another computational advantage of dynamical systems is their allowance for pattern completion: partial input that pushes the state into an appropriate basin of attraction is sufficient to lead to the execution of the full pattern of activity. In the motor domain, Li et al. (2016) tasked mice to locate objects by whisking, and then during movement preparation, the experimenters optogenetically suppressed large portions of the premotor cortical network. They found that the premotor network was able to compensate for the missing activity consistent with pattern completion by a dynamic attractor, leading to motor behavior being largely unaffected. For sensory systems, such dynamical pattern completion may be critical to provide stable categorical perception in the face of noisy and dynamic input, such as perceptual “closure” of occluded objects (Doniger et al., 2000; Tang et al., 2018), and could underlie some illusions, such as illusory contours (Altschuler et al., 2012). Aberrations in the dynamic landscapes that support these completion processes may help to explain some disorders of perception, such as sensory hallucinations with psychosis (Waters et al., 2014) or dementia (Barnes and David, 2001), and elevated sensitivity in sensory processing disorder or Autism spectrum disorders (Marco et al., 2011). On the other end of the spectrum, overly stable dynamics could also be problematic. For example, one interpretation of obsessive-compulsive disorder (OCD) is as a tendency for overly strong attraction of neurophysiological limit cycles guiding behavior (Rolls et al., 2008). While high-level behaviors receive much of the attention in the study of OCD, deficits in low-level visual processing and perceptual decision-making have also been reported (Gonçalves et al., 2010; Kim et al., 2008). A general change in dynamic stability could provide a unifying framework for understanding this constellation of symptoms, and point to perceptual assays that could be used as biomarkers for mental disorders.
While much of the study of dynamics in motor and premotor cortex has concerned the planning and execution of movements, there has been recent interest in how premotor dynamics support value-based decision-making. For example, Wang et al. (2023) tasked monkeys to pick between offered rewards of different magnitudes and delays, signified by different symbolic visual cues, while the experimenters recorded population activity in lateral prefrontal cortex. Similar to our approach, the researchers estimated the attractive strength of dynamic attractors from the residuals of individual-trial neural population state space trajectories. They found that the strength of dynamic attraction was related to the consistency of animals’ decisions in the task. Our current results in visual cortex are largely consistent with this previous finding in prefrontal cortex, and further enable us to dissect animals’ behavior at a finer-grained scale. Specifically, the stable dynamics underlying consistent decisions that Wang et al. (2023) observed could be consistent with what we termed “premeditated” false alarms in this task, as well as confident judgements of correctly detected targets. It is possible that the stable dynamics in visual cortex associated with these premeditated false alarms are inherited from prefrontal feedback. However, we also found evidence that periods of low stability can “make or break” animals perceptual judgements on our task, suggesting a different class of false alarm behavior based in visual misperception.
We found that for trials with relatively low stability (i.e., not likely to result in premeditated false alarms), the relationship between dynamic stability and false alarm rate varied in a reliable way over time since the preceding stimulus. Namely, the relationship started out weak, but grew to a significant peak at regular and repeated intervals (∼11–12.5 Hz; Fig. 9a). This periodic relationship could be consistent with the system traversing a limit cycle that approaches an attractor boundary separating perceptual from motoric states. The 10–12.5 Hz frequency we observed corresponds to the so-called alpha band that has been linked to attentional suppression of visual processing (Snyder and Foxe, 2010; Banerjee et al., 2011; Foxe and Snyder, 2011; Mathewson et al., 2011). Neural oscillations have also been implicated in the growing evidence in support of a “rhythmic” theory of attention that holds that theta oscillations organize alternate time periods suitable for perceptual processing and motoric action, and the current results are certainly consistent with this framework (Fiebelkorn et al., 2011; Fiebelkorn and Kastner, 2019; Aussel et al., 2023). Such an alternation between perceptual and motoric processing phases could also be related to our observation in one monkey that the usual direct relationship between stability and response time at short delays inverted for delays around 150 ms or more (Fig. 5).
Taken together, the current results add to the growing appreciation of the computational role for dynamical systems in neuroscience by linking dynamical stability in visual cortex to perceptual decision-making behavior. Improved understanding of neurophysiological dynamics will likely be critical for intervening in brain function, such as to treat complex mental illnesses. For example, rather than trying to precisely impose a particular pattern of neural activity on the brain through highly targeted stimulation or inactivation, one feasible approach may be to rather shape the dynamic landscape so that neural activity naturally unfolds along more favorable trajectories. Further, monitoring the dynamic stability of neural activity may enable people to monitor for potential errors of perception or decision-making that are critical for navigating daily life.
Footnotes
A.C.S. was supported by NIH grants K99/R00EY025768, R01EY028811 and R01EY011749; a NARSAD Young Investigator award from the Brain & Behavior Research Foundation; and an Alfred P. Sloan Foundation research fellowship. Experimentation was performed by A.C.S. while a postdoctoral fellow in the laboratory of Matthew A. Smith at the University of Pittsburgh (now at the Carnegie Mellon University). We thank Dr. Smith for his support, including funding (NIH grants R01MH118929, R01EB026953, R01EY022928 and P30EY008098; NSF NCS BCS 1954107/1734916; Research to Prevent Blindness; and the Eye and Ear Foundation of Pittsburgh). The authors would like to thank Ms. Samantha Schmitt for assistance with surgery and data collection, and Dinah McAlly for feedback on dynamical systems analyses.
The authors declare no competing financial interests.
- Correspondence should be addressed to Adam C. Snyder at adam.snyder{at}rochester.edu.
