Experimental setup and trial-averaged neural responses

We trained two rhesus macaques on a center-out reaching task in which they controlled an on-screen cursor using a planar manipulandum (Fig. 1a). Each session consisted of both 1-Target and 2-Target trials, randomly interspersed. On 2-Target trials the monkey first positioned the cursor in the central target, after which two additional targets appeared located 180° apart with respect to the center (Fig. 1c, left). These targets remained on screen for between 750 and 1000 ms (Target On), then disappeared for 250–500 ms (Target Blank) before a single target reappeared for 250–500 ms (Cue). Finally, the central target disappeared, the second outer target reappeared, and a tone cued the monkey to reach to the originally cued target (Go). 1-Target trials followed the same basic structure, except that the monkey was only ever shown one outer target (Fig. 1d, left). On roughly 10% of 2-Target trials (Free-Choice trials) we omitted the Cue epoch, and instead instructed the monkey to reach immediately after the Target Blank epoch (Fig. 1c, bottom). In all conditions, the monkeys made approximately straight reaches to the targets (Fig. 1c, d, right).

Fig. 1 Experimental setup. a Monkeys used a planar manipulandum to control a cursor. b Array placement in dorsal premotor (PMd) and primary motor (M1) cortex (CS central sulcus, AS arcuate sulcus, PCD precentral dimple, IPS intraparietal sulcus). Dashed lines correspond to approximate locations of sulcal landmarks that were obscured by the boundaries of the intraoperative craniotomy. c Task events during 2-Target trials and resulting cursor trajectories. The monkeys were initially presented with two opposing targets. On most trials (top), the correct target was displayed at the start of the Cue epoch; roughly 10% did not contain a Cue epoch (Free-Choice, bottom). On these trials, the monkeys were forced to select one of the two targets with no information about which would lead to reward. d Same as in c for 1-Target trials. The monkey image in a was created by Paul Wanda for use in this paper. All rights reserved Full size image

Throughout each session, we recorded the activity of discriminated neurons in both PMd and primary motor cortex (M1) using chronically implanted 96-electrode arrays (Blackrock microsystems). We calculated firing rates by filtering the spike trains with a causal, half-Gaussian kernel before downsampling to 40 Hz. Most PMd neurons appeared directionally tuned throughout the planning phases (i.e., Target On, Target Blank, and Cue epochs) of the 1-Target task. To summarize the population-wide responses, we calculated a preferred direction for each neuron using a standard cosine model25. We then used those preferred directions to categorize the response of each neuron on every trial as either pro-PD (target at preferred direction), anti-PD (target opposite preferred direction), or orthogonal-PD (target orthogonal to preferred direction). The traces in Fig. 2a show the average of all pro-PD and anti-PD activity across 1-Target trials after subtracting orthogonal-PD activity to account for changes not due to reach direction. The resulting plot reveals an increase in pro-PD activity shortly after target presentation and a decrease in anti-PD activity, corroborating previous findings of sustained, planning-related activity in PMd during reaching26,27,28,29,30. We repeated this procedure for 2-Target trials and found an increase in both pro-PD and anti-PD activity (Fig. 2b), seeming to indicate dual representation of both targets, as previously reported9,10,11,12,13.

Fig. 2 Apparent dual representation from trial averaging. a Average activity traces of neurons with preferred directions aligned (solid) and anti-aligned (dashed) with the reach direction across all 1-Target trials. Activity of neurons with preferred directions orthogonal to cue direction has been subtracted. Shading represents bootstrapped 95% confidence. b Average traces (as in a) for all 2-Target trials. c Histograms showing the percentage of activity during pro-PD and anti-PD trials that exceeded the median activity observed on orthogonal-PD trials. Rightward skew on 2-Target trials (blue) suggests simultaneous representation. p-Values correspond to the null hypothesis that the distribution mean is 50% (t-test). d Analysis as in c for a simulation of an unbiased guessing approach using 1-Target data. e Analysis as in c for a simulation of a biased guessing approach using 1-Target data Full size image

Single-neuron tests of dual representation

We further tested the nature of the apparent dual representation effect across 2-Target trials using the control analysis first described by Cisek and Kalaska11. Briefly, on each trial we labeled the planning-related activity as described above (pro-PD, anti-PD, and orthogonal-PD), and calculated the percentage of pro-PD and anti-PD activity that exceeded the median orthogonal-PD activity. Since this metric grouped pro-PD and anti-PD activity together, a dataset consisting only of single-target representations should have resulted in values around 50% (pro-PD activity would exceed the orthogonal-PD median threshold but anti-PD activity would not). Indeed, the black histogram in Fig. 2c—which represents the activity during 1-Target trials—shows that the proportion of high pro-PD and anti-PD activity across neurons was not significantly different from 50% (t-test, p = 0.1). In contrast, the distribution of high activity on 2-Target trials (Fig. 2c, blue) was skewed significantly toward 100% (t-test, p < 10−9), consistent with activity related to both targets—the result expected of a dual representation paradigm.

Although the results from Fig. 2a–c seem to provide convincing evidence of dual representation, we considered the possibility that they were instead caused by target biases during the planning phase. The analysis in Fig. 2c implicitly assumes a null hypothesis of unbiased guessing, in which the subject randomly selects one of the two displayed targets at the start of each trial. However, there is another possible guessing-based approach, which we term biased guessing. Under a biased guessing paradigm, the subject still only ever creates an initial plan to one target, but that plan is almost always to the same target. For example, for every 2-Target trial with a left and right target, the subject might start by planning a reach to the right (switching later if cued to the left target). We simulated datasets for both of these guessing-based approaches (see Methods) to determine whether the analysis from Fig. 2c could correctly identify that they contained only single-reach plans. For the unbiased guessing dataset, the analysis returned a distribution of high pro-PD and anti-PD activity that was not significantly different from 50% (Fig. 2d; t-test, p = 0.13), correctly ruling out the possibility of dual representation. However, for the biased guessing dataset, the analysis returned a highly right-skewed distribution (Fig. 2e; t-test, p < 10 −10). This result strongly—but incorrectly—suggests the presence of dual representation. Thus, while the analysis from Fig. 2c can discount the possibility of an unbiased guess-and-switch approach, it cannot rule out the possibility that the monkeys employed a single-plan strategy with strong biases in the initial plans.

Population-based approach to single-trial reach plan decoding

The conflicting interpretations in Fig. 2 indicate that methods based on the trial-averaged responses of single neurons can lead to incorrect conclusions about the nature of neural responses on individual trials. To disambiguate the initial target deliberation requires that planning-related neural responses be evaluated at the level of single trials. Array recordings allow the large number of recorded neurons, rather than a large number of trials, be used to compensate for the stochastic neural noise. As a first step, we used principal component analysis (PCA) to reduce the population’s activity to a de-noised, 10-dimensional neural state14,16,22,31,32,33,34. Figure 3a shows the evolution of three dimensions of this state for left and right 1-Target trials, superimposed on the neural states observed across all left and right 1-Target trials. Even in three dimensions, the reach directions are separable, indicating that a low-dimensionality-based approach can provide a useful readout of instantaneous reach planning.

Fig. 3 Low-dimensional neural states on 1-Target trials. a Low-dimensional neural state trajectories throughout individual left (red) and right (blue) 1-Target trials. Blue and red clusters reflect all neural states visited during 1-Target trials to rightward and leftward targets, respectively. Colored, labeled markers indicate the first time points in each trial epoch. b Proximity plot (x-axis: proximity to the rightward cluster; y-axis: proximity to leftward cluster) for the example trials from a, with corresponding trial event markers. c Proximity plot of Target Blank activity over all 1-Target trials, monkey C. Inset density plot shows that most points lie along the x- and y-axes. d Same as in c for monkey M Full size image

To quantify the extent of target-related activity within the neural state space, we developed a proximity metric based on the Mahalanobis distance to clusters associated with each reach direction (see Methods). As an example, take a point in the leftward trial trace (red) from Fig. 3a. We can calculate its proximity to the leftward reach cluster (red point cloud) as well as its proximity to the rightward reach cluster (blue point cloud). Plotting these two values against each other for all points along the example leftward reach neural state trajectory results in the red trace in Fig. 3b. Repeating for the rightward trial in Fig. 3a gives rise to the blue trace in Fig. 3b. Excursions along the y- and x-axes can be interpreted as evolving leftward and rightward reach plans, respectively. To display the results from multiple target axes, we arbitrarily chose the x-axis to represent half of the targets (at 0°, 45°, 90°, and 135°) and the y-axis to the other half. Over all sessions and reach directions, we successfully classified the final reach direction from neural data collected during the Target Blank epoch of 1-Target trials for both monkey C (Fig. 3c, 97%) and monkey M (Fig. 3d, 98%).

Neural state test of dual representation

Since the state space proximity metric proved capable of accurately describing population-wide planning on 1-Target trials, we next applied it to activity on 2-Target trials. To ensure that the method could differentiate between different types of planning, we first simulated three potential models: dual-target; averaged-plan; and stay-or-switch. The dual-target and averaged-plan models reflect mechanisms by which PMd could represent two reach directions simultaneously. Alternatively, the stay-or-switch model represents the case in which PMd plans only a single reach at a given time. For all models, we simulated activity only during the Target Blank epoch.

To model dual-target representation, we first fit cosine tuning curves to 1-Target data for all neurons. We transformed those single-target tuning curves into bimodal, dual representation curves to match the response types reported by Cisek and Kalaska11. Figure 4a shows a schematic of averaged responses (as in Fig. 2) and representative 1-Target (unimodal) and 2-Target (bimodal) tuning curves. From the bimodal curves, we simulated activity for the left/right target pair from Fig. 3a; the resulting neural state was close to both the left- and right-plan clusters (Fig. 4b). Across all target pairs and sessions, simulated dual-target neural states tended to lie near both reach direction clusters (Fig. 4c, points close to diagonal).

Fig. 4 Model predictions of low-dimensional states. a Illustration of pro-PD (solid) and anti-PD (dashed) activity on a 2-Target trial under a dual-target model based on Cisek and Kalaska11. Inset shows example 1-Target (gray) and 2-Target (purple) turning curves. b Simulated activity from the model in a for a left/right trial results in a low-dimensional neural state between the left and right 1-Target planning states. c Proximity plot of the simulated simultaneous representation states for all target axes. Symbol color corresponds to monkey (black, monkey C; gray, monkey M). d–f Same for averaged-plan model. g–i Same for stay-or-switch model Full size image

The averaged-plan model represented another variant of dual representation; each neuron’s response reflected the average of its responses to each target individually. Its simulated activity was qualitatively similar to the dual-target model (Fig. 4d–f), with neural states near both clusters.

Neural responses for the third model (stay-or-switch) corresponded to only one reach plan at any given time (Fig. 4g); the associated neural states (Fig. 4h) and proximity plots (Fig. 4i) were indistinguishable from the 1-Target condition. The clear difference in results between simulated dual- and single-representation models thus demonstrated the ability of our population-based proximity metric to identify dual representation in single-trial neural activity.

In Fig. 5a, we show the neural states observed during two epochs—Target Blank and Go—across all left/right 2-Target trials from the example session in Fig. 3a. At the time of movement (Fig. 5a, right plot) the neural states clearly reflected the cued direction. However, during the earlier Target Blank epoch (Fig. 5a, left plot), they appeared to indicate a rightward reach plan. The proximity plots incorporating all 10 dimensions of the neural state confirm the appearance of the two-dimensional projection: pre-Cue activity almost always reflected a rightward reach (Fig. 5b, left—high density along x- and y-axes). Across all targets and sessions, the neural states during the Go epoch accurately reflected the cued reach directions (Fig. 5c, d, right plots). However, during the Target Blank epoch, the proximity plots suggest a mix of cued and anti-cued reach plans. This is expected, since the monkeys did not yet know which target was correct. Of note, the proximity plots reveal excursions mainly along the axes, as in 1-Target trials. In the scatter plots, this effect is more apparent for monkey M (Fig. 5d, left), but density plot insets reveal that both monkeys exhibited what appears to be largely single-target planning activity.

Fig. 5 Low-dimensional neural states on 2-Target trials. a Neural states during planning (left plot) and movement execution (right plot) for all left/right target trials during an example session. Filled red circles correspond to trials with a cue to the left target, filled blue circles a cue to the right target. Open circles represent 1-Target left (red) and right (blue) trials. b Proximity plots of the left/right 2-Target trials in a. c Left: proximity plots of planning activity (Target Blank epoch) for all 2-Target trials, monkey C. Inset heat map shows the high concentration of points along the x- and y-axes. Right: proximity plots of execution-related activity (Go epoch) for all 2-Target trials, monkey C. d Same as c for monkey M Full size image

To quantify the extent to which the observed neural states represented single or dual reach plans, we developed a new metric from the calculated proximities, called the dual representation index (DRI; see Methods). Figure 6a shows the 1-Target proximity plot from Fig. 3c overlaid with a contour plot of the DRI metric. The DRI is bounded by zero (along either axis) and one (upper right corner), with highest values nearest the diagonal (indicative of dual representation; Fig. 4c, f). We first calculated the DRI for neural states observed during the Target Blank epoch on 1-Target trials. The resulting histogram for monkey C is shown in Fig. 6b. DRI < 0.2 captured all but 3% of 1-Target planning for monkey C, and all but 1% for monkey M. We then calculated DRI for both actual (Fig. 6e, f; black) and simulated 2-Target neural states (Fig. 6e, f; gray). While DRI for the two simulated models largely exceeded 0.2 (84%, monkey C; 87%, monkey M), the percentage of actual 2-Target activity above the threshold was very low (6%, monkey C; 3%, monkey M). Thus, although the trial-averaged results from Fig. 2 suggested the presence of dual representation on 2-Target trials, we found no such evidence in single-trial population activity. This result held even if we restricted our analysis to only the subpopulation of neurons with trial-averaged responses most strongly indicative of dual representation (see Supplementary Note 2 and Supplementary Figure 2).

Fig. 6 Testing for dual representation in low-dimensional states. a Proximity plot of 1-Target trials for monkey C from Fig. 3c, overlaid with a contour plot of the dual representation index (DRI). b Histogram of DRI values from a. A post hoc upper threshold of DRI = 0.2 (vertical dashed line) captured all but 3% of 1-Target activity for monkey C and all but 1% for monkey M. c Histogram of DRI values for all 2-Target trials (black), monkey C. Purple bars reflect simulations from both the dual-target model and the averaged-plan model. d Same as c for monkey M Full size image

Target preferences during 2-Target planning

The results from the above analyses suggest that even on 2-Target trials, the monkeys planned for only one reach at a time. To track the evolution of these plans, we calculated the difference over time between the proximities to the pair of relevant reach direction clusters. The resulting difference (∆Proximity) provided an estimate of the direction and strength of the instantaneous reach plan. This metric was more conservative than a probability-based classifier in that it was less likely to report spurious reach plans having low strength (see Supplementary Figures 3 and 4). Figure 7a shows example single-trial target decodes using this metric for left/right, 2-Target trials. At the time of movement execution (Go epoch) reaches to the left were clearly distinguishable from those to the right. However, activity early in the trials overwhelmingly (88%) resembled rightward reach plans. Both monkeys had similarly skewed preferences (Fig. 7b). However, these preferences were inconsistent across sessions and did not always follow a clear hemispatial bias. On the first session, monkey M had an up/right preference. Over the next two sessions, those preferences appeared to rotate to the downward and leftward directions (Fig. 7c, bottom row). Monkey C had similar preferences during the first two sessions, but completely opposite preferences for two of the four target pairs on the third session (Fig. 7c, top row). The inconsistency of the planning preferences, both within and across subjects, suggests that they arose as part of conscious task strategies rather than from an ingrained predilection for minimizing exertion or some other physiological cost function35,36,37.

Fig. 7 Preferential reach planning in PMd during two-target trials. a ΔProximity traces for all left/right trials in an example session (monkey C, session 1). Blue traces indicate those for which the monkey was cued to the left. Red traces indicate trials cued to the right. During the Target Blank epoch, 88% of activity indicated a rightward reach plan. Activity prior to Target Blank epoch is aligned to Target On. Activity during the Target Blank epoch is aligned to Cue appearance. Activity after Cue appearance is aligned to the Go cue. b Distribution of neural preferences across target axes from all sessions (black, monkey C; gray, monkey M). c Neural preferences across sessions. For each axis, radial length represents the observed preference Full size image

We considered the possibility that the decoded biases during early planning periods resulted from anisometries in the proximity metric across reach directions, and thus did not accurately reflect the instantaneous plan. To address this, we compared each monkey’s decoded target preferences on cued 2-Target trials to their actual choice biases on Free-Choice trials. Over all 16 left/right Free-Choice trials from the session in Fig. 7, monkey C reached to the right target 11 times (69%, Fig. 8a). This rightward choice bias mirrored the preference observed in the initial planning activity on cued 2-Target trials (88%, Fig. 7a). Across monkeys, we found a strong correspondence between the target preferences decoded from cued 2-Target neural activity and the actual reach direction on Free-Choice trials (Fig. 8b). Additionally, reach plans decoded from primary motor cortex (M1) matched those from PMd (see Supplementary Note 1 and Supplementary Figure 1) further indicating that the neural state decoding accurately reflected the monkeys’ instantaneous reach plans.

Fig. 8 Neural preferences match Free-Choice behavior. a ΔProximity traces for all left/right Free-Choice trials in the example session from Fig. 4a. The monkey chose the rightward target on 11 of the 16 trials. b Across all sessions, the monkeys’ decisions on Free-Choice trials for each axis correlated with their planning preferences decoded from cued 2-Target trials. Black symbols correspond to monkey C, gray symbols to monkey M. Symbol shape corresponds to the different sessions, as in Fig. 7c. c Bar plot indicating the degree to which Target Blank period activity successfully predicted the monkeys’ choices on Free-Choice trials for each session and target axis. Black bars correspond to monkey C, gray to monkey M. Error bars represent 95% confidence bounds calculated from the standard error Full size image

On average, the monkeys had a 75:25% target preference during planning (Fig. 7b). Thus, at times, they began planning to move to a target they did not generally favor. While the results from Fig. 8b show that preferences in early planning activity were largely predictive of Free-Choice movement preferences, it was unclear how well the planning activity on a single Free-Choice trial might correlate with the eventual movement decision. Were initial plans made to favored targets more likely to be carried through to execution than those made to non-favored targets? To answer this question, we identified the favored targets during the Target Blank epoch on 2-Target trials. We then compared the direction decoded during Target Blank on each Free-Choice trial with the eventual reach direction. We found no difference between trials with initial plans to favored targets compared to non-favored targets; neural activity for both was equally predictive (Fig. 8c). Thus, while the monkeys did exhibit clear session-wide target preferences, it was the initial plan on any given Free-Choice trial that best predicted the chosen reach direction.

Plan strength and reaction time

Our findings suggest the existence of only single-reach plans, but the strengths of those plans varied widely across trials. Consider the left/right responses in Fig. 7a. Most early trial activity clearly indicated rightward reach plans. However, some activity suggested leftward (negative ∆Proximity) or weak-to-nonexistent plans (∆Proximity near zero). Due to the conservative nature of the ∆Proximity metric (see Supplementary Note 3 and Supplementary Figures 3 and 4), large magnitudes—either positive or negative—could only arise from neural states close to a given reach direction cluster. Due to the lack of evidence for dual representation in our data (Fig. 6), low magnitudes could only arise from neural states unassociated with any specific reach plan. We predicted that the magnitudes of the decoded reach plans on individual trials would correlate with some aspect of the kinematics of the executed movement. To test this, we compared the average magnitude of ∆Proximity in a 100 ms window preceding the Go epoch on each cued, 2-Target trial to the subsequent movement reaction time. Figure 9a shows this relationship for left-cued reaches on an example session. Reaction times were markedly shorter when ∆Proximity indicated a strong leftward plan at the time of the Go cue, and longer when it indicated a rightward plan. This negative correlation between decoded plan strength to the cued target and reaction time occurred for both monkeys (Fig. 9b; linear mixed effects model accounting for differences across reach directions and sessions; monkey C: coeff = –127, F-test p = 0.0036; monkey M: coeff = –159, F-test p ≈ 0) and is similar to observations in previous studies12,31,38. We found a similar negative correlation between ∆Proximity directly preceding the Go cue and reaction time on Free-Choice trials (Fig. 9c, d; monkey C: coeff = –241, F-test p = 0.0017; monkey M: coeff = –108, F-test p = 0.0266).

Fig. 9 Correlation between pre-Go neural state and reaction time. a Reaction time as a function of the strength of the reach representation in PMd calculated 100 ms prior to the Go cue for all leftward reaches on two-target trials during a single session. Reaction times decreased as the decoded strength of the neural representation increased. b Histogram of the slopes (as calculated in a) for all target axes from all sessions (monkey C, black; monkey M, gray). c As in a for all reaches to the upper left target during Free-Choice trials. Reaction time decreased with the strength of the decoded representation. d As in b for Free-Choice trials Full size image

Reach planning on error trials

Although both monkeys understood the 2-Target task, at times they chose the incorrect—i.e., non-cued—target (monkey C: 16%, monkey M: 27%). We examined the progression of reach plans during these error trials to reveal potential sources of incorrect movement choices. Using the reach plans decoded early (Target Blank) and late (Cue) in the trial, we characterized three types of errors, which together described over 97% of all errors. During type 1 errors, the monkey maintained a consistent reach plan throughout, not deviating even after receiving a cue to the opposite target (Fig. 10a, heavy trace). During type 2 errors, the monkey switched to the correct plan after cue presentation, but then later reverted to his initial incorrect plan upon receiving the Go cue (Fig. 10b, heavy trace). During type 3 errors, the monkey switched to the incorrect reach plan at the last second, despite having planned correctly throughout the trial (Fig. 10c, heavy trace). Despite different error rates between monkeys, the high incidence of type 1 and 2 errors suggests that both monkeys had an aversion to switching away from their initial reach plans. This was true whether that initial plan was to a favored target or to a non-favored target (Fig. 10d; filled vs. open bars).