Infinite-horizon OFC model of the brain’s control behavior in BMI.

A BMI system can be modeled as an optimal feedback-control system [26, 37–39]. Similar to natural sensorimotor control [40–42], when controlling a BMI, the brain (controller) selects the next neural command based on the feedback (e.g., visual) of the current state of the prosthetic device (e.g., cursor) and the task goal. For example, when moving a cursor on the computer screen towards a visual target (Fig 1A and 1B), the goal is to reach the target and stop there. We thus model the brain in closed-loop BMI control as an optimal feedback-controller and use this model to predict the brain’s control commands during CLDA. This model can be constructed by defining an approximate forward dynamics model, quantifying the task goals as cost functions, and modeling the visual feedback. The BMI architecture uses this OFC model of the brain’s control behavior to infer the subject’s intended kinematics and to adaptively update the decoder parameter estimates.

We denote the sequence of kinematic states by x₀, ⋯ ,x_t and assume that they evolve according to the linear dynamical model (1) This is the forward dynamics model with parameters A and B that we need to select appropriately, e.g., by fitting them based on the subject’s manual movements. Here u_t is the brain’s control command at time t and w_t is a zero-mean white Gaussian state noise with covariance matrix W, which represents the uncertainty in the forward model (in prior BMI work with Kalman filters for example, the prior model did not include the Bu_t−1 term). We denote the decoded kinematics at time t, which is displayed to the subject, by x_t|t. We assume that the subject perfectly observes x_t|t, i.e., that the visual feedback is noiseless and instantaneous. We also implicitly assume that the brain has obtained an internal forward model of the dynamics of movement in response to control commands u_t in the task. Evidence for formation of such internal models has been presented in prior studies using motor control tasks [42] and more recently using BMI tasks [43].

To predict the brain’s intended control command and consequently the intended kinematics, we formulate a cost function that quantifies the goal of the task and then minimize its expected value over choices of u_t. Target-directed movement trajectories during proficient control are dependent on the desired movement duration. Hence in our work on combined decoding of target and trajectory in target-directed movements and when decoder parameters were known [26, 37, 39], we formed a finite-horizon cost function; we then decoded the trajectory by jointly estimating the movement kinematics and its horizon (i.e., duration) from neural activity. In a CLDA technique, however, parameter estimates are poor initially and hence the decoder cannot estimate the intended kinematics accurately. Consequently, we cannot estimate the intended horizon from neural activity. Moreover, targets may not be reached during the initial trials because of poor control. Hence to develop a model of the brain’s control behavior that can be used as an intention estimator during CLDA, instead of constructing a finite-horizon cost function and decoding the horizon, we form an infinite-horizon cost function. This choice is also motivated by recent motor control studies that have suggested infinite-horizon models [44–46] as a possible alternative to the finite-horizon ones [40, 41].

In our experiments, we take the state to be x_t = [d_t,v_t]^T, where the components represent the cursor’s position and velocity in the two dimensions. Denoting the target position by d*, we form the cost function as (2) where the three terms in the sum enforce positional accuracy, stopping condition, and energetic efficiency, respectively. The stopping condition is included in the cost function since the subject is required to stop at the target for 250ms. Hence a movement that just passes through the target without stopping at the target does not result in a reward. The efficiency cost puts a penalty on large velocity commands. The weights w_r and w_v can be first empirically approximated such that the OFC model produces trajectories similar to the monkey’s natural trajectories. These weights can be then validated and refined experimentally as shown in the Results section. Given the linear Gaussian state-space model in Eq (1) and the quadratic cost function in Eq (2), the optimal control solution u_t at each time that minimizes the expected cost is given by a linear function of the controller’s (brain’s) estimate of the state at that time [47]. This is the standard linear-quadratic-Gaussian (LQG) solution. Given the assumption of noiseless visual feedback, the controller’s (brain’s) estimate of the state at each time is equal to the actual displayed state on the screen, x_t|t, and hence OFC-PPF solves for the intended control as (3) where x* = [d*,0]^T is the target state for position and velocity, and L is the steady-state solution to the discrete form of the algebraic Riccati equation found recursively and offline [47]. This optimal feedback control policy can be interpreted as the subject’s corrective control command in response to the deviation of the visual feedback of the current prosthetic state from the target state.

Point process model of the spikes.

Adaptive OFC-PPF uses a point process observation model of the spiking activity in closed loop. To do so, it bins the spikes in small intervals Δ that contain at most one spike (taken to be 5ms here). This generates a discrete time-series of 0’s and 1’s (Fig 1C). This discrete time-series is modeled as a point process [33–35]. The point process model enables the brain to control the BMI with every binary spike event and at a much faster time-scale compared to the commonly-used closed-loop BMI decoders, e.g., the Wiener filter or the Kalman filter. While it is possible to fit the point process parameters by designing a batch-based technique that runs on the time-scale of minutes (using the generalized-linear models (GLM) maximum likelihood methods), this would result in a slow rate of update for the parameters. Hence we use the point process modeling framework to design an algorithm that adapts the decoder parameters with every binary spike event and at a much faster time-scale compared to batch-based techniques that are often used in BMI decoders. We will demonstrate in the Results section that this spike-event-based adaptation time-scale results in much faster convergence compared to the slower time-scale of existing batch-based methods.

We denote the neural observations of the ensemble of C neurons by N₁, ⋯ ,N_t where is the binary spike events of the C neurons at time t. We assume that neurons’ activities are conditionally independent given the intended kinematics. Hence the point process observation model (similar to an inhomogeneous Poisson process) for the ensemble is given by [33–35] (4) Here Δ is the time interval used to bin the spikes, taken to be small enough to contain at most one spike, is the instantaneous firing rate of neuron c at time t, and is the model parameters for neuron c that need to be estimated via CLDA (see below). Motivated by cosine tuning models of the motor cortex [35, 48, 49], we take for each neuron as a log-linear function of velocity in the two dimensions (5) where is the parameter in this model. Note that this model can equivalently be written as (6) where θ_t is the movement direction at time t, is the preferred direction and is the modulation depth.

Spike-event-based adaptation using OFC-PPF.

We now combine the OFC and PPF models to develop the adaptive OFC-PPF architecture. The architecture consists of one recursive Bayesian decoder for the kinematics and one decoder for each neuron’s parameters.

To estimate the parameters, we need to accurately infer the intended velocity and solve for values that best describe the observed neural activity in response to this intention under the observation model (4). Initially, however, the output of the kinematic decoder is not an accurate estimate of the intended velocity because of poor decoder parameter estimates. Hence during the adaptation process and to estimate the parameters, we use the infinite-horizon OFC model of the brain to infer its velocity intention. All this model needs is knowledge of the task goal and of the visual feedback to the subject, which are both independent of the quality of the kinematic decoder. The visual feedback is just the decoded kinematics x_t|t and the task goal is quantified as in Eq (2). Hence the intended kinematics at each time, denoted by , are found from Eqs (3) and (1) as (7) The weights in the cost function (2) can be approximately chosen such that the OFC model (7) reaches the target with a movement duration similar to the monkey’s natural movement duration. We can also experimentally test the choice of the weights in the cost function as discussed in the Results section. We experimentally tested two different types of cost functions with different assumptions about neural mechanisms for control. These findings were used to select the BMI cost function.

Given the inferred velocity intention Eq (7), we need to fit the parameters of the point process model. One way to fit these would be to use batch-based methods [20, 21], such as SmoothBatch, to find the parameters of the point process model using GLM maximum-likelihood techniques [35]. For example, we can design a SmoothBatch algorithm that finds the maximum-likelihood estimate of the point process parameters in Eq (5) in batches of 90 sec length using GLM methods, and average these batch estimates over time with a half-life of 180 sec [21]. However, this approach would only update the decoder parameters and improve the decoder quality on the time-scale of minutes, which is the batch length. To allow the BMI to update the decoder parameters with every spike event, we instead develop an adaptive algorithm by building a recursive Bayesian decoder for the parameters.

A recursive Bayesian decoder consists of a prior model on the unknown states—i.e., the tuning parameters for each neuron here—and an observation model relating the neural activity to these states. The observation model is given by Eq (4). We construct the prior model for the parameters of each neuron as a random-walk state-space model given by (8) where q_t is white Gaussian noise with covariance matrix Q. We used the random-walk prior model since it provides us with a dynamic model with minimal assumption and with adequate uncertainty. The only assumption of a random-walk model is continuity in the evolution of parameters. Moreover, the random-walk model incorporates adequate uncertainty (e.g., to account for model mismatch) through its stochastic noise term q_t.

The choice of Q dictates the learning rate of the adaptive decoder [50]. The development of a principled algorithm for selection of the optimal learning rate or Q is the topic of our future work [50]; this selection can be guided by the approximate lower and upper bounds on parameter values given by neurophysiological and physical constraints, and refined using experimental tuning.

Given the prior and the observation models, we can write the recursions of the point process decoder for the parameters, which consist of a prediction step and an update step [34, 39]. Let’s denote the one step prediction mean by , the prediction covariance by , the minimum mean-squared error (MMSE) estimate by , and its covariance by . From Eq (8), the prediction step of OFC-PPF for the parameters is found as (9) (10) Since the observation model is a point process, to find the update step we make a Gaussian approximation to the posterior [34]. We have provided the recursions of a general PPF in S2 Text and shown how the parameter decoder can be obtained from these recursions given the log-linear rate function in Eq (5). The update step for the instantaneous firing rate function in Eq (5) can be found as (11) (12) where (see Eq (5)), and (i.e., the intended velocity) is given as in Eq (7). Hence adaptive OFC-PPF estimates each neuron’s parameters at each time step using Eqs (9)–(12).

Intuitively, in the prediction step Eqs (9) and (10) we use the random-walk state model in Eq (8) to move the parameter estimate forward in time. Since the random-walk model enforces continuity, the predicted parameters in Eq (9) are the same as the previous estimated parameters; but the prediction covariance in Eq (10) is larger to account for uncertainty and model-mismatch. In the update step Eqs (11) and (12), the estimate is found by making a correction or update to the prediction. To do so, we compare the actual spike observation at time t, (whether 1 or 0), with the predicted probability of having a spike at time t, (predicted because we use the predicted parameter to compute this probability). Note that this predicted probability is also equivalent to the predicted expected number of spikes at time t, as we have a Bernoulli random variable per bin. Hence the correction is (1- predicted probability of a spike)—or equivalently (1-predicted expected value of the number of spikes)—if a spike occurs and (0- predicted probability of a spike)—or equivalently (0-predicted expected value of the number of spikes)—if no spike occurs. If a spike occurs and the predicted probability of a spike is high, this correction is small (since our predicted parameter was probably close to the true value) and vice versa. Therefore the estimate is a combination of the prediction and the correction terms (see also S3 Text).

It is important to note that adaptive OFC-PPF does not perform joint estimation of parameters and kinematics as is done in the simulation studies in [34, 51]. Instead, given the poor initial parameter estimates and hence the poor initial kinematic decoder, we rely on the OFC model to provide the intended kinematics to the parameter estimator as in Eq (7). This ensures that the poor decoded kinematics do not disrupt the adaptation of the parameters. The disruption in parameter convergence can happen as a result of joint estimation even if a goal-directed prior kinematic model is used to guide the decoded kinematics towards the target (for example the OFC goal-directed model in our assisted training paradigm; see below). This is because, unlike our approach, joint estimation requires a prior joint distribution to be placed on the kinematics and parameters. While this prior joint distribution can be pre-selected in a simulation study, it cannot be easily defined in actual BMI experiments as parameters and their uncertainty are initially unknown. But a joint estimator is sensitive to this prior joint distribution and to the relative uncertainty placed on the initial parameters and kinematics. This relative uncertainty is dictated by the relative noise covariances in the prior models of kinematics and parameters in Eqs (1) and (8), and by the selected covariances on their initial estimates. For example, if parameters are initially poor but not enough noise is placed on their prior model, the joint estimator will likely not converge as it assumes that the parameters are closer to the true values than they actually are; hence it will make most of the update to the decoded kinematics while assuming the wrong parameters. This worsens the estimate of the kinematic intention, which in turn further disrupts the parameter estimation. In contrast, adaptive OFC-PPF convergence does not depend on the initial kinematic decoder quality; the only way the decoded kinematics enter the adaptation process is by providing the visual feedback term in the OFC model since the monkey indeed observes these decoded kinematics regardless of their quality.

It is also important to note that in our architecture the estimation of each neuron’s parameters is independent of other neurons and only requires the OFC-inferred intention. Hence the parameter decoders for each neuron can run in parallel if need be, making it readily scalable to many channels of recording. Moreover, the state dimension is relatively small (3 in this work) for each parameter decoder and hence the estimation is not computationally demanding. For example, our system could be run in experiments with 20–30 neurons and 5ms bins within MATLAB even using a serial implementation of parameter decoders.

Autonomous and dynamic assisted training using the OFC-PPF paradigm.

To enable the BMI to perform general movements (e.g., curved jumps or straight target-directed movements), once decoder parameters converge we use a random-walk prior model (c.f. Eq (13) with L_a = 0 and Eq (19)) in the kinematics decoder. This random-walk prior model only enforces two general rules, which apply to many types of movements, without any additional assumptions: 1) velocity evolution in time is correlated, i.e., there is correlation between velocity vectors at two adjacent time points; 2) position is the integral of velocity. Given the poor initial parameter estimates, however, an initial random-walk kinematic decoder often generates trajectories that are far from the intended trajectories. This may result in decoded trajectories that are biased towards a specific region of space, and consequently cause slower convergence in decoder parameters by not allowing the decoder to explore the space. Moreover, this may result in low initial success rates and hence in reduced subject engagement in the task, which can consequently lead to failure in parameter convergence.

Here we develop a new dynamic assisted training technique within the OFC-PPF paradigm that allows the subject to explore the space even with poor initial parameters, and hence results in consistent parameter convergence across sessions. Assisted training has been used in prior studies to help subjects reach targets with a poor decoder (e.g., [6, 11, 36]). Current methods either add to the decoded velocity vector an assistive vector that directs straight towards the target, or subtract from the decoded velocity vector a vector perpendicular to the straight line to the target, thus attenuating the deviation. These methods often continuously or manually change the ratio of the assistive vector to the decoded vector in the sum to adjust how much assistance is provided to the subject. These ad-hoc approaches can make convergence trainer-dependent and significantly reduce robustness. Highly variable levels of assistance can also complicate the interpretation of performance during adaptation. It is, therefore, important to develop an assisted training technique that provides a systematic way to change the level of assistance before parameter convergence, and also enables a way to compute a chance level assisted performance, the comparison to which may provide a potential approach to assess user’s engagement during assistance. Moreover, while current methods often set a constant speed for the assistive vector, it is important to provide an approach to adjust the prosthetic speed systematically in a given trial. Finally, it could be beneficial to incorporate more naturalistic modulations of speed compared to current manipulations (such as adding to the decoded vector), which for example do not enforce a stopping condition at the target.

Our new OFC-based assisted training technique automatically and dynamically adjusts the assistance level based on subject’s performance, and can provide a way to calculate a chance level performance during assisted training; this may in turn have the potential to assess subject engagement during assistance. The assist technique automatically iterates between assist and test periods and stops assistance once proficient performance is reached. The OFC-based assisted training also automatically adjusts the speed at each time step based on the current kinematic feedback. It also enforces stopping at the target. Finally, it can be combined with the OFC-PPF spike-event-based adaptation and intention estimation in a modular fashion and does not interfere with the process of adaptation.

The OFC-based assisted training works by incorporating the target information in the kinematics decoder using an optimal feedback-controlled prior kinematics model instead of the random-walk model (Fig 2). This results in a target-directed decoder that, in addition to enforcing continuity, reflects the subject’s goal to reach the instructed target in the decoded kinematics [26, 39]. Specifically, we build the prior model of our target-directed decoder using Eqs (1) and (3) as (13) Note that L_a depends on the cost function chosen in Eq (2) for assisted training and need not be equal to L, which is used for intention estimation. Indeed, to change the level of assistance dynamically, we systematically change L_a depending on the subject’s performance as we describe below. In contrast, L for intention estimation remains constant throughout the adaptation process.

Given the prior state-space model in Eq (13) and the observation model in Eq (4), we can find the recursions of the kinematics decoder similar to what we have derived for a feedback-controlled point process decoder for target-directed movements [26, 39]. Let’s denote the one step prediction mean by x_t|t−1 = E(x_t|N_{1: t−1}), the prediction covariance by Λ_xt|t−1, the MMSE estimate that is displayed to the subject by x_t|t, and its covariance by Λ_xt|t. Using Eq (13), the prediction step of OFC-PPF for the kinematics is found as (14) (15) The decoder update step for the log-linear rate function in Eq (5) as we have shown in S2 Text and derived previously [26] is given by (16) (17) where , since the observation model assumes velocity tuning only and no tuning to position (see also [34] for a general treatment). Note that, as before, are the estimated parameters found in Eq (12). Hence, during assisted training, adaptive OFC-PPF decodes the kinematics using Eqs (14)–(17). In this work we use a special case of the above by implementing a velocity PPF; this means that in the update steps in Eqs (16) and (17), we only update the velocity and set the position equal to the predicted position in Eq (14), which is equal to the integral of the decoded velocity (this is in the same spirit as a velocity KF; see the specific choices of A and B below).

Similar to the parameter recursions in Eqs (9)–(12), these kinematic recursions are obtained from the same general form given in S2 Text, but this time by taking the parameters as known and decoding the kinematics instead. Since all C neurons are informative of the kinematics, the kinematic decoder incorporates all neurons’ spiking activities. For C neurons and assuming that their activities are independent conditioned on the kinematic state, the correction term simply becomes the sum of the correction terms for each neuron. In the prediction step, we use the prior model of kinematics in Eq (13) (either assisted or non-assisted) to predict the kinematics at time t based on the estimated kinematics at time t−1. In the update step, we correct this prediction based on the difference between the spike observations of all neurons and their predicted probability of having a spike at time t, i.e., . This is the predicted probability since the predicted kinematics v_t|t−1 is used to compute it. Note that here we consider as given and decode the kinematics. The more informative the spiking activity is about the kinematics, i.e., the larger is for a neuron, the more weight is placed on the correction term for that neuron. If the spiking activity is not informative at all for a neuron, or , then that neuron’s spiking activity will not affect the decoded kinematics (see also S3 Text).

The assisted training paradigm can dynamically change the level of assistance. To decrease the level of assistance, we change L_a by increasing w_v and w_r in the cost function in Eq (2). Increasing these weights increases the time it takes for the state-space model in Eq (13) to reach the target. A longer arrival time at the target is equivalent to a lower level of assistance since the subject would need to take the cursor to the target by relying more on its neural activity as opposed to the prior model (c.f., Eqs (14) and (17). Motivated by [44], we pick (18) where τ is a time constant. Hence we change the level of assistance by changing this single parameter τ. As τ → ∞, L_a → 0, the state-space model in Eq (13) becomes equivalent to a random-walk state-space model, and hence assistance stops.

The dynamic assisted training paradigm proceeds as follows (Fig 2). We first decide on a discrete set of assistance levels corresponding to a discrete set of τ’s, and on a time period to decode using each level of assisted training. We start the adaptive OFC-PPF from the highest assist level and decrease the assist level one by one while the subject is performing the task and parameters are being updated. After the time period for the lowest assist level ends, we initiate a test period in which the subject controls the BMI with no assistance, i.e., using a random-walk state-space model in Eq (13) corresponding to τ → ∞. We evaluate the subject’s performance during this test period. Based on this non-assisted level of performance, the system decides on whether assistance should continue and if so, what level of assistance it should restart at. The process enters a new assist period and repeats until non-assisted performance exceeds a desired threshold. Note that parameter adaptation continues even after assistance stops. Indeed we can set the performance threshold, which is used to decide whether to continue the assistance, below the maximum steady-state performance that happens once parameters fully converge.

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Fig 2. Adaptive OFC-PPF flow-chart.

(A) The architecture proceeds with decoding as follows. The decoder parameters are first initialized as desired. The architecture then starts a period of combined assisted training and spike-event-based closed-loop adaptation. Once non-assisted performance in a test period exceeds a desired threshold, assistance stops and a random-walk PPF (termed here RW-PPF) is used for control. Spike-event-based adaptation continues until performance saturates. At that point, adaptation stops and the random-walk PPF with the converged parameters is used by the subject for volitional control of movements in various tasks. The green parts of the flow-chart show the dynamic assisted training procedure. (B) The architecture during the different stages of adaptation and assisted training.

https://doi.org/10.1371/journal.pcbi.1004730.g002

Chance level performance computation during assisted training.

While providing assisted training, it is often difficult to assess whether subjects are engaged in the task. This is because a high level of assist could result in good performance even in the absence of volitional control by the subject. In addition to providing an automatic way to conduct dynamic assisted training, our architecture provides a way to compute the chance level performance during assisted training. The ability to compute this chance level may have the potential to assess subject engagement during assisted training in a principled manner. We calculate the chance level performance at each assistance level by running the adaptive OFC-PPF while the subject’s monitor is off and hence the subject cannot be engaged in the task. In this case, the adaptive OFC-PPF performance is purely due to the assisted state-space model. If a subject’s performance is significantly larger than the corresponding chance level performance during a given assist level, this may indicate that the subject is engaged in the task. This could in turn be useful both for identifying assist levels that enable subject engagement and for post-hoc interpretation of performance during assistance. We have shown the chance level performance with assistance in green in Fig 3. We can see that performance with assistance is above the 99% chance level; consistent with this, the monkey’s performance converges. In this monkey, assisted training always allowed it to converge to a good decoder. We did not observe instances of the monkey giving up with assisted training (in contrast to without assisted training). Had we observed sessions in which the decoder did not converge, it would have been interesting to confirm that the assisted performance would fall below chance level in such sessions. While in principle this computational approach to find the chance level assisted performance may allow us to assess engagement, we need additional experiments with a less motivated animal to fully test the idea. This will be the focus of our future investigations.

State-space model for 2D cursor movements.

While the OFC-PPF development above is general to any state-space model, in this work we pick the forward dynamics model in Eq (1) as (19) (20) (21) where a and w are fit to the monkey’s own end-point cursor kinematics using maximum-likelihood estimation [21]. Moreover, we use a velocity decoder, i.e., we decode the velocity and obtain the position deterministically by integrating the decoded velocity in each dimension using x_t = Ax_t−1, i.e., and similarly for the vertical position.

Adaptive OFC-PPF: A fully modular closed-loop BMI architecture.

The complete flow chart for the adaptive OFC-PPF architecture is shown in Fig 2. The architecture proceeds with decoding as follows. The decoder parameters are first initialized as desired. The architecture then starts a period of combined assisted training and spike-event-based closed-loop adaptation. Once non-assisted performance exceeds a desired threshold, assistance stops and a random-walk PPF is used for control. Spike-event-based adaptation continues until performance saturates. At that point, adaptation stops and the random-walk PPF with the converged parameters is used.

It is important to note that the adaptive OFC-PPF architecture is fully modular. First, the intention estimation module is fully independent of the rest of the architecture. For example, one can elect to use prior methods of intention estimation [20] without modifying any other OFC-PPF modules. The assisted training module is also fully separate from the rest of the architecture and its use is optional. In particular, OFC assisted training and intention estimation are separate modules and can use different cost functions and can be used independently. Moreover, the spike-event-based method of adaptation is a module independent of the kinematics decoder and intention estimation. For example, one can use the SmoothBatch method for updating the parameters while keeping the rest of the architecture intact.

Surgery and electrophysiology.

A male rhesus macaque (Macaca mulatta) was chronically implanted with arrays of 128 Teflon-coated tungsten microwire electrodes (35 μm diameter, 500 μm spacing, 8 × 16 configuration; Innovative Neurophysiology, Durham, NC). The arrays targeted the arm and hand areas of the primary motor cortex (M1) and dorsal premotor cortex (PMd) of each hemisphere. Localization of target areas was performed using stereotactic coordinates and implants were typically positioned at a depth of 2.5 mm.

Neural activity was recorded using a 128-channel MAP system (Plexon, Inc., Dallas, TX, USA). For real-time BMI control, channel-level activity was used, which was defined by setting thresholds for each channel (5.5 standard deviations from the mean signal amplitude) and using online sorting software to define unit templates that captured all incoming neural activity on the channel. Thresholds were set at the beginning of each session based on 1–2 min of neural activity recorded as the animal sat quietly. After defining channel thresholds, the online sorting client was used to define unit templates. Templates were typically defined that captured all threshold crossings. In the rare event that channel-level activity showed clearly separable units that could not be adequately captured in a single sorting template, the channel was split into two units. The use of templates allowed for real-time rejection of non-neuronal artifacts during BMI sessions. BMI was controlled by 15–20 multi-units on each day. We used 5ms as we found that more than 1 spike rarely occurred within a single 5ms bin (less than 0.6% of the bins).

All procedures were conducted in compliance with the National Institutes of Health Guide for the Care and Use of Laboratory Animals and were approved by the University of California, Berkeley Institutional Animal Care and Use Committee.

Decoder initialization.

Decoder parameters were initialized either by fitting them using neural activity recorded as the subject passively viewed a cursor moving through the center-out task during a visual feedback session (referred to as visual feedback seed) [21], or they were initialized arbitrarily by randomly permuting the visual feedback seed across neurons.

Behavioral tasks.

Center-out task. The monkey performed a self-paced delayed center-out reaching task under BMI control (Fig 1A and 1B). During BMI control, its arm was confined within a primate chair. Trials were initiated by moving to the center target. Upon entering the center, one of eight peripheral targets appeared. After a brief hold, a “go” cue (center target changing color) indicated to the subject to initiate a reach to the peripheral target. Successful trials required a movement to and brief hold at the central target to initialize a trial, followed by a movement to and brief hold at the peripheral target, and were rewarded by a liquid reward. Failure to acquire the target within a specified window or to hold the cursor within the target for the duration of the hold period resulted in an error, and the trial was repeated. To meet the hold requirement, the monkey had to maintain the cursor within the target for the full hold period upon entering it; this is stricter than some prior tasks [20] since the subject had no opportunity to correct for exiting the target before the completion of the hold period. The monkey had to actively return the cursor to the center to initialize new trials after success or failure. Target directions were presented in a blocked pseudo-randomized order. Targets were circular with 1.2 cm radius and were uniformly distributed about a circle of 13 cm diameter. Hold time requirements at the center and at the targets were 250 ms and the subject had 3–10 s to complete the movement from the central to the peripheral target.

Target-jump task. The monkey also performed a target-jump task that consisted of the normal center-out trials interleaved with jump trials. In one type of target-jump task, a jump trial occurred with a probability of 25% and in it the target changed randomly to one of the other 7 targets 500 ms after the cursor left the center. In the other type of target-jump task, a jump trial occurred with a probability of 17% and could be one of 5 jump types (displayed later in Figures in Results); again the jump occurred 500 ms after the cursor left the center.

Target-to-target task. The monkey also performed a target-to-target movement task in one session. This task required the monkey to perform a point-to-point movement similar to the center-out task. However, this time, there was no center target and the initial and end target locations could be different from the center-out task (displayed later in Figures in Results).

Behavioral metrics.

BMI performance was quantified using both task-level and kinematic metrics. The main task metric used was success rate (number of successful trials completed per minute), which takes into account both speed and accuracy. We also calculated the trial percent correct (percentage of initiated trials resulting in success). Steady-state success rate was calculated over the best ten minutes of a session and steady-state percent correct was calculated over the best 100 trials per session for all decoders to minimize the effect of motivation variation. In addition to steady-state success rate, we also assess decoder adaptation via the success rate evolution over time by calculating it in non-overlapping 2 min windows. Movement kinematics were quantified using movement error and reach time metrics. Movement error for a given trial was defined as the average perpendicular deviation from a straight-line reach between the central and peripheral target. Reach time was calculated as the time from leaving the central target to arriving at the peripheral target. Average reach time and movement error metrics for a session were calculated in the same manner as the percent correct metric.