As you read this text, your eyes make saccades that guide your fovea from one word to the next. Accuracy of these movements require the brain to monitor and learn from visual errors. A current model suggests that learning is supported by two different adaptive processes, one fast (high error sensitivity, low retention), and the other slow (low error sensitivity, high retention). Here, we searched for signatures of these hypothesized processes and found that following experience of a visual error, there was an adaptive change in the motor commands of the subsequent saccade. Surprisingly, this adaptation was not uniformly expressed throughout the movement. Rather, after experience of a single error, the adaptive response in the subsequent trial was limited to the deceleration period. After repeated exposure to the same error, the acceleration period commands also adapted, and exhibited resistance to forgetting during set-breaks. In contrast, the deceleration period commands adapted more rapidly, but suffered from poor retention during these same breaks. State-space models suggested that acceleration and deceleration periods were supported by a shared adaptive state which re-aimed the saccade, as well as two separate processes which resembled a two-state model: one that learned slowly and contributed primarily via acceleration period commands, and another that learned rapidly but contributed primarily via deceleration period commands.

Previous research shows that human eye movements can serve as a valuable source of information about the structural elements of the oculomotor system and they also can open a window to the neural functions and cognitive mechanisms related to visual attention and perception. The research field of eye movement-driven biometrics explores the extraction of individual-specific characteristics from eye movements and their employment for recognition purposes. In this work, we present a study for the incorporation of dynamic saccadic features into a model of eye movement-driven biometrics. We show that when these features are added to our previous biometric framework and tested on a large database of 322 subjects, the biometric accuracy presents a relative improvement in the range of 31.6--33.5% for the verification scenario, and in range of 22.3--53.1% for the identification scenario. More importantly, this improvement is demonstrated for different types of visual stimulus (random dot, text, video), indicating the enhanced robustness offered by the incorporation of saccadic vigor and acceleration cues.

Voluntary motor commands produce two kinds of consequences. Initially, a sensory consequence is observed in terms of activity in our primary sensory organs (e.g., vision, proprioception). Subsequently, the brain evaluates the sensory feedback and produces a subjective measure of utility or usefulness of the motor commands (e.g., reward). As a result, comparisons between predicted and observed consequences of motor commands produce two forms of prediction error. How do these errors contribute to changes in motor commands? Here, we considered a reach adaptation protocol and found that when high quality sensory feedback was available, adaptation of motor commands was driven almost exclusively by sensory prediction errors. This form of learning had a distinct signature: as motor commands adapted, the subjects altered their predictions regarding sensory consequences of motor commands, and generalized this learning broadly to neighboring motor commands. In contrast, as the quality of the sensory feedback degraded, adaptation of motor commands became more dependent on reward prediction errors. Reward prediction errors produced comparable changes in the motor commands, but produced no change in the predicted sensory consequences of motor commands, and generalized only locally. Because we found that there was a within subject correlation between generalization patterns and sensory remapping, it is plausible that during adaptation an individual's relative reliance on sensory vs. reward prediction errors could be inferred. We suggest that while motor commands change because of sensory and reward prediction errors, only sensory prediction errors produce a change in the neural system that predicts sensory consequences of motor commands.

Our motor system changes due to causes that span multiple timescales. For example, muscle response can change because of fatigue, a condition where the disturbance has a fast timescale or because of disease where the disturbance is much slower. Here we hypothesize that the nervous system adapts in a way that reflects the temporal properties of such potential disturbances. According to a Bayesian formulation of this idea, movement error results in a credit assignment problem: what timescale is responsible for this disturbance? The adaptation schedule influences the behavior of the optimal learner, changing estimates at different timescales as well as the uncertainty. A system that adapts in this way predicts many properties observed in saccadic gain adaptation. It well predicts the timecourses of motor adaptation in cases of partial sensory deprivation and reversals of the adaptation direction.

We describe the design, testing and tools to build parametric models of a six-legged cockroach-like robot for velocity control without precise knowledge on the robot's geometry or its inertia. Robot legs were made by Shape Deposition Manufacturing and were compliant at the "knee". These kinds of robots usually have a limited number of actuators and a small number of low-cost sensors. Consequently, they are difficult to control with analytic models. Our goal was to design a very fast robot that could run in a straight line over short distances at a desired velocity. We incorporated such legs into a novel body design, where position and orientation of the legs were chosen to enhance static stability. Robot design proved to be robust, as the machine did not suffer any failure in over 20,000 runs. We found that body-pitch angle was a crucial parameter in the control of running speed. To control this angle, we built a parametric model that related leg orientation to pitch angle. We experimented with various leg stiffness parameters, and built a comprehensive parametric model that quantified performance as a function of this parameter, as well as body-pitch angle, ground slope, and body mass. When these parameters were optimized, the robot consistently achieved a speed of six body lengths per second, even when pulling a large load in the form of a trailer cart.

Reaching movements require the brain to generate motor com- mands that rely on an internal model of the task's dynamics. Here we consider the errors that subjects make early in their reaching trajectories to various targets as they learn an internal model. Us- ing a framework from function approximation, we argue that the sequence of errors should reflect the process of gradient descent. If so, then the sequence of errors should obey hidden state transitions of a simple dynamical system. Fitting the system to human data, we find a surprisingly good fit accounting for 98% of the variance. This allows us to draw tentative conclusions about the basis ele- ments used by the brain in transforming sensory space to motor commands. To test the robustness of the results, we estimate the shape of the basis elements under two conditions: in a traditional learning paradigm with a consistent force field, and in a random sequence of force fields where learning is not possible. Remarkably, we find that the basis remains invariant. 1 Introduction It appears that in constructing the motor commands to guide the arm toward a target, the brain relies on an internal model (IM) of the dynamics of the task that it learns through practice [1]. The IM is presumably a system that transforms a desired limb trajectory in sensory coordinates to motor commands. The motor commands in turn create the complex activation of muscles necessary to cause action. A major issue in motor control is to infer characteristics of the IM from the actions of subjects. Recently, we took a first step toward mathematically characterizing the IM's rep- resentation in the brain [2]. We analyzed the sequence of errors made by subjects on successive movements as they reached to targets while holding a robotic arm. The robot produced a force field and subjects learned to compensate for the field (presumably by constructing an IM) and eventually produced straight movements within the field. Our analysis sought to draw conclusions about the structure of the IM from the sequence of errors generated by the subjects. For instance, in a velocity-dependent force field (such as the fields we use), the IM must be able to encode velocity in order to anticipate the upcoming force. We hoped that the e#ect of errors in one direction on subsequent movements in other directions would give information about the width of the elements which the IM used in encoding velocity. For example, if the basis elements were narrow, then movements in a given direction would result in little or no change in performance in neighboring directions. Wide basis elements would mean appropriately larger e#ects. We hypothesized that an estimate of the width of the basis elements could be cal- culated by fitting the time sequence of errors to a set of equations representing a dynamical system. The dynamical system assumed that error in a movement resulted from a di#erence between the IM's approximation and the actual environ- ment, an assumption that has recently been corroborated [3]. The error in turn changed the IM, a#ecting subsequent movements:

Biological sensorimotor systems are not static maps that transform input (sensory information) into output (motor behavior). Evi(cid:173) dence from many lines of research suggests that their representa(cid:173) tions are plastic, experience-dependent entities. While this plastic(cid:173) ity is essential for flexible behavior, it presents the nervous system with difficult organizational challenges. If the sensorimotor system adapts itself to perform well under one set of circumstances, will it then perform poorly when placed in an environment with different demands (negative transfer)? Will a later experience-dependent change undo the benefits of previous learning (catastrophic inter(cid:173) ference)? We explore the first question in a separate paper in this volume (Shadmehr et al. 1995). Here we present psychophysical and computational results that explore the question of catastrophic interference in the context of a dynamic motor learning task. Un(cid:173) der some conditions, subjects show evidence of catastrophic inter(cid:173) ference. Under other conditions, however, subjects appear to be immune to its effects. These results suggest that motor learning can undergo a process of consolidation. Modular neural networks are well suited for the demands of learning multiple input/output mappings. By incorporating the notion of fast- and slow-changing connections into a modular architecture, we were able to account for the psychophysical results. 20 Tom Brashers-Krug, Reza Shadmelzr, Emanuel Todorov

Experiments were performed to reveal some of the computational properties of the human motor memory system. We show that as humans practice reaching movements while interacting with a novel mechanical environment, they learn an internal model of the inverse dynamics of that environment. Subjects show recall of this model at testing sessions 24 hours after the initial practice. The representation of the internal model in memory is such that there is interference when there is an attempt to learn a new inverse dynamics map immediately after an anticorrelated mapping was learned. We suggest that this interference is an indication that the same computational elements used to encode the first inverse dynamics map are being used to learn the second mapping. We predict that this leads to a forgetting of the initially learned skill.

The cerebellar model articulation controller (CMAC) (Albus 1975) is applied for learning the inverse dynamics of a simulated two joint, planar arm. The actuators were antagonistic muscles, which acted as feedback controllers for each joint. We use this example to demonstrate some limitations of the control paradigm used in earlier applications of the CMAC (e.g., Miller et al. 1987, 1990): the CMAC learns dynamics of the arm and not those of the feedback system. We suggest an alternate approach, one in which the CMAC learns to manipulate the feedback controller's input, producing a virtual trajectory, rather the controller's output, which is torque. Several experiments are performed that suggest that the CMAC learns to compensate for the dynamics of the plant, as well as the controller.

The feasibility of developing a neural network to perform nonlinear Bayesian estimation from sparse data is explored using an example from clinical pharmacology. The problem involves estimating parameters of a dynamic model describing the pharmacokinetics of the bronchodilator theophylline from limited plasma concentration measurements of the drug obtained in a patient. The estimation performance of a backpropagation trained network is compared to that of the maximum likelihood estimator as well as the maximum a posteriori probability estimator. In the example considered, the estimator prediction errors (model parameters and outputs) obtained from the trained neural network were similar to those obtained using the nonlinear Bayesian estimator.

We have studied the scratch reflex in order to better understand the strategy that the spinal neural structures use to program limb movements. A network is proposed for the positioning and rhythmic portions of the scratch reflex in the deafferented preparation. This model is based on Berkinblit's hypotheses regarding organization of neurons constituting the spinal central pattern generator (CPG) for this behavior. We offer a mechanism by which the initial position of the hindlimb can influence the output of the CPG in the immobilized animal.