A generative learning model for saccade adaptation.

Plasticity in the oculomotor system ensures that saccadic eye movements reliably meet their visual goals-to bring regions of interest into foveal, high-acuity vision. Here, we present a comprehensive description of sensorimotor learning in saccades. We induced continuous adaptation of saccade amplitudes using a double-step paradigm, in which participants saccade to a peripheral target stimulus, which then undergoes a surreptitious, intra-saccadic shift (ISS) as the eyes are in flight. In our experiments, the ISS followed a systematic variation, increasing or decreasing from one saccade to the next as a sinusoidal function of the trial number. Over a large range of frequencies, we confirm that adaptation gain shows (1) a periodic response, reflecting the frequency of the ISS with a delay of a number of trials, and (2) a simultaneous drift towards lower saccade gains. We then show that state-space-based linear time-invariant systems (LTIS) represent suitable generative models for this evolution of saccade gain over time. This state-equation algorithm computes the prediction of an internal (or hidden state-) variable by learning from recent feedback errors, and it can be compared to experimentally observed adaptation gain. The algorithm also includes a forgetting rate that quantifies per-trial leaks in the adaptation gain, as well as a systematic, non-error-based bias. Finally, we study how the parameters of the generative models depend on features of the ISS. Driven by a sinusoidal disturbance, the state-equation admits an exact analytical solution that expresses the parameters of the phenomenological description as functions of those of the generative model. Together with statistical model selection criteria, we use these correspondences to characterize and refine the structure of compatible state-equation models. We discuss the relation of these findings to established results and suggest that they may guide further design of experimental research across domains of sensorimotor adaptation.

Saccadic adaptation to a systematically varying disturbance.

Saccadic adaptation maintains the correct mapping between eye movements and their targets, yet the dynamics of saccadic gain changes in the presence of systematically varying disturbances has not been extensively studied. Here we assessed changes in the gain of saccade amplitudes induced by continuous and periodic postsaccadic visual feedback. Observers made saccades following a sequence of target steps either along the horizontal meridian (Two-way adaptation) or with unconstrained saccade directions (Global adaptation). An intrasaccadic step-following a sinusoidal variation as a function of the trial number (with 3 different frequencies tested in separate blocks)-consistently displaced the target along its vector. The oculomotor system responded to the resulting feedback error by modifying saccade amplitudes in a periodic fashion with similar frequency of variation but lagging the disturbance by a few tens of trials. This periodic response was superimposed on a drift toward stronger hypometria with similar asymptotes and decay rates across stimulus conditions. The magnitude of the periodic response decreased with increasing frequency and was smaller and more delayed for Global than Two-way adaptation. These results suggest that-in addition to the well-characterized return-to-baseline response observed in protocols using constant visual feedback-the oculomotor system attempts to minimize the feedback error by integrating its variation across trials. This process resembles a convolution with an internal response function, whose structure would be determined by coefficients of the learning model. Our protocol reveals this fast learning process in single short experimental sessions, qualifying it for the study of sensorimotor learning in health and disease.

The neural representation of speed in macaque area MT/V5.

Tuning for speed is one key feature of motion-selective neurons in the middle temporal visual area of the macaque cortex (MT, or V5). The present paper asks whether speed is coded in a way that is invariant to the shape of the moving stimulus, and if so, how. When tested with single sine-wave gratings of different spatial and temporal frequencies, MT neurons show a continuum in the degree to which preferred speed depends on spatial frequency. There is some dependence in 75% of MT neurons, and the other 25% maintain speed tuning despite changes in spatial frequency. When tested with stimuli constructed by adding two superimposed sine-wave gratings, the preferred speed of MT neurons becomes less dependent on spatial frequency. Analysis of these responses reveals a speed-tuning nonlinearity that selectively enhances the responses of the neuron when multiple spatial frequencies are present and moving at the same speed. Consistent with the presence of the nonlinearity, MT neurons show speed tuning that is close to form-invariant when the moving stimuli comprise square-wave gratings, which contain multiple spatial frequencies moving at the same speed. We conclude that the neural circuitry in and before MT makes no explicit attempt to render MT neurons speed-tuned for sine-wave gratings, which do not occur in natural scenes. Instead, MT neurons derive form-invariant speed tuning in a way that takes advantage of the multiple spatial frequencies that comprise moving objects in natural scenes.

Effect of form cues on 1D and 2D motion pooling.

Local-motion information can provide either 1-dimensional (1D) or 2-dimensional (2D) solutions. 1D signals occur when the aperture problem has not been solved, so each signal is an estimate of the local-orthogonal component of the object's motion. 2D signals occur when the aperture problem has been solved, so each signal is an estimate of the object's motion. Previous research (JoV, 2009, 9, 1-25) has shown that 1D and 2D signals are pooled differently, via intersection-of-constraints (IOC) and vector-average processes, respectively. Previous research (e.g. Vis. Res., 2003, 2290-2301) has also indicated that form cues can influence how motion signals are perceived. We investigated whether forms cues can affect the pooling of motion signals and whether they differentially affect the pooling of 1D and 2D signals. Global-Gabor (GG) and global-plaid (GP) stimuli were used. These stimuli consist of multiple apertures that contain either Gabors or plaids, respectively. In the GG stimulus the global solution is defined by having the Gabor carriers move (1D signals) such that they are consistent with a single IOC-defined solution. In the GP stimuli the plaid motion (2D signals) are consistent with a vector-average solution defined by a Gaussian distribution. Form cues can be introduced by adding orientation information to the apertures that is either consistent (aligned with) or inconsistent (orthogonal to) with the global-solution. With the 1D stimuli, form cues affect how the motion signals are pooled, with motion being perceived in the direction defined by the orientation cue. Orientation cues had no direct effect on the pooling of the 2D signals.

Adaptation state of the local-motion-pooling units determines the nature of the motion aftereffect to transparent motion.

When observers adapt to a transparent-motion stimulus, the resulting motion aftereffect (MAE) is typically in the direction opposite to the vector average of the component directions. It has been proposed that the reason for this is that it is the adaptation state at the local-level (i.e. of the local-motion-pooling units) that determines the nature of the MAE (Vidnyanszky et al. Trends in Cognitive Sciences, 6(4), 157-161). The adapting stimuli used in these experiments typically consisted of random-dot kinematograms, with each dot being able to move over the entire viewing aperture. Here we used spatially-localised global-plaid stimuli which enabled us, over the course of adaptation, to present either one of both motion directions at each local region. A unidirectional MAE was perceived when two motion directions were presented at each location and a transparent MAE was perceived when a single direction was presented. These results support the notion that it is the adaptation state at the local-motion-pooling level that determines the nature of the MAE to transparent motion stimuli.

No interaction of first- and second-order signals in the extraction of global-motion and optic-flow.

Edwards and Badcock (Vision Research 35, 2589, 1995) argued for independent first-order (FO) and second-order (SO) motion systems up to and including the global-motion level. That study used luminance (which they called FO) and contrast (SO) modulated dots. They found that SO noise dots did not mask signal extraction with luminance increment dots while luminance increment dots did mask SO signal extraction. However, they argued this asymmetry was not due to a combined FO-SO pathway, but rather due to the fact that the luminance-modulated dots, being also local variations in contrast, are both FO and SO stimuli. We test their claim of FO and SO independence by using a stimulus that can generate pure FO and SO signals, specifically one consisting of multiple Gabors (the global-Gabor stimulus) in which the Gaussian envelopes are static and the carriers drift. The carrier can either be luminance-modulated (FO) or contrast-modulated (SO) and motion signals from the randomly-oriented local Gabors must be combined to detect the global-motion vector. Results show no cross-masking of FO and SO signals, thus supporting the hypothesis of independent FO and SO systems up to and including the level extracting optic-flow.

Neuronal responses to moving targets in monkey frontal eye fields.

Due to delays in visuomotor processing, eye movements directed toward moving targets must integrate both target position and velocity to be accurate. It is unknown where and how target velocity information is incorporated into the planning of rapid (saccadic) eye movements. We recorded the activity of neurons in frontal eye fields (FEFs) while monkeys made saccades to stationary and moving targets. A substantial fraction of FEF neurons was found to encode not only the initial position of a moving target, but the metrics (amplitude and direction) of the saccade needed to intercept the target. Many neurons also encoded target velocity in a nearly linear manner. The quasi-linear dependence of firing rate on target velocity means that the neuronal response can be directly read out to compute the future position of a target moving with constant velocity. This is demonstrated using a quantitative model in which saccade amplitude is encoded in the population response of neurons tuned to retinal target position and modulated by target velocity.

Computing vector differences using a gain field-like mechanism in monkey frontal eye field.

Signals related to eye position are essential for visual perception and eye movements, and are powerful modulators of sensory responses in many regions of the visual and oculomotor systems. We show that visual and pre-saccadic responses of frontal eye field (FEF) neurons are modulated by initial eye position in a way suggestive of a multiplicative mechanism (gain field). Furthermore the slope of the eye position sensitivity tends to be negatively correlated with preferred retinal position across the population. A model with Gaussian visual receptive fields and linear-rectified eye position gain fields accounts for a large portion of the variance in the recorded data. Using physiologically derived parameters, this model is able to subtract the gaze shift from the vector representing the retinal location of the target. This computation might be used to maintain a memory of target location in space during ongoing eye movements. This updated spatial memory can be read directly from the locus of the peak of activity across the retinotopic map of FEF and it is the result of a vector subtraction between retinal target location when flashed and subsequent eye displacement in the dark.

Visual remapping by vector subtraction: analysis of multiplicative gain field models.

Saccadic eye movements remain spatially accurate even when the target becomes invisible and the initial eye position is perturbed. The brain accomplishes this in part by remapping the remembered target location in retinal coordinates. The computation that underlies this visual remapping is approximated by vector subtraction: the original saccade vector is updated by subtracting the vector corresponding to the intervening eye movement. The neural mechanism by which vector subtraction is implemented is not fully understood. Here, we investigate vector subtraction within a framework in which eye position and retinal target position signals interact multiplicatively (gain field). When the eyes move, they induce a spatial modulation of the firing rates across a retinotopic map of neurons. The updated saccade metric can be read from the shift of the peak of the population activity across the map. This model uses a quasi-linear (half-rectified) dependence on the eye position and requires the slope of the eye position input to be negatively proportional to the preferred retinal position of each neuron. We derive analytically this constraint and study its range of validity. We discuss how this mechanism relates to experimental results reported in the frontal eye fields of macaque monkeys.