Effector-dependent stochastic reference frame transformations alter decision-making

Abstract

Psychophysical, motor control, and modeling studies have revealed that sensorimotor reference frame transformations (RFTs) add variability to transformed signals. For perceptual decision-making, this phenomenon could decrease the fidelity of a decision signal's representation or alternatively improve its processing through stochastic facilitation. We investigated these two hypotheses under various sensorimotor RFT constraints. Participants performed a time-limited, forced-choice motion discrimination task under eight combinations of head roll and/or stimulus rotation while responding either with a saccade or button press. This paradigm, together with the use of a decision model, allowed us to parameterize and correlate perceptual decision behavior with eye-, head-, and shoulder-centered sensory and motor reference frames. Misalignments between sensory and motor reference frames produced systematic changes in reaction time and response accuracy. For some conditions, these changes were consistent with a degradation of motion evidence commensurate with a decrease in stimulus strength in our model framework. Differences in participant performance were explained by a continuum of eye-head-shoulder representations of accumulated motion evidence, with an eye-centered bias during saccades and a shoulder-centered bias during button presses. In addition, we observed evidence for stochastic facilitation during head-rolled conditions (i.e., head roll resulted in faster, more accurate decisions in oblique motion for a given stimulus-response misalignment). We show that perceptual decision-making and stochastic RFTs are inseparable within the present context. We show that by simply rolling one's head, perceptual decision-making is altered in a way that is predicted by stochastic RFTs.

Figure 1.

Potential roles of noise in perceptual decision-making. Six separate perceptual decision processes (three different evidential certainties with head upright/rolled) are simulated within a drift–diffusion framework for leftward target motion (see shaded curves in inset). One possible role for RFT noise is in the degradation of motion evidence certainty (modeled by Gaussian distributions), which can be seen in the inset. Another possible role for RFT noise is in stochastic facilitation of the decision dynamics (dotted lines). Leftward color-matched arrows represent theoretical influence of stochastic facilitation on response times. Evidence accumulation in this illustrative model is represented by the summed log ratios for random draws from each distribution, biased in the leftward direction and with uniform noise added to the signal.

Figure 2.

Task and paradigm. (A) Participants performed the task under one of eight conditions—four for each response type (saccade or button), organized in a block design. These were combinations of head and/or congruent screen rotations, giving rise to visual motion that was separable across eye, head, and shoulder (screen) reference frames. (B) Each trial consisted of a fixation (500 ms), motion (up to 1,500 ms), and decision epoch. Participants were instructed to determine the direction (left or right) of coherently moving dots randomly chosen at 20%, 10%, or 2% coherence and make their decision using either a horizontal saccade or a button press as quickly and accurately as possible.

Figure 3.

Single participant cumulative RT distributions. Across coherence levels (columns), specific patterns in RTs across rotational conditions (color-coded, see legend) are shown for Participant 7. Differences in the order of these RT distributions can be seen when comparing saccade (top row) to button responses (bottom row).

Figure 4.

Psychometric and chronometric functions. Group-level psychometric and chronometric functions revealed that speed and accuracy were not traded off across rotation conditions, as participants were generally less accurate (psychometric functions, left column) and also slower (chronometric functions, right column) under rotated conditions. In the chronometric plots, each point represents the group average of the LATER fit parameter µ approximating the median reaction time of each condition at each motion strength. Left insets show the discrimination thresholds (thr), which represent the threshold coherence (%) at which participants chose the correct direction 75% of the time for the 2AFC task. Right insets also show the discrimination slope (slo), which approximates the sensitivity to motion strength.

Figure 5.

Variability of rotational effects on performance across participants. Changes in reaction time (top row), percent error (middle row), and reward rate (bottom row) across coherence level (columns), with left axes representing scale for single participant changes (colored line segments, see legend for participant numbers) and right axes representing group-level average changes across rotation conditions (color-coded bars). Each vertex of the line segments represents one rotation condition, in line with the colored bars at the bottom.

Figure 6.

Reference frame predictions and analysis. (A) Response type–specific reference frame prediction matrices. Each cell represents a specific reference frame and the predicted effect size for the corresponding rotation condition. For example, if motion evidence were coded according to an eye-centered reference frame, for the condition in which only the motion stimulus were rotated (condition nH-S), we would expect a large (black shading) reference frame transformation-induced stochastic effect on the coded evidence signal in both saccade and button response conditions. (B) Participant R-squared coefficients for correlation analysis between prediction matrices in panel (A) and observed changes in reaction time (top row), percent error (middle row), and reward rate (bottom row), across coherence levels (columns). Participant color code is the same as in previous figures, and black symbols represent across-participant means. Open circles and filled squares represent R-squared coefficients for saccade responses and for button responses, respectively. Pure eye-centered (red), head-centered (blue), and shoulder-centered (green) reference frame predictions are represented with large filled circles. Note that we have plotted the eye–shoulder projection of this 3D space (thus the head R² axis is along the origin).

Figure 7.

Stochastic facilitation for decisions under H-nS conditions versus nH-S conditions. Delta reaction times (left), percent errors (middle), and reward rates (right) for H-nS for saccades (filled bars) and button presses (open bars). Asterisks represent significant differences from nH-S conditions using a paired t test.