Optimising strategies on the numberline task
David Aagten-Murphy, Guido Marco Cicchini and David Burr
The ability to correctly indicate the location of a numerical magnitude on a linear scale, the numberline task, has frequently been measured as a proxy for mathematical abilities. There are several caveats to this measure, particularly when using digits, as learning and cognitive strategy appear to play a large role in performance. Here we parametrically examined a variety of numberlines - differing in scale, direction, length and the origin and endpoint of magnitudes covered - to identify various different sources of error. Furthermore we utilised dot clouds as well as digits to identify differences in behaviour between estimated and absolute numerosity judgements respectively. Overall the various numberline perturbations were best explained by a modified performance-optimizing Bayesian model, where judgement errors were minimised by incorporating a prior, defined by a probability density function comprising a combination of physical features of the numberline, particularly its endpoint and centre. Little evidence supported the notion of 'logarithmic coding'. These results demonstrate the presence of non-numerical optimising strategies on the numberline task, which have implications for subjects with difficulties in mathematics, where poorer performance may correlate with difficulty in applying an optimal strategy.
How children deal with risk in a visuomotor task
Tessa Dekker, Julia Jones and Marko Nardini
Human adults can take uncertainty in their sensory and motor systems into account to maximize gain in rewarded visuomotor tasks. It is unclear when or how humans learn their own sensory and motor capabilities, or become able to use this information to make optimal decisions under risk. To explore the development of these abilities, we applied a Bayesian decision-making framework that captures adults'movement strategy choices (Trommershäuser et al., 2003, JOSA A, 1419-1433) to a child-friendly, rewarded visuo-motor task. Six- to 11-year-old children and adults earned points by rapidly touching a target on a screen, while avoiding a partially overlapping penalty region. Spatial configurations of the penalty and target and penalty size were varied. To choose the gain maximizing-strategy in each condition, subjects must represent and take into account their own visuo-motor uncertainty. Adults chose movement strategies close to those maximizing expected gain in response to changes in penalty location and size. Children showed changes in strategy when risk was introduced, but selected pointing strategies that were further from optimal. These results suggest that optimal decision making under risk takes surprisingly long to develop. Children may have inaccurate representations of own variability, of probability, and/or of value in the task.
Saccade trajectory of a perceptual decision is influenced most by the last evidence viewed
Clare Lyne, Eugene McSorely and Rachel McCloy
Where to saccade is a frequent perceptual decision. Research using random dot kinematograms (RDKs) shows increasing motion coherence indicating a choice leads to saccade trajectory deviating further away from the non-selected target (McSorley & McCloy, 2009, Experimental Brain Research, 198, 513-20). Here, we examine whether the temporal window over which participants integrate information affects saccade metrics. The window is ~100ms; when useful information is presented after this, performance falls to chance (Ludwig et al, 2005b, Journal of Neuroscience, 25 (43), 9907-12). Participants made a saccade to the target indicated by motion within an RDK, which contained a window of high coherence information among random motion, the position of which varied along the trial. It was hypothesised that when the window was at the beginning of the trial, there would be increased deviation away from the non-selected target and better performance as it would be incorporated into the decision. There were no differences in performance or saccade metrics. A second experiment carried out detailed analysis of the timings. Performance did not vary, but saccade trajectory deviated away significantly more when the window was at the end of the trial. This suggests the final evidence has the most impact on saccade trajectory.
Integration of extraretinal and visual information for perceptual decisions across eye movements
Florian Ostendorf and Ray Dolan
We continuously move our eyes when we inspect a visual scene. For the successful integration of visual information into a coherent scene representation the visuomotor system needs to deal with these constant self-induced perceptual changes and distinguish them from external motion. Internal forward models may help to solve this problem: The brain may use an internal monitoring signal associated with an oculomotor command to predict the visual consequences of the corresponding eye movement and compare this prediction with the actual perceptual outcome. Space integration across eye movements has been classically studied in sparse visual environments. However, visual scenes in everyday life typically contain a rich structure of spatial relational information, providing additional cues to disambiguate self-induced from external changes of perceptual input. We asked normal subjects to perform a simple perceptual decision on the apparent displacement of a visual target, jumping unpredictably in sync with a saccadic eye movement. In a critical test condition, the target object was presented together with flanker objects. Perceptual decisions in this condition could also take into account the spatial distance between target and flankers. Results support the notion that subjects combine internal monitoring and visual relational information in an efficient manner, weighting these information sources depending on their respective reliability.
What happens early in ultra-rapid object recognition?
Torsten Stemmler, Karoline Spang and Manfred Fahle
Human observers are remarkably fast in detecting animals in complex natural scenes. One possible explanation is that fast visual recognition may rely on the sequence of cortical arrival times of spikes according to a temporal order code. We tested this possible explanation by scrambling temporal scene information, distributing image presentations on pixel by pixel basis on several consecutive frames at high presentation rate (150 Hz) while keeping overall image information constant. Stimuli were presented at a CRT screen for up to 100 ms, separated in maximally 15 frames, and subjects in a first experiment pushed one of two buttons to indicate, in a 2AFC task, whether the image to the left or else in the one to the right of the fixation point contained an animal. Participants responded by a saccade in the second experiment, with or else without a temporal gap between fixation point and stimulus presentation. We did not find significant differences in overall reaction times and performance levels between simultaneous versus temporally scrambled presentations, and only performance of less frequent ultra-fast responses declined moderately as a function of early image content, not supporting the notion of a general use of cortical arrival times for pattern recognition.
Effect of gender membership on sequential decision of face attractiveness
Aki Kondo, Kohske Takahashi and Katsumi Watanabe
When we make decisions for sequentially presented items, each decision is biased by the stimulus and decision in the preceding trials (the sequential effect; Holland & Lockhead, 1968, Perception & Psychophysics, 3, 409-414). In a mixed-category sequence, the sequential effect is stronger when the stimuli of current and preceding trials fall under the same category (Ward, 1985, Perception & Psychophysics, 38, 512-522). In the present study, we investigated whether the gender membership of faces would affect on the sequential effect. Forty-eight pictures of male and female faces were presented successively. Participants rated attractiveness, roundness, or intelligence of each face on a 7-point scale. The sequential effect was observed irrespective of the property to be judged. However, the sequential effect was enhanced in the same-category trials only for the attractiveness judgement, not for the roundness judgement or the intelligence judgement. These findings suggest that the gender of faces serves as a cue for forming category representation when face attractiveness is of interest, and hence the category formation in sequential decision is adaptive process depending on the property to be judged.
How different choice methods affect perceptual decision bias
Shigeaki Nishina, Dongho Kim and Takeo Watanabe
Decisions based on visual patterns are not only based on immediate visual signals but also on the observer's knowledge about what is likely to be shown. Perceptual decision making is thus not purely perceptual. It has been found that such bias is observed differently in 2AFC and 2IFC tasks in terms of time span within which past information is accumulated, even when experimental settings are identical except that the instruction to the subjects were given accordingly [Kim et al. 2009, Journal of Vision 9(8):827]. The results show that while a decision as to when an event happens is partially determined by immediate past events, a decision as to what feature is presented is determined by an accumulation of longer past experiences, suggesting different mechanisms underlying those two types of tasks although they are statistically identical. Here we propose a probabilistic model based on a diffusion model that can explain the difference effectively in terms of both short-term and long-term aspects of the decision process. The model indicates that different decision thresholds would underlie the observed different biases. We also discuss how this difference may affect experimental designs in general.
Time scale of evidence integration in visual motion decisions
Pia Jentgens, Thomas Pfeffer, Konstantinos Tsetsos, Marius Usher and Tobias Donner
Current computational models of perceptual decisions postulate that choices are based on the temporal integration of sensory information. When the stimulus duration is controlled by the environment, the optimal strategy is to integrate all the evidence provided. We tested whether human observers do so during judgments about the net motion of random dot kinematograms. We presented random dot kinematograms for various durations and at various levels of motion strength and computed psychophysical thresholds for each stimulus duration. The time scale of perfect integration was estimated as the duration, for which thresholds decrease with stimulus duration with a slope of approximately -0.5 in log-log coordinates. We compared the integration time scale across different 'task sets': yes-no motion detection and up/down motion discrimination; up/down discrimination with fixed stimulus-response (SR) mapping and with trial-to-trial variations in SR mapping. Under fixed SR-mapping, observers integrated information nearly perfectly across at least 3 s. Further, the integration time scales were independent of discrimination/detection, but time scales decreased (to ~500 ms) when the SR mapping varied from trial to trial. We conclude that the integration time scale in perceptual choice, can be long, dependent on the automaticity of the SR mapping. This dependence may reflect capacity limits.
Temporal integration in visual motion detection with temporal uncertainty
Thomas Pfeffer, Konstantinos Tsetsos, Pia Jentgens, Tomas Knapen, Marius Usher and Tobias H. Donner
Computational models postulate that perceptual choices are based on the temporal integration of sensory signals. So far, this computation has commonly been probed in tasks, in which the level of sensory evidence is constant. However, in natural environments sensory evidence varies in an unpredictable fashion. We characterized how humans integrate coherent random dot motion signals embedded in a stream of flickering noise (0% motion coherence), introducing temporal uncertainty about the start of the signal. Motion signals of varying duration (between 120 - 960 ms) and coherence levels occurred at random latencies within a 4 s noise stream, or not at all (25% of trials). In different conditions, blocked by session, signal durations were mostly short (120 ms) or mostly long (960 ms). Subjects'detection thresholds decreased monotonically as a function of signal duration up to 960 ms, consistent with temporal integration even under temporal uncertainty. The dependency of the integration timescale on the presence of temporal uncertainty and the prevalent stimulus duration will be examined by means of a simple computational model of the decision process.
The estimation of short durations and an objective measure of observer performance evaluation
Simon Cropper, Alan Johnston and Aurelio Bruno
We examined observers' ability to judge short durations and then reflect upon their own performance. Observers responded to 2 identical presentations of a drifting sine grating 4 deg above fixation. They initiated presentation with a button-press, and released the button when they considered the stimulus to be half-way through. The intervals ranged between 0.5 and 2 secs and the duration conditions were blocked. Subjects were asked to indicate their 'most accurate estimate'of the two. Observers consistently over-estimated the true duration. This standing error was not proportional to interval length. As expected there was no significant difference in variance (or mean) between the first and second interval. When trials were grouped by objective performance the 'ideal'estimates had a significantly smaller variance. However, when grouped on observer section the 'best'estimates also had a significantly lower variance compared to the worst, indicating observer awareness of decisional noise on a trial-by-trial basis. The difference in variance between selected and rejected trial provides an objective measure of performance evaluation and an alternative to subjective confidence ratings. One implication of this study is that improved performance through perceptual learning may involved learning a model of observer noise.