The relationship between initial threshold, learning, and generalization in perceptual learning.

We investigated the origin of two previously reported general rules of perceptual learning. First, the initial discrimination thresholds and the amount of learning were found to be related through a Weber-like law. Second, increased training length negatively influenced the observer's ability to generalize the obtained knowledge to a new context. Using a five-day training protocol, separate groups of observers were trained to perform discrimination around two different reference values of either contrast (73% and 30%) or orientation (25° and 0°). In line with previous research, we found a Weber-like law between initial performance and the amount of learning, regardless of whether the tested attribute was contrast or orientation. However, we also showed that this relationship directly reflected observers' perceptual scaling function relating physical intensities to perceptual magnitudes, suggesting that participants learned equally on their internal perceptual space in all conditions. In addition, we found that with the typical five-day training period, the extent of generalization was proportional to the amount of learning, seemingly contradicting the previously reported diminishing generalization with practice. This result suggests that the negative link between generalization and the length of training found in earlier studies might have been due to overfitting after longer training and not directly due to the amount of learning per se.

How to reward animals based on their subjective percepts: A Bayesian approach to online estimation of perceptual biases.

Elucidating the neural basis of perceptual biases, such as those produced by visual illusions, can provide powerful insights into the neural mechanisms of perceptual inference. However, studying the subjective percepts of animals poses a fundamental challenge: unlike human participants, animals cannot be verbally instructed to report what they see, hear, or feel. Instead, they must be trained to perform a task for reward, and researchers must infer from their responses what the animal perceived. However, animals' responses are shaped by reward feedback, thus raising the major concern that the reward regimen may alter the animal's decision strategy or even intrinsic perceptual biases. We developed a method that estimates perceptual bias during task performance and then computes the reward for each trial based on the evolving estimate of the animal's perceptual bias. Our approach makes use of multiple stimulus contexts to dissociate perceptual biases from decision-related biases. Starting with an informative prior, our Bayesian method updates a posterior over the perceptual bias after each trial. The prior can be specified based on data from past sessions, thus reducing the variability of the online estimates and allowing it to converge to a stable estimate over a small number of trials. After validating our method on synthetic data, we apply it to estimate perceptual biases of monkeys in a motion direction discrimination task in which varying background optic flow induces robust perceptual biases. This method overcomes an important challenge to understanding the neural basis of subjective percepts.

Statistical Learning in Vision.

Vision and learning have long been considered to be two areas of research linked only distantly. However, recent developments in vision research have changed the conceptual definition of vision from a signal-evaluating process to a goal-oriented interpreting process, and this shift binds learning, together with the resulting internal representations, intimately to vision. In this review, we consider various types of learning (perceptual, statistical, and rule/abstract) associated with vision in the past decades and argue that they represent differently specialized versions of the fundamental learning process, which must be captured in its entirety when applied to complex visual processes. We show why the generalized version of statistical learning can provide the appropriate setup for such a unified treatment of learning in vision, what computational framework best accommodates this kind of statistical learning, and what plausible neural scheme could feasibly implement this framework. Finally, we list the challenges that the field of statistical learning faces in fulfilling the promise of being the right vehicle for advancing our understanding of vision in its entirety.

Development of Preschoolers' Understanding of Zero.

While knowledge on the development of understanding positive integers is rapidly growing, the development of understanding zero remains not well-understood. Here, we test several components of preschoolers' understanding of zero: Whether they can use empty sets in numerical tasks (as measured with comparison, addition, and subtraction tasks); whether they can use empty sets soon after they understand the cardinality principle (cardinality-principle knowledge is measured with the give-N task); whether they know what the word "zero" refers to (tested in all tasks in this study); and whether they categorize zero as a number (as measured with the smallest-number and is-it-a-number tasks). The results show that preschoolers can handle empty sets in numerical tasks as soon as they can handle positive numbers and as soon as, or even earlier than, they understand the cardinality principle. Some also know that these sets are labeled as "zero." However, preschoolers are unsure whether zero is a number. These results identify three components of knowledge about zero: operational knowledge, linguistic knowledge, and meta-knowledge. To account for these results, we propose that preschoolers may understand numbers as the properties of items or objects in a set. In this view, zero is not regarded as a number because an empty set does not include any items, and missing items cannot have any properties, therefore, they cannot have the number property either. This model can explain why zero is handled correctly in numerical tasks even though it is not regarded as a number.

Statistically defined visual chunks engage object-based attention.

Although objects are the fundamental units of our representation interpreting the environment around us, it is still not clear how we handle and organize the incoming sensory information to form object representations. By utilizing previously well-documented advantages of within-object over across-object information processing, here we test whether learning involuntarily consistent visual statistical properties of stimuli that are free of any traditional segmentation cues might be sufficient to create object-like behavioral effects. Using a visual statistical learning paradigm and measuring efficiency of 3-AFC search and object-based attention, we find that statistically defined and implicitly learned visual chunks bias observers' behavior in subsequent search tasks the same way as objects defined by visual boundaries do. These results suggest that learning consistent statistical contingencies based on the sensory input contributes to the emergence of object representations.

A common probabilistic framework for perceptual and statistical learning.

System-level learning of sensory information is traditionally divided into two domains: perceptual learning that focuses on acquiring knowledge suitable for fine discrimination between similar sensory inputs, and statistical learning that explores the mechanisms that develop complex representations of unfamiliar sensory experiences. The two domains have been typically treated in complete separation both in terms of the underlying computational mechanisms and the brain areas and processes implementing those computations. However, a number of recent findings in both domains call in question this strict separation. We interpret classical and more recent results in the general framework of probabilistic computation, provide a unifying view of how various aspects of the two domains are interlinked, and suggest how the probabilistic approach can also alleviate the problem of dealing with widely different types of neural correlates of learning. Finally, we outline several directions along which our proposed approach fosters new types of experiments that can promote investigations of natural learning in humans and other species.

Unimodal statistical learning produces multimodal object-like representations.

The concept of objects is fundamental to cognition and is defined by a consistent set of sensory properties and physical affordances. Although it is unknown how the abstract concept of an object emerges, most accounts assume that visual or haptic boundaries are crucial in this process. Here, we tested an alternative hypothesis that boundaries are not essential but simply reflect a more fundamental principle: consistent visual or haptic statistical properties. Using a novel visuo-haptic statistical learning paradigm, we familiarised participants with objects defined solely by across-scene statistics provided either visually or through physical interactions. We then tested them on both a visual familiarity and a haptic pulling task, thus measuring both within-modality learning and across-modality generalisation. Participants showed strong within-modality learning and 'zero-shot' across-modality generalisation which were highly correlated. Our results demonstrate that humans can segment scenes into objects, without any explicit boundary cues, using purely statistical information.

Symbolic Number Comparison Is Not Processed by the Analog Number System: Different Symbolic and Non-symbolic Numerical Distance and Size Effects.

HIGHLIGHTS We test whether symbolic number comparison is handled by an analog noisy system.Analog system model has systematic biases in describing symbolic number comparison.This suggests that symbolic and non-symbolic numbers are processed by different systems. Dominant numerical cognition models suppose that both symbolic and non-symbolic numbers are processed by the Analog Number System (ANS) working according to Weber's law. It was proposed that in a number comparison task the numerical distance and size effects reflect a ratio-based performance which is the sign of the ANS activation. However, increasing number of findings and alternative models propose that symbolic and non-symbolic numbers might be processed by different representations. Importantly, alternative explanations may offer similar predictions to the ANS prediction, therefore, former evidence usually utilizing only the goodness of fit of the ANS prediction is not sufficient to support the ANS account. To test the ANS model more rigorously, a more extensive test is offered here. Several properties of the ANS predictions for the error rates, reaction times, and diffusion model drift rates were systematically analyzed in both non-symbolic dot comparison and symbolic Indo-Arabic comparison tasks. It was consistently found that while the ANS model's prediction is relatively good for the non-symbolic dot comparison, its prediction is poorer and systematically biased for the symbolic Indo-Arabic comparison. We conclude that only non-symbolic comparison is supported by the ANS, and symbolic number comparisons are processed by other representation.

Interference Between Number Magnitude and Parity.

Interference between number magnitude and other properties can be explained by either an analogue magnitude system interfering with a continuous representation of the other properties or by discrete, categorical representations in which the corresponding number and property categories interfere. In this study, we investigated whether parity, a discrete property which supposedly cannot be stored on an analogue representation, could interfere with number magnitude. We found that in a parity decision task the magnitude interfered with the parity, highlighting the role of discrete representations in numerical interference. Additionally, some participants associated evenness with large values, while others associated evenness with small values, therefore, a new interference index, the dual index was introduced to detect this heterogeneous interference. The dual index can be used to reveal any heterogeneous interference that were missed in previous studies. Finally, the magnitude-parity interference did not correlate with the magnitude-response side interference (Spatial-Numerical Association of Response Codes [SNARC] effect) or with the parity-response side interference (Markedness Association of Response Codes [MARC] effect), suggesting that at least some of the interference effects are not the result of the stimulus property markedness.

The Source of the Symbolic Numerical Distance and Size Effects.

Human number understanding is thought to rely on the analog number system (ANS), working according to Weber's law. We propose an alternative account, suggesting that symbolic mathematical knowledge is based on a discrete semantic system (DSS), a representation that stores values in a semantic network, similar to the mental lexicon or to a conceptual network. Here, focusing on the phenomena of numerical distance and size effects in comparison tasks, first we discuss how a DSS model could explain these numerical effects. Second, we demonstrate that the DSS model can give quantitatively as appropriate a description of the effects as the ANS model. Finally, we show that symbolic numerical size effect is mainly influenced by the frequency of the symbols, and not by the ratios of their values. This last result suggests that numerical distance and size effects cannot be caused by the ANS, while the DSS model might be the alternative approach that can explain the frequency-based size effect.