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  • Information from Lay-Language Summaries is Embargoed Until the Conclusion of the Scientific Presentation

    456—Multisensory: Spatial Factors in Cross-Modal Processing

    Monday, November 11, 2013, 1:00 pm - 5:00 pm

    456.13: Near optimal multisensory integration of approximate numbers

    Location: Halls B-H

    ">I. KANITSCHEIDER1, A. BROWN2, M. B. RYAN2, *A. POUGET3,1, A. CHURCHLAND2;
    1Basic Neurosci., Univ. of Geneva, Geneva, Switzerland; 2Cold Spring Harbor Lab., Cold Spring Harbor, NY; 3Brain and Cognitive Sci., Univ. Rochester, ROCHESTER, NY

    Abstract Body: There is considerable evidence that animals and humans possess an approximate number sense, believed to be the precursor of complex symbolic manipulation of numbers developed by humans. The approximate number sense allows us to perceive numerosity in sensory scenes, but what does our brain represent: a scalar estimate of numerosity or a probability distribution over numerosity? The latter would automatically encode the uncertainty associated with our perception of numerosity, and would also predict that when we combine information about numerosity across senses, or add numerosity within a modality, we do so by performing probabilistic inferences, as opposed to simple arithmetic operations over scalar estimates.
    To explore this issue, we designed a novel task to determine whether subjects can perform optimal inference about numerosity based on multisensory inputs. We trained human subjects on a sequential numerosity task in which they had to decide whether a test stimulus had a larger or smaller numerosity than a fixed reference. Depending on the trial, the numerosity was presented either as a sequence of visual flashes, as a sequence of auditory tones, or both. Furthermore we varied the reliability of the stimulus by adding noise to both visual and auditory conditions, either blocked across trials or on a trial-by-trial basis. We controlled for low-level stimulus attributes like stimulus rate and duration to ensure that subjects based their decisions solely on numerosity.
    Across subjects, we see a clear improvement in the multisensory condition at a given noise level compared to the unisensory conditions at the same noise level. Using a bootstrap analysis, we further show that the magnitude of improvement is close to what would have been predicted by a statistically optimal cue combination. These findings provide evidence that the brain is able to both extract and represent probability distributions of numerical estimates from the statistics of their unisensory presentation.
    Furthermore, our results support the notion that the approximate number sense allows subjects to represent, compare and manipulate numerical estimates independently of sensory modality. In the past, this has been mainly explored by comparing numerosity comparison performance of subjects across and within modalities (e.g. Barth, Kanwisher & Spelke, 2003). The ability of subjects to integrate numerosity from different modalities, as shown by our results, provides novel evidence for the abstractness of the approximate number sense.

    Lay Language Summary: Groups of female lions can assess whether they are outnumbered by a group of lion intruders into their territory based on the number of roars they hear. The lions’ ability relies on the approximate number sense, an intuitive sense of quantity shared among animal species as diverse as monkeys, rats, pigeons, dolphins and raccoons. In humans, this sense allows us to quickly estimate the number of jellybeans in a jar or the number of people in a supermarket checkout line and is believed to be the basis of our capability to understand abstract math.
    But how does the brain represent intuitive numbers? One possibility would be that it simply extracts a precise number from a sensory scene, which can be further processed if necessary according to the rules of addition and subtraction. The real world, however, is often confusing. In many situations, evidence about number will be uncertain and a more sophisticated strategy would be to represent and process not only the number itself but also its reliability. If the reliability of a number estimate is available, the brain can achieve better results by acting like a clever statistician who would follow the rules of probabilistic inference, a mathematical paradigm which allows giving more weight to reliable information than to unreliable one.
    Whether reliability of intuitive numbers is processed by the brain can be tested by a framework called “multisensory integration”. Multisensory integration directly tests whether subjects are able to weigh stimulus information according to its reliability by presenting the same stimulus to multiple senses. In our case, human subjects watched a sequence of visual flashes and auditory tones and reported whether the number of events where higher or lower than ten. The flashes and tones were presented so rapidly that our subjects were not able to explicitly count them but only had an intuitive sense of how many events they perceived.
    We then compared subjects’ performance on two types of trials: In multisensory trials, both flashes and tones were present, while in unisensory trials, subjects either saw only flashes or heard only tones. If subjects are indeed able to represent numbers probabilistically, they should do better on multisensory trials than on unisensory trials: Since both flashes and tones are potentially useful information for subjects to base their decision on, they should get it right more often when both types of information are present.
    Moreover, if the brain acts like the clever statistician mentioned above, we cannot only qualitatively predict that subjects improve on multisensory trials, but we can quantitatively predict the size of the improvement. This prediction is called “optimal multisensory integration” and can be mathematically derived from the theory of probabilistic inference. Our results show that subjects come very close to the mathematically optimal performance. These findings provide evidence that the brain not only processes intuitive numbers according to simple arithmetic rules, but is able to also make efficient use of the reliabilities of intuitive numbers.

    Information from Lay-Language Summaries is Embargoed Until the Conclusion of the Scientific Presentation

    456—Multisensory: Spatial Factors in Cross-Modal Processing

    Monday, November 11, 2013, 1:00 pm - 5:00 pm

    456.13: Near optimal multisensory integration of approximate numbers

    Location: Halls B-H

    ">I. KANITSCHEIDER1, A. BROWN2, M. B. RYAN2, *A. POUGET3,1, A. CHURCHLAND2;
    1Basic Neurosci., Univ. of Geneva, Geneva, Switzerland; 2Cold Spring Harbor Lab., Cold Spring Harbor, NY; 3Brain and Cognitive Sci., Univ. Rochester, ROCHESTER, NY

    Abstract Body: There is considerable evidence that animals and humans possess an approximate number sense, believed to be the precursor of complex symbolic manipulation of numbers developed by humans. The approximate number sense allows us to perceive numerosity in sensory scenes, but what does our brain represent: a scalar estimate of numerosity or a probability distribution over numerosity? The latter would automatically encode the uncertainty associated with our perception of numerosity, and would also predict that when we combine information about numerosity across senses, or add numerosity within a modality, we do so by performing probabilistic inferences, as opposed to simple arithmetic operations over scalar estimates.
    To explore this issue, we designed a novel task to determine whether subjects can perform optimal inference about numerosity based on multisensory inputs. We trained human subjects on a sequential numerosity task in which they had to decide whether a test stimulus had a larger or smaller numerosity than a fixed reference. Depending on the trial, the numerosity was presented either as a sequence of visual flashes, as a sequence of auditory tones, or both. Furthermore we varied the reliability of the stimulus by adding noise to both visual and auditory conditions, either blocked across trials or on a trial-by-trial basis. We controlled for low-level stimulus attributes like stimulus rate and duration to ensure that subjects based their decisions solely on numerosity.
    Across subjects, we see a clear improvement in the multisensory condition at a given noise level compared to the unisensory conditions at the same noise level. Using a bootstrap analysis, we further show that the magnitude of improvement is close to what would have been predicted by a statistically optimal cue combination. These findings provide evidence that the brain is able to both extract and represent probability distributions of numerical estimates from the statistics of their unisensory presentation.
    Furthermore, our results support the notion that the approximate number sense allows subjects to represent, compare and manipulate numerical estimates independently of sensory modality. In the past, this has been mainly explored by comparing numerosity comparison performance of subjects across and within modalities (e.g. Barth, Kanwisher & Spelke, 2003). The ability of subjects to integrate numerosity from different modalities, as shown by our results, provides novel evidence for the abstractness of the approximate number sense.

    Lay Language Summary: Groups of female lions can assess whether they are outnumbered by a group of lion intruders into their territory based on the number of roars they hear. The lions’ ability relies on the approximate number sense, an intuitive sense of quantity shared among animal species as diverse as monkeys, rats, pigeons, dolphins and raccoons. In humans, this sense allows us to quickly estimate the number of jellybeans in a jar or the number of people in a supermarket checkout line and is believed to be the basis of our capability to understand abstract math.
    But how does the brain represent intuitive numbers? One possibility would be that it simply extracts a precise number from a sensory scene, which can be further processed if necessary according to the rules of addition and subtraction. The real world, however, is often confusing. In many situations, evidence about number will be uncertain and a more sophisticated strategy would be to represent and process not only the number itself but also its reliability. If the reliability of a number estimate is available, the brain can achieve better results by acting like a clever statistician who would follow the rules of probabilistic inference, a mathematical paradigm which allows giving more weight to reliable information than to unreliable one.
    Whether reliability of intuitive numbers is processed by the brain can be tested by a framework called “multisensory integration”. Multisensory integration directly tests whether subjects are able to weigh stimulus information according to its reliability by presenting the same stimulus to multiple senses. In our case, human subjects watched a sequence of visual flashes and auditory tones and reported whether the number of events where higher or lower than ten. The flashes and tones were presented so rapidly that our subjects were not able to explicitly count them but only had an intuitive sense of how many events they perceived.
    We then compared subjects’ performance on two types of trials: In multisensory trials, both flashes and tones were present, while in unisensory trials, subjects either saw only flashes or heard only tones. If subjects are indeed able to represent numbers probabilistically, they should do better on multisensory trials than on unisensory trials: Since both flashes and tones are potentially useful information for subjects to base their decision on, they should get it right more often when both types of information are present.
    Moreover, if the brain acts like the clever statistician mentioned above, we cannot only qualitatively predict that subjects improve on multisensory trials, but we can quantitatively predict the size of the improvement. This prediction is called “optimal multisensory integration” and can be mathematically derived from the theory of probabilistic inference. Our results show that subjects come very close to the mathematically optimal performance. These findings provide evidence that the brain not only processes intuitive numbers according to simple arithmetic rules, but is able to also make efficient use of the reliabilities of intuitive numbers.