Brezis Noam, Bronfman Zohar Z, Usher Marius
School of Psychology, Tel Aviv University, Tel Aviv 69978, Israel
School of Psychology and Cohn Institute for the History and Philosophy of Science and Ideas, Tel Aviv University, Tel Aviv 69978, Israel
Neural Comput. 2018 Feb;30(2):428-446. doi: 10.1162/neco_a_01037. Epub 2017 Nov 21.
Humans possess a remarkable ability to rapidly form coarse estimations of numerical averages. This ability is important for making decisions that are based on streams of numerical or value-based information, as well as for preference formation. Nonetheless, the mechanism underlying rapid approximate numerical averaging remains unknown, and several competing mechanism may account for it. Here, we tested the hypothesis that approximate numerical averaging relies on perceptual-like processes, instantiated by population coding. Participants were presented with rapid sequences of numerical values (four items per second) and were asked to convey the sequence average. We manipulated the sequences' length, variance, and mean magnitude and found that similar to perceptual averaging, the precision of the estimations improves with the length and deteriorates with (higher) variance or (higher) magnitude. To account for the results, we developed a biologically plausible population-coding model and showed that it is mathematically equivalent to a population vector. Using both quantitative and qualitative model comparison methods, we compared the population-coding model to several competing models, such as a step-by-step running average (based on leaky integration) and a midrange model. We found that the data support the population-coding model. We conclude that humans' ability to rapidly form estimations of numerical averages has many properties of the perceptual (intuitive) system rather than the arithmetic, linguistic-based (analytic) system and that population coding is likely to be its underlying mechanism.
人类拥有一种非凡的能力，能够迅速对数值平均数形成粗略估计。这种能力对于基于数值流或基于价值的信息做出决策以及偏好形成都很重要。尽管如此，快速近似数值平均背后的机制仍然未知，可能有几种相互竞争的机制可以解释它。在这里，我们测试了这样一个假设，即近似数值平均依赖于由群体编码实例化的类似感知的过程。向参与者呈现快速的数值序列（每秒四个项目），并要求他们传达序列的平均值。我们操纵了序列的长度、方差和平均大小，发现与感知平均类似，估计的精度随着长度的增加而提高，随着（更高的）方差或（更高的）大小而降低。为了解释这些结果，我们开发了一个具有生物学合理性的群体编码模型，并表明它在数学上等同于一个群体向量。使用定量和定性的模型比较方法，我们将群体编码模型与几个相互竞争的模型进行了比较，例如逐步移动平均值（基于泄漏积分）和中值模型。我们发现数据支持群体编码模型。我们得出结论，人类快速形成数值平均估计的能力具有感知（直观）系统而非算术、基于语言（分析）系统的许多特性，并且群体编码可能是其潜在机制。
