心理数量表征：计算模型研究

Because number is a core construct underlying much intelligent behavior, the representation of number is a topic of great interest in cognitive neuroscience and psychology. Number cognition has been investigated with a diversity of methods, including single-cell recording, neuroimaging, and (developmental) behavioral paradigms. Here, we aim to investigate and understand the representation of number by means of computational modeling. Based on previous empirical work, two core systems of number representation have been proposed (Feigenson, Dehaene, & Spelke, 2004): an approximate system for computations involving large numbers, and a more precise object file system that codes small numbers. However, the nature of these two core systems of number has remained unspecified. In the first study, we evaluate whether a previous absolute number representation (e.g., the number of objects in a set) computational model can incorporate the two core systems. Furthermore, because the field has been dominated by investigations of absolute number representation, the second study is dedicated to illuminating aspects of representations involving proportions (ratios of quantities). The correlation between absolute number representation and proportion representation, and the nature of proportion representations are still elusive. We propose a gain-field model of proportion representation to shed light on the neural and computational basis of proportion representation.

在最近的认知神经科学和心理学研究中，数量表征是一个引起广泛关注的研究主题；研究者通过单神经元记录、神经影像以及发展心理研究等不同方法对其进行了研究。在本项目中，我们试图通过计算模型来研究和理解数量表征：(1)虽然已经有大量研究考察了双数量表征系统的假设(Feigenson, Dehaene, & Spelke, 2004)： 一个近似大数表征系统和一个精确客体档案小数表征系统。但这两个系统的计算功能的实质依旧不清楚。因此，本项目核心内容之一是扩展现有绝对数量表征(例如，一集合物体的数目)计算模型，来帮助人类更好地理解双数量表征系统的假设。(2)最近，对复杂数量表征(例如，比率)的研究也越来越多。但迄今为止，绝对量表征和比率表征的相互关系，以及大脑如何表征像比率这样比较复杂的数量还不是很清楚。因此，本项目核心内容之二是提出比率的增益域模型来帮助人类更好地理解比率表征的神经科学和计算科学基础。

在最近的认知神经科学和心理学研究中，数学能力发展和学习以及数量表征是一个引起广泛关注的研究主题。本项目组采用行为、fMRI技术以及计算模型等研究手段，从心理数量表征这条主线出发考察了数量表征的神经编码机制。主要内容包括：（1）心理数量的总和编码和位置编码的神经机制，以及非符号数量表征方式的计算模型的实现；（2）复杂数量表征，数字比率表征的神经计算模型；（3）数量运算——空间的交互效应的起源，这种效应的发生阶段，单纯呈现运算符号能否能诱发个体注意的空间转移；（4）数量中值切分的神经机制研究，心理数字线和物理线的切分是否有不同切分机制。