It's a small dimensional world after all: Comment on "The unreasonable effectiveness of small neural ensembles in high-dimensional brain" by Alexander N. Gorban et al.
It's a small dimensional world after all: Comment on "The unreasonable effectiveness of small neural ensembles in high-dimensional brain" by Alexander N. Gorban et al.
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毕竟这是一个小维度的世界：Alexander N. Gorban 等人对“高维大脑中小型神经集合的不合理有效性”的评论。
DOI：
10.1016/j.plrev.2019.03.015
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发表时间：
2019
影响因子：
11.7
通讯作者：
Kreiman,Gabriel
中科院分区：
文献类型：
--
作者：
Kreiman,Gabriel
The curse of dimensionality refers to the exponential growth in volume in high dimensional spaces, making efficient sampling and drawing conclusions from sparse sampling extremely challenging (Bellman 1957, Vapnik 1995). The difficulties of high-dimensional spaces are particularly prevalent in Neuroscience, where they are manifested in at least three different forms:(1) The number of possible stimuli and task conditions is infinite;(2) In large animals, the number of neurons is many orders of magnitude larger than the numbers that can be currently studied experimentally;(3) By and large, most modeling tools to think about neural data are founded on intuitions from small dimensional worlds.Consider a specific example: the goal is to characterize how information is represented along ventral visual cortex in monkeys, the areas critical for visual object recognition, by presenting images and recording neuronal activity. The number of possible images is infinite. Even restricting the question to small image patches of size 100× 100 pixels and 256 shades of gray, there are many more such images than the estimated number of stars in the observable universe. The number remains astronomically large even if we restrict the analysis to patches of images cropped from photographs on the internet to impose naturalistic constraints. Even without considering other variables such as the age, state, and goals of the animal, task demands, and other experimental conditions, characterizing this stimulus space is daunting to say the least. To make matters more complicated, to investigate the neural representation in visual cortex, traditional studies have relied on studying one neuron at a time; state-of-the-art techniques can push these numbers to hundreds and perhaps soon thousands of simultaneously recorded neurons. Yet, the number of neurons in macaque ventral visual cortex is on the order of several hundred million. These challenges have not prevented publication of a large number of studies about correlations and interpretation of the map between neuronal responses and visual stimuli. Are we deluding ourselves in thinking that we might be able to infer and model brain function by scrutinizing the activity of a handful of neurons in response to a small number of stimuli?
