发育中视觉皮层自发对称破缺的机制
Mechanisms for spontaneous symmetry breaking in developing visual cortex
摘要：
为了让大脑识别图像中的局部方向，神经元必须自发地打破其响应函数的平移和旋转对称性-这是无监督学习的典型例子。生物学中无监督学习的主要框架是赫布原理，但赫布学习如何打破这种对称性是一个长期存在的生物物理学之谜。理论研究一致认为，这需要输入到视觉皮层，以反转它们在长距离上的相关性的相对大小。经验测量已经徒劳地寻找这样的反转，并报告相反的情况是正确的。我们正式的问题，通过厄米化的多层模型，它映射到一个问题的零温度相变。在新的相图中，只要（1）经常性的相互作用足够长，（2）赫布竞争被适当地考虑，两种对称性都会自发地破缺。对称性破缺的相关机制是来自同一传入细胞的连接之间的竞争。这种竞争，而不是输入的结构，能够触发图像处理所需的对称性破坏阶段。我们提供了分析预测的相对大小的相关长度尺度需要这种新的机制发生。这些结果使实验观察与赫布范式相一致，揭示了视觉皮层发育的新机制，并有助于我们对学习和对称性破缺之间关系的理解。
英文摘要：
For the brain to recognize local orientations within images, neurons must spontaneously break the translation and rotation symmetry of their response functions -- an archetypal example of unsupervised learning. The dominant framework for unsupervised learning in biology is Hebb's principle, but how Hebbian learning could break such symmetries is a longstanding biophysical riddle. Theoretical studies agree that this should require inputs to visual cortex to invert the relative magnitude of their correlations at long distances. Empirical measurements have searched in vain for such an inversion, and report the opposite to be true. We formally approach the question through the hermitianization of a multi-layer model, which maps it into a problem of zero-temperature phase transitions. In the emerging phase diagram, both symmetries break spontaneously as long as (1) recurrent interactions are sufficiently long-range and (2) Hebbian competition is duly accounted for. The relevant mechanism for symmetry breaking is competition among connections sprouting from the same afferent cell. Such competition, and not the structure of the inputs, is capable of triggering the broken-symmetry phase required by image processing. We provide analytic predictions on the relative magnitudes of the relevant length-scales needed for this novel mechanism to occur. These results reconcile experimental observations to the Hebbian paradigm, shed light on a new mechanism for visual cortex development, and contribute to our growing understanding of the relationship between learning and symmetry breaking.
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