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 argue that this requires inputs to the 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 multilayer model, which maps it into a problem of zero-temperature phase transitions. In the emerging phase diagram, both symmetries break spontaneously as long as (i) recurrent interactions are sufficiently long range and (ii) Hebbian competition is duly accounted for. A key ingredient for symmetry breaking is competition among connections sprouting from the same afferent cell. Such a competition, along with simple monotonic falloff of input correlations with distance, 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.

中文翻译：

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视觉皮层发育过程中自发对称性破坏的机制

为了让大脑识别图像中的局部方向，神经元必须自发地破坏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谜团。理论研究认为，这需要视觉皮层的输入来反转它们在远距离的相关性的相对大小。经验测量徒劳地寻找这种倒置并报告相反的情况。我们通过多层模型的 Hermitianization 正式处理该问题，将其映射为零温度相变问题。在新兴的相图中，只要（i）重复的相互作用范围足够长并且（ii）适当地考虑到赫布竞争，这两种对称性都会自发地破坏。对称性破坏的一个关键因素是从同一个传入细胞发芽的连接之间的竞争。这种竞争，以及输入相关性与距离的简单单调衰减，能够触发图像处理所需的破坏对称阶段。我们对这种新机制发生所需的相关长度尺度的相对大小提供了分析预测。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坏之间关系的理解不断加深。