视觉定向选择性环模型中的错觉
Illusions in the Ring Model of visual orientation selectivity
摘要：
定向调谐的环模型是人类新皮层中视觉区V1的超柱的动力学模型，其被设计成通过局部，即，皮质-皮质计算调谐曲线是该动力学模型的稳态解，即与时间无关。环模型的一个重要假设是，输入到V1的LGN弱调谐到视网膜方向，并且V1中的局部计算使这种调谐变得尖锐。由于描述环模型的方程在突触权重分布中相对于作用于刺激的视网膜取向的特定组具有内置的等方差性质，因此该模型实际上编码了相对于彼此任意平移的无限数量的调谐曲线。通过使用轨道空间缩减技术，我们重写的规范形式的模型方程作为多项式的函数，是不变的关于这个组的行动。这使我们能够结合等变分歧理论与一个有效的数值连续方法，以计算调谐曲线的环模型预测。令人惊讶的是，这些调谐曲线中的一些并不适应刺激。我们将其解释为神经错觉，并以数值方式显示它们如何通过简单的动力学刺激诱导。这些神经错觉是该模型的重要生物预测。如果它们能在实验中被观察到，这将是支持环模型的一个优点。我们还展示了我们的理论分析如何通过将模型预测与已发表的实验观测结果进行比较来非常简单地指定模型参数的范围。
英文摘要：
The Ring Model of orientation tuning is a dynamical model of a hypercolumn of visual area V1 in the human neocortex that has been designed to account for the experimentally observed orientation tuning curves by local, i.e., cortico-cortical computations. The tuning curves are stationary, i.e. time independent, solutions of this dynamical model. One important assumption underlying the Ring Model is that the LGN input to V1 is weakly tuned to the retinal orientation and that it is the local computations in V1 that sharpen this tuning. Because the equations that describe the Ring Model have built-in equivariance properties in the synaptic weight distribution with respect to a particular group acting on the retinal orientation of the stimulus, the model in effect encodes an infinite number of tuning curves that are arbitrarily translated with respect to each other. By using the Orbit Space Reduction technique we rewrite the model equations in canonical form as functions of polynomials that are invariant with respect to the action of this group. This allows us to combine equivariant bifurcation theory with an efficient numerical continuation method in order to compute the tuning curves predicted by the Ring Model. Surprisingly some of these tuning curves are not tuned to the stimulus. We interpret them as neural illusions and show numerically how they can be induced by simple dynamical stimuli. These neural illusions are important biological predictions of the model. If they could be observed experimentally this would be a strong point in favour of the Ring Model. We also show how our theoretical analysis allows to very simply specify the ranges of the model parameters by comparing the model predictions with published experimental observations.
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