Krommenhoek K P, Wiegerinck W A
Department of Medical Physics and Biophysics, University of Nijmegen, The Netherlands.
Biol Cybern. 1998 Jun;78(6):465-77. doi: 10.1007/s004220050450.
Saccadic averaging is the phenomenon that two simultaneously presented retinal inputs result in a saccade with an endpoint located on an intermediate position between the two stimuli. Recordings from neurons in the deeper layers of the superior colliculus have revealed neural correlates of saccade averaging, indicating that it takes place at this level or upstream. Recently, we proposed a neural network for internal feedback in saccades. This neural network model is different from other models in that it suggests the possibility that averaging takes place in a stage upstream of the colliculus. The network consists of output units representing the neural map of the deeper layers of the superior colliculus and hidden layers imitating areas in the posterior parietal cortex. The deeper layers of the superior colliculus represent the motor error of a desired saccade, e.g. an eye movement to a visual target. In this article we show that averaging is an emergent property of the proposed network. When two retinal targets with different intensities are simultaneously presented to the network, the activity in the output layer represents a single motor error with a weighted average value. Our goal is to understand the mechanism of weighted averaging in this neural network. It appears that averaging in the model is caused by the linear dependence of the net input, received by the hidden units, on retinal error, independent of its retinal coding format. For nonnormalized retinal error inputs, also the nonlinearity between the net input and the activity of the hidden units plays a role in the averaging process. The averaging properties of the model are in agreement with physiological experiments if the hypothetical retinal error input map is normalized. The neural network predicts that if this normalization is overruled by electrical stimulation, averaging still takes place. However, in this case--as a consequence of the feedback task--the location of the resulting saccade depends on the initial eye position and the total intensity/current applied at the two locations. This could be a way to verify the neural network model. If the assumptions for the model are valid, a physiological implication of this paper is that averaging of saccades takes place upstream of the superior colliculus.
扫视平均是指两个同时呈现的视网膜输入会导致一次扫视，其终点位于两个刺激之间的中间位置的现象。对上丘深层神经元的记录揭示了扫视平均的神经关联，表明它发生在这个水平或上游水平。最近，我们提出了一个用于扫视内部反馈的神经网络。这个神经网络模型与其他模型的不同之处在于，它提出了平均可能发生在丘上一个阶段的可能性。该网络由代表上丘深层神经图谱的输出单元和模仿后顶叶皮层区域的隐藏层组成。上丘深层代表期望扫视的运动误差，例如眼睛向视觉目标的移动。在本文中，我们表明平均是所提出网络的一种涌现特性。当将两个具有不同强度的视网膜目标同时呈现给网络时，输出层的活动代表一个具有加权平均值的单一运动误差。我们的目标是了解这个神经网络中加权平均的机制。看来模型中的平均是由隐藏单元接收到的净输入对视网膜误差的线性依赖性引起的，与视网膜编码格式无关。对于未归一化的视网膜误差输入，净输入与隐藏单元活动之间的非线性在平均过程中也起作用。如果假设的视网膜误差输入图谱被归一化，模型的平均特性与生理实验一致。神经网络预测，如果这种归一化被电刺激推翻，平均仍然会发生。然而，在这种情况下——作为反馈任务的结果——所得扫视的位置取决于初始眼位以及在两个位置施加的总强度/电流。这可能是验证神经网络模型的一种方法。如果模型的假设有效，本文的一个生理学含义是扫视平均发生在上丘的上游。
