Mazzoni P, Andersen R A, Jordan M I
Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology, Cambridge 02139.
Cereb Cortex. 1991 Jul-Aug;1(4):293-307. doi: 10.1093/cercor/1.4.293.
Area 7a of the posterior parietal cortex of the primate brain is concerned with representing head-centered space by combining information about the retinal location of a visual stimulus and the position of the eyes in the orbits. An artificial neural network was previously trained to perform this coordinate transformation task using the backpropagation learning procedure, and units in its middle layer (the hidden units) developed properties very similar to those of area 7a neurons presumed to code for spatial location (Andersen and Zipser, 1988; Zipser and Andersen, 1988). We developed two neural networks with architecture similar to Zipser and Andersen's model and trained them to perform the same task using a more biologically plausible learning procedure than backpropagation. This procedure is a modification of the Associative Reward-Penalty (AR-P) algorithm (Barto and Anandan, 1985), which adjusts connection strengths using a global reinforcement signal and local synaptic information. Our networks learn to perform the task successfully to any degree of accuracy and almost as quickly as with backpropagation, and the hidden units develop response properties very similar to those of area 7a neurons. In particular, the probability of firing of the hidden units in our networks varies with eye position in a roughly planar fashion, and their visual receptive fields are large and have complex surfaces. The synaptic strengths computed by the AR-P algorithm are equivalent to and interchangeable with those computed by backpropagation. Our networks also perform the correct transformation on pairs of eye and retinal positions never encountered before. All of these findings are unaffected by the interposition of an extra layer of units between the hidden and output layers. These results show that the response properties of the hidden units of a layered network trained to perform coordinate transformations, and their similarity with those of area 7a neurons, are not a specific result of backpropagation training. The fact that they can be obtained by a more biologically plausible learning rule corroborates the validity of this neural network's computational algorithm as a plausible model of how area 7a may perform coordinate transformations.
灵长类大脑后顶叶皮质的7a区通过整合视觉刺激的视网膜位置信息和眼睛在眼眶中的位置信息来表征以头部为中心的空间。之前曾使用反向传播学习程序训练一个人工神经网络来执行这种坐标转换任务，并且其中间层（隐藏单元）中的神经元所呈现出的特性与推测用于编码空间位置的7a区神经元的特性非常相似（安德森和齐普泽，1988；齐普泽和安德森，1988）。我们开发了两个架构与齐普泽和安德森模型相似的神经网络，并使用一种比反向传播更符合生物学原理的学习程序训练它们执行相同的任务。这个程序是对关联奖励-惩罚（AR-P）算法（巴托和阿南丹，1985）的一种修改，该算法使用全局强化信号和局部突触信息来调整连接强度。我们的网络能够成功地以任何精度执行任务，并且几乎与使用反向传播时一样快，而且隐藏单元所呈现出的反应特性与7a区神经元的特性非常相似。特别是，我们网络中隐藏单元的放电概率随眼睛位置以大致平面的方式变化，并且它们的视觉感受野很大且具有复杂的表面。由AR-P算法计算出的突触强度与由反向传播计算出的突触强度等效且可互换。我们的网络还能对之前从未遇到过的眼睛和视网膜位置对进行正确的转换。所有这些发现都不受在隐藏层和输出层之间插入额外一层单元的影响。这些结果表明，经过训练执行坐标转换的分层网络隐藏单元的反应特性，以及它们与7a区神经元特性的相似性，并非反向传播训练的特定结果。它们可以通过一种更符合生物学原理的学习规则获得这一事实，证实了这个神经网络计算算法作为7a区可能执行坐标转换方式的合理模型的有效性。
