Arbib M A, Amari S
J Theor Biol. 1985 Jan 7;112(1):123-55. doi: 10.1016/s0022-5193(85)80120-x.
Section 1 lists 12 points which must be addressed by neural models of sensorimotor coordination. Section 2 addresses the problem of extrapolating motor output from noisy data or from sensory input. The Pellionisz-Llinas cerebellar lookahead module addresses this problem for the noise-free case, and we suggest theoretical and experimental tests of the model; we then suggest the investigation of neural analogs of the Kalman-Bucy filter. Section 3 offers a brief exposition of mechanics in a tensor framework to provide the irreducible minimum of mathematical machinery to evaluate the Pellionisz-Llinás tensor theory of brain function and to suggest fruitful new hypotheses. Our critique of this theory in section 4 leads us to conclude that what they offer is based on metaphorical use of terminology from Euclidean tensors, not on rigorous application of the mathematics of tensor analysis. The central claim of their theory--that the input is a covariant intention vector transformed by a metric tensor encoded in the cerebellum to a contravariant execution vector--has not been substantiated and probably cannot be substantiated. However, we do point the way to further use of tensor analysis in the study of neural control of movement. The concluding section then returns to the points raised in section 1 with a highly selective survey of models of cerebellum and tectum.
第1节列出了感觉运动协调的神经模型必须解决的12个要点。第2节讨论了从噪声数据或感觉输入中推断运动输出的问题。佩利奥尼斯-利纳雷斯小脑前瞻性模块解决了无噪声情况下的这个问题，我们提出了该模型的理论和实验测试；然后我们建议对卡尔曼-布西滤波器的神经类似物进行研究。第3节在张量框架中简要阐述了力学，以提供评估大脑功能的佩利奥尼斯-利纳雷斯张量理论所需的最少数学工具，并提出富有成果的新假设。我们在第4节对该理论的批评使我们得出结论，他们所提供的内容是基于对欧几里得张量术语的隐喻性使用，而不是基于张量分析数学的严格应用。他们理论的核心主张——输入是一个协变意图向量，通过编码在小脑中的度量张量转换为一个逆变执行向量——尚未得到证实，而且可能无法得到证实。然而，我们确实指出了在运动神经控制研究中进一步使用张量分析的方向。结论部分然后通过对小脑和顶盖模型的高度选择性综述，回到了第1节提出的要点。
