Investigation of Possible Neural Architectures Underlying Information-Geometric Measures
Investigation of Possible Neural Architectures Underlying Information-Geometric Measures
复制标题
信息几何测量下可能的神经架构的研究
作者：
M. Tatsuno;M. Okada
最近提出了一种新的分析方法，基于信息几何，这种方法可能会提供有用的见解，神经集团内的统计相互作用。然而，由于问题的不适定性，信息几何度量与神经交互结构之间的联系尚未阐明。在这里，可能的神经架构的信息几何措施进行了调查，使用一个孤立的对和一个孤立的三重模型神经元。通过假设平衡态的存在，我们推导出解析的信息几何参数和这些简单的神经结构之间的关系。对于对称网络，一阶和二阶信息几何参数分别表示外部输入和神经元之间的底层连接，前提是对数线性模型中用于参数估计的神经元数量和网络中的神经元数量相同。然而，对于非对称网络，这些参数取决于每个神经元的内在连接和外部输入。此外，我们推导了两个神经元相互作用的信息几何参数和传统的互相关度量之间的关系。我们还表明，信息几何参数的变化取决于对数线性模型中的参数估计假设的神经元的数量。这一发现表明，有必要仔细研究信息几何方法。本文还讨论了一种选择合适正交坐标的可能准则。本文指出了基于模型的方法的重要性，并阐明了信息几何应用于神经网络分析的潜在神经结构。
A novel analytical method based on information geometry was recently proposed, and this method may provide useful insights into the statistical interactions within neural groups. The link between information-geometric measures and the structure of neural interactions has not yet been elucidated, however, because of the ill-posed nature of the problem. Here, possible neural architectures underlying information-geometric measures are investigated using an isolated pair and an isolated triplet of model neurons. By assuming the existence of equilibrium states, we derive analytically the relationship between the information-geometric parameters and these simple neural architectures. For symmetric networks, the first- and second-order information-geometric parameters represent, respectively, the external input and the underlying connections between the neurons provided that the number of neurons used in the parameter estimation in the log-linear model and the number of neurons in the network are the same. For asymmetric networks, however, these parameters are dependent on both the intrinsic connections and the external inputs to each neuron. In addition, we derive the relation between the information-geometric parameter corresponding to the two-neuron interaction and a conventional cross-correlation measure. We also show that the information-geometric parameters vary depending on the number of neurons assumed for parameter estimation in the log-linear model. This finding suggests a need to examine the information-geometric method carefully. A possible criterion for choosing an appropriate orthogonal coordinate is also discussed. This article points out the importance of a model-based approach and sheds light on the possible neural structure underlying the application of information geometry to neural network analysis.
影响因子：
56.9
作者：
WILSON, MA;MCNAUGHTON, BL
通讯作者：
MCNAUGHTON, BL