Minimal embedding dimension bounds for receptive fields
نویسنده
چکیده
Curto, et. al., in 2013 outlined the neural ring, and neural ideal for describing receptive field structures of groups of neurons. In this paper we review their results, and explores some bounds that the algebraic and simplicial complex structures induce on the minimal embedding dimension of the receptive fields.
منابع مشابه
Characterization and Minimal Embeddings of Connected Neural Codes
We give a complete characterization of receptive field codes realizable by connected receptive fields and their minimal embedding dimensions. In particular, we show that all connected codes are realizable in dimension at most three. To our knowledge, this is the first family of receptive field codes for which the exact characterization and minimal embedding dimension is known.
متن کاملNeural Networks with Local Receptive Fields and Superlinear VC Dimension
Local receptive field neurons comprise such well-known and widely used unit types as radial basis function (RBF) neurons and neurons with center-surround receptive field. We study the Vapnik-Chervonenkis (VC) dimension of feedforward neural networks with one hidden layer of these units. For several variants of local receptive field neurons, we show that the VC dimension of these networks is sup...
متن کاملEssential Dimension of Separable Algebras Embedding in a Fixed Central Simple Algebra
One of the key problems in non-commutative algebra is the classification of central simple algebras and more generally of separable algebras over fields, i.e., Azumaya-algebras whose center is étale over the given field. In this paper we fix a central simple F -algebra A of prime power degree and study seperable algebras over extensions K/F , which embed in AK . The type of such an embedding is...
متن کاملNeural Networks with Local Receptive
Local receptive eld neurons comprise such well-known and widely used unit types as radial basis function neurons and neurons with center-surround receptive eld. We study the Vapnik-Chervonenkis (VC) dimension of feedforward neural networks with one hidden layer of these units. For several variants of local receptive eld neurons we show that the VC dimension of these networks is superlinear. In ...
متن کاملModel Based Method for Determining the Minimum Embedding Dimension from Solar Activity Chaotic Time Series
Predicting future behavior of chaotic time series system is a challenging area in the literature of nonlinear systems. The prediction's accuracy of chaotic time series is extremely dependent on the model and the learning algorithm. On the other hand the cyclic solar activity as one of the natural chaotic systems has significant effects on earth, climate, satellites and space missions. Several m...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2014