Gaussian information bottleneck and the non-perturbative renormalization group
Gaussian information bottleneck and the non-perturbative renormalization group
复制标题
高斯信息瓶颈和非微扰重整化群
DOI：
10.1088/1367-2630/ac395d
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发表时间：
2022
影响因子：
3.3
通讯作者：
Palmer, Stephanie E.
中科院分区：
文献类型：
--
作者：
Kline, Adam G.;Palmer, Stephanie E.
重整化群(RG)是一类用于解释相互作用的多体系统的集体物理的理论技术。有人提出，RG形式主义可能有助于在传统物理背景之外的复杂系统中发现和解释新出现的低维结构，例如在生物学或计算机科学中。在这种情况下，已经使用的一种常见的降维框架是信息瓶颈(IB)，其中的目标是压缩输入信号X，同时最大化其具有某种随机相关性的互信息。可变Y的信息瓶颈已被应用于脊椎动物和无脊椎动物处理系统中，以表征对外部世界未来运动的最优编码。最近的其他工作表明，二聚体模型的RG方案可以被试图解决类似IB的问题的神经网络“发现”。这份手稿探讨了IB和任何现有的RG公式是否在形式上等价。一类软截断非摄动RG技术由一族非确定粗化映射族定义，从而可以形式地映射到IB上，反之亦然。具体而言，本文的讨论完全局限于高斯统计(GIB)，对于它，IB有精确的、封闭的解。在此约束下，GIB具有半群结构，其中连续变换保持IB-最优。此外，可以识别与GIB相关联的RG截止方案。我们的结果表明，IB可用于在RG手术中强加“大尺度”结构的概念，如生物功能。
The renormalization group (RG) is a class of theoretical techniques used to explain the collective physics of interacting, many-body systems. It has been suggested that the RG formalism may be useful in finding and interpreting emergent low-dimensional structure in complex systems outside of the traditional physics context, such as in biology or computer science. In such contexts, one common dimensionality-reduction framework already in use is information bottleneck (IB), in which the goal is to compress an'input'signal X while maximizing its mutual information with some stochastic'relevance'variable Y. IB has been applied in the vertebrate and invertebrate processing systems to characterize optimal encoding of the future motion of the external world. Other recent work has shown that the RG scheme for the dimer model could be'discovered'by a neural network attempting to solve an IB-like problem. This manuscript explores whether IB and any existing formulation of RG are formally equivalent. A class of soft-cutoff non-perturbative RG techniques are defined by families of non-deterministic coarsening maps, and hence can be formally mapped onto IB, and vice versa. For concreteness, this discussion is limited entirely to Gaussian statistics (GIB), for which IB has exact, closed-form solutions. Under this constraint, GIB has a semigroup structure, in which successive transformations remain IB-optimal. Further, the RG cutoff scheme associated with GIB can be identified. Our results suggest that IB can be used to impose a notion of'large scale'structure, such as biological function, on an RG procedure.
驱动无序系统中非平衡相变的重正化群分析
DOI：
--
发表时间：
2019
期刊：
Springer Theses
影响因子：
--
作者：
T. Haga
通讯作者：
T. Haga
DOI：
--
发表时间：
2006
期刊：
--
影响因子：
--
作者：
Iroon Polytechniou-
通讯作者：
Iroon Polytechniou-