Optimisation via encodings: a renormalisation group perspective
Difficult, in particular NP-complete, optimization problems are traditionally solved approximately using search heuristics. These are usually slowed down by the rugged landscapes encountered, because local minima arrest the search process. Cover-encoding maps were devised to circumvent this problem by transforming the original landscape to one that is free of local minima and enriched in near-optimal solutions. By definition, these involve the mapping of the original (larger) search space into smaller subspaces, by processes that typically amount to a form of coarse-graining. In this paper, we explore the details of this coarse-graining using formal arguments, as well as concrete examples of cover-encoding maps, that are investigated analytically as well as computationally. Our results strongly suggest that the coarse-graining involved in cover-encoding maps bears a strong resemblance to that encountered in renormalisation group schemes. Given the apparently disparate nature of these two formalisms, these strong similarities are rather startling, and suggest deep mathematical underpinnings that await further exploration.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Abstraction requires breadth: a renormalisation group approach
Abstraction is the process of extracting the essential features from raw data while ignoring irrelevant details. This is similar to the process of focusing on large-scale properties, systematically removing irrelevant sm…
Criticality & Deep Learning II: Momentum Renormalisation Group
Guided by critical systems found in nature we develop a novel mechanism consisting of inhomogeneous polynomial regularisation via which we can induce scale invariance in deep learning systems. Technically, we map our dee…
Deep LearningIterative Magnitude Pruning as a Renormalisation Group: A Study in The Context of The Lottery Ticket Hypothesis
This thesis delves into the intricate world of Deep Neural Networks (DNNs), focusing on the exciting concept of the Lottery Ticket Hypothesis (LTH). The LTH posits that within extensive DNNs, smaller, trainable subnetwor…
Transferability of Winning Lottery Tickets in Neural Network Differential Equation Solvers
Recent work has shown that renormalisation group theory is a useful framework with which to describe the process of pruning neural networks via iterative magnitude pruning. This report formally describes the link between…
Renormalisation Group Methods for Effective Epidemiological Models
Epidemiological models describe the spread of an infectious disease within a population. They capture microscopic details on how the disease is passed on among individuals in various different ways, while making predicti…