Negative spherical perceptron
Mihailo Stojnic

TL;DR
This paper extends the analysis of spherical perceptrons to the negative threshold case, providing new insights into its storage capacity and suggesting it may be more combinatorially complex than the positive case.
Contribution
It introduces a novel mechanism to analyze negative spherical perceptrons and offers the first detailed study of their storage capacity.
Findings
Negative spherical perceptrons may be more combinatorial in nature.
The analysis confirms the complexity of the negative case.
Results suggest the negative case is a harder challenge than the positive one.
Abstract
In this paper we consider the classical spherical perceptron problem. This problem and its variants have been studied in a great detail in a broad literature ranging from statistical physics and neural networks to computer science and pure geometry. Among the most well known results are those created using the machinery of statistical physics in \cite{Gar88}. They typically relate to various features ranging from the storage capacity to typical overlap of the optimal configurations and the number of incorrectly stored patterns. In \cite{SchTir02,SchTir03,TalBook} many of the predictions of the statistical mechanics were rigorously shown to be correct. In our own work \cite{StojnicGardGen13} we then presented an alternative way that can be used to study the spherical perceptrons as well. Among other things we reaffirmed many of the results obtained in \cite{SchTir02,SchTir03,TalBook} and…
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Taxonomy
TopicsNeural Networks and Applications · Blind Source Separation Techniques · Topological and Geometric Data Analysis
