From 1863b8b84356fa645dafb42dc9fe4028d825e54f Mon Sep 17 00:00:00 2001 From: couchot Date: Tue, 16 Jun 2015 10:19:23 +0200 Subject: [PATCH 1/1] ++ --- chaosANN.tex | 33 +++++++++------------------------ main.pdf | Bin 1980602 -> 1979020 bytes 2 files changed, 9 insertions(+), 24 deletions(-) diff --git a/chaosANN.tex b/chaosANN.tex index 1754b80..cdcd912 100644 --- a/chaosANN.tex +++ b/chaosANN.tex @@ -152,34 +152,19 @@ $\left(x_1^0,\dots,x_n^0\right)$ et $S \in [n]^{\mathds{N}}$, il produit exactement les même sorties que les itérations de $F_{f_u}$ avec une condition initiale $\left((x_1^0,\dots, x_n^0),S\right) \in \mathds{B}^n \times [n]^{\mathds{N}}$. Les itérations de $F_{f_u}$ -sont donc un modèle formel de ce genre de réseau de neurones. -Pour vérifier s'il est chaotique, il suffit ainsi +sont donc un modèle formel de cette classe de réseau de neurones. +Pour vérifier si un de ces représentants est chaotique, il suffit ainsi de vérifier si le graphe d'itérations $\textsc{giu}(f)$ est fortement connexe. -\section{Suitability of Feedforward Neural Networks -for Predicting Chaotic and Non-chaotic Behaviors} - -In the context of computer science different topic areas have an -interest in chaos, as for steganographic -techniques~\cite{1309431,Zhang2005759}. Steganography consists in -embedding a secret message within an ordinary one, while the secret -extraction takes place once at destination. The reverse ({\it i.e.}, -automatically detecting the presence of hidden messages inside media) -is called steganalysis. Among the deployed strategies inside -detectors, there are support vectors -machines~\cite{Qiao:2009:SM:1704555.1704664}, neural -networks~\cite{10.1109/ICME.2003.1221665,10.1109/CIMSiM.2010.36}, and -Markov chains~\cite{Sullivan06steganalysisfor}. Most of these -detectors give quite good results and are rather competitive when -facing steganographic tools. However, to the best of our knowledge -none of the considered information hiding schemes fulfills the Devaney -definition of chaos~\cite{Devaney}. Indeed, one can wonder whether -detectors continue to give good results when facing truly chaotic -schemes. More generally, there remains the open problem of deciding -whether artificial intelligence is suitable for predicting topological -chaotic behaviors. +\section{Un réseau de neurones peut-il approximer un +des itération unaires chaotiques?} + +Cette section s'intéresse à étudier le comportement d'un réseau de neurones +face à des itérations unaires chaotiques, comme définies à +la section~\ref{sec:TIPE12}. + \subsection{Representing Chaotic Iterations for Neural Networks} \label{section:translation} diff --git a/main.pdf b/main.pdf index 18dbdd693edc286a6d17fb20e8c0be6cc597cd53..02648a4fe891499de46d3728eb08bf003e9ae52e 100644 GIT binary patch delta 58520 zcmZtNQ*bU!v?k!#wr$(CogLe@@x`|7WXHB`?bx<$%zx%o&DC5yRb748SF5|%yE^YZ zV~#xUP%(*w(pr~suJQ}$aDNZq#@PxLRuET<#Hz(aw1ZeYOfBvMWZq6};v?&2Y` z_HRl@eTwV`qU*FOQV3l+rDauBRo(o8YSM1DERuS*v?3@ZfU`0qz5XGtt<2@_iz#OJ| zVu(CoDjFmsBtQ^s9u7boC&_G;GGo9T4HvIGrCDF<3MqGiRFMpZ)+~ z5`;|t1e3BM3NRHru!X6BA)^p6bX{nOFxe>Ph>kFzp9ZQuGV-Qia+Q79V3`;4l> 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