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On Lyapunov exponents and adversarial perturbation [article]

Vinay Uday Prabhu, Nishant Desai, John Whaley
2018 arXiv   pre-print
adversarial perturbation.  ...  In this paper, we would like to disseminate a serendipitous discovery involving Lyapunov exponents of a 1-D time series and their use in serving as a filtering defense tool against a specific kind of deep  ...  adversarially perturbed and randomly perturbed images.  ... 
arXiv:1802.06927v1 fatcat:myi3reglobdnvkme6ywzp4ws7u

Approaching Adversarial Example Classification with Chaos Theory

Anibal Pedraza, Oscar Deniz, Gloria Bueno
2020 Entropy  
Adversarial examples are one of the most intriguing topics in modern deep learning. Imperceptible perturbations to the input can fool robust models.  ...  In our experiments, we show that the Lyapunov exponents (an established measure of chaoticity), which have been recently proposed for classification of adversarial examples, are not robust to image processing  ...  We explain this based on the relationship between entropy and positive Lyapunov exponents, which in fact are the most discriminant ones.  ... 
doi:10.3390/e22111201 pmid:33286969 pmcid:PMC7712112 fatcat:q27dkrzpgzg2pep7oyrdzxsvl4

A Dependent Variable Harmonically Coupled Chaotic System for a Pseudorandom bit Generator

Qi Wu, J. Heled, A. Yuan
2018 MATEC Web of Conferences  
Linear complexity and cipher space are analyzed at last. All the results demonstrate that the proposed generator possesses excellent properties. 1  ...  Afterwards, a pseudorandom bit generator is proposed based on it. Next, we employ five statistic tests to evaluate the pseudo randomness of generated sequences.  ...  then the Lyapunov exponents for system (6) In Figure 2 , the two Lyapunov exponents are depicted with lines and points, respectively.  ... 
doi:10.1051/matecconf/201817303074 fatcat:a736juc3kjbibowlumgo7rzzfq

Stochastic Security: Adversarial Defense Using Long-Run Dynamics of Energy-Based Models [article]

Mitch Hill, Jonathan Mitchell, Song-Chun Zhu
2021 arXiv   pre-print
from which the EOT attack naturally follows, and 3) state-of-the-art adversarial defense for naturally-trained classifiers and competitive defense compared to adversarially-trained classifiers on Cifar  ...  We focus on defending naturally-trained classifiers using Markov Chain Monte Carlo (MCMC) sampling with an Energy-Based Model (EBM) for adversarial purification.  ...  Ordered systems have a maximal Lyapunov exponent that is either negative or 0, while chaotic systems have positive Lyapunov exponents.  ... 
arXiv:2005.13525v2 fatcat:dtrckl6sgvfd7oey6oh3tqmkfi

Transient Response of Hybrid Boolean Networks as Physical Unclonable Functions [article]

Noeloikeau Charlot, Daniel Canaday, Andrew Pomerance, Daniel J. Gauthier
2020 arXiv   pre-print
In this work, we present a novel PUF design composed of a chaotic Boolean network implemented on a field-programmable gate array, capable of generating challenge-response pairs in as little as 10 ns.  ...  property protection and device authentication to secret key exchange.  ...  Lyapunov Exponent The Lyapunov exponent of a system is a measure of the rate at which two nearby points in phase space diverge.  ... 
arXiv:1907.12542v2 fatcat:dvs3cowwpjbqxcfoxrhwc4kfly

Random Number Generators Founded on Signal and Information Theory [chapter]

David P. Maher, Robert J. Rance
1999 Lecture Notes in Computer Science  
The strength of a cryptographic function depends on the amount of entropy in the cryptovariables that are used as keys.  ...  To address these problems, we have developed new theory and we have invented and implemented some new techniques.  ...  Mathematically, a positive Lyapunov exponent defines chaos. In discrete time, the Lyapunov exponent is defined as the averaged logarithm of the absolute value of gain each cycle.  ... 
doi:10.1007/3-540-48059-5_19 fatcat:kqliydlqybewrjlgkhxsmdmhjy

Combining data assimilation and machine learning to emulate a dynamical model from sparse and noisy observations: a case study with the Lorenz 96 model [article]

Julien Brajard , Laurent Bertino Nansen Center, Thormøhlensgate 47, Bergen, Norway, Dept of Meteorology, University of Reading, Mathematical Institute, University of Utrecht, CEREA, joint laboratory École des Ponts ParisTech and EDF R D, Université Paris-Est, Champs-sur-Marne, France)
2020 arXiv   pre-print
A novel method, based on the combination of data assimilation and machine learning is introduced.  ...  The surrogate model shows short-term forecast skills up to two Lyapunov times, the retrieval of positive Lyapunov exponents as well as the more energetic frequencies of the power density spectrum.  ...  CEREA and LOCEAN are members of Institut Pierre-Simon Laplace (IPSL).  ... 
arXiv:2001.01520v1 fatcat:572rmchpizhzhljdn2v4ccynze

Optimal input representation in neural systems at the edge of chaos [article]

Guillermo B. Morales, Miguel A. Muñoz
2021 arXiv   pre-print
of the rank, with an exponent close to unity, a result that has been indeed experimentally verified in neurons of the mouse visual cortex.  ...  Here, we elaborate on a recent theoretical result, which establishes that the spectrum of covariance matrices of neural networks representing complex inputs in a robust way needs to decay as a power-law  ...  with a very small difference in their initial conditions: λ = lim k→∞ 1 k log γ k γ 0 (4) where λ is termed the maximum Lyapunov exponent (MLE), γ 0 is the initial distance between the perturbed and unperturbed  ... 
arXiv:2107.05709v1 fatcat:ej7hul45lffntcb4h453sqnbay

Noisy Recurrent Neural Networks [article]

Soon Hoe Lim, N. Benjamin Erichson, Liam Hodgkinson, Michael W. Mahoney
2021 arXiv   pre-print
Our theory is supported by empirical results which demonstrate that the RNNs have improved robustness with respect to various input perturbations.  ...  We find that, under reasonable assumptions, this implicit regularization promotes flatter minima; it biases towards models with more stable dynamics; and, in classification tasks, it favors models with  ...  Hodgkinson, and M. W. Mahoney would like to acknowledge the IARPA (contract W911NF20C0035), ARO, NSF, and and ONR via its BRC on RandNLA for providing partial support of this work.  ... 
arXiv:2102.04877v3 fatcat:vfwxcpjc25bfvd7d5gvy7iqa7i

Noise-Response Analysis of Deep Neural Networks Quantifies Robustness and Fingerprints Structural Malware [article]

N. Benjamin Erichson, Dane Taylor, Qixuan Wu, Michael W. Mahoney
2021 arXiv   pre-print
In particular, DNNs can be designed to have backdoors that allow an adversary to easily and reliably fool an image classifier by adding a pattern of pixels called a trigger.  ...  weights and activation pathways).  ...  NBE and MWM would like to acknowledge the UC Berkeley CLTC, ARO, IARPA, NSF, and ONR for providing partial support of this work.  ... 
arXiv:2008.00123v2 fatcat:54q7xf2wg5ey5covluyidetc4q

Adversarial decision strategies in multiple network phased oscillators: the Blue-Green-Red Kuramoto-Sakaguchi model [article]

Mathew Zuparic, Maia Angelova, Ye Zhu, Alexander Kalloniatis
2020 arXiv   pre-print
The agents are coupled on three networks of differing topologies, with interactions modulated by different cross-population frustrations, internal and cross-network couplings.  ...  We compare this to a numerical solution for a range of internal and cross-network coupling parameters to investigate various synchronisation regimes and critical thresholds.  ...  This research was a collaboration between the Commonwealth of Australia (represented by the Defence Science and Technology Group) and Deakin University through a Defence Science Partnerships agreement.  ... 
arXiv:2011.09759v1 fatcat:q5punx4jjrdbhkyfdggwaaekmm

Chaos of Learning Beyond Zero-sum and Coordination via Game Decompositions [article]

Yun Kuen Cheung, Yixin Tao
2020 arXiv   pre-print
We take on a game decomposition approach and answer the question affirmatively.  ...  Among other results, we propose a notion of "matrix domination" and design a linear program, and use them to characterize bimatrix games where MWU is Lyapunov chaotic almost everywhere.  ...  ) is Lyapunov chaotic in S δ with Lyapunov exponent θ 2 δ 2 2(n 1 +n 2 ) ǫ 2 .  ... 
arXiv:2008.00540v1 fatcat:h64qsnztbbb5fa2qs3ikb67yo4

Dynamic Assignment Control of a Closed Queueing Network under Complete Resource Pooling [article]

Siddhartha Banerjee, Yash Kanoria, Pengyu Qian
2020 arXiv   pre-print
Further, there is an SMW policy that achieves the optimal loss exponent among all assignment policies, and we analytically specify this policy in terms of the demand arrival rates for all origin-destination  ...  Simulations of ride-hailing based on the NYC taxi dataset demonstrate excellent performance.  ...  on this Lyapunov function is exponent optimal.  ... 
arXiv:1803.04959v3 fatcat:uj7lo77l35cb5b5ktsqwc2ldva

Teams as Complex Adaptive Systems: Reviewing 17 Years of Research

Pedro J. Ramos-Villagrasa, Pedro Marques-Quinteiro, José Navarro, Ramón Rico
2017 Small Group Research  
To help fully incorporate the logic of teams as CAS in the science of teams, we review extant research on teams approached from a nonlinear dynamical system theory.  ...  This review contributes to teams' theory and practice by offering ways to identify both research methods and managing techniques that scholars and practitioners may apply to study and manage teams as CAS  ...  ., to use Lyapunov exponents; .  ... 
doi:10.1177/1046496417713849 fatcat:ufdvrsihgbgi5fpojxzr2mzg34

Latent Representations of Dynamical Systems: When Two is Better Than One [article]

Max Tegmark
2019 arXiv   pre-print
component analysis and all other approaches that use a single latent representation, and discuss the intuitive reason why two representations are better than one.  ...  We show that the information-theoretically optimal approach uses different mappings for present and future, in contrast to state-of-the-art machine-learning approaches where both mappings are the same.  ...  Lyapunov exponents) are predictive but unpredictable, while those in unstable equilibria (with positive Lyapunov exponents) are unpredictive but predictable.  ... 
arXiv:1902.03364v2 fatcat:4dy2qoug45dilkgtvbzwrlrcpq
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