ترغب بنشر مسار تعليمي؟ اضغط هنا

Neural Networks and Chaos: Construction, Evaluation of Chaotic Networks, and Prediction of Chaos with Multilayer Feedforward Networks

68   0   0.0 ( 0 )
 نشر من قبل Christophe Guyeux
 تاريخ النشر 2016
  مجال البحث الهندسة المعلوماتية
والبحث باللغة English




اسأل ChatGPT حول البحث

Many research works deal with chaotic neural networks for various fields of application. Unfortunately, up to now these networks are usually claimed to be chaotic without any mathematical proof. The purpose of this paper is to establish, based on a rigorous theoretical framework, an equivalence between chaotic iterations according to Devaney and a particular class of neural networks. On the one hand we show how to build such a network, on the other hand we provide a method to check if a neural network is a chaotic one. Finally, the ability of classical feedforward multilayer perceptrons to learn sets of data obtained from a dynamical system is regarded. Various Boolean functions are iterated on finite states. Iterations of some of them are proven to be chaotic as it is defined by Devaney. In that context, important differences occur in the training process, establishing with various neural networks that chaotic behaviors are far more difficult to learn.



قيم البحث

اقرأ أيضاً

We introduce a new structure for memory neural networks, called feedforward sequential memory networks (FSMN), which can learn long-term dependency without using recurrent feedback. The proposed FSMN is a standard feedforward neural networks equipped with learnable sequential memory blocks in the hidden layers. In this work, we have applied FSMN to several language modeling (LM) tasks. Experimental results have shown that the memory blocks in FSMN can learn effective representations of long history. Experiments have shown that FSMN based language models can significantly outperform not only feedforward neural network (FNN) based LMs but also the popular recurrent neural network (RNN) LMs.
Conventional artificial neural networks are powerful tools in science and industry, but they can fail when applied to nonlinear systems where order and chaos coexist. We use neural networks that incorporate the structures and symmetries of Hamiltonia n dynamics to predict phase space trajectories even as nonlinear systems transition from order to chaos. We demonstrate Hamiltonian neural networks on the canonical Henon-Heiles system, which models diverse dynamics from astrophysics to chemistry. The power of the technique and the ubiquity of chaos suggest widespread utility.
We explore chaos in the Kuramoto model with multimodal distributions of the natural frequencies of oscillators and provide a comprehensive description under what conditions chaos occurs. For a natural frequency distribution with $M$ peaks it is typic al that there is a range of coupling strengths such that oscillators belonging to each peak form a synchronized cluster, but the clusters do not globally synchronize. We use collective coordinates to describe the inter- and intra-cluster dynamics, which reduces the Kuramoto model to $2M-1$ degrees of freedom. We show that under some assumptions, there is a time-scale splitting between the slow intracluster dynamics and fast intercluster dynamics, which reduces the collective coordinate model to an $M-1$ degree of freedom rescaled Kuramoto model. Therefore, four or more clusters are required to yield the three degrees of freedom necessary for chaos. However, the time-scale splitting breaks down if a cluster intermittently desynchronizes. We show that this intermittent desynchronization provides a mechanism for chaos for trimodal natural frequency distributions. In addition, we use collective coordinates to show analytically that chaos cannot occur for bimodal frequency distributions, even if they are asymmetric and if intermittent desynchronization occurs.
The dynamics of an extremely diluted neural network with high order synapses acting as corrections to the Hopfield model is investigated. As in the fully connected case, the high order terms may strongly improve the storage capacity of the system. Th e dynamics displays a very rich behavior, and in particular a new chaotic phase emerges depending on the weight of the high order connections $epsilon$, the noise level $T$ and the network load defined as the rate between the number of stored patterns and the mean connectivity per neuron $alpha =P/C$.
502 - B. Cessac , T. Vieville 2008
We present a mathematical analysis of a networks with Integrate-and-Fire neurons and adaptive conductances. Taking into account the realistic fact that the spike time is only known within some textit{finite} precision, we propose a model where spikes are effective at times multiple of a characteristic time scale $delta$, where $delta$ can be textit{arbitrary} small (in particular, well beyond the numerical precision). We make a complete mathematical characterization of the model-dynamics and obtain the following results. The asymptotic dynamics is composed by finitely many stable periodic orbits, whose number and period can be arbitrary large and can diverge in a region of the synaptic weights space, traditionally called the edge of chaos, a notion mathematically well defined in the present paper. Furthermore, except at the edge of chaos, there is a one-to-one correspondence between the membrane potential trajectories and the raster plot. This shows that the neural code is entirely in the spikes in this case. As a key tool, we introduce an order parameter, easy to compute numerically, and closely related to a natural notion of entropy, providing a relevant characterization of the computational capabilities of the network. This allows us to compare the computational capabilities of leaky and Integrate-and-Fire models and conductance based models. The present study considers networks with constant input, and without time-dependent plasticity, but the framework has been designed for both extensions.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا