Neurodynamics and Neural Networks

2019 ◽  
pp. 276-307
Author(s):  
David D. Nolte
Keyword(s):  
Homoclinic Orbits ◽  
Recurrent Network ◽  
Basins Of Attraction ◽  
Hopfield Network ◽  
Network Architectures ◽  
Recurrent Networks ◽  
Delta Rule ◽  
Artificial Neurons ◽  
Simple Features ◽  
Associative Recall

Individual neurons are modelled as nonlinear oscillators that rely on bistability and homoclinic orbits to produce spiking potentials. Simplified mathematical models, like the Fitzhugh–Nagumo and NaK models, capture successively more sophisticated behavior of individual neurons, such as thresholds and spiking. Artificial neurons are introduced that are composed of three simple features: summation of inputs, referencing to a threshold, and saturating output. Artificial networks of neurons are defined through specific network architectures that included the perceptron, feedforward networks with hidden layers that are trained using the Delta Rule, and recurrent networks with feedback. A prevalent example of a recurrent network is the Hopfield network, which performs operations such as associative recall. The dynamic trajectories of the Hopfield network have basins of attraction in state space that correspond to stored memories.

Recurrent Neural Networks with Small Weights Implement Definite Memory Machines

2003 ◽  
Vol 15 (8) ◽  
pp. 1897-1929 ◽  
Author(s):  
Barbara Hammer ◽  
Peter Tiňo
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Experimental Studies ◽  
Activation Function ◽  
Transition Function ◽  
Recurrent Network ◽  
Point Of View ◽  
Recurrent Networks ◽  
Contraction Parameter ◽  
Arbitrary Precision

Recent experimental studies indicate that recurrent neural networks initialized with “small” weights are inherently biased toward definite memory machines (Tiňno, Čerňanský, & Beňušková, 2002a, 2002b). This article establishes a theoretical counterpart: transition function of recurrent network with small weights and squashing activation function is a contraction. We prove that recurrent networks with contractive transition function can be approximated arbitrarily well on input sequences of unbounded length by a definite memory machine. Conversely, every definite memory machine can be simulated by a recurrent network with contractive transition function. Hence, initialization with small weights induces an architectural bias into learning with recurrent neural networks. This bias might have benefits from the point of view of statistical learning theory: it emphasizes one possible region of the weight space where generalization ability can be formally proved. It is well known that standard recurrent neural networks are not distribution independent learnable in the probably approximately correct (PAC) sense if arbitrary precision and inputs are considered. We prove that recurrent networks with contractive transition function with a fixed contraction parameter fulfill the so-called distribution independent uniform convergence of empirical distances property and hence, unlike general recurrent networks, are distribution independent PAC learnable.

JAZZ MELODY GENERATION USING RECURRENT NETWORKS AND REINFORCEMENT LEARNING

2006 ◽  
Vol 15 (04) ◽  
pp. 623-650
Author(s):  
JUDY A. FRANKLIN
Keyword(s):  
Reinforcement Learning ◽  
Dynamic Systems ◽  
Recurrent Neural Networks ◽  
Short Term Memory ◽  
State Of The Art ◽  
Recurrent Network ◽  
Recurrent Networks ◽  
Short Term ◽  
Long Short Term Memory ◽  
Lstm Network

Recurrent (neural) networks have been deployed as models for learning musical processes, by computational scientists who study processes such as dynamic systems. Over time, more intricate music has been learned as the state of the art in recurrent networks improves. One particular recurrent network, the Long Short-Term Memory (LSTM) network shows promise for learning long songs, and generating new songs. We are experimenting with a module containing two inter-recurrent LSTM networks to cooperatively learn several human melodies, based on the songs' harmonic structures, and on the feedback inherent in the network. We show that these networks can learn to reproduce four human melodies. We then present as input new harmonizations, so as to generate new songs. We describe the reharmonizations, and show the new melodies that result. We also present a hierarchical structure for using reinforcement learning to choose LSTM modules during the course of melody generation.

scholarly journals Learning Beyond Finite Memory in Recurrent Networks of Spiking Neurons

2006 ◽  
Vol 18 (3) ◽  
pp. 591-613 ◽  
Author(s):  
Peter Tiňo ◽  
Ashely J. S. Mills
Keyword(s):  
Extraction Procedure ◽  
Recurrent Network ◽  
Spiking Neurons ◽  
Fading Memory ◽  
Recurrent Networks ◽  
Spiking Neuron ◽  
Neuron Networks ◽  
Gradient Based ◽  
Temporal Structures ◽  
Spiking Neuron Networks

We investigate possibilities of inducing temporal structures without fading memory in recurrent networks of spiking neurons strictly operating in the pulse-coding regime. We extend the existing gradient-based algorithm for training feedforward spiking neuron networks, SpikeProp (Bohte, Kok, & La Poutré, 2002), to recurrent network topologies, so that temporal dependencies in the input stream are taken into account. It is shown that temporal structures with unbounded input memory specified by simple Moore machines (MM) can be induced by recurrent spiking neuron networks (RSNN). The networks are able to discover pulse-coded representations of abstract information processing states coding potentially unbounded histories of processed inputs. We show that it is often possible to extract from trained RSNN the target MM by grouping together similar spike trains appearing in the recurrent layer. Even when the target MM was not perfectly induced in a RSNN, the extraction procedure was able to reveal weaknesses of the induced mechanism and the extent to which the target machine had been learned.

scholarly journals Estimation of Dynamical Neuron Nets’ Errors for Measuring Systems

2018 ◽  
pp. 33-35
Author(s):  
Leit Akhmed Mustafa Al Ravashdekh ◽  
I. Ruzhentsev
Keyword(s):  
Dynamic Systems ◽  
Kalman Filters ◽  
Learning Algorithm ◽  
Measurement Data ◽  
Recurrent Network ◽  
Digital Measurement ◽  
Network Architectures ◽  
Navigation Systems ◽  
Measuring Systems ◽  
Satellite Navigation Systems

In the work based on the analysis of application of satellite navigation systems for determining position of moving traffic objects is proposed during the processing of the digital measurement data using artificial neural network. To perform modeling of nonlinear dynamic systems, it is suggested to use recurrent network architectures and a learning algorithm based on the theory of Kalman filters.

scholarly journals Homeostatic activity-dependent tuning of recurrent networks for robust propagation of activity

2015 ◽  
Author(s):  
Julijana Gjorgjieva ◽  
Jan Felix Evers ◽  
Stephen Eglen
Keyword(s):  
Spontaneous Activity ◽  
Activity Patterns ◽  
Network Connectivity ◽  
Recurrent Network ◽  
Recurrent Networks ◽  
Synaptic Growth ◽  
Network Output ◽  
Homeostatic Model ◽  
Weak Connectivity ◽  
Activity Dependent

Developing neuronal networks display spontaneous rhythmic bursts of action potentials that are necessary for circuit organization and tuning. While spontaneous activity has been shown to instruct map formation in sensory circuits, it is unknown whether it plays a role in the organization of motor networks that produce rhythmic output. Using computational modeling we investigate how recurrent networks of excitatory and inhibitory neuronal populations assemble to produce robust patterns of unidirectional and precisely-timed propagating activity during organism locomotion. One example is provided by the motor network in Drosophila larvae, which generates propagating peristaltic waves of muscle contractions during crawling. We examine two activity-dependent models which tune weak network connectivity based on spontaneous activity patterns: a Hebbian model, where coincident activity in neighboring populations strengthens connections between them; and a homeostatic model, where connections are homeostatically regulated to maintain a constant level of excitatory activity based on spontaneous input. The homeostatic model tunes network connectivity to generate robust activity patterns with the appropriate timing relationships between neighboring populations. These timing relationships can be modulated by the properties of spontaneous activity suggesting its instructive role for generating functional variability in network output. In contrast, the Hebbian model fails to produce the tight timing relationships between neighboring populations required for unidirectional activity propagation, even when additional assumptions are imposed to constrain synaptic growth. These results argue that homeostatic mechanisms are more likely than Hebbian mechanisms to tune weak connectivity based on local activity patterns in a recurrent network for rhythm generation and propagation.

EQUILIBRIUM AND ATTRACTIVITY ANALYSIS FOR A CLASS OF HETERO-ASSOCIATIVE NEURAL MEMORIES

1996 ◽  
Vol 07 (03) ◽  
pp. 287-304
Author(s):  
DONQ-LIANG LEE ◽  
WEN-JUNE WANG
Keyword(s):  
High Performance ◽  
Sufficient Conditions ◽  
High Capacity ◽  
Neural Model ◽  
Recall Rate ◽  
Basins Of Attraction ◽  
Holographic Memory ◽  
Proposed Model ◽  
Training Pair ◽  
Associative Recall

Based on the natural structure of Kosko’s Bidirectional Associative Memories (BAM), a high-performance, high-capacity associative neural model is proposed which is capable of simultaneous hetero-associative recall. The proposed model, Modified Bidirectional Decoding Strategy (MBDS), improves the recall rate by adding some association fascicles to Kosko’s BAM. The association fascicles are sparse coding neuron structures that provide activating strengths between two neuron fields (say, field X and field Y). The sufficient conditions for a state to become an equilibrium state of the MBDS network is derived. Based on these results, we discuss the basins of attraction of the training pairs in one iteration. The upper bound of the number of error bits which can be tolerated by MBDS is also derived. Because the attractivity of a stored training pair can be increased markedly with the aid of its corresponding association fascicles, we recommend a high capacity realization of MBDS, Bidirectional Holographic Memory (BHM), so that each training pair is stored uniquely and directly in the connection weights rather than encoded in a correlation matrix. Finally, computer simulations demonstrate the attractiveness of three different realizations of MBDS to verify our results.

scholarly journals Forex exchange rate forecasting using deep recurrent neural networks

2020 ◽  
Vol 2 (1-2) ◽  
pp. 69-96 ◽  
Author(s):  
Alexander Jakob Dautel ◽  
Wolfgang Karl Härdle ◽  
Stefan Lessmann ◽  
Hsin-Vonn Seow
Keyword(s):  
Neural Network ◽  
Deep Learning ◽  
Exchange Rate ◽  
Language Processing ◽  
Short Term Memory ◽  
Recurrent Network ◽  
Network Architectures ◽  
Exchange Rate Forecasting ◽  
Trading Model ◽  
Gated Recurrent Units

Abstract Deep learning has substantially advanced the state of the art in computer vision, natural language processing, and other fields. The paper examines the potential of deep learning for exchange rate forecasting. We systematically compare long short-term memory networks and gated recurrent units to traditional recurrent network architectures as well as feedforward networks in terms of their directional forecasting accuracy and the profitability of trading model predictions. Empirical results indicate the suitability of deep networks for exchange rate forecasting in general but also evidence the difficulty of implementing and tuning corresponding architectures. Especially with regard to trading profit, a simpler neural network may perform as well as if not better than a more complex deep neural network.

A DISCRETE FULLY RECURRENT NETWORK OF MAX PRODUCT UNITS FOR ASSOCIATIVE MEMORY AND CLASSIFICATION

2002 ◽  
Vol 12 (03n04) ◽  
pp. 247-262 ◽  
Author(s):  
ROELOF K. BROUWER
Keyword(s):  
Fixed Points ◽  
Associative Memory ◽  
Recurrent Network ◽  
Connection Matrix ◽  
Recurrent Networks ◽  
Associative Memories ◽  
Product Operation ◽  
Linear Threshold ◽  
Fully Connected

This paper defines the truncated normalized max product operation for the transformation ofstates of a network and provides a method for solving a set of equations based on this operation. The operation serves as the transformation for the set of fully connected units in a recurrent network that otherwise might consist of linear threshold units. Component values of the state vector and ouputs of the units take on the values in the set {0, 0.1, …, 0.9, 1}. The result is a much larger state space given a particular number of units and size of connection matrix than for a network based on threshold units. Since the operation defined here can form the basis of transformations in a recurrent network with a finite number of states, fixed points or cycles are possible and the network based on this operation for transformations can be used as an associative memory or pattern classifier with fixed points taking on the role of prototypes. Discrete fully recurrent networks have proven themselves to be very useful as associative memories and as classifiers. However they are often based on units that have binary states. The effect of this is that the data to be processed consisting of vectors in ℜn have to be converted to vectors in {0, 1}m with m much larger than n since binary encoding based on positional notation is not feasible. This implies a large increase in the number of components. The effect can be lessened by allowing more states for each unit in our network. The network proposed demonstrates those properties that are desirable in an associative memory very well as the simulations show.

scholarly journals Object Reconstruction Based on Attentive Recurrent Network from Single and Multiple Images

2021 ◽  
Author(s):  
Zishu Gao ◽  
En Li ◽  
Zhe Wang ◽  
Guodong Yang ◽  
Jiwu Lu ◽  
...  
Keyword(s):  
Recurrent Network ◽  
Alternative Methods ◽  
Network Architectures ◽  
Applied Learning ◽  
Surface Textures ◽  
Reconstruction Methods ◽  
Localization And Mapping ◽  
Computationally Intensive ◽  
3D Volume ◽  
Residual Block

AbstractThe application of traditional 3D reconstruction methods such as structure-from-motion and simultaneous localization and mapping are typically limited by illumination conditions, surface textures, and wide baseline viewpoints in the field of robotics. To solve this problem, many researchers have applied learning-based methods with convolutional neural network architectures. However, simply utilizing convolutional neural networks without taking other measures into account is computationally intensive, and the results are not satisfying. In this study, to obtain the most informative images for reconstruction, we introduce a residual block to a 2D encoder for improved feature extraction, and propose an attentive latent unit that makes it possible to select the most informative image being fed into the network rather than choosing one at random. The recurrent visual attentive network is injected into the auto-encoder network using reinforcement learning. The recurrent visual attentive network pays more attention to useful images, and the agent will quickly predict the 3D volume. This model is evaluated based on both single- and multi-view reconstructions. The experiment results show that the recurrent visual attentive network increases prediction performance in a way that is superior to other alternative methods, and our model has desirable capacity for generalization.

scholarly journals Asset price dynamics in a financial market with fundamentalists and chartists

2001 ◽  
Vol 6 (2) ◽  
pp. 69-99 ◽  
Author(s):  
Carl Chairella ◽  
Roberto Dieci ◽  
Laura Gardini
Keyword(s):  
Financial Market ◽  
Asset Price ◽  
Homoclinic Orbits ◽  
Basins Of Attraction ◽  
Two Dimensional ◽  
Global Bifurcations ◽  
Critical Curves ◽  
Qualitative Structure ◽  
Local And Global Bifurcations ◽  
Noninvertible Maps

In this paper we consider a model of the dynamics of speculative markets involving the interaction of fundamentalists and chartists. The dynamics of the model are driven by a two-dimensional map that in the space of the parameters displays regions of invertibility and noninvertibility. The paper focuses on a study of local and global bifurcations which drastically change the qualitative structure of the basins of attraction of several, often coexistent, attracting sets. We make use of the theory of critical curves associated with noninvertible maps, as well as of homoclinic bifurcations and homoclinic orbits of saddles in regimes of invertibility.

Sign in / Sign up

Export Citation Format

Share Document