Stability and encoding properties of two-layer nonlinear feedback neural networks are examined. Bidirectionality, forward and backard information flow, is introduced in neural nets to produce two-way associative search for stored associations (A, B, ). Passing information through M gives one direction; passing it through its transpose M r gives the other. A bidirectional associative memory. (BAM) behaves as a hetero- associative content addressable memory (CAM), storing and recalling the vector pairs (A1, Bi),-..,(Am Bin) , where .4 {0,1}"and B We prove that every n-by-p matrix M is a bidirectionally stable heteroas- sociative CAM for both binary/bipolar and continuous neurons a, and hi. When the BAM neurons are activated, the network quickly evolves to a stable state of two-pattern reverberation, or resonance. The stable reverberation corresponds to a system energy local minimum. Heteroassociafive inlormation is encoded iu a BAM by summing correlation matrices. The BAM storage capact .ty for reliable recall is roughly m < niin(n, p). No more heteroassociafive pairs can be 'reliably stored and recalled than the lesser of the dimensions of the pattern spaces (0,1 }"and 0,1 } P. The Appendix shos that it is better on average to use bipolar {- 1,i} coding than binary. {0,1 } coding of heteroassociative pairs (.4, B,). BAM encoding and decoding are combined in the adaptive BAM, which extends global bidirectional stabflit), to realtime unsupervised learning. Temporal patterns (AE,--., A,,) are represented as ordered lists of binary/bipolar vectors and stored in a temporal associative memory (TAM) n-by- matrix M as a limit cycle of the dynamical system. Forward recall proceeds through M, backward recall through M r . Temporal patterns are stored by summing contiguous bipolar...

The interplay between experiments and theoretical approaches can support the exploration of the function of neuronal circuits in the cortex. In this review we exemplify such a proceeding with a study on the functional role of spike timing and gamma-oscillations, and their relation to associative activity feedback through cortex-intrinsical synaptic connections. We first discern the theoretical approaches in general that have been most important in brain research, in particular, those approaches focusing on the biophysical, the functional, and the computational aspect. It is demonstrated how results from computational model studies on different levels of abstraction can constrain the functionality of associative memory expected in real cortical neuronal circuits. These constraints will be used to implement a computational model of associative memory on the base of biophysically elaborated compartmental neurons developed by Pinsky and Rinzel [43]. We run simulation experiments...

This article presents an approximation method to reduce the spatiotemporal behavior of localized activation peaks (also called "bumps") in nonlinear neural #eld equations to a set of coupled ordinary differential equations (ODEs) for only the amplitudes and tuning widths of these peaks. This enables a simpli#ed analysis of steady-state receptive #elds and their stability, as well as spatiotemporal point spread functions and dynamic tuning properties. A lowest-order approximation for peak amplitudes alone shows that much of the well-studied behavior of small neural systems (e.g., the Wilson-Cowan oscillator) should carry over to localized solutions in neural #elds. Full spatiotemporal response pro#les can further be reconstructed from this low-dimensional approximation. The method is applied to two standard neural #eld models: a one-layer model with difference-of-gaussians connectivity kernel and a two-layer excitatoryinhibitory network. Similar models have been previously employed in numerical studies addressing orientation tuning of cortical simple cells. Explicit formulas for tuning properties, instabilities, and oscillation frequencies are given, and exemplary spatiotemporal response functions, reconstructed from the low-dimensional approximation, are compared with full network simulations

In this paper, we explore the dynamical features of a neural network model which presents two types of adaptative parameters : the classical weights between the units and the time constants associated with each artificial neuron. The purpose of this study is to provide a strong theoretical basis for modeling and simulating dynamic recurrent neural networks. In order to achieve this, we study the effect of the statistical distribution of the weights and of the time constants on the network dynamics and we make a statistical analysis of the neural transformation. We examine the network power spectra (to draw some conclusions over the frequential behavior of the network) and we compute the stability regions to explore the stability of the model. We show that the network is sensitive to the variations of the mean values of the weights and the time constants (because of the temporal aspects of the learned tasks). Nevertheless, our results highlight the improvements in the network dynamics d...

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