Modeling spatial–temporal operations with context-dependent associative memories

We organize our behavior and store structured information with many procedures that require the coding of spatial and temporal order in specific neural modules. In the simplest cases, spatial and temporal relations are condensed in prepositions like “below” and “above”, “behind” and “in front of”, or “before” and “after”, etc. Neural operators lie beneath these words, sharing some similarities with logical gates that compute spatial and temporal asymmetric relations. We show how these operators can be modeled by means of neural matrix memories acting on Kronecker tensor products of vectors. The complexity of these memories is further enhanced by their ability to store episodes unfolding in space and time. How does the brain scale up from the raw plasticity of contingent episodic memories to the apparent stable connectivity of large neural networks? We clarify this transition by analyzing a model that flexibly codes episodic spatial and temporal structures into contextual markers capable of linking different memory modules.     

Flexible Memory Networks

Networks of neurons in some brain areas are flexible enough to encode new memories quickly. Using a standard firing rate model of recurrent networks, we develop a theory of flexible memory networks. Our main results characterize networks having the maximal number of flexible memory patterns, given a constraint graph on the network’s connectivity matrix. Modulo a mild topological condition, we find a close connection between maximally flexible networks and rank 1 matrices. The topological condition is H ₁(X;ℤ)=0, where X is the clique complex associated to the network’s constraint graph; this condition is generically satisfied for large random networks that are not overly sparse. In order to prove our main results, we develop some matrix-theoretic tools and present them in a self-contained section independent of the neuroscience context.     

Dynamics and bifurcations of two coupled neural oscillators with different connection types

In this paper we present an oscillatory neural network composed of two coupled neural oscillators of the Wilson-Cowan type. Each of the oscillators describes the dynamics of average activities of excitatory and inhibitory populations of neurons. The network serves as a model for several possible network architectures. We study how the type and the strength of the connections between the oscillators affect the dynamics of the neural network. We investigate, separately from each other, four possible connection types (excitatory→excitatory, excitatory→inhibitory, inhibitory→excitatory, and inhibitory→inhibitory) and compute the corresponding bifurcation diagrams. In case of weak connections (small strength), the connection of populations of different types lead to periodicin-phase oscillations, while the connection of populations of the same type lead to periodicanti-phase oscillations. For intermediate connection strengths, the networks can enter quasiperiodic or chaotic regimes, and can also exhibit multistability. More generally, our analysis highlights the great diversity of the response of neural networks to a change of the connection strength, for different connection architectures. In the discussion, we address in particular the problem of information coding in the brain using quasiperiodic and chaotic oscillations. In modeling low levels of information processing, we propose that feature binding should be sought as a temporally coherent phase-locking of neural activity. This phase-locking is provided by one or more interacting convergent zones and does not require a central “top level” subcortical circuit (e.g. the septo-hippocampal system). We build a two layer model to show that although the application of a complex stimulus usually leads to different convergent zones with high frequency oscillations, it is nevertheless possible to synchronize these oscillations at a lower frequency level using envelope oscillations. This is interpreted as a feature binding of a complex stimulus.     

Behavioral and neural analysis of associative learning in the honeybee: a taste from the magic well

Equipped with a mini brain smaller than one cubic millimeter and containing only 950,000 neurons, honeybees could be indeed considered as having rather limited cognitive abilities. However, bees display a rich and interesting behavioral repertoire, in which learning and memory play a fundamental role in the framework of foraging activities. We focus on the question of whether adaptive behavior in honeybees exceeds simple forms of learning and whether the neural mechanisms of complex learning can be unraveled by studying the honeybee brain. Besides elemental forms of learning, in which bees learn specific and univocal links between events in their environment, bees also master different forms of non-elemental learning, including categorization, contextual learning and rule abstraction, both in the visual and in the olfactory domain. Different protocols allow accessing the neural substrates of some of these learning forms and understanding how complex problem solving can be achieved by a relatively simple neural architecture. These results underline the enormous richness of experience-dependent behavior in honeybees, its high flexibility, and the fact that it is possible to formalize and characterize in controlled laboratory protocols basic and higher-order cognitive processing using an insect as a model. This paper is dedicated to the memory of Guillermo ‘Willy’ Zaccardi (1972–2007), disciple and friend beyond time and distance, who will always be remembered with a smile.     

Learning related interactions among neuronal systems involved in memory processes

Functional neuroimaging techniques using positron emission tomography (PET) and functional magnetic resonance imaging (fMRI) have provided new insights in our understanding of brain function from the molecular to the systems level. While subtraction strategy based data analyses have revealed the involvement of distributed brain regions in memory processes, covariance analysis based data analysis strategies allow functional interactions between brain regions of a neuronal network to be assessed. The focus of this chapter is to (1) establish the functional topography of episodic and working memory processes in young and old normal volunteers, (2) to assess functional interactions between modules of networks of brain regions by means of covariance based analyses and systems level modelling and (3) to relate neuroimaging data to the underpinning neural networks. Male normal young and old volunteers without neurological or psychiatric illness participated in neuroimaging studies (PET, fMRI) on working and episodic memory. Distributed brain areas are involved in memory processes (episodic and working memory) in young volunteers and show much of an overlap with respect to the network components. Systems level modelling analyses support the hypothesis of bihemispheric, asymmetric networks subserving memory processes and revealed both similarities in general and differences in the interactions between brain regions during episodic encoding and retrieval as well as working memory. Changes in memory function with ageing are evident from studies in old volunteers activating more brain regions compared to young volunteers and revealing more and stronger influences of prefrontal regions. We finally discuss the way in which the systems level models based on PET and fMRI results have implications for the understanding of the underlying neural network functioning of the brain.     

Dynamics control of semantic processes in a hierarchical associative memory

 A neural mechanism for control of dynamics and function of associative processes in a hierarchical memory system is demonstrated. For the representation and processing of abstract knowledge, the semantic declarative memory system of the human brain is considered. The dynamics control mechanism is based on the influence of neuronal adaptation on the complexity of neural network dynamics. Different dynamical modes correspond to different levels of the ultrametric structure of the hierarchical memory being invoked during an associative process. The mechanism is deterministic but may also underlie free associative thought processes. The formulation of an abstract neural network model of hierarchical associative memory utilizes a recent approach to incorporate neuronal adaptation. It includes a generalized neuronal activation function recently derived by a Hodgkin-Huxley-type model. It is shown that the extent to which a hierarchically organized memory structure is searched is controlled by the neuronal adaptability, i.e. the strength of coupling between neuronal activity and excitability. In the brain, the concentration of various neuromodulators in turn can regulate the adaptability. An autonomously controlled sequence of bifurcations, from an initial exploratory to a final retrieval phase, of an associative process is shown to result from an activity-dependent release of neuromodulators. The dynamics control mechanism may be important in the context of various disorders of the brain and may also extend the range of applications of artificial neural networks. Received: 19 April 1995/Accepted in revised form: 8 August 1995     

Memories in context

Context-dependent associative memories are models that allow the retrieval of different vectorial responses given a same vectorial stimulus, depending on the context presented to the memory. The contextualization is obtained by doing the Kronecker product between two vectorial entries to the associative memory: the key stimulus and the context. These memories are able to display a wide variety of behaviors that range from all the basic operations of the logical calculus (including fuzzy logics) to the selective extraction of features from complex vectorial patterns. In the present contribution, we show that a context-dependent memory matrix stores a large amount of possible virtual associative memories, that awaken in the presence of a context. We show how the vectorial context allows a memory matrix to be representable in terms of its singular-value decomposition. We describe a neural interpretation of the model in which the Kronecker product is performed on the same neurons that sustain the memory. We explored, with numerical experiments, the reliability of chains of contextualized associations. In some cases, random disconnection produces the emergence of oscillatory behaviors of the system. Our results show that associative chains retain their performances for relatively large dimensions. Finally, we analyze the properties of some modules of context-dependent autoassociative memories inserted in recursive nets: the perceptual autoorganization in the presence of ambiguous inputs (e.g. the disambiguation of the Necker’s cube figure), the construction of intersection filters, and the feature extraction capabilities.     

Dynamic searching in the brain

Cognitive functions rely on the extensive use of information stored in the brain, and the searching for the relevant information for solving some problem is a very complex task. Human cognition largely uses biological search engines, and we assume that to study cognitive function we need to understand the way these brain search engines work. The approach we favor is to study multi-modular network models, able to solve particular problems that involve searching for information. The building blocks of these multimodular networks are the context dependent memory models we have been using for almost 20 years. These models work by associating an output to the Kronecker product of an input and a context. Input, context and output are vectors that represent cognitive variables. Our models constitute a natural extension of the traditional linear associator. We show that coding the information in vectors that are processed through association matrices, allows for a direct contact between these memory models and some procedures that are now classical in the Information Retrieval field. One essential feature of context-dependent models is that they are based on the thematic packing of information, whereby each context points to a particular set of related concepts. The thematic packing can be extended to multimodular networks involving input-output contexts, in order to accomplish more complex tasks. Contexts act as passwords that elicit the appropriate memory to deal with a query. We also show toy versions of several ‘neuromimetic’ devices that solve cognitive tasks as diverse as decision making or word sense disambiguation. The functioning of these multimodular networks can be described as dynamical systems at the level of cognitive variables.     

Cell assembly dynamics in detailed and abstract attractor models of cortical associative memory

Summary During the last few decades we have seen a convergence among ideas and hypotheses regarding functional principles underlying human memory. Hebb’s now more than fifty years old conjecture concerning synaptic plasticity and cell assemblies, formalized mathematically as attractor neural networks, has remained among the most viable and productive theoretical frameworks. It suggests plausible explanations for Gestalt aspects of active memory like perceptual completion, reconstruction and rivalry. We review the biological plausibility of these theories and discuss some critical issues concerning their associative memory functionality in the light of simulation studies of models with palimpsest memory properties. The focus is on memory properties and dynamics of networks modularized in terms of cortical minicolumns and hypercolumns. Biophysical compartmental models demonstrate attractor dynamics that support cell assembly operations with fast convergence and low firing rates. Using a scaling model we obtain reasonable relative connection densities and amplitudes. An abstract attractor network model reproduces systems level psychological phenomena seen in human memory experiments as the Sternberg and von Restorff effects. We conclude that there is today considerable substance in Hebb’s theory of cell assemblies and its attractor network formulations, and that they have contributed to increasing our understanding of cortical associative memory function. The criticism raised with regard to biological and psychological plausibility as well as low storage capacity, slow retrieval etc has largely been disproved. Rather, this paradigm has gained further support from new experimental data as well as computational modeling.     

Dynamical correlation patterns and corresponding community structure in neural spontaneous activity at criticality

It has been considered that the state in the vicinity of a critical point, which is the point between ordered and disordered states, can underlie and facilitate information processing of the brain in various aspects. In this research, we numerically study the influence of criticality on one aspect of brain information processing, i.e., the community structure, which is an important characteristic of complex networks. We examine community structure of the functional connectivity in simulated brain spontaneous activity, which is based on dynamical correlations between neural activity patterns at different positions. The brain spontaneous activity is simulated by a neural field model whose parameter covers subcritical, critical, and supercritical regions. Then, the corresponding dynamical correlation patterns and community structure are compared. In the critical region, we found some distinctive properties, namely high correlation and correlation switching, high modularity and a low number of modules, high stability of the dynamical functional connectivity, and moderate flexibility of the community structure across temporal scales. We also discuss how these characteristics might improve information processing of the brain.     

What can we teach Lymnaea and what can Lymnaea teach us?

This review describes the advantages of adopting a molluscan complementary model, the freshwater snail Lymnaea stagnalis, to study the neural basis of learning and memory in appetitive and avoidance classical conditioning; as well as operant conditioning of its aerial respiratory and escape behaviour. We firstly explored ‘what we can teach Lymnaea’ by discussing a variety of sensitive, solid, easily reproducible and simple behavioural tests that have been used to uncover the memory abilities of this model system. Answering this question will allow us to open new frontiers in neuroscience and behavioural research to enhance our understanding of how the nervous system mediates learning and memory. In fact, from a translational perspective, Lymnaea and its nervous system can help to understand the neural transformation pathways from behavioural output to sensory coding in more complex systems like the mammalian brain. Moving on to the second question: ‘what can Lymnaea teach us?’, it is now known that Lymnaea shares important associative learning characteristics with vertebrates, including stimulus generalization, generalization of extinction and discriminative learning, opening the possibility to use snails as animal models for neuroscience translational research.     

Memory Deficit in Mice Administered Aluminum–maltolate Complex

Recently, aluminum (Al) has been identified as one of the environmental factors responsible for cause certain nerve degeneration diseases, particularly, Alzheimer’s disease (AD). However, the relationship between Al and AD is controversial. We previously examined whether Al induced neurotoxin in the brain of mice when aluminum–maltolate complex (ALM) was administered daily for 120 days. Our results revealed that Al accumulated in the brain induced oxidative stress, and the nerve degeneration was detected in the brain of the ALM-treated group. On the basis of these results, we have tried to examine whether the incorporated Al affects memory in mice with regard to an indicator of spatial memory deficits depending on the chemical forms of Al, namely, as an ion (AlCl₃) and in the form of a complex (ALM). We administered saline, AlCl₃, and ALM at a concentration of 40 μmol Al/kg body weight to mice by daily ip injections for 60 days. We assessed spatial memory by a water maze task and determined the Al levels in the brain of the mice by the neutron activation analysis method. Spatial memory deficit as an indicator of the swimming time was related to Al accumulation in the brain of mice; the chemical form of the Al compound was important in order to exhibit the memory deficit in mice; the uptake of Al is higher in mice when it is administered in a complex form than in an ionic form.     

A hybrid neural network of addressable and content-addressable memory

We investigate the memory structure and retrieval of the brain and propose a hybrid neural network of addressable and content-addressable memory which is a special database model and can memorize and retrieve any piece of information (a binary pattern) both addressably and content-addressably. The architecture of this hybrid neural network is hierarchical and takes the form of a tree of slabs which consist of binary neurons with the same array. Simplex memory neural networks are considered as the slabs of basic memory units, being distributed on the terminal vertexes of the tree. It is shown by theoretical analysis that the hybrid neural network is able to be constructed with Hebbian and competitive learning rules, and some other important characteristics of its learning and memory behavior are also consistent with those of the brain. Moreover, we demonstrate the hybrid neural network on a set of ten binary numeral patters     

Robot control and the evolution of modular neurodynamics

Summary A modular approach to neural behavior control of autonomous robots is presented. It is based on the assumption that complex internal dynamics of recurrent neural networks can efficiently solve complex behavior tasks. For the development of appropriate neural control structures an evolutionary algorithm is introduced, which is able to generate neuromodules with specific functional properties, as well as the connectivity structure for a modular synthesis of such modules. This so called ENS ³-algorithm does not use genetic coding. It is primarily designed to develop size and connectivity structure of neuro-controllers. But at the same time it optimizes also parameters of individual networks like synaptic weights and bias terms. For demonstration, evolved networks for the control of miniature Khepera robots are presented. The aim is to develop robust controllers in the sense that neuro-controllers evolved in a simulator show comparably good behavior when loaded to a real robot acting in a physical environment. Discussed examples of such controllers generate obstacle avoidance and phototropic behaviors in non-trivial environments.     

Elements for a general memory structure: properties of recurrent neural networks used to form situation models

We study how individual memory items are stored assuming that situations given in the environment can be represented in the form of synaptic-like couplings in recurrent neural networks. Previous numerical investigations have shown that specific architectures based on suppression or max units can successfully learn static or dynamic stimuli (situations). Here we provide a theoretical basis concerning the learning process convergence and the network response to a novel stimulus. We show that, besides learning “simple” static situations, a nD network can learn and replicate a sequence of up to n different vectors or frames. We find limits on the learning rate and show coupling matrices developing during training in different cases including expansion of the network into the case of nonlinear interunit coupling. Furthermore, we show that a specific coupling matrix provides low-pass-filter properties to the units, thus connecting networks constructed by static summation units with continuous-time networks. We also show under which conditions such networks can be used to perform arithmetic calculations by means of pattern completion.     

Context-dependent associations in linear distributed memories

In this article we present a method that allows conditioning of the response of a linear distributed memory to a variable context. This method requires a system of two neural networks. The first net constructs the Kronecker product between the vector input and the vector context, and the second net supports a linear associative memory. This system is easily adaptable for different goals. We analyse here its capacity for the conditional extraction of features from a complex perceptual input, its capacity to perform quasi-logical operations (for instance, of the kind of “exclusive-or”), and its capacity to structurate a memory for temporal sequences which access is conditioned by the context. Finally, we evaluate the potential importance of the capacity to establish arbitrary contexts, for the evolution of biological cognitive systems. Part of this study has been presented in a preliminary version at the XVI Reunión Científica de la Sociedad Argentina de Biofísica, Tigre, Argentina, December 1987.     

A generalized locomotion CPG architecture based on oscillatory building blocks

 Neural oscillation is one of the most extensively investigated topics of artificial neural networks. Scientific approaches to the functionalities of both natural and artificial intelligences are strongly related to mechanisms underlying oscillatory activities. This paper concerns itself with the assumption of the existence of central pattern generators (CPGs), which are the plausible neural architectures with oscillatory capabilities, and presents a discrete and generalized approach to the functionality of locomotor CPGs of legged animals. Based on scheduling by multiple edge reversal (SMER), a primitive and deterministic distributed algorithm, it is shown how oscillatory building block (OBB) modules can be created and, hence, how OBB-based networks can be formulated as asymmetric Hopfield-like neural networks for the generation of complex coordinated rhythmic patterns observed among pairs of biological motor neurons working during different gait patterns. It is also shown that the resulting Hopfield-like network possesses the property of reproducing the whole spectrum of different gaits intrinsic to the target locomotor CPGs. Although the new approach is not restricted to the understanding of the neurolocomotor system of any particular animal, hexapodal and quadrupedal gait patterns are chosen as illustrations given the wide interest expressed by the ongoing research in the area. Received: 14 June 2002 / Accepted: 18 February 2003 / Published online: 20 May 2003 Correspondence to: Z. Yang (e-mail: zhijun.yang@ed.ac.uk) Acknowledgements. This work was partially supported by CNPq, the Brazilian Research Agency, under support number 143032/96-8. We are grateful for the helpful discussions with Prof. V.C. Barbosa, Dr. A.E. Xavier, Dr. M.S. Dutra, and Dr. A.F.R. Araújo. The donations of FPGA hardware and software from XILINX Incorporation under the order No. XUP2930 and XUP3576 are also highly appreciated.     

White Matter Integrity Supports BOLD Signal Variability and Cognitive Performance in the Aging Human Brain

Decline in cognitive performance in old age is linked to both suboptimal neural processing in grey matter (GM) and reduced integrity of white matter (WM), but the whole-brain structure-function-cognition associations remain poorly understood. Here we apply a novel measure of GM processing–moment-to-moment variability in the blood oxygenation level-dependent signal (SD_BOLD)—to study the associations between GM function during resting state, performance on four main cognitive domains (i.e., fluid intelligence, perceptual speed, episodic memory, vocabulary), and WM microstructural integrity in 91 healthy older adults (aged 60-80 years). We modeled the relations between whole-GM SD_BOLD with cognitive performance using multivariate partial least squares analysis. We found that greater SD_BOLD was associated with better fluid abilities and memory. Most of regions showing behaviorally relevant SD_BOLD (e.g., precuneus and insula) were localized to inter- or intra-network “hubs” that connect and integrate segregated functional domains in the brain. Our results suggest that optimal dynamic range of neural processing in hub regions may support cognitive operations that specifically rely on the most flexible neural processing and complex cross-talk between different brain networks. Finally, we demonstrated that older adults with greater WM integrity in all major WM tracts had also greater SD_BOLD and better performance on tests of memory and fluid abilities. We conclude that SD_BOLD is a promising functional neural correlate of individual differences in cognition in healthy older adults and is supported by overall WM integrity.     

Article for analog vector algebra computation

We introduce the concept of an analog neural network represented by chemical operations performed on strands of DNA. This new type of DNA computing has the advantage that it should be fault tolerant and thus more immune to DNA hybridization errors than a Boolean DNA computer. We describe a particular set of DNA operations to effect the interconversion of electrical and DNA data and to represent the Hopfield associative memory and the feed-forward neural network of Rumelhart et al. We speculate that networks containing as many as 10(9) neurons might be feasible.     

An Effective Logical Cache for a Clustered LRC-Based DSM System

As local-area workstation networks are widely available, the idea of offering a software distributed shared memory (SDSM) system across interconnects of clusters is quite an attractive alternative for compute-intensive applications. However, the higher cost of sending a message over an inter-cluster link compared to an intra-cluster one can limit applications' performance on a multi-cluster SDSM system. In this paper, we present the extensions that we have added to the SDSM TreadMarks, which provides the lazy release consistency (LRC) memory model, in order to adapt it to a loosely-coupled cluster-based platform. We have implemented a logical per-cluster cache that exploits cluster locality. By accessing the cache of its cluster, a processor can share data previously requested by a second processor of its cluster, thereby, minimizing, the cost of inter-cluster communication.