Retrospective and prospective persistent activity induced by Hebbian learning in a recurrent cortical network

Going beyond a mean-field model for the learning cortex: second-order statistics

Mean-field models of the cortex have been used successfully to interpret the origin of features on the electroencephalogram under situations such as sleep, anesthesia, and seizures. In a mean-field scheme, dynamic changes in synaptic weights can be considered through fluctuation-based Hebbian learning rules. However, because such implementations deal with population-averaged properties, they are not well suited to memory and learning applications where individual synaptic weights can be important. We demonstrate that, through an extended system of equations, the mean-field models can be developed further to look at higher-order statistics, in particular, the distribution of synaptic weights within a cortical column. This allows us to make some general conclusions on memory through a mean-field scheme. Specifically, we expect large changes in the standard deviation of the distribution of synaptic weights when fluctuation in the mean soma potentials are large, such as during the transitions between the "up" and "down" states of slow-wave sleep. Moreover, a cortex that has low structure in its neuronal connections is most likely to decrease its standard deviation in the weights of excitatory to excitatory synapses, relative to the square of the mean, whereas a cortex with strongly patterned connections is most likely to increase this measure. This suggests that fluctuations are used to condense the coding of strong (presumably useful) memories into fewer, but dynamic, neuron connections, while at the same time removing weaker (less useful) memories.

Variability in neuronal activity in primate cortex during working memory tasks

Persistent elevated neuronal activity has been identified as the neuronal correlate of working memory. It is generally assumed in the literature and in computational and theoretical models of working memory that memory-cell activity is stable and replicable; however, this assumption may be an artifact of the averaging of data collected across trials, and needs experimental verification. In this study, we introduce a classification scheme to characterize the firing frequency trends of cells recorded from the cortex of monkeys during performance of working memory tasks. We examine the frequency statistics and variability of firing during baseline and memory periods. We also study the behavior of cells on individual trials and across trials, and explore the stability of cellular firing during the memory period. We find that cells from different firing-trend classes possess markedly different statistics. We also find that individual cells show substantial variability in their firing behavior across trials, and that firing frequency also varies markedly over the course of a single trial. Finally, the average frequency distribution is wider, the magnitude of the frequency increases from baseline to memory smaller, and the magnitude of frequency decreases larger than is generally assumed. These results may serve as a guide in the evaluation of current theories of the cortical mechanisms of working memory.

Period-two cycles in a feedforward layered neural network model with symmetric sequence processing

The effects of dominant sequential interactions are investigated in an exactly solvable feedforward layered neural network model of binary units and patterns near saturation in which the interaction consists of a Hebbian part and a symmetric sequential term. Phase diagrams of stationary states are obtained and a phase of cyclic correlated states of period two is found for a weak Hebbian term, independently of the number of condensed patterns c.

Temporal integration by stochastic recurrent network dynamics with bimodal neurons

Temporal integration of externally or internally driven information is required for a variety of cognitive processes. This computation is generally linked with graded rate changes in cortical neurons, which typically appear during a delay period of cognitive task in the prefrontal and other cortical areas. Here, we present a neural network model to produce graded (climbing or descending) neuronal activity. Model neurons are interconnected randomly by AMPA-receptor-mediated fast excitatory synapses and are subject to noisy background excitatory and inhibitory synaptic inputs. In each neuron, a prolonged afterdepolarizing potential follows every spike generation. Then, driven by an external input, the individual neurons display bimodal rate changes between a baseline state and an elevated firing state, with the latter being sustained by regenerated afterdepolarizing potentials. When the variance of background input and the uniform weight of recurrent synapses are adequately tuned, we show that stochastic noise and reverberating synaptic input organize these bimodal changes into a sequence that exhibits graded population activity with a nearly constant slope. To test the validity of the proposed mechanism, we analyzed the graded activity of anterior cingulate cortex neurons in monkeys performing delayed conditional Go/No-go discrimination tasks. The delay-period activities of cingulate neurons exhibited bimodal activity patterns and trial-to-trial variability that are similar to those predicted by the proposed model.

The effects of perceptual history on memory of visual objects

We investigated how the recognition and perception of memory-stored visual objects are influenced by cumulative experience with similar stimuli. The memory of a face was established by training observers to identify a set of faces as either "friends" or "non-friends". Subsequently, for multiple daily sessions, observers continued to perform this identification task, in which presented faces included a sequence of morphed faces, gradually transforming from a friend face (source) to another initially distinguishable non-friend face (target), interleaved with other faces. Initially observers identified only the first part of the morph sequence as "friends". In experimental conditions for which the initial "friends" portion was at least 54% of the sequence, this portion increased along repeated daily practice, until eventually most of the sequence was identified as "friends". After this practice, perceived similarity between source and target faces was much higher than the average similarity between the other face images. These effects did not occur when the morph images were shown in random order using a similar protocol. In addition, corresponding recognition confusions between source and target faces were found. Our findings suggest that memories of objects can be changed as a result of exposure to similar stimuli and show the dependency of these changes on the order in which stimuli are presented and on their level of similarity.

Impact of spatiotemporally correlated images on the structure of memory

How does experience modify what we store in long-term memory? Is it an effect of unattended experience or does it require supervision? What role is played by temporal correlations in the input stream? We present a plastic recurrent network in which memory of faces is initially embedded and then, in the absence of supervision, the presentation of temporally correlated faces drastically changes long-term memory. We model and interpret the results of recent experiments and provide predictions for future testing. The stimuli are frames of a morphing film, interpolating between two memorized faces: If the temporal order of presentation of the frame stimuli is random, then the structure of memory is basically unaffected by synaptic plasticity (memory preservation). If the temporal order is sequential, then all image frames are classified as the same memory (memory collapse). The empirical findings are reproduced in the simulated dynamics of the network, in which the evolution of neural activity is conditioned by the associated synaptic plasticity (learning). The results are captured by theoretical analysis, which leads to predictions concerning the critical parameters of the stimuli; a third phase is identified in which memory is erased (forgetting).

Seizures and Antiepileptic Drugs: Does Exposure Alter Normal Brain Development?

Seizures and antiepileptic drugs (AEDs) affect brain development and have long-term neurological consequences. The specific molecular and cellular changes, the precise timing of their influence during brain development, and the full extent of the long-term consequences of seizures and AEDs exposure have not been established. This review critically assesses both the basic and clinical science literature on the effects of seizures and AEDs on the developing brain and finds that evidence exists to support the hypothesis that both seizures and antiepileptic drugs influence a variety of biological process, at specific times during development, which alter long-term cognition and epilepsy susceptibility. More research, both clinical and experimental, is needed before changes in current clinical practice, based on the scientific data, can be recommended.

Computational algorithms and neuronal network models underlying decision processes

Animals or humans often encounter such situations in which they must choose their behavioral responses to be made in the near or distant future. Such a decision is made through continuous and bidirectional interactions between the environment surrounding the brain and its internal state or dynamical processes. Therefore, decision making may provide a unique field of researches for studying information processing by the brain, a biological system open to information exchanges with the external world. To make a decision, the brain must analyze pieces of information given externally, past experiences in a similar situation, possible behavioral responses, and predicted outcomes of the individual responses. In this article, we review results of recent experimental and theoretical studies of neuronal substrates and computational algorithms for decision processes.

The role of short-term depression in sustained neural activity in the prefrontal cortex: a simulation study

Recent experimental researches have suggested that sustained neural activity in the prefrontal cortex is a process of memory retention in decision making. Previous theoretical studies indicate that a balance between recurrent excitation and feedback inhibition is important for sustaining the activity. To investigate a plausible balancing mechanism, we simulated a biophysically realistic network model. Our model shows that short-term depression (STD) enables the network to sustain its activity despite the presence of long-term inhibition by GABA(B) receptors and that the sustained firing rates have a bell-shaped dependence on the degree of STD. By analyzing the neural network dynamics, we show that the bell-shaped dependence on STD is formed by destabilizing the balance with either excessive or insufficient STD. We also show that the optimal degree of STD has a linear relationship with the neural network size. These results suggest that STD provides a balancing mechanism and controls levels of sustained activities of various size networks.

A review of the integrate-and-fire neuron model: II. Inhomogeneous synaptic input and network properties

The integrate-and-fire neuron model describes the state of a neuron in terms of its membrane potential, which is determined by the synaptic inputs and the injected current that the neuron receives. When the membrane potential reaches a threshold, an action potential (spike) is generated. This review considers the model in which the synaptic input varies periodically and is described by an inhomogeneous Poisson process, with both current and conductance synapses. The focus is on the mathematical methods that allow the output spike distribution to be analyzed, including first passage time methods and the Fokker-Planck equation. Recent interest in the response of neurons to periodic input has in part arisen from the study of stochastic resonance, which is the noise-induced enhancement of the signal-to-noise ratio. Networks of integrate-and-fire neurons behave in a wide variety of ways and have been used to model a variety of neural, physiological, and psychological phenomena. The properties of the integrate-and-fire neuron model with synaptic input described as a temporally homogeneous Poisson process are reviewed in an accompanying paper (Burkitt in Biol Cybern, 2006).

Single neurons in the medial prefrontal cortex of the rat exhibit tonic and phasic coding during trace fear conditioning

Trace fear conditioning is a learning task that requires the association of an auditory conditioned stimulus (CS) and a shock unconditioned stimulus (US) that are separated by a 20-s trace interval. Single neuron activity was recorded from the prelimbic and infralimbic areas of the medial prefrontal cortex in rats during trace fear conditioning or nonassociative unpaired training. Prelimbic neurons showed learning-related increases in activity to the CS and US, whereas infralimbic neurons showed learning-related decreases in activity to these stimuli. A subset of prelimbic neurons exhibited sustained increases in activity during the trace interval. These sustained prelimbic responses may provide a bridging code that allows for overlapping representations of CS and US information within the trace fear conditioning circuit.

A model for integrating elementary neural functions into delayed-response behavior

It is well established that various cortical regions can implement a wide array of neural processes, yet the mechanisms which integrate these processes into behavior-producing, brain-scale activity remain elusive. We propose that an important role in this respect might be played by executive structures controlling the traffic of information between the cortical regions involved. To illustrate this hypothesis, we present a neural network model comprising a set of interconnected structures harboring stimulus-related activity (visual representation, working memory, and planning), and a group of executive units with task-related activity patterns that manage the information flowing between them. The resulting dynamics allows the network to perform the dual task of either retaining an image during a delay (delayed-matching to sample task), or recalling from this image another one that has been associated with it during training (delayed-pair association task). The model reproduces behavioral and electrophysiological data gathered on the inferior temporal and prefrontal cortices of primates performing these same tasks. It also makes predictions on how neural activity coding for the recall of the image associated with the sample emerges and becomes prospective during the training phase. The network dynamics proves to be very stable against perturbations, and it exhibits signs of scale-invariant organization and cooperativity. The present network represents a possible neural implementation for active, top-down, prospective memory retrieval in primates. The model suggests that brain activity leading to performance of cognitive tasks might be organized in modular fashion, simple neural functions becoming integrated into more complex behavior by executive structures harbored in prefrontal cortex and/or basal ganglia.

Before we do anything, our brain must construct neural representations of the operations required. Imaging and recording techniques are indeed providing ever more detailed insight into how different regions of the brain contribute to behavior. However, it has remained elusive exactly how these various regions then come to cooperate with each other, thus organizing the brain-scale activity patterns needed for even the simplest planned tasks. In the present work, the authors propose a neural network model built around the hypothesis of a modular organization of brain activity, where relatively autonomous basic neural functions useful at a given moment are recruited and integrated into actual behavior. At the heart of the model are regulating structures that restrain information from flowing freely between the different cortical areas involved, releasing it instead in a controlled fashion able to produce the appropriate response. The dynamics of the network, simulated on a computer, enables it to pass simple cognitive tests while reproducing data gathered on primates carrying out these same tasks. This suggests that the model might constitute an appropriate framework for studying the neural basis of more general behavior.

Beyond bistability: Biophysics and temporal dynamics of working memory

Working memory has often been modeled and conceptualized as a kind of binary (bistable) memory switch, where stimuli turn on plateau-like persistent activity in subsets of cells, in line with many in vivo electrophysiological reports. A potentially related form of bistability, termed up- and down-states, has been studied with regard to its synaptic and ionic basis in vivo and in reduced cortical preparations. Also single cell mechanisms for producing bistability have been proposed and investigated in brain slices and computationally. Recently, however, it has been emphasized that clear plateau-like bistable activity is rather rare during working memory tasks, and that neurons exhibit a multitude of different temporally unfolding activity profiles and temporal structure within their spiking dynamics. Hence, working memory seems to be a highly dynamical neural process with yet unknown mappings from dynamical to computational properties. Empirical findings on ramping activity profiles and temporal structure will be reviewed, as well as neural models that attempt to account for it and its computational significance. Furthermore, recent in vivo, neural culture, and in vitro preparations will be discussed that offer new possibilities for studying the biophysical mechanisms underlying computational processes during working memory. These preparations have revealed additional evidence for temporal structure and spatio-temporally organized attractor states in cortical networks, as well as for specific computational properties that may characterize synaptic processing during high-activity states as during working memory. Together such findings may lay the foundations for highly dynamical theories of working memory based on biophysical principles.

Heterogeneity in the pyramidal network of the medial prefrontal cortex

The prefrontal cortex is specially adapted to generate persistent activity that outlasts stimuli and is resistant to distractors, presumed to be the basis of working memory. The pyramidal network that supports this activity is unknown. Multineuron patch-clamp recordings in the ferret medial prefrontal cortex showed a heterogeneity of synapses interconnecting distinct subnetworks of different pyramidal cells. One subnetwork was similar to the pyramidal network commonly found in primary sensory areas, consisting of accommodating pyramidal cells interconnected with depressing synapses. The other subnetwork contained complex pyramidal cells with dual apical dendrites displaying nonaccommodating discharge patterns; these cells were hyper-reciprocally connected with facilitating synapses displaying pronounced synaptic augmentation and post-tetanic potentiation. These cellular, synaptic and network properties could amplify recurrent interactions between pyramidal neurons and support persistent activity in the prefrontal cortex.

Memory of Ordinal Number Categories in Macaque Monkeys

What mechanism underlies serial order memory? Studying preverbal serial memory shows that macaque monkeys reproducing a sequence of items can acquire knowledge of item ordinal position. In our previous experiment, macaques were repeatedly presented with image lists (first shown sequentially and then simultaneously on a touch screen together with a distractor chosen randomly from other lists). The task was to touch list images in the correct order. The monkeys' natural tendency was to categorize images by their ordinal position or number because their most common error was touching the distractor when it had the same ordinal number (in its own list) as the correct image. Item-to-item associations were used to complete the categorization strategy. Proposing a dynamic image-salience hypothesis for serial recall (based on category-to-image influence and a salience computation for identifying touch targets), we now study the category label characteristics in the context of this hypothesis.

We found that these category labels are absolute, ordinal-number-based categories (first, second, etc.), not relative memorized as relative distance from the beginning and the end of the list, and not based on fixed ranking of reward contingency/image familiarity. Even isolated from item–item associations, the categories demonstrate category tuning (as well as the corresponding overlap of adjacent ordinal number codes). Moreover, monkeys choose images by proximity of their category to the current touch number, irrespective of the accuracy of the preceding choice. Category tuning itself is symmetric relative to correct ordinal position, but is skewed by other factors (reward, etc.). Tuning width increases with list length, with a concurrent increased use of item-to-item associations for determining touch order.

Dynamic functional tuning of nonlinear cortical networks

The mammalian neocortex is a highly complex and nonlinear dynamic system. One of its most prominent features is an omnipresent spontaneous neuronal activity. Here the possible functional role of this global background for cognitive flexibility is studied in a prototypic mean-field model area. It is demonstrated that the level of global background current efficiently controls the stimulus-response threshold and the stability and properties of short-term memory states. Moreover, it can dynamically gate arbitrary cortical subnetworks, when applied to parts of the area as a weak bias signal. These results suggest a central functional role of the level of background activation: the dynamic functional tuning of neocortical circuits.

A neural network model for trace conditioning

We studied the dynamics of a neural network that has both recurrent excitatory and random inhibitory connections. Neurons started to become active when a relatively weak transient excitatory signal was presented and the activity was sustained due to the recurrent excitatory connections. The sustained activity stopped when a strong transient signal was presented or when neurons were disinhibited. The random inhibitory connections modulated the activity patterns of neurons so that the patterns evolved without recurrence with time. Hence, a time passage between the onsets of the two transient signals was represented by the sequence of activity patterns. We then applied this model to represent the trace eye blink conditioning, which is mediated by the hippocampus. We assumed this model as CA3 of the hippocampus and considered an output neuron corresponding to a neuron in CA1. The activity pattern of the output neuron was similar to that of CA1 neurons during trace eye blink conditioning, which was experimentally observed.

Computational and in vitro studies of persistent activity: edging towards cellular and synaptic mechanisms of working memory

Persistent neural activity selective to features of an extinct stimulus has been identified as the neural correlate of working memory processes. The precise nature of the physiological substrate for this self-sustained activity is still unknown. In the last few years, this problem has gathered experimental together with computational neuroscientists in a quest to identify the cellular and network mechanisms involved. I introduce here the attractor theory framework within which current persistent activity computational models are built, and I then review the main physiological mechanisms that have been linked thereby to persistent activity and working memory. Open computational and physiological issues with these models are discussed, together with their potential experimental validation in current in vitro models of persistent activity.

Active Maintenance of Associative Mnemonic Signal in Monkey Inferior Temporal Cortex

We investigated the contribution of the inferior temporal (IT) cortical neurons to the active maintenance of internal representations. The activity of single neurons in the IT cortex was recorded while the monkeys performed a sequential-type associative memory task in which distractor stimuli interrupted the delay epoch between the cue and target (paired-associate) stimuli. For each neuron, information about each stimulus conveyed by the delay activity was estimated as a coefficient of multiple regression analysis. We found that target information derived from long-term memory (LTM) persisted despite the distractors. By contrast, cue information derived from the visual system was attenuated and frequently replaced by distractor information. These results suggest that LTM-derived information required for upcoming behavior is actively maintained in the IT neurons, whereas visually derived information tends to be updated irrespective of behavioral relevance.

Neural dynamics of cross-modal and cross-temporal associations

We have studied a neurodynamic model of cross-modal and cross-temporal associations. We show that a network of integrate-and-fire neurons can generate spiking activity with realistic dynamics during the delay period of a paired associates task. In particular, the activity of the model resembles reported data from single-cell recordings in the prefrontal cortex.

Learning in realistic networks of spiking neurons and spike-driven plastic synapses

We have used simulations to study the learning dynamics of an autonomous, biologically realistic recurrent network of spiking neurons connected via plastic synapses, subjected to a stream of stimulus-delay trials, in which one of a set of stimuli is presented followed by a delay. Long-term plasticity, produced by the neural activity experienced during training, structures the network and endows it with active (working) memory, i.e. enhanced, selective delay activity for every stimulus in the training set. Short-term plasticity produces transient synaptic depression. Each stimulus used in training excites a selective subset of neurons in the network, and stimuli can share neurons (overlapping stimuli). Long-term plasticity dynamics are driven by presynaptic spikes and coincident postsynaptic depolarization; stability is ensured by a refresh mechanism. In the absence of stimulation, the acquired synaptic structure persists for a very long time. The dependence of long-term plasticity dynamics on the characteristics of the stimulus response (average emission rates, time course and synchronization), and on the single-cell emission statistics (coefficient of variation) is studied. The study clarifies the specific roles of short-term synaptic depression, NMDA receptors, stimulus representation overlaps, selective stimulation of inhibition, and spike asynchrony during stimulation. Patterns of network spiking activity before, during and after training reproduce most of the in vivo physiological observations in the literature.

Mean field and capacity in realistic networks of spiking neurons storing sparsely coded random memories

Mean-field (MF) theory is extended to realistic networks of spiking neurons storing in synaptic couplings of randomly chosen stimuli of a given low coding level. The underlying synaptic matrix is the result of a generic, slow, long-term synaptic plasticity of two-state synapses, upon repeated presentation of the fixed set of the stimuli to be stored. The neural populations subtending the MF description are classified by the number of stimuli to which their neurons are responsive (multiplicity). This involves 2p + 1 populations for a network storing p memories. The computational complexity of the MF description is then significantly reduced by observing that at low coding levels (f), only a few populations remain relevant: the population of mean multiplicity - pf and those of multiplicity of order square root pf around the mean. The theory is used to produce (predict) bifurcation diagrams (the onset of selective delay activity and the rates in its various stationary states) and to compute the storage capacity of the network (the maximal number of single items used in training for each of which the network can sustain a persistent, selective activity state). This is done in various regions of the space of constitutive parameters for the neurons and for the learning process. The capacity is computed in MF versus potentiation amplitude, ratio of potentiation to depression probability and coding level f. The MF results compare well with recordings of delay activity rate distributions in simulations of the underlying microscopic network of 10,000 neurons.

Multi-item Working Memory — A Behavioral Study

Macaque monkeys were trained to recognize the repetition of one of the images already seen in a sequence of random length. On average, performance decreased with sequence length. However, this was due to a complex combination of factors, as follows: performance was found to decrease with the separation in the sequence of the test (repetition image) from the cue (its first appearance in the sequence), for trials with sequences of fixed length. In contrast, performance improved as a function of sequence length, for equal cue-test separations. Reaction times followed a complementary trend: they increased with cue-test separation and decreased with sequence length. The frequency of false positives (FPs) indicates that images are not always removed from working memory between successive trials, and that the monkeys rarely confuse different images. The probability of miss errors depends on number of intervening stimulus presentations, while FPs depend on elapsed time. A simple two-state stochastic model of multi-item working memory is proposed that guides the account for the main effects of performance and false positives, as well as their interaction. In the model, images enter WM when they are presented, or by spontaneous jump-in. Misses are due to spontaneous jump-out of images previously seen.

Climbing neuronal activity as an event-based cortical representation of time

The brain has the ability to represent the passage of time between two behaviorally relevant events. Recordings from different areas in the cortex of monkeys suggest the existence of neurons representing time by increasing (climbing) activity, which is triggered by a first event and peaks at the expected time of a second event, e.g., a visual stimulus or a reward. When the typical interval between the two events is changed, the slope of the climbing activity adapts to the new timing. We present a model in which the climbing activity results from slow firing rate adaptation in inhibitory neurons. Hebbian synaptic modifications allow for learning the new time interval by changing the degree of firing rate adaptation. This event-based representation of time is consistent with Weber's law in interval timing, according to which the error in estimating a time interval is proportional to the interval length.

Neural representation of interval time

Animals can predict the time of occurrence of a forthcoming event relative to a preceding stimulus, i.e. the interval time between those two, given previous learning experience with the temporal contingency between them. Accumulating evidence suggests that a particular pattern of neural activity observed during tasks involving fixed temporal intervals might carry interval time information: the activity of some cortical and subcortical neurons ramps up slowly and linearly during the interval, like a temporal integrator, and peaks around the time at which the event is due to occur. The slope of this climbing activity, and hence the peak time, adjusts to the length of a temporal interval during repetitive experience with it. Various neural mechanisms for producing climbing activity with variable slopes, representing the length of learned intervals, are discussed.

The effects of seizures on the connectivity and circuitry of the developing brain

Recurring seizures in infants and children are often associated with cognitive deficits, but the reason for the learning difficulties is unclear. Recent studies in several animal models suggest that seizures themselves may contribute in important ways to these deficits. Other studies in animals have shown that recurring seizures result in dendritic spine loss. This change, coupled with a down-regulation in NMDA receptor subunit expression, suggests that repetitive seizures may interrupt the normal development of glutamatergic synaptic transmission. We hypothesize that homeostatic, neuroprotective processes are induced by recurring early-life seizures. These processes, by diminishing glutamatergic synaptic transmission, are aimed at preventing the continuation of seizures. However, by preventing the normal development of glutamatergic synapses, and particularly NMDA receptor-mediated synaptic transmission, such homeostatic processes also reduce synaptic plasticity and diminish the ability of neuronal circuits to learn and store memories.