Publications

Learning is a multi-faceted phenomenon of critical importance and hence attracted a great deal of research, both experimental and theoretical. In this review, we will consider some of the paradigmatic examples of learning and discuss the common themes in theoretical learning research, such as levels of modeling and their corresponding relation to experimental observations and mathematical ideas common to different types of learning.

Numerous studies analyzed the performance of participants in free recall of randomly assembled lists of words with the focus on the average number of words recalled for different experimental parameters such as list length, presentation speed, etc. The distribution of performance around the mean was not systematically studied, even though it is well-known that recall is an unpredictable process resulting in highly variable results over different trials. We recently introduced the mathematical model of free recall that reproduced well the average performance of human participants in experiments with randomly assembled lists of words or short sentences. The model assumes that during recall, each memory item currently recalled triggers a recall of a next item based on the random symmetric matrix of similarity measures between items in the list. When applying the model to experimental data, a crucial assumption was made that upon presentation, a certain fraction of presented items remain in memory that are candidates for recall, and that the number of such items can be estimated with recognition experiments performed by the same group of participants under identical conditions of item presentation as in the recall experiments. It is not clear whether this assumption is valid under different experimental paradigms and with different groups of participants. Here we propose that calculating the variance of recall performance allows one to formulate interesting predictions that can be tested without performing recognition experiments. Comparison of model predictions with experimental data on young and old participants indicates that the same recall algorithm is involved in both groups, even though old participants may have fewer candidate memory items for recall after presentation.

Memorizing time of an event may employ two processes (i) encoding of the absolute time of events within an episode, (ii) encoding of its relative order. Here we study interaction between these two processes. We performed experiments in which one or several items were presented, after which participants were asked to report the time of occurrence of items. When a single item was presented, the distribution of reported times was quite wide. When two or three items were presented, the relative order among them strongly affected the reported time of each of them. Bayesian theory that takes into account the memory for the events order is compatible with the experimental data, in particular in terms of the effect of order on absolute time reports. Our results suggest that people do not deduce order from memorized time, instead people’s memory for absolute time of events relies critically on memorized order of the events.

Visual encoding (how stimuli evoke neuronal responses) is known to progress from low to high levels. Decoding (how responses lead to perception), in contrast, is less understood but is widely assumed to follow the same, low-to-high-level hierarchy. According to this assumption, orientation decoding must occur in low-level areas such as V1, and consequently, two orientations on opposite sides of the fixation should not interact with each other perceptually. However, Ding et al (PNAS, 2017) provided evidence against the assumption and proposed that visual decoding may follow the opposite, high-to-low-level hierarchy in working memory. If two orientations on opposite sides of the fixation are both task relevant and enter a high-level working-memory area in a delay period, then they should interact with each other. We tested this prediction. Subjects maintained central fixation when two lines with an orientation difference of 5° were flashed on opposite sides of the fixation, with a center-to-center distance of 16° of visual angle. Their eye positions were monitored with an infrared eye tracker and trials with broken fixation were aborted. After a delay, subjects reported the two orientations by drawing and adjusting an indicator line at the fixation. In one condition, the indicator line disappeared after the first report, and was redrawn for the second report, to minimize potential interference. We found that the two lines showed a large and significant repulsion between them, demonstrating the predicted cross-fixation interactions in working memory. The pattern was consistent across 14 subjects. Control conditions and analyses ruled out alternative explanations such as interactions across trials on the same side of the fixation. Moreover, we quantitatively accounted for the repulsion with the retrospective Bayesian decoding model in Ding et al. We conclude that our results support the theory that visual perception may be viewed as high-to-low-level decoding in working memory.

Recurrent and feedback networks are capable of holding dynamic memories. Nonetheless, training a network for that task is challenging. In order to do so, one should face non-linear propagation of errors in the system. Small deviations from the desired dynamics due to error or inherent noise might have a dramatic effect in the future. A method to cope with these difficulties is thus needed. In this work we focus on recurrent networks with linear activation functions and binary output unit. We characterize its ability to reproduce a temporal sequence of actions over its output unit. We suggest casting the temporal learning problem to a perceptron problem. In the discrete case a finite margin appears, providing the network, to some extent, robustness to noise, for which it performs perfectly (i.e. producing a desired sequence for an arbitrary number of cycles flawlessly). In the continuous case the margin approaches zero when the output unit changes its state, hence the network is only able to reproduce the sequence with slight jitters. Numerical simulation suggest that in the discrete time case, the longest sequence that can be learned scales, at best, as square root of the network size. A dramatic effect occurs when learning several short sequences in parallel, that is, their total length substantially exceeds the length of the longest single sequence the network can learn. This model easily generalizes to an arbitrary number of output units, which boost its performance. This effect is demonstrated by considering two practical examples for sequence learning. This work suggests a way to overcome stability problems for training recurrent networks and further quantifies the performance of a network under the specific learning scheme.

Human memory can store large amount of information. Nevertheless, recalling is often a challenging task. In a classical free recall paradigm, where participants are asked to repeat a briefly presented list of words, people make mistakes for lists as short as 5 words. We present a model for memory retrieval based on a Hopfield neural network where transition between items are determined by similarities in their long-term memory representations. Meanfield analysis of the model reveals stable states of the network corresponding (1) to single memory representations and (2) intersection between memory representations. We show that oscillating feedback inhibition in the presence of noise induces transitions between these states triggering the retrieval of different memories. The network dynamics qualitatively predicts the distribution of time intervals required to recall new memory items observed in experiments. It shows that items having larger number of neurons in their representation are statistically easier to recall and reveals possible bottlenecks in our ability of retrieving memories. Overall, we propose a neural network model of information retrieval broadly compatible with experimental observations and is consistent with our recent graphical model (Romani et al., 2013).

In serial recall experiments, human subjects are requested to retrieve a list of words in the same order as they were presented. In a classical study, participants were reported to recall more words from study lists composed of short words compared to lists of long words, the word length effect. The world length effect was also observed in free recall experiments, where subjects can retrieve the words in any order. Here we analyzed a large dataset from free recall experiments of unrelated words, where short and long words were randomly mixed, and found a seemingly opposite effect: long words are recalled better than the short ones. We show that our recently proposed mechanism of associative retrieval can explain both these observations. Moreover, the direction of the effect depends solely on the way study lists are composed.

NAKeywords: short-term plasticity, phenomenological model, neural information processing, associative memory, network dynamics, neural field model,continuous attractor neural network

Networks with continuous set of attractors are considered to be a paradigmatic model for parametric working memory (WM), but require fine tuning of connections and are thus structurally unstable. Here we analyzed the network with ring attractor, where connections are not perfectly tuned and the activity state therefore drifts in the absence of the stabilizing stimulus. We derive an analytical expression for the drift dynamics and conclude that the network cannot function as WM for a period of several seconds, a typical delay time in monkey memory experiments. We propose that short-term synaptic facilitation in recurrent connections significantly improves the robustness of the model by slowing down the drift of activity bump. Extending the calculation of the drift velocity to network with synaptic facilitation, we conclude that facilitation can slow down the drift by a large factor, rendering the network suitable as a model of WM.

Continuous attractor networks are used to model the storage and representation of analog quantities, such as position of a visual stimulus. The storage of multiple continuous attractors in the same network has previously been studied in the context of self-position coding. Several uncorrelated maps of environments are stored in the synaptic connections, and a position in a given environment is represented by a localized pattern of neural activity in the corresponding map, driven by a spatially tuned input. Here we analyze networks storing a pair of correlated maps, or a morph sequence between two uncorrelated maps. We find a novel state in which the network activity is simultaneously localized in both maps. In this state, a fixed cue presented to the network does not determine uniquely the location of the bump, i.e. the response is unreliable, with neurons not always responding when their preferred input is present. When the tuned input varies smoothly in time, the neuronal responses become reliable and selective for the environment: the subset of neurons responsive to a moving input in one map changes almost completely in the other map. This form of remapping is a non-trivial transformation between the tuned input to the network and the resulting tuning curves of the neurons. The new state of the network could be related to the formation of direction selectivity in one-dimensional environments and hippocampal remapping. The applicability of the model is not confined to self-position representations; we show an instance of the network solving a simple delayed discrimination task.

Inter-pyramidal synaptic connections are characterized by a wide range of EPSP amplitudes. Although repeatedly observed at different brain regions and across layers, little is known about the synaptic characteristics that contribute to this wide range. In particular, the range could potentially be accounted for by differences in all three parameters of the quantal model of synaptic transmission, i.e. the number of release sites, release probability and quantal size. Here, we present a rigorous statistical analysis of the transmission properties of excitatory synaptic connections between layer-5 pyramidal neurons of the somato-sensory cortex. Our central finding is that the EPSP amplitude is strongly correlated with the number of estimated release sites, but not with the release probability or quantal size. In addition, we found that the number of release sites can be more than an order of magnitude higher than the typical number of synaptic contacts for this type of connection. Our findings indicate that transmission at stronger synaptic connections is mediated by multiquantal release from their synaptic contacts. We propose that modulating the number of release sites could be an important mechanism in regulating neocortical synaptic transmission.

The synchronous oscillatory activity characterizing many neurons in a network is often considered to be a mechanism for representing, binding, conveying, and organizing information. A number of models have been proposed to explain high-frequency oscillations, but the mechanisms that underlie slow oscillations are still unclear. Here, we show by means of analytical solutions and simulations that facilitating excitatory (E_f) synapses onto interneurons in a neural network play a fundamental role, not only in shaping the frequency of slow oscillations, but also in determining the form of the up and down states observed in electrophysiological measurements. Short time constants and strong E_f synapse-connectivity were found to induce rapid alternations between up and down states, whereas long time constants and weak E_f synapse connectivity prolonged the time between up states and increased the up state duration. These results suggest a novel role for facilitating excitatory synapses onto interneurons in controlling the form and frequency of slow oscillations in neuronal circuits.

We propose a model of the primary auditory cortex (A1), in which each iso-frequency column is represented by a recurrent neural network with short-term synaptic depression. Such networks can emit Population Spikes, in which most of the neurons fire synchronously for a short time period. Different columns are interconnected in a way that reflects the tonotopic map in A1, and population spikes can propagate along the map from one column to the next, in a temporally precise manner that depends on the specific input presented to the network. The network, therefore, processes incoming sounds by precise sequences of population spikes that are embedded in a continuous asynchronous activity, with both of these response components carrying information about the inputs and interacting with each other. With these basic characteristics, the model can account for a wide range of experimental findings. We reproduce neuronal frequency tuning curves, whose width depends on the strength of the intracortical inhibitory and excitatory connections. Non-simultaneous two-tone stimuli show forward masking depending on their temporal separation, as well as on the duration of the first stimulus. The model also exhibits non-linear suppressive interactions between sub-threshold tones and broad-band noise inputs, similar to the hypersensitive locking suppression recently demonstrated in auditory cortex. We derive several predictions from the model. In particular, we predict that spontaneous activity in primary auditory cortex gates the temporally locked responses of A1 neurons to auditory stimuli. Spontaneous activity could, therefore, be a mechanism for rapid and reversible modulation of cortical processing.

Recognizing specific spatiotemporal patterns of activity, which take place at timescales much larger than the synaptic transmission and membrane time constants, is a demand from the nervous system exemplified, for instance, by auditory processing. We consider the total synaptic input that a single readout neuron receives on presentation of spatiotemporal spiking input patterns. Relying on the monotonic relation between the mean and the variance of a neuron's input current and its spiking output, we derive learning rules that increase the variance of the input current evoked by learned patterns relative to that obtained from random background patterns. We demonstrate that the model can successfully recognize a large number of patterns and exhibits a slow deterioration in performance with increasing number of learned patterns. In addition, robustness to time warping of the input patterns is revealed to be an emergent property of the model. Using a leaky integrate-and-fire realization of the readout neuron, we demonstrate that the above results also apply when considering spiking output.

Attractor neural network theory has been proposed as a theory for long-term memory. Recent studies of hippocampal place cells, including a study by Leutgeb et al. in this issue of Neuron, address the potential role of attractor dynamics in the formation of hippocampal representations of spatial maps.

Performance in perceptual tasks improves with repetition (perceptual learning), eventually reaching a saturation level. Typically, when perceptual learning effects are studied, stimulus parameters are kept constant throughout the training and during the pre- and post-training tests. Here we investigate whether learning by repetition transfers to testing conditions in which the practiced stimuli are randomly interleaved during the post-training session. We studied practice effects with a contrast discrimination task, employing a number of training methods: (i) practice with a single, fixed pedestal (base-contrast), (ii) practice with several pedestals, and (iii) practice with several pedestals that included a spatial context. Pre-and post-training tests were carried out with the base contrast randomized across trials, under conditions of contrast uncertainty. The results showed that learning had taken place with the fixed pedestal method (i) and with the context method (iii), but only the latter survived the uncertainty test. In addition, we were able to identify a very fast learning phase in contrast discrimination that improved performance under uncertainty. We contend that learned tasks that do not pass the uncertainty test involve modification of decision strategies that require exact knowledge of the stimulus.

Spontaneous cortical activity-ongoing activity in the absence of intentional sensory input-has been studied extensively, using methods ranging from EEG (electroencephalography), through voltage sensitive dye imaging, down to recordings from single neurons. Ongoing cortical activity has been shown to play a critical role in development, and must also be essential for processing sensory perception, because it modulates stimulus-evoked activity, and is correlated with behaviour. Yet its role in the processing of external information and its relationship to internal representations of sensory attributes remains unknown. Using voltage sensitive dye imaging, we previously established a close link between ongoing activity in the visual cortex of anaesthetized cats and the spontaneous firing of a single neuron. Here we report that such activity encompasses a set of dynamically switching cortical states, many of which correspond closely to orientation maps. When such an orientation state emerged spontaneously, it spanned several hypercolumns and was often followed by a state corresponding to a proximal orientation. We suggest that dynamically switching cortical states could represent the brain's internal context, and therefore reflect or influence memory, perception and behaviour.

Depending on the precise temporal relationship between their spiking activities, connections between neurons could be modified in opposite directions. Although the functional implications of this spike-timing-dependent plasticity are not clear, several theoretical studies have indicated that it could underlie important effects such as sequence learning, predictive learning and balancing excitation and inhibition. To explore fully this novel form of synaptic plasticity, it is crucial to understand how the modification builds up over the consecutive spikes of presynaptic and postsynaptic neurons. In the absence of solid data, many theorists assumed a linear summation model. However, recent experiments specifically devised to study this issue have demonstrated that the effects of the consecutive spikes on the overall modification steadily decline, indicating strong non-linearities in the corresponding learning rules.

This chapter focuses on the emergence of feature selectivity from lateral interactions in the visual cortex. The tuning properties of neurons responding to oriented moving stimuli result from the interplay between excitation on a short length scale and inhibition dominating at larger distances. The chapter reviews models for the dynamics of activities in cortex that are based on stereotyped intracortical interactions. These models stood at the very beginning of the mathematical description of collective phenomena in the brain. The dynamics of these models may have far-reaching consequences and explains a variety of experimental findings. The chapter shows that they might provide a novel explanation for the early development of feature maps in the visual cortex. In chains and two-dimensional neuronal layers, a Mexican-hat shaped coupling induces localized activation patterns. This simple dynamics can be related to response properties of neurons in primary visual cortex. The chapter shows that this approach can also explain the shape of orientation and direction maps as well as the relation of columnar structures to receptive field size and movement.

We investigated the dynamics of localized excitatory and inhibitory populations coupled by dynamic synapses. The synaptic connections exhibit fast depression and facilitation as recently observed in neocortex. Phase plane analysis and numerical simulations are used to investigate population responses to various stimuli. In particular, we analyze the fixed point structure, their stability as a function of input currents. We find parameter sets for which the system exhibits anomalous behavior, by decreasing the activity of both excitatory and inhibitory populations in response to an increase of the inhibitory input current. (C) 2000 Elsevier Science B.V. All rights reserved.

The relation between the activity of a single neocortical neuron and the dynamics of the network in which it is embedded was explored by single-unit recordings and real-time optical imaging. The firing rate of a spontaneously active single neuron strongly depends on the instantaneous spatial pattern of ongoing population activity in a large cortical area. Very similar spatial patterns of population activity were observed both when the neuron fired spontaneously and when it was driven by its optimal stimulus. The evoked patterns could be used to reconstruct the spontaneous activity of single neurons.

The efficacy of synaptic transmission between two neurons changes as a function of the history of previous activations of the synaptic connection. This history dependence can be characterized by examining the dependence of transmission on the frequency of stimulation. In this framework synaptic plasticity can also be examined in terms of changes in the frequency dependence of transmission and not merely in terms of synaptic strength which constitutes only a linear scaling mechanism. Recent work shows that the frequency dependence of transmission determines the content of information transmitted between neurons and that synaptic modifications can change the content of information transmitted. Multipatch-clamp recordings revealed that the frequency dependence of transmission is potentially unique for each synaptic connection made by a single axon and that the class of pre-postsynaptic neuron determines the class of frequency dependence (activity independent), while the unique activity relationship between any two neurons could determine the precise values of the parameters within a specific class (activity dependent). The content of information transmitted between neurons is also formalized to provide synaptic transfer functions which can be used to determine the role of the synaptic connection within a network of neurons. It is proposed that deriving synaptic transfer functions is crucial in order to understand the link between synaptic transmission and information processing within networks of neurons and to understand the link between synaptic plasticity and learning and memory.

At early stages in visual processing cells respond to local stimuli with specific features such as orientation and spatial frequency. Although the receptive fields of these cells have been thought to be local and independent, recent physiological and psychophysical evidence has accumulated, indicating that the cells participate in a rich network of local connections. Thus, these local processing units can integrate information over much larger parts of the visual field; the pattern of their response to a stimulus apparently depends on the context presented. To explore the pattern of lateral interactions in human visual cortex under different context conditions we used a novel chain lateral masking detection paradigm, in which human observers performed a detection task in the presence of different length chains of high-contrast-flanked Gabor signals. The results indicated a nonmonotonic relation of the detection threshold with the number of flankers. Remote flankers had a stronger effect on target detection when the space between them was filled with other flankers, indicating that the detection threshold is caused by dynamics of large neuronal populations in the neocortex, with a major interplay between excitation and inhibition. We considered a model of the primary visual cortex as a network consisting of excitatory and inhibitory cell populations, with both short- and long-range interactions. The model exhibited a behavior similar to the experimental results throughout a range of parameters. Experimental and modeling results indicated that long-range connections play an important role in visual perception, possibly mediating the effects of context.

The transmission across neocortical synapses changes dynamically as a function of presynaptic activity [1]. A switch in the manner in which a complex signal, such as a burst of presynaptic action potentials, is transmitted between two neocortical layer 5 pyramidal neurons was observed after coactivation of both neurons. The switch involved a redistribution of synaptic efficacy during the burst such that the synapses transmitted more effectively only the first action potential in the burst. A computational analysis reveals that this modification in dynamically changing transmission enables pyramidal neurons to extract a rich array of dynamic features of ongoing activity in network of pyramidal neurons, such as the onset and amplitude of abrupt synchronized frequency transitions in groups of presynaptic neurons, the size of the group of neurons involved and the degree of synchrony. These synapses transmit information about dynamic features by causing transient increases of postsynaptic current which have characteristic amplitudes and durations. At the same time, the ability of synapses to signal the sustained level of presynaptic activity is limited to a narrow range of low frequencies, which become even narrower after synaptic modification.

We have explored a network model of cortical microcircuits based on integrate-and-fire neurons in a regime where the reset following a spike is small, recurrent excitation is balanced by feedback inhibition, and the activity is highly irregular. This regime cannot be described by a mean-field theory based on average activity levels because essential features of the model depend on fluctuations from the average. We propose a new way of scaling the strength of synaptic interaction with the size of the network: rather than scale the amplitude of the synapse we scale the neurotransmitter release probabilities with the number of inputs to keep the average input constant. This is consistent with the low transmitter release probability observed in a majority of hippocampal synapses. Another prominent feature of this regime is the ability of the network to switch rapidly between different states, as demonstrated in a model based on an orientation columns in the mammalian visual cortex. Both network and intrinsic properties of neurons contribute to achieving the balance condition that allows rapid state switching.

Interpreting recent single-unit recordings of delay activities in delayed match-to-sample experiments in anterior ventral temporal (AVT) cortex of monkeys in terms of reverberation dynamics, we present a model neural network of quasi-realistic elements that reproduces the empirical results in great detail. Information about the contiguity of successive stimuli in the training sequence, representing the fact that training is done on a set of uncorrelated stimuli presented in a fixed temporal sequence, is embedded in the synaptic structure. The model reproduces quite accurately the correlations between delay activity distributions corresponding to stimulation with the uncorrelated stimuli used for training. It reproduces also the activity distributions of spike rates on sample cells as a function of the stimulating pattern. It is, in our view, the first time that a computational phenomenon, represented on the neurophysiological level, is reproduced in all its quantitative aspects.The model is then used to make predictions about further features of the physiology of such experiments. Those include further properties of the correlations, features of selective cells as discriminators of stimuli provoking different delay activity distributions, and activity distributions among the neurons in a delay activity produced by a given pattern. The model has predictive implications also for the dependence of the delay activities on different training protocols. Finally, we discuss the perspectives of the interplay between such models and neurophysiology as well as its limitations and possible extensions.

Systems of globally coupled oscillators often display states of full synchrony in which all oscillators are phase locked. It is shown that for globally coupled oscillators with neuronlike pulse interactions, the phase-locked state is unstable to inhomogeneity in the local frequency. For weak inhomogeneity the system breaks into two subpopulations: one that is phase locked and another one that consists of aperiodic oscillators. The fraction of the unlocked population remains finite in the limit of vanishing inhomogeneity.

Single-neuron spike dynamics is reconsidered in a situation in which the neural afferent spike input, originating from non-specific spontaneous activity, is very large compared with the input produced by specific (task related) operation of a cortical module. This the authors argue is the situation prevailing in associative cortex. It is shown that the Frolov-Cowan 'point approximation' can be derived systematically in this case, even in the presence of shunting inhibition.The same type of logic is then applied to the cable theory equation for the neuron. Also, here under low ratio of signal to spontaneous activity in the input, the dynamics linearizes, leading to an integrate-and-fire behaviour for the effective neuron. This element sums its synaptic inputs linearly. Its parameters are the resting parameters of the bare neuron, renormalized by the heavy barrage of impinging spontaneous activity. The only remnant of the geometric structure of the dendritic tree is an effective weakening of the postsynaptic potential due to the spatial decay of the spike influence, travelling from the synapse to the spike-emitting part of the membrane, and a time delay for the arrival of the peak of the spike influence.This description can then be re-expressed in terms of rates. The role of the low rates of the selectively spiking neurons is found to be essential at many stages in the argument.

We apply the theory of chaotic regimes for asymmetric networks to the case of highly diluted neural networks with Hebb learning rule. We find the critical capacity and the transition point to chaos.

The simple learning algorithm in the neural network with binary synapses, which take one step for storing one pattern is considered. The resulting model turns out to be palimpsestic, and the number of patterns which can be effectively retrieved is L~N1/2.

We extend the analysis of asymmetric diluted networks to the case of low-activity level. The same learning algorithm which was used for the symmetric model turns out to be successful. The use of “V-variables” (V = 0; 1) leads to significant enhancing of the storage capacity. The overloading phase transition is found to be of the first order, which means good retrieval quality in all associative memory phases. The intensity of time-dependent nonthermal noise can be diminished considerably by the appropriate choice of the neural threshold. Some sort of “universality” of the performance of the networks with low-activity level can be noted.