Recurrent network of perceptrons with three state synapses achieves competitive classification on real inputs

We describe an attractor network of binary perceptrons receiving inputs from a retinotopic visual feature layer. Each class is represented by a random subpopulation of the attractor layer, which is turned on in a supervised manner during learning of the feed forward connections. These are discrete three state synapses and are updated based on a simple field dependent Hebbian rule. For testing, the attractor layer is initialized by the feedforward inputs and then undergoes asynchronous random updating until convergence to a stable state. Classification is indicated by the sub-population that is persistently activated. The contribution of this paper is two-fold. This is the first example of competitive classification rates of real data being achieved through recurrent dynamics in the attractor layer, which is only stable if recurrent inhibition is introduced. Second, we demonstrate that employing three state synapses with feedforward inhibition is essential for achieving the competitive classification rates due to the ability to effectively employ both positive and negative informative features

Inhomogeneous sparseness leads to dynamic instability during sequence memory recall in a recurrent neural network model.

Theoretical models of associative memory generally assume most of their parameters to be homogeneous across the network. Conversely, biological neural networks exhibit high variability of structural as well as activity parameters. In this paper, we extend the classical clipped learning rule by Willshaw to networks with inhomogeneous sparseness, i.e., the number of active neurons may vary across memory items. We evaluate this learning rule for sequence memory networks with instantaneous feedback inhibition and show that little surprisingly, memory capacity degrades with increased variability in sparseness. The loss of capacity, however, is very small for short sequences of less than about 10 associations. Most interestingly, we further show that, due to feedback inhibition, too large patterns are much less detrimental for memory capacity than too small patterns

A Mathematical Analysis of Memory Lifetime in a simple Network Model of Memory

We study the learning of an external signal by a neural network and the time to forget it when this network is submitted to other signals considered as noise. The presentation of an external stimulus changes the state of the synapses in a network of binary neurons. Multiple presentations of a unique signal leads to its learning. Then, the presentation of other signals also changes the synaptic weight (during the forgetting time). We study the number of external signals to which the network can be submitted until the initial signal is considered as forgotten. We construct an estimator of the initial signal thanks to the synaptic currents. In our model, these synaptic currents evolve as Markov chains. We study mathematically these Markov chains and obtain a lower bound on the number of external stimulus that the network can receive before the initial signal is forgotten. We finally present numerical illustrations of our results

Does computational neuroscience need new synaptic learning paradigms?

Computational neuroscience is dominated by a few paradigmatic models, but it remains an open question whether the existing modelling frameworks are sufficient to explain observed behavioural phenomena in terms of neural implementation. We take learning and synaptic plasticity as an example and point to open questions, such as one-shot learning and acquiring internal representations of the world for flexible planning

A Mathematical Analysis of Memory Lifetime in a simple Network Model of Memory

We study the learning of an external signal by a neural network and the time to forget it when this network is submitted to noise. The presentation of an external stimulus to the recurrent network of binary neurons may change the state of the synapses. Multiple presentations of a unique signal leads to its learning. Then, during the forgetting time, the presentation of other signals (noise) may also modify the synaptic weights. We construct an estimator of the initial signal thanks to the synaptic currents and define by this way a probability of error. In our model, these synaptic currents evolve as Markov chains. We study the dynamics of these Markov chains and obtain a lower bound on the number of external stimuli that the network can receive before the initial signal is considered as forgotten (probability of error above a given threshold). Our results hold for finite size networks as well as in the large size asymptotic. Our results are based on a finite time analysis rather than large time asymptotic. We finally present numerical illustrations of our results

Memory capacity in the hippocampus

Neural assemblies in hippocampus encode positions. During rest, the hippocam- pus replays sequences of neural activity seen during awake behavior. This replay is linked to memory consolidation and mental exploration of the environment. Re- current networks can be used to model the replay of sequential activity. Multiple sequences can be stored in the synaptic connections. To achieve a high mem- ory capacity, recurrent networks require a pattern separation mechanism. Such a mechanism is global remapping, observed in place cell populations. A place cell fires at a particular position of an environment and is silent elsewhere. Multiple place cells usually cover an environment with their firing fields. Small changes in the environment or context of a behavioral task can cause global remapping, i.e. profound changes in place cell firing fields. Global remapping causes some cells to cease firing, other silent cells to gain a place field, and other place cells to move their firing field and change their peak firing rate. The effect is strong enough to make global remapping a viable pattern separation mechanism. We model two mechanisms that improve the memory capacity of recurrent net- works. The effect of inhibition on replay in a recurrent network is modeled using binary neurons and binary synapses. A mean field approximation is used to de- termine the optimal parameters for the inhibitory neuron population. Numerical simulations of the full model were carried out to verify the predictions of the mean field model. A second model analyzes a hypothesized global remapping mecha- nism, in which grid cell firing is used as feed forward input to place cells. Grid cells have multiple firing fields in the same environment, arranged in a hexagonal grid. Grid cells can be used in a model as feed forward inputs to place cells to produce place fields. In these grid-to-place cell models, shifts in the grid cell firing patterns cause remapping in the place cell population. We analyze the capacity of such a system to create sets of separated patterns, i.e. how many different spatial codes can be generated. The limiting factor are the synapses connecting grid cells to place cells. To assess their capacity, we produce different place codes in place and grid cell populations, by shuffling place field positions and shifting grid fields of grid cells. Then we use Hebbian learning to increase the synaptic weights be- tween grid and place cells for each set of grid and place code. The capacity limit is reached when synaptic interference makes it impossible to produce a place code with sufficient spatial acuity from grid cell firing. Additionally, it is desired to also maintain the place fields compact, or sparse if seen from a coding standpoint. Of course, as more environments are stored, the sparseness is lost. Interestingly, place cells lose the sparseness of their firing fields much earlier than their spatial acuity. For the sequence replay model we are able to increase capacity in a simulated recurrent network by including an inhibitory population. We show that even in this more complicated case, capacity is improved. We observe oscillations in the average activity of both excitatory and inhibitory neuron populations. The oscillations get stronger at the capacity limit. In addition, at the capacity limit, rather than observing a sudden failure of replay, we find sequences are replayed transiently for a couple of time steps before failing. Analyzing the remapping model, we find that, as we store more spatial codes in the synapses, first the sparseness of place fields is lost. Only later do we observe a decay in spatial acuity of the code. We found two ways to maintain sparse place fields while achieving a high capacity: inhibition between place cells, and partitioning the place cell population so that learning affects only a small fraction of them in each environment. We present scaling predictions that suggest that hundreds of thousands of spatial codes can be produced by this pattern separation mechanism. The effect inhibition has on the replay model is two-fold. Capacity is increased, and the graceful transition from full replay to failure allows for higher capacities when using short sequences. Additional mechanisms not explored in this model could be at work to concatenate these short sequences, or could perform more complex operations on them. The interplay of excitatory and inhibitory populations gives rise to oscillations, which are strongest at the capacity limit. The oscillation draws a picture of how a memory mechanism can cause hippocampal oscillations as observed in experiments. In the remapping model we showed that sparseness of place cell firing is constraining the capacity of this pattern separation mechanism. Grid codes outperform place codes regarding spatial acuity, as shown in Mathis et al. (2012). Our model shows that the grid-to-place transformation is not harnessing the full spatial information from the grid code in order to maintain sparse place fields. This suggests that the two codes are independent, and communication between the areas might be mostly for synchronization. High spatial acuity seems to be a specialization of the grid code, while the place code is more suitable for memory tasks. In a detailed model of hippocampal replay we show that feedback inhibition can increase the number of sequences that can be replayed. The effect of inhibition on capacity is determined using a meanfield model, and the results are verified with numerical simulations of the full network. Transient replay is found at the capacity limit, accompanied by oscillations that resemble sharp wave ripples in hippocampus. In a second model Hippocampal replay of neuronal activity is linked to memory consolidation and mental exploration. Furthermore, replay is a potential neural correlate of episodic memory. To model hippocampal sequence replay, recurrent neural networks are used. Memory capacity of such networks is of great interest to determine their biological feasibility. And additionally, any mechanism that improves capacity has explanatory power. We investigate two such mechanisms. The first mechanism to improve capacity is global, unspecific feedback inhibition for the recurrent network. In a simplified meanfield model we show that capacity is indeed improved. The second mechanism that increases memory capacity is pattern separation. In the spatial context of hippocampal place cell firing, global remapping is one way to achieve pattern separation. Changes in the environment or context of a task cause global remapping. During global remapping, place cell firing changes in unpredictable ways: cells shift their place fields, or fully cease firing, and formerly silent cells acquire place fields. Global remapping can be triggered by subtle changes in grid cells that give feed-forward inputs to hippocampal place cells. We investigate the capacity of the underlying synaptic connections, defined as the number of different environments that can be represented at a given spatial acuity. We find two essential conditions to achieve a high capacity and sparse place fields: inhibition between place cells, and partitioning the place cell population so that learning affects only a small fraction of them in each environments. We also find that sparsity of place fields is the constraining factor of the model rather than spatial acuity. Since the hippocampal place code is sparse, we conclude that the hippocampus does not fully harness the spatial information available in the grid code. The two codes of space might thus serve different purposes