Slow stochastic Hebbian learning of classes of stimuli in a recurrent neural network

We study unsupervised Hebbian learning in a recurrent network in which synapses have a finite number of stable states. Stimuli received by the network are drawn at random at each presentation from a set of classes. Each class is defined as a cluster in stimulus space, centred on the class prototype. The presentation protocol is chosen to mimic the protocols of visual memory experiments in which a set of stimuli is presented repeatedly in a random way. The statistics of the input stream may be stationary, or changing. Each stimulus induces, in a stochastic way, transitions between stable synaptic states. Learning dynamics is studied analytically in the slow learning limit, in which a given stimulus has to be presented many times before it is memorized, i.e. before synaptic modifications enable a pattern of activity correlated with the stimulus to become an attractor of the recurrent network. We show that in this limit the synaptic matrix becomes more correlated with the class prototypes than with any of the instances of the class. We also show that the number of classes that can be learned increases sharply when the coding level decreases, and determine the speeds of learning and forgetting of classes in the case of changes in the statistics of the input stream

Inter-trial neuronal activity in inferior temporal cortex: a putative vehicle to generate long-term visual associations.

When monkeys perform a delayed match-to-sample task, some neurons in the anterior inferotemporal cortex show sustained activity following the presentation of specific visual stimuli, typically only those that are shown repeatedly. When sample stimuli are shown in a fixed temporal order, the few images that evoke delay activity in a given neuron are often neighboring stimuli in the sequence, suggesting that this delay activity may be the neural correlate of associative long-term memory. Here we report that stimulus-selective sustained activity is also evident following the presentation of the test stimulus in the same task. We use a neural network model to demonstrate that persistent stimulus-selective activity across the intertrial interval can lead to similar mnemonic representations (distributions of delay activity across the neural population) for neighboring visual stimuli. Thus, inferotemporal cortex may contain neural machinery for generating long-term stimulus-stimulus associations

Efficient Partitioning of Memory Systems and Its Importance for Memory Consolidation

Long-term memories are likely stored in the synaptic weights of neuronal networks in the brain. The storage capacity of such networks depends on the degree of plasticity of their synapses. Highly plastic synapses allow for strong memories, but these are quickly overwritten. On the other hand, less labile synapses result in long-lasting but weak memories. Here we show that the trade-off between memory strength and memory lifetime can be overcome by partitioning the memory system into multiple regions characterized by different levels of synaptic plasticity and transferring memory information from the more to less plastic region. The improvement in memory lifetime is proportional to the number of memory regions, and the initial memory strength can be orders of magnitude larger than in a non-partitioned memory system. This model provides a fundamental computational reason for memory consolidation processes at the systems level

The computational role of structure in neural activity and connectivity

One major challenge of neuroscience is finding interesting structures in a seemingly disorganized neural activity. Often these structures have computational implications that help to understand the functional role of a particular brain area. Here we outline a unified approach to characterize these structures by inspecting the representational geometry and the modularity properties of the recorded activity, and show that this approach can also reveal structures in connectivity. We start by setting up a general framework for determining geometry and modularity in activity and connectivity and relating these properties with computations performed by the network. We then use this framework to review the types of structure found in recent works on model networks performing three classes of computations

Learning in neural networks with material synapses

We discuss the long term maintenance of acquired memory in synaptic connections of a perpetually learning electronic device. This is affected by ascribing each synapse a finite number of stable states in which it can maintain for indefinitely long periods. Learning uncorrelated stimuli is expressed as a stochastic process produced by the neural activities on the synapses. In several interesting cases the stochastic process can be analyzed in detail, leading to a clarification of the performance of the network, as an associative memory, during the process of uninterrupted learning. The stochastic nature of the process and the existence of an asymptotic distribution for the synaptic values in the network imply generically that the memory is a palimpsest but capacity is as low as log N for a network of N neurons. The only way we find for avoiding this tight constraint is to allow the parameters governing the learning process (the coding level of the stimuli; the transition probabilities for potentiation and depression and the number of stable synaptic levels) to depend on the number of neurons. It is shown that a network with synapses that have two stable states can dynamically learn with optimal storage efficiency, be a palimpsest, and maintain its (associative) memory for an indefinitely long time provided the coding level is low and depression is equilibrated against potentiation. We suggest that an option so easily implementable in material devices would not have been overlooked by biology. Finally we discuss the stochastic learning on synapses with variable number of stable synaptic states

Long Memory Lifetimes Require Complex Synapses and Limited Sparseness

Theoretical studies have shown that memories last longer if the neural representations are sparse, that is, when each neuron is selective for a small fraction of the events creating the memories. Sparseness reduces both the interference between stored memories and the number of synaptic modifications which are necessary for memory storage. Paradoxically, in cortical areas like the inferotemporal cortex, where presumably memory lifetimes are longer than in the medial temporal lobe, neural representations are less sparse. We resolve this paradox by analyzing the effects of sparseness on complex models of synaptic dynamics in which there are metaplastic states with different degrees of plasticity. For these models, memory retention in a large number of synapses across multiple neurons is significantly more efficient in case of many metaplastic states, that is, for an elevated degree of complexity. In other words, larger brain regions allow to retain memories for significantly longer times only if the synaptic complexity increases with the total number of synapses. However, the initial memory trace, the one experienced immediately after memory storage, becomes weaker both when the number of metaplastic states increases and when the neural representations become sparser. Such a memory trace must be above a given threshold in order to permit every single neuron to retrieve the information stored in its synapses. As a consequence, if the initial memory trace is reduced because of the increased synaptic complexity, then the neural representations must be less sparse. We conclude that long memory lifetimes allowed by a larger number of synapses require more complex synapses, and hence, less sparse representations, which is what is observed in the brain

Internal Representation of Task Rules by Recurrent Dynamics: The Importance of the Diversity of Neural Responses

Neural activity of behaving animals, especially in the prefrontal cortex, is highly heterogeneous, with selective responses to diverse aspects of the executed task. We propose a general model of recurrent neural networks that perform complex rule-based tasks, and we show that the diversity of neuronal responses plays a fundamental role when the behavioral responses are context-dependent. Specifically, we found that when the inner mental states encoding the task rules are represented by stable patterns of neural activity (attractors of the neural dynamics), the neurons must be selective for combinations of sensory stimuli and inner mental states. Such mixed selectivity is easily obtained by neurons that connect with random synaptic strengths both to the recurrent network and to neurons encoding sensory inputs. The number of randomly connected neurons needed to solve a task is on average only three times as large as the number of neurons needed in a network designed ad hoc. Moreover, the number of needed neurons grows only linearly with the number of task-relevant events and mental states, provided that each neuron responds to a large proportion of events (dense/distributed coding). A biologically realistic implementation of the model captures several aspects of the activity recorded from monkeys performing context-dependent tasks. Our findings explain the importance of the diversity of neural responses and provide us with simple and general principles for designing attractor neural networks that perform complex computation