Analog Memories in a Balanced Rate-Based Network of E-I Neurons

Abstract The persistent and graded activity often observed in cortical circuits is sometimes seen as a signature of autoassociative retrieval of memories stored earlier in synaptic efficacies. However, despite decades of theoretical work on the subject, the mechanisms that support the storage and retrieval of memories remain unclear. Previous proposals concerning the dynamics of memory networks have fallen short of incorporating some key physiological constraints in a unified way. Specifically, some models violate Dale's law (i.e. allow neurons to be both excitatory and inhibitory), while some others restrict the representation of memories to a binary format, or induce recall states in which some neurons fire at rates close to saturation. We propose a novel control-theoretic framework to build functioning attractor networks that satisfy a set of relevant physiological constraints. We directly optimize networks of excitatory and inhibitory neurons to force sets of arbitrary analog patterns to become stable fixed points of the dynamics. The resulting networks operate in the balanced regime, are robust to corruptions of the memory cue as well as to ongoing noise, and incidentally explain the reduction of trial-to-trial variability following stimulus onset that is ubiquitously observed in sensory and motor cortices. Our results constitute a step forward in our understanding of the neural substrate of memory

Neural Network Capacity with Delta Learning and Linear Thresholds

This thesis examines the memory capacities of generalized neural networks. Hopfield networks trained with Hebbian learning as well as networks additionally adjusted with Delta learning are investigated in their binary forms and extended with linear thresholding. These are examined to better understand the capacity of the human brain and the capabilities of artificial intelligence. Greater artificial neural network capacity allows for more computation with less storage space. New methods are proposed to increase Hopfield network capacities, and the scalability of these methods is also examined in respect to size of the network. The ability to recall entire patterns from stimulation of a single neuron is also examined for the increased capacity networks.Computer Scienc

Information Processing Using Circulant Matrices

Circulant matrices may be used to process certain kinds of signals in computer science applications. Specifically, they can be used as signal transforms. In this thesis several new applications of circulant matrices are described. New results have been obtained in number theoretic Hilbert transform (NHT), which is a generalization of discrete Hilbert transform (DHT).The NHT matrix generates ideal orthogonal sequences named as random residue sequences, since the NHT matrix with its transpose computes all correlation in the block. Random residue sequences can be used as carriers for wireless communications. We also investigate applications of circulant matrices to store and reproduce patterns as neural memories.Computer Scienc

Mixed Selectivity via Unsupervised Learning in Neural Networks

Mixed selectivity characterises neurons that simultaneously respond to different input stimuli. Neurons with mixed selectivity have been observed in multiple brain regions, and are hypothesised to play important roles in neural computation. Recently, both experimental and theoretical work demonstrated the importance of mixed selectivity in context-dependent decision tasks. This thesis extends existing theoretical work on mixed selectivity, arguing for a general and statistical role of mixed selectivity in learning complex dependencies of input stimuli. This role can be motivated from unsupervised learning of generative models, and is exhibited in increased mutual information between the stimuli and their neural representation. This argument is supported empirically using simulation of a sequence disambiguation task that incorporated key aspects of related behaviour experiments. Mixed selectivity neurons that resembled hippocampal place cells were emerged from models optimised only for behaviour. To understand these results, as well as to generalise the findings to a wider range of computations, I provided a formal connection between learning robust models and mixed selectivity

Improving Associative Memory in a Network of Spiking Neurons

In this thesis we use computational neural network models to examine the dynamics and functionality of the CA3 region of the mammalian hippocampus. The emphasis of the project is to investigate how the dynamic control structures provided by inhibitory circuitry and cellular modification may effect the CA3 region during the recall of previously stored information. The CA3 region is commonly thought to work as a recurrent auto-associative neural network due to the neurophysiological characteristics found, such as, recurrent collaterals, strong and sparse synapses from external inputs and plasticity between coactive cells. Associative memory models have been developed using various configurations of mathematical artificial neural networks which were first developed over 40 years ago. Within these models we can store information via changes in the strength of connections between simplified model neurons (two-state). These memories can be recalled when a cue (noisy or partial) is instantiated upon the net. The type of information they can store is quite limited due to restrictions caused by the simplicity of the hard-limiting nodes which are commonly associated with a binary activation threshold. We build a much more biologically plausible model with complex spiking cell models and with realistic synaptic properties between cells. This model is based upon some of the many details we now know of the neuronal circuitry of the CA3 region. We implemented the model in computer software using Neuron and Matlab and tested it by running simulations of storage and recall in the network. By building this model we gain new insights into how different types of neurons, and the complex circuits they form, actually work. The mammalian brain consists of complex resistive-capacative electrical circuitry which is formed by the interconnection of large numbers of neurons. A principal cell type is the pyramidal cell within the cortex, which is the main information processor in our neural networks. Pyramidal cells are surrounded by diverse populations of interneurons which have proportionally smaller numbers compared to the pyramidal cells and these form connections with pyramidal cells and other inhibitory cells. By building detailed computational models of recurrent neural circuitry we explore how these microcircuits of interneurons control the flow of information through pyramidal cells and regulate the efficacy of the network. We also explore the effect of cellular modification due to neuronal activity and the effect of incorporating spatially dependent connectivity on the network during recall of previously stored information. In particular we implement a spiking neural network proposed by Sommer and Wennekers (2001). We consider methods for improving associative memory recall using methods inspired by the work by Graham and Willshaw (1995) where they apply mathematical transforms to an artificial neural network to improve the recall quality within the network. The networks tested contain either 100 or 1000 pyramidal cells with 10% connectivity applied and a partial cue instantiated, and with a global pseudo-inhibition.We investigate three methods. Firstly, applying localised disynaptic inhibition which will proportionalise the excitatory post synaptic potentials and provide a fast acting reversal potential which should help to reduce the variability in signal propagation between cells and provide further inhibition to help synchronise the network activity. Secondly, implementing a persistent sodium channel to the cell body which will act to non-linearise the activation threshold where after a given membrane potential the amplitude of the excitatory postsynaptic potential (EPSP) is boosted to push cells which receive slightly more excitation (most likely high units) over the firing threshold. Finally, implementing spatial characteristics of the dendritic tree will allow a greater probability of a modified synapse existing after 10% random connectivity has been applied throughout the network. We apply spatial characteristics by scaling the conductance weights of excitatory synapses which simulate the loss in potential in synapses found in the outer dendritic regions due to increased resistance. To further increase the biological plausibility of the network we remove the pseudo-inhibition and apply realistic basket cell models with differing configurations for a global inhibitory circuit. The networks are configured with; 1 single basket cell providing feedback inhibition, 10% basket cells providing feedback inhibition where 10 pyramidal cells connect to each basket cell and finally, 100% basket cells providing feedback inhibition. These networks are compared and contrasted for efficacy on recall quality and the effect on the network behaviour. We have found promising results from applying biologically plausible recall strategies and network configurations which suggests the role of inhibition and cellular dynamics are pivotal in learning and memory