Noise modulation of synaptic weights in a biological neural network

Reconfigurable Filtering of Neuro-Spike Communications Using Synthetically Engineered Logic Circuits

High-frequency firing activity can be induced either naturally in a healthy brain as a result of the processing of sensory stimuli or as an uncontrolled synchronous activity characterizing epileptic seizures. As part of this work, we investigate how logic circuits that are engineered in neurons can be used to design spike filters, attenuating high-frequency activity in a neuronal network that can be used to minimize the effects of neurodegenerative disorders such as epilepsy. We propose a reconfigurable filter design built from small neuronal networks that behave as digital logic circuits. We developed a mathematical framework to obtain a transfer function derived from a linearization process of the Hodgkin-Huxley model. Our results suggest that individual gates working as the output of the logic circuits can be used as a reconfigurable filtering technique. Also, as part of the analysis, the analytical model showed similar levels of attenuation in the frequency domain when compared to computational simulations by fine-tuning the synaptic weight. The proposed approach can potentially lead to precise and tunable treatments for neurological conditions that are inspired by communication theory.

Stability Analysis and Application for Delayed Neural Networks Driven by Fractional Brownian Noise

This paper deals with two types of the stability problem for the delayed neural networks driven by fractional Brownian noise (FBN). The existence and the uniqueness of the solution to the main system with respect to FBN are proved via fixed point theory. Based on Hilbert-Schmidt operator theory and analytic semigroup principle, the mild solution of the stochastic neural networks is obtained. By applying the stochastic analytic technique and some well-known inequalities, the asymptotic stability criteria and the exponential stability condition are established. Both numerical example and practical application for synchronization control of multiagent system are provided to illustrate the effectiveness and potential of the proposed techniques.

The Dropout Learning Algorithm

Dropout is a recently introduced algorithm for training neural network by randomly dropping units during training to prevent their co-adaptation. A mathematical analysis of some of the static and dynamic properties of dropout is provided using Bernoulli gating variables, general enough to accommodate dropout on units or connections, and with variable rates. The framework allows a complete analysis of the ensemble averaging properties of dropout in linear networks, which is useful to understand the non-linear case. The ensemble averaging properties of dropout in non-linear logistic networks result from three fundamental equations: (1) the approximation of the expectations of logistic functions by normalized geometric means, for which bounds and estimates are derived; (2) the algebraic equality between normalized geometric means of logistic functions with the logistic of the means, which mathematically characterizes logistic functions; and (3) the linearity of the means with respect to sums, as well as products of independent variables. The results are also extended to other classes of transfer functions, including rectified linear functions. Approximation errors tend to cancel each other and do not accumulate. Dropout can also be connected to stochastic neurons and used to predict firing rates, and to backpropagation by viewing the backward propagation as ensemble averaging in a dropout linear network. Moreover, the convergence properties of dropout can be understood in terms of stochastic gradient descent. Finally, for the regularization properties of dropout, the expectation of the dropout gradient is the gradient of the corresponding approximation ensemble, regularized by an adaptive weight decay term with a propensity for self-consistent variance minimization and sparse representations.

Neuropoiesis: proposal for a connectionistic neurobiology

Given current assumptions about the biology of neural organization, some connectionists believe that it may not be possible to accurately model the brain's neural architecture. We have identified five restrictive neurobiological dogmas that we believe have limited the exploration of more fundamental correlations between computational and biological neural networks. We postulate that: 1) the dendritic tree serves as a synapse storage device rather than a simple summation device; 2) connection strength between neurons depends on the number and location of synapses of similar weight, not on synapses of variable weights; 3) axonal sprouting occurs regularly in adult organisms; 4) the postsynaptic genome directly controls the presynaptic cell via mRNA, rather than indirectly by the expression of NCAMs, reverse neurotransmitters, etc.; 5) dendritic spines serve a trophic function by controlling development of new sprouts via a process we term retroduction. We entertain an alternative formulation of a computational neural element that is fully consistent with modern neuroscience research. We then show how our model neuron can learn under Hebbian conditions, and extend the model to explain non-Hebbian, one-trial learning. This work is significant because by stretching the theoretical boundaries of modern neuroscience, we show how connectionists can potentially create new, more biologically-based neural elements which, when, interconnected into networks, exhibit not only properties of existing backpropagation networks, but other physiological properties as well.