Order-Based Representation in Random Networks of Cortical Neurons

The wide range of time scales involved in neural excitability and synaptic transmission might lead to ongoing change in the temporal structure of responses to recurring stimulus presentations on a trial-to-trial basis. This is probably the most severe biophysical constraint on putative time-based primitives of stimulus representation in neuronal networks. Here we show that in spontaneously developing large-scale random networks of cortical neurons in vitro the order in which neurons are recruited following each stimulus is a naturally emerging representation primitive that is invariant to significant temporal changes in spike times. With a relatively small number of randomly sampled neurons, the information about stimulus position is fully retrievable from the recruitment order. The effective connectivity that makes order-based representation invariant to time warping is characterized by the existence of stations through which activity is required to pass in order to propagate further into the network. This study uncovers a simple invariant in a noisy biological network in vitro; its applicability under in vivo constraints remains to be seen

A feedback model of perceptual learning and categorisation

Top-down, feedback, influences are known to have significant effects on visual information processing. Such influences are also likely to affect perceptual learning. This article employs a computational model of the cortical region interactions underlying visual perception to investigate possible influences of top-down information on learning. The results suggest that feedback could bias the way in which perceptual stimuli are categorised and could also facilitate the learning of sub-ordinate level representations suitable for object identification and perceptual expertise

Dynamical Entropy Production in Spiking Neuron Networks in the Balanced State

We demonstrate deterministic extensive chaos in the dynamics of large sparse networks of theta neurons in the balanced state. The analysis is based on numerically exact calculations of the full spectrum of Lyapunov exponents, the entropy production rate and the attractor dimension. Extensive chaos is found in inhibitory networks and becomes more intense when an excitatory population is included. We find a strikingly high rate of entropy production that would limit information representation in cortical spike patterns to the immediate stimulus response.Comment: 4 pages, 4 figure

Decorrelation of neural-network activity by inhibitory feedback

Correlations in spike-train ensembles can seriously impair the encoding of information by their spatio-temporal structure. An inevitable source of correlation in finite neural networks is common presynaptic input to pairs of neurons. Recent theoretical and experimental studies demonstrate that spike correlations in recurrent neural networks are considerably smaller than expected based on the amount of shared presynaptic input. By means of a linear network model and simulations of networks of leaky integrate-and-fire neurons, we show that shared-input correlations are efficiently suppressed by inhibitory feedback. To elucidate the effect of feedback, we compare the responses of the intact recurrent network and systems where the statistics of the feedback channel is perturbed. The suppression of spike-train correlations and population-rate fluctuations by inhibitory feedback can be observed both in purely inhibitory and in excitatory-inhibitory networks. The effect is fully understood by a linear theory and becomes already apparent at the macroscopic level of the population averaged activity. At the microscopic level, shared-input correlations are suppressed by spike-train correlations: In purely inhibitory networks, they are canceled by negative spike-train correlations. In excitatory-inhibitory networks, spike-train correlations are typically positive. Here, the suppression of input correlations is not a result of the mere existence of correlations between excitatory (E) and inhibitory (I) neurons, but a consequence of a particular structure of correlations among the three possible pairings (EE, EI, II)

A generative spike train model with time-structured higher order correlations

Emerging technologies are revealing the spiking activity in ever larger neural ensembles. Frequently, this spiking is far from independent, with correlations in the spike times of different cells. Understanding how such correlations impact the dynamics and function of neural ensembles remains an important open problem. Here we describe a new, generative model for correlated spike trains that can exhibit many of the features observed in data. Extending prior work in mathematical finance, this generalized thinning and shift (GTaS) model creates marginally Poisson spike trains with diverse temporal correlation structures. We give several examples which highlight the model's flexibility and utility. For instance, we use it to examine how a neural network responds to highly structured patterns of inputs. We then show that the GTaS model is analytically tractable, and derive cumulant densities of all orders in terms of model parameters. The GTaS framework can therefore be an important tool in the experimental and theoretical exploration of neural dynamics

Nonlinear Hebbian learning as a unifying principle in receptive field formation

The development of sensory receptive fields has been modeled in the past by a variety of models including normative models such as sparse coding or independent component analysis and bottom-up models such as spike-timing dependent plasticity or the Bienenstock-Cooper-Munro model of synaptic plasticity. Here we show that the above variety of approaches can all be unified into a single common principle, namely Nonlinear Hebbian Learning. When Nonlinear Hebbian Learning is applied to natural images, receptive field shapes were strongly constrained by the input statistics and preprocessing, but exhibited only modest variation across different choices of nonlinearities in neuron models or synaptic plasticity rules. Neither overcompleteness nor sparse network activity are necessary for the development of localized receptive fields. The analysis of alternative sensory modalities such as auditory models or V2 development lead to the same conclusions. In all examples, receptive fields can be predicted a priori by reformulating an abstract model as nonlinear Hebbian learning. Thus nonlinear Hebbian learning and natural statistics can account for many aspects of receptive field formation across models and sensory modalities

Why Neurons Have Thousands of Synapses, A Theory of Sequence Memory in Neocortex

Neocortical neurons have thousands of excitatory synapses. It is a mystery how neurons integrate the input from so many synapses and what kind of large-scale network behavior this enables. It has been previously proposed that non-linear properties of dendrites enable neurons to recognize multiple patterns. In this paper we extend this idea by showing that a neuron with several thousand synapses arranged along active dendrites can learn to accurately and robustly recognize hundreds of unique patterns of cellular activity, even in the presence of large amounts of noise and pattern variation. We then propose a neuron model where some of the patterns recognized by a neuron lead to action potentials and define the classic receptive field of the neuron, whereas the majority of the patterns recognized by a neuron act as predictions by slightly depolarizing the neuron without immediately generating an action potential. We then present a network model based on neurons with these properties and show that the network learns a robust model of time-based sequences. Given the similarity of excitatory neurons throughout the neocortex and the importance of sequence memory in inference and behavior, we propose that this form of sequence memory is a universal property of neocortical tissue. We further propose that cellular layers in the neocortex implement variations of the same sequence memory algorithm to achieve different aspects of inference and behavior. The neuron and network models we introduce are robust over a wide range of parameters as long as the network uses a sparse distributed code of cellular activations. The sequence capacity of the network scales linearly with the number of synapses on each neuron. Thus neurons need thousands of synapses to learn the many temporal patterns in sensory stimuli and motor sequences.Comment: Submitted for publicatio