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Population rate coding in recurrent neuronal networks consisting of neurons with mixed excitatory-inhibitory synapses

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NONLINEAR DYNAMICS 2020年第3期100卷 2673-2686页

作者： Sun, Xiaojuan Si, Hao Beijing Univ Posts & Telecommun Sch Sci Beijing 100876 Peoples R China

neural coding is a key problem in neuroscience aimed to understand the information processing mechanism in brain. Among the classical theories of neural coding, population rate coding has been studied widely in many works. In computational studies, neurons are usually classified into excitatory or inhibitory ones. Excitatory neurons have excitatory output synapses, and inhibitory neurons have inhibitory output synapses. However, according to physiological observations, neurons potentially have both types of output synapses. Thus, in this paper, neuronal networks consisting of neurons with mixed excitatory-inhibitory synapses are constructed to investigate the population rate coding fidelity of neuronal systems. It is revealed that, under intermediate values of recurrent probability, inhibitory-excitatory strength ratio, and noise intensity, the performance of population rate coding could be improved by both excitatory synaptic strength and synaptic time constant. It is indicated that external stimuli can be encoded in the form of population firing rate by the studied neuronal networks very well. What is more exciting is that we find the neuronal networks considered in our work have higher coding efficiency than the traditional ones. Therefore, neurons with mixed excitatory-inhibitory synapses may be much more rational.

关键词： neural coding Population rate coding Recurrent neuronal network

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Techniques for temporal detection of neural sensitivity to external stimulation

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BIOLOGICAL CYBERNETICS 2009年第4期100卷 289-297页

作者： Rodriguez, Francisco B. Huerta, Ramon Univ Autonoma Madrid Escuela Politecn Super Dpto Ingn Informat GNB E-28049 Madrid Spain Univ Calif San Diego Inst Nonlinear Sci La Jolla CA 92093 USA

We propose a simple measure of neural sensitivity for characterizing stimulus coding. Sensitivity is defined as the fraction of neurons that show positive responses to n stimuli out of a total of N. To determine a positive response, we propose two methods: Fisherian statistical testing and a data-driven Bayesian approach to determine the response probability of a neuron. The latter is non-parametric, data-driven, and captures a lower bound for the probability of neural responses to sensory stimulation. Both methods are compared with a standard test that assumes normal probability distributions. We applied the sensitivity estimation based on the proposed method to experimental data recorded from the mushroom body (MB) of locusts. We show that there is a broad range of sensitivity that the MB response sweeps during odor stimulation. The neurons are initially tuned to specific odors, but tend to demonstrate a generalist behavior towards the end of the stimulus period, meaning that the emphasis shifts from discrimination to feature learning.

关键词： Sensitivity Bayes test neural response Olfaction Statistical testing neural coding Fisher test Likelihood ratio test

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Combining frequency and time domain approaches to systems with multiple spike train input and output

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BIOLOGICAL CYBERNETICS 2009年第6期100卷 459-474页

作者： Brillinger, D. R. Lindsay, K. A. Rosenberg, J. R. Univ Glasgow Div Neurosci & Biomed Syst Glasgow G12 8QQ Lanark Scotland Univ Glasgow Dept Math Glasgow G12 8QW Lanark Scotland Univ Calif Berkeley Dept Stat Berkeley CA 94720 USA

A frequency domain approach and a time domain approach have been combined in an investigation of the behaviour of the primary and secondary endings of an isolated muscle spindle in response to the activity of two static fusimotor axons when the parent muscle is held at a fixed length and when it is subjected to random length changes. The frequency domain analysis has an associated error process which provides a measure of how well the input processes can be used to predict the output processes and is also used to specify how the interactions between the recorded processes contribute to this error. Without assuming stationarity of the input, the time domain approach uses a sequence of probability models of increasing complexity in which the number of input processes to the model is progressively increased. This feature of the time domain approach was used to identify a preferred direction of interaction between the processes underlying the generation of the activity of the primary and secondary endings. In the presence of fusimotor activity and dynamic length changes imposed on the muscle, it was shown that the activity of the primary and secondary endings carried different information about the effects of the inputs imposed on the muscle spindle. The results presented in this work emphasise that the analysis of the behaviour of complex systems benefits from a combination of frequency and time domain methods.

关键词： Multiple spike trains neural coding Maximum likelihood Canonical coherence Muscle spindle Multivariate point processes

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Small-world networks in neuronal populations: A computational perspective

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neural NETWORKS 2013年 44卷 143-156页

作者： Zippo, Antonio G. Gelsomino, Giuliana Van Duin, Pieter Nencini, Sara Caramenti, Gian Carlo Valente, Maurizio Biella, Gabriele E. M. CNR Inst Mol Bioimaging & Physiol Milan Italy Univ Milan Dept Comp Sci Milan Italy CNR Inst Biomed Technol Milan Italy

The analysis of the brain in terms of integrated neural networks may offer insights on the reciprocal relation between structure and information processing. Even with inherent technical limits, many studies acknowledge neuron spatial arrangements and communication modes as key factors. In this perspective, we investigated the functional organization of neuronal networks by explicitly assuming a specific functional topology, the small-world network. We developed two different computational approaches. Firstly, we asked whether neuronal populations actually express small-world properties during a definite task, such as a learning task. For this purpose we developed the Inductive Conceptual Network (ICN), which is a hierarchical bio-inspired spiking network, capable of learning invariant patterns by using variable-order Markov models implemented in its nodes. As a result, we actually observed small-world topologies during learning in the ICN. Speculating that the expression of small-world networks is not solely related to learning tasks, we then built a de facto network assuming that the information processing in the brain may occur through functional small-world topologies. In this de facto network, synchronous spikes reflected functional small-world network dependencies. In order to verify the consistency of the assumption, we tested the null-hypothesis by replacing the small-world networks with random networks. As a result, only small world networks exhibited functional biomimetic characteristics such as timing and rate codes, conventional coding strategies and neuronal avalanches, which are cascades of bursting activities with a power-law distribution. Our results suggest that small-world functional configurations are liable to underpin brain information processing at neuronal level. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Neuronal assemblies Information abstraction Machine learning Small-world networks Neuronal avalanches neural coding

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Computational role of structure in neural activity and connectivity

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TRENDS IN COGNITIVE SCIENCES 2024年第7期28卷 677-690页

作者： Ostojic, Srdjan Fusi, Stefano PSL Res Univ Lab Neurosci Cognit & Computat INSERM U960 Ecole Normale Super F-75005 Paris France Columbia Univ Ctr Theoret Neurosci New York NY 10032 USA Columbia Univ Zuckerman Mind Brain Behav Inst New York NY USA Columbia Univ Dept Neurosci New York NY USA Columbia Univ Kavli Inst Brain Sci New York NY USA

One major challenge of neuroscience is identifying structure in seemingly disorganized neural activity. Different types of structure have different computational implications that can help neuroscientists understand the functional role of a particular brain area. Here, we outline a unified approach to characterize structure by inspecting the representational geometry and the modularity properties of the recorded activity and show that a similar approach can also reveal structure 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 studies of model networks performing three classes of computations.

关键词： neural coding neural representations neural network models

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Non-uniform quantization of neural spike sequences through an information distortion measure

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NEUROCOMPUTING 2001年 38卷 175-181页

作者： Dimitrov, AG Miller, JP Aldworth, Z Gedeon, T Montana State Univ Ctr Computat Biol Bozeman MT 59717 USA Montana State Univ Dept Math Sci Bozeman MT 59717 USA

There have been various suggestions about how information is encoded in neural spike trains: by the number of spikes, by the temporal correlations, or by complete patterns. The latter scheme is most general, and encompasses many others. However, the search for pattern codes requires exponentially more data than the search for mean rate or correlation codes. Here we describe a method that enables optimal use of whatever quantity of data is available. This method allows spike trains to be studied with variable, non-uniform temporal precision. Precision is optimized to provide a best lower bound for the information content of spike patterns given the available data. (C) 2001 Elsevier Science B.V. All rights reserved.

关键词： neural coding quantization information theory cricket

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Bayesian Entropy Estimation for Countable Discrete Distributions

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JOURNAL OF MACHINE LEARNING RESEARCH 2014年 15卷 2833-2868页

作者： Archer, Evan Park, Il Memming Pillow, Jonathan W. Univ Texas Austin Ctr Perceptual Syst Austin TX 78712 USA Max Planck Inst Biol Cybernet D-72076 Tubingen Germany Univ Texas Austin Dept Psychol Div Stat & Sci Computat Neurobiol Sect Austin TX 78712 USA

We consider the problem of estimating Shannon's entropy H from discrete data, in cases where the number of possible symbols is unknown or even countably infinite. The Pitman-Yor process, a generalization of Dirichlet process, provides a tractable prior distribution over the space of countably infinite discrete distributions, and has found major applications in Bayesian non-parametric statistics and machine learning. Here we show that it provides a natural family of priors for Bayesian entropy estimation, due to the fact that moments of the induced posterior distribution over H can be computed analytically. We derive formulas for the posterior mean (Bayes' least squares estimate) and variance under Dirichlet and Pitman-Yor process priors. Moreover, we show that a fixed Dirichlet or Pitman-Yor process prior implies a narrow prior distribution over H, meaning the prior strongly determines the entropy estimate in the under-sampled regime. We derive a family of continuous measures for mixing Pitman-Yor processes to produce an approximately flat prior over H. We show that the resulting "Pitman-Yor Mixture" (PYM) entropy estimator is consistent for a large class of distributions. Finally, we explore the theoretical properties of the resulting estimator, and show that it performs well both in simulation and in application to real data.

关键词： entropy information theory Bayesian estimation Bayesian nonparametrics Dirichlet process Pitman-Yor process neural coding

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Multineuron spike train analysis with R-convolution linear combination kernel

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neural NETWORKS 2018年 102卷 67-77页

作者： Tezuka, Taro Univ Tsukuba Ctr Artificial Intelligence Res 1-1-1 Tennodai Tsukuba Ibaraki Japan Univ Tsukuba Fac Lib Informat & Media Sci 1-1-1 Tennodai Tsukuba Ibaraki Japan

A spike train kernel provides an effective way of decoding information represented by a spike train. Some spike train kernels have been extended to multineuron spike trains, which are simultaneously recorded spike trains obtained from multiple neurons. However, most of these multineuron extensions were carried out in a kernel-specific manner. In this paper, a general framework is proposed for extending any single-neuron spike train kernel to multineuron spike trains, based on the R-convolution kernel. Special subclasses of the proposed R-convolution linear combination kernel are explored. These subclasses have a smaller number of parameters and make optimization tractable when the size of data is limited. The proposed kernel was evaluated using Gaussian process regression for multineuron spike trains recorded from an animal brain. It was compared with the sum kernel and the population Spikernel, which are existing ways of decoding multineuron spike trains using kernels. The results showed that the proposed approach performs better than these kernels and also other commonly used neural decoding methods. A novel way of extending any single spike train kernel to multineuron spike trains is proposed. Subclasses of a kernel having fewer parameters are introduced, making optimization more feasible. Gaussian process regression with the kernel outperformed other existing decoding methods. (c) 2018 Elsevier Ltd. All rights reserved.

关键词： Spike trains neural coding Kernel methods Gaussian process regression

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NEUROCOMPUTING 2002年 44卷 121-126页

作者： Kuhn, A Rotter, S Aertsen, A Univ Freiburg D-79104 Freiburg Germany

Correlation of neuronal activities is widely observed in the central nervous system and is likely to play a key role in its functioning. It is, thus, essential to understand the effects of correlated synaptic input on the response of neurons. Here, we model neuronal input as correlated Poisson processes. and assess their impact on the leaky integrate-and-fire neuron. We found that neuronal output firing rate typically is a non-monotonic function of the input correlation, and propose that the response of neurons is critically dependent on the input ensemble statistics. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： correlation integrate-and-fire input statistics neural coding

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Surrogate gradient scaling for directly training spiking neural networks

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APPLIED INTELLIGENCE 2023年第23期53卷 27966-27981页

作者： Chen, Tao Wang, Shu Gong, Yu Wang, Lidan Duan, Shukai Southwest Univ Coll Artificial Intelligence Chongqing 400715 Peoples R China Chongqing Key Lab Brain Inspired Comp & Intelligent Control Chongqing 400715 Peoples R China Natl & Local Joint Engn Lab Intelligent Transmiss Chongqing 400715 Peoples R China Chongqing Brain Sci Collaborat Innovat Ctr Chongqing 400715 Peoples R China

Spiking neural networks (SNNs) are considered to be biologically plausible and can yield high energy efficiency when implemented on neuromorphic hardware due to their highly sparse asynchronous binary event-driven nature. Recently, surrogate gradient (SG) approaches have enabled SNNs to be trained from scratch with backpropagation (BP) algorithms under a deep learning framework. However, a popular SG approach known as straight-through estimator (STE), which only propagates the same gradient information, does not take into account the activation differences between the membrane potentials and output spikes. To address this issue, we propose surrogate gradient scaling (SGS), which scales up or down the gradient information of the membrane potential according to the sign of the gradient of the spiking neuron output and the difference between the membrane potential and the output of the spiking neuron. This SGS approach can also be applied to unimodal functions that propagate different gradient information from the output spikes to the input membrane potential. In addition, SNNs trained directly from scratch suffer from poor generalization performance, and we introduce Lipschitz regularization (LR), which is incorporated into the loss function. It not only improves the generalization performance of SNNs but also makes them more robust to noise. Extensive experimental results on several popular benchmark datasets (CIFAR10, CIFAR100 and CIFAR10-DVS) show that our approach not only outperforms the SOTA but also has lower inference latency. Remarkably, our SNNs can lead to 34x, 29x, and 17x computation energy savings compared to standard Artificial neural networks (ANNs) on above three datasets.

关键词： Neuromorphic computing Lipschitz regularization Energy efficient Noisy robust neural coding Image recognition

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